Microconstrictions - OPUS 4

Microconstrictions Quantification of cell mechanical properties with a sensitive and high-throughput microfluidic device

Der Naturwissenschaftlichen Fakultät der Friedrich-Alexander-Universität Erlangen-N¨ urnberg zur Erlangung des Doktorgrades Dr. rer. nat.

vorgelegt von Janina Renate Lange aus N¨ urnberg

Als Dissertation genehmigt von der Naturwissenschaftlichen Fakultät der Friedrich-Alexander-Universität Erlangen-N¨ urnberg Tag der m¨ undlichen Pr¨ ufung: 15.12.2017

Vorsitzender des Promotionsorgans: Prof. Dr. Georg Kreimer Gutachter/innen: 1. Prof. Dr. Ben Fabry 2. Prof. Dr. Hans-G¨ unther Döbereiner

Abstract

This thesis describes a method for quantifying the passive mechanical properties of suspended cells with a microfluidic device consisting of a parallel array of micron-sized constrictions. Using a high-speed camera, the flow speed, cell deformation and cell entry time into a constriction were measured while cells passed through the microconstriction array (∼ 100 cells/min). From the flow speed and the occupation state of the constrictions with cells, the driving pressure across each constriction was continuously computed. Cell entry time into microconstrictions decreased with increasing driving pressure and decreasing cell size according to a power-law. From this power-law relationship, cell elasticity and fluidity (power-law exponent) were estimated. A more detailed analysis confirmed that cells have non-linear material properties, which means that cell stiffness increases with increasing stress and strain, for example. To avoid biased measurements due to stress and strain stiffening, 2-dimensional histogram matching was developed, which compares only cell populations from two measurements that experienced both the same stress and the same strain. The high sensitivity of the setup to cell cytoskeletal and cell nuclear changes was then shown with drugs that depolymerize or stabilize these cell components. Moreover, the influence of both measurement and culture parameters on cell mechanical properties was investigated systematically and revealed that most parameters, for instance measurement medium and timing, must be tightly controlled. Finally, through a fluorescence extension of the setup, the correlation of cell mechanical properties with fluorescently tagged intracellular proteins was achieved. An increase in cell stiffness and a decrease in cell fluidity in a dose-dependent manner was found for the overexpression of the nuclear proteins histone 2B and lamin A. In summary, in this work, passive cell mechanical properties were analyzed with a microconstriction setup on a quantitative and high-throughput basis. Therefore, it builds the foundation of a widespread use of this measurement tool in biology and medicine.

Zusammenfassung

Die vorliegende Arbeit beschreibt eine Methode zur Quantifizierung der passiven mechanischen Eigenschaften suspendierter Zellen. Daf¨ ur wurde ein mikrofluidisches Messger¨ at bestehend aus einer parallelen Anordnung von mikrometergroßen Engstellen, sog. ”Microconstrictions”, benutzt. Während Zellen durch die Messvorrichtung gepumpt wurden, wurde deren Flussgeschwindigkeit, Deformation und Eintrittszeit in eine Microconstriction mit einer Hochgeschwindigkeitskamera gemessen (∼ 100 Zellen/min). Durch die gemessene Flussgeschwindigkeit wurde der Druckabfall u ¨ber jede Microconstriction zu jedem Messzeitpunkt berechnet, wof¨ ur ebenfalls die Besetzungszustände der restlichen Microconstrictions ber¨ ucksichtigt wurden. Die Eintrittszeit von Zellen in eine Microconstriction nahm mit zunehmendem Druck ab, und mit zunehmender Zellgr¨ oße zu, was durch ein Potenzgesetz beschrieben werden konnte. Durch den Potenz-Zusammenhang konnten die elastische Zellsteifigkeit und die Zellfluidit¨ at (Potenzexponent) berechnet werden. Eine detaillierte Analyse best¨ atigte, dass Zellen nicht-lineare Materialeigenschaften aufweisen. Beispielsweise erh¨ oht sich die Zellsteifigkeit mit zunehmendem Druck oder zunehmender Deformation. Um zu verhindern, dass Microconstriction-Messungen durch diese Druck- oder Verformungsversteifung verfälscht wurden, wurde ein Verfahren zum zweidimensionalen Histogrammabgleich entwickelt. Dadurch werden nur Zellpopulationen aus Messungen verglichen, welche sowohl denselben Druck, als auch dieselbe Deformation erfuhren. Weiterhin wurde ¨ die Empfindlichkeit des Messaufbaus gegen¨ uber Anderungen der zellmechanischen Eigenschaften des Zellzytoskeletts oder des Zellkerns u ¨berpr¨ uft. Daf¨ ur wurden die mechanischen Eigenschaften bestimmter Zellkomponenten durch depolymerisierende oder stabilisierende Chemikalien verändert, was mit Microconstrictions erfolgreich detektiert werden konnte. Zudem wurde der Einfluss von Zellkultur und Messparametern auf die resultierenden zellmechanischen Eigenschaften systematisch untersucht. Dieses Experiment zeigte, dass die meisten Parameter, zum Beispiel das Messmedium und der zeitliche Ablauf der Messung, streng kontrolliert werden m¨ ussen. Zuletzt wurde durch eine Fluoreszenzerweiterung des Messaufbaus eine Korrelation von Zellmechanik und

dem Expressionslevel einzelner zelleigener Proteine ermöglicht. Dabei wurde eine Korrelation zwischen erhöhter Zellsteifigkeit und verringerter Zellfluidität mit steigenden Expressionsspiegeln der zellnukleären Proteine Histon 2B und Lamin A gefunden.

Zusammenfassend wurde in dieser Arbeit die passive

Zellmechanik mit einem Microconstriction-Aufbau mit hohem Messdurchsatz quantifiziert. Sie bildet daher die Grundlage f¨ ur eine weitverbreitete Nutzung dieser Messtechnik in der biologischen und medizinischen Forschung und Diagnostik.

Contents 1 Introduction 1.1 Aims of this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1

1.2

Techniques for measurements of cell mechanical properties . . . . . . . . . .

3

1.3

Historical development of microconstriction setups . . . . . . . . . . . . . .

7

2 Methods and methodological evaluations 11 2.1 Development of a microconstriction setup . . . . . . . . . . . . . . . . . . . 11 2.1.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2

2.1.2

Soft lithography process . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.1.3

Characterization of channel dimensions . . . . . . . . . . . . . . . . 17

2.1.4

Stability of channel geometry . . . . . . . . . . . . . . . . . . . . . . 19

2.1.5

Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Measurement process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.1 Measurement preparation and clean-up . . . . . . . . . . . . . . . . 22 2.2.2

2.3

2.4

2.5

Video recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Evaluation of cell mechanical properties . . . . . . . . . . . . . . . . . . . . 24 2.3.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.2

Measurement parameters . . . . . . . . . . . . . . . . . . . . . . . . 29

2.3.3

Calculation of stress and strain . . . . . . . . . . . . . . . . . . . . . 32

2.3.4

Power-law rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Correlation of cell mechanical properties with protein expression . . . . . . 42 2.4.1 Fluorescence setup extension . . . . . . . . . . . . . . . . . . . . . . 43 2.4.2

Image recording with synchronized cameras . . . . . . . . . . . . . . 44

2.4.3

Image analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Cell systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.5.1 K562 leukemia cells . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.5.2

DLD-1 colon carcinoma cells . . . . . . . . . . . . . . . . . . . . . . 47

3 Investigations of cell mechanics 3.1 Influence of microconstriction measurements on cell morphology, viability,

49

and proliferation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.1.1 Influence on cell morphology . . . . . . . . . . . . . . . . . . . . . . 50 3.1.2 3.2

Influence on cell viability and proliferation . . . . . . . . . . . . . . . 51

Validation of power-law behavior . . . . . . . . . . . . . . . . . . . . . . . . 53

i

CONTENTS

3.3

3.2.1

Analysis of single cell deformation . . . . . . . . . . . . . . . . . . . 53

3.2.2

Power-law behavior of tentry vs. ǫmax /∆p of a cell population . . . . 55

Investigations of stress and strain stiffening . . . . . . . . . . . . . . . . . . 56 3.3.1 Extension of power-law rheology with stress and strain stiffening . . 58 3.3.2

3.4

2-dimensional histogram matching . . . . . . . . . . . . . . . . . . . 58

Comparison of different strain measures . . . . . . . . . . . . . . . . . . . . 61 3.4.1 2- and 3-dimensional area expansion moduli . . . . . . . . . . . . . . 63 3.4.2

1-dimensional stretch measures . . . . . . . . . . . . . . . . . . . . . 65

3.4.3

1-dimensional compressive measures . . . . . . . . . . . . . . . . . . 67

3.5

Systematic error of cell mechanical properties . . . . . . . . . . . . . . . . . 68

3.6

Sensitivity of microconstriction measurements to mechanical changes of cell cytoskeleton and nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.7

Soft glassy rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.8

Influence of measurement and culture parameters on measurements of cell mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.9

Validation of fluorescence setup . . . . . . . . . . . . . . . . . . . . . . . . 86 3.9.1 Combined calcein staining and cytochalasin D softening . . . . . . . 86 3.9.2

Impact of laser illumination on cell mechanics . . . . . . . . . . . . . 88

4 Biomedical applications 91 4.1 Correlation of cell mechanical properties with cell invasiveness . . . . . . . . 91 4.2

Influence of Hoechst staining on cell mechanics . . . . . . . . . . . . . . . . 95

4.3

Influence of myosin-II on cell mechanical properties . . . . . . . . . . . . . . 97

4.4

Influence of αvβ3 and αIIbβ3 integrin on cell mechanical properties . . . . 99

4.5

Influence of p21 on cell mechanical properties . . . . . . . . . . . . . . . . . 106

4.6

Influence of GBP-1 on cell mechanical properties . . . . . . . . . . . . . . . 109

4.7

Influence of particulate matter on cell mechanical properties . . . . . . . . . 116

4.8

Influence of histone 2B on cell mechanical properties . . . . . . . . . . . . . 119

4.9

Influence of lamin A on cell mechanical properties . . . . . . . . . . . . . . 121

5 Summary and outlook

125

Bibliography

131

ii

6 Appendix 6.1 Generation of microfluidic setup

143 . . . . . . . . . . . . . . . . . . . . . . . . 143

6.2

Measurement process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

6.3

Cell culture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

6.4

Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

List of abbreviations

151

List of figures

153

List of publications

155

CONTENTS

iv

1

Introduction 1.1

Aims of this work

During the last decades, a growing interest in physical properties of cells has emerged. Many essential biological processes in our bodies are not only governed and mediated by chemical cell-cell signaling, but also by cell mechanics, like cell migration, force generation, and adhesion. While migrating, cells chemically or mechanically interact with each other, i.e. they push and pull other cells, and thereby often move collectively [1]. In the course of embryogenesis, for example, cells collectively follow chemical gradients to form our limbs and organs [2, 3]. Throughout wound healing, cells close a tissue gap to stop bleeding and protect the body against invading bacteria [4–6]. Similarly, in the course of cancer progression, cells leave a primary tumor, traverse the extracellular matrix (ECM) and enter a blood vessel. Then, they travel to a distant location of the body and form metastases [7, 8]. Next to macroscopic processes like muscle contraction and heart beat, cells need to generate forces during migration processes when they encounter obstacles that pose a steric hindrance [9]. In the case of metastasis formation, for example, cells have to repeatedly squeeze themselves through the pores of the ECM [7, 8]. After activation through inflammatory cues, suspended immune cells adhere to the walls of blood vessels, and finally cross the endothelial barrier and enter the tissue [10]. In all of these cases, cells do not behave like rigid bodies, but constantly change their shape and deform themselves. For cell deformation, not only active cell mechanics, but also passive cell properties, like cell elasticity and viscosity, play a crucial role. Hereby, the amount of force cells need to deform themselves strongly depends on their deformability. The passive mechanics of cells, however, has long been thought to be largely unimportant for most body processes. Macroscopic structures, like calcified bones and the extracellular tissue, provide stability and structure for our bodies, whereas cells are comparatively soft [11]. Only for the last two decades, passive cell deformability has been more and more appreciated as a readout of complex intracellular processes, which are normally difficult to observe

1

1. INTRODUCTION

for a researcher. Passive cell mechanical properties were found to be especially correlated with the overexpression or knockout of cytoskeletal and nuclear proteins [12]. During the cell cycle, for example, cells were found to reach their highest stiffness in the mitotic phase after chromatin condensation [13]. In the course of stem cell differentiation, suspended myeloid cells stiffen, as they build up their cytoskeleton and increase its contractility to migrate into the ECM [14]. Moreover, changes in bulk cell mechanics could also be correlated with several diseases. Sickel-cell anaemia does not only change the shape of erythrocytes, but also stiffens them and makes them clogg blood vessels [15]. Contrastingly, the development of malign cells in the course of cancerogenesis was correlated with cell softening, which might simplify cell invasion into the ECM during metastasis formation [16, 17]. The study of cell deformability might not only be used to diagnose diseases, but could also provide ways to stop their progression. Cell mechanics could be monitored and deliberately changed in pharmaceutical studies to stop cells from invading the ECM, or to soften blood cells and prevent them from clogging blood vessels. There exist several approaches to investigate passive cell mechanics. A cell can be deformed to a certain extent, and the required force is measured. Secondly, a known force can be applied to a cell, and its resulting deformation is observed. Finally, a known force and deformation can be applied, and the required deformation time of the cell is monitored. In general, cell mechanical measurements are technically challenging. First, single cells are very small, and have a diameter of only 5-30 µm. Secondly, they were found to be much softer than the macroscopic connective tissue of the human body. Therefore, measurement tools for passive cell mechanics must apply small forces at a micrometer scale. However, the accuracy of the production of mechanical components is limited to several dozens of micrometers with conventional methods. This is why specialized production techniques like soft lithography are required [18]. Additionally, in previous studies, cells were found to be heterogeneous, for example concerning their size and gene expression [10, 19]. Thus, mechanical measurements have to be conducted with a high throughput to gain statistically significant results. Moreover, the measurements have to be reproducible to enable systematic investigations of large samples. Therefore, all influencing environmental and measurement parameters must be first known, and then be tightly controlled. In terms of environmental parameters, you could think of the nutrients, which the cells are fed before measurements. Concerning the measurement parameters, the applied stresses and strains should be measured, so that cell mechanical responses cannot only be compared on a qualitative basis, but quantified in terms of material properties. Otherwise, results from independent measurements or different measurement techniques cannot be compared. It was the aim of this thesis to develop a high-throughput, quantitative measurement tool for passive cell mechanical properties, which is at the same time low-cost and easy to handle for scientific standards. These requirements are very well satisfied by a microflu2

1.2 Techniques for measurements of cell mechanical properties

idic microconstriction assay. Hereby cells in suspension are flushed through micron-scale constrictions and their deformation into these constrictions is monitored and quantified based on a theory of visco-elastic materials. After its development, the microconstriction assay was furthermore calibrated and applied in biological and medical studies. Through a fluorescence extension of the setup, cell mechanical properties could finally be correlated with the expression levels of intracellular proteins. Parts of this thesis were published in Biophysical Journal as Lange et al., 2015 [20], Lautscham, ... Lange, ... et al., 2015 [21] and Lange et al., 2017 [22], and in BBRC as Lange et al., 2016 [23].

1.2

Techniques for measurements of cell mechanical properties

During the last decades a wide range of biophysical cell rheometers was developed. All measurement methods observe the mechanical response of cells to the application of stress and/or strain according to one of the three following principles: • A cell is deformed by a certain strain and the necessary stress is measured. • A stress is applied for a certain time and the induced cell deformation is measured. • A defined stress and a defined strain are applied and the time the cell takes until reaching a certain deformation is measured. Stress and strain can be applied through tension, for example pulling at a cell, through compression, for example by poking a cell with a cantilever, or through shear, for example by shearing a cell between two parallel plates (comp. to Sec. 2.3.1.1). A summary of several commonly used measurement techniques for cell mechanical properties can be found in Fig. 1.1. All presented measurement methods differ concerning their way of stress and strain application. Moreover, they apply different amounts of stress and strain over different times, which results in widely varying stress- and strain-rates. They all have differing advantages and disadvantages, and are optimized for certain applications. Some of them are very adaptable concerning their stress rates, others are less flexible, for example in terms of the amount of strain they exert on the investigated cells. Generally, two groups of measurement techniques can be distinguished: measurement methods on adherent cells and measurement methods on non-adherent cells. Cell adhesion to a substrate is the natural state of mesenchymal cells, for example fibroblasts, epithelial and endothelial cells. With a measurement method on adherent cells, the cell cytoskeleton of these cell polulations can be probed in-situ, without the necessity of lifting them off of the substrate, for instance through trypsinization. However, naturally suspended cells, such as blood cells, have to be glued to the substrate [24], or restricted in microwells [25] for the use of adherent measurement techniques. 3

1. INTRODUCTION

Method

Characteristics

References

+adherent cells +high frequency range (0.01-1,000 Hz) +high throughput (~100 cells in parallel) +temporal/spacial resolution

Wang et al., 1993 Fabry et al., 2001 Laudadio et al., 2005 Deng et al., 2006

+adherent cells +spacial resolution +range of appl. forces and ind. depths - low throughput (30 samples/h) +high range of appl. pres. and strains (pore size) - suspended cells - mechanical deformations -stress fluctuations through clogging

Microconstrictions

+high throughput (>10,000 cells/h) +med. range of appl. stresses (pressure) and strains (pore size) +quantitative evaluation possible - suspended cells - mechanical deformations (clogging)

Magnetic twisting cytometry

Magnetic tweezers

Reid et al., 1976 Worthen et al., 1989 Dongping et al., 2015

Mak et al., 2013 Byun et al., 2012 Rowat et al., 2013 Nyberg et al., 2016

Figure 1.1: Selection of cell mechanical measurement techniques, including their advantages (+), disadvantages (-) and references. Links to full references can be found in the main text. Figure layout adapted from [11] and extended.

4

1.2 Techniques for measurements of cell mechanical properties

One of the oldest measurement techniques on adherent cells is magnetic twisting cytometry. For magnetic twisting cytometry, magnetic beads (1-5 µm in diameter) are incorporated into the cell cytoskeleton by endocytosis. Then, a magnetic torque at a high range of frequencies is applied and the bead displacements are evaluated optically [26–29]. The elastic and viscous material properties surrounding the bead can be calculated from the bead displacements. Thereby, the mechanics of different cell components, for example the cell periphery and the cell nucleus, can be measured independently. Moreover, a large amount of cells can be probed in parallel (approx. 100/measurement), which enables a high measurement throughput. However, the exact attachment mechanism and/or the point of anchoring of the beads to the cytoskeleton is often unclear, which may result in unknown origins of the measurement results [27]. Furthermore, magnetic tweezers can be used to investigate cell mechanical properties. Magnetic tweezers also exert a magnetic force on a magnetic bead incorporated into the cell cytoskeleton of adherent cells. In contrast to magnetic twisting cytometry, the direction of the applied stress can be tuned finely, and thus allows for a big variation of measurements. Again, different cell components can be measured independently. Also, the attachment of the beads to the cytoskeleton is often unclear. Concerning measurement throughput, only one cell can be probed at a time, so the measurement throughput is limited to approx. < 50 cells/h [30–32]. One of the most applied and thus calibrated measurement methods is atomic force microscopy (AFM). Hereby a flexible cantilever indents the surface of an adherent cell with nanometer spacial resolution. The exact shape of the cantilever tip determines the stress and strain distribution in the material. By observing the cantilever deflection through the reflection of a laser beam, a stress-strain curve of the investigated material is recorded and its Young’s modulus can be calculated through Hertz’s model. On the downside, AFM measurements require a costly setup with finely tuned mechanical components and highly experienced researchers. Moreover, the measurement throughput is limited to < 20 cells/h [33–37]. As a last measurement technique on adherent cells, microplate rheometers should be mentioned. Microplate rheometers compress, stretch or shear a cell, which is adhered to two parallel plates located at a distance of approx. 10 µm. Either one of the plates is used as a force sensor, or the cell shape is monitored for different applied tensile, compressive or shear forces, which usually allows for qualitative comparisons between cell lines or cell treatments. As the cell has to adhere for a few minutes up to several hours on the two plates, the throughput is highly limited to a few cells per hour [38–40]. Additionally, there are microfluidic measurement techniques for investigating cell mechanical properties. Instead of transporting the measurement device to the cells, for example the cantilever with AFM measurements, cells are quickly transported to the location of measurement through microfluidic flows. This means that only cells in suspension can be probed with microfluidic measurement techniques. Examples for cells in suspension 5

1. INTRODUCTION

are naturally suspended cells, such as erythrocytes and neutrophils, or naturally adherent cells brought into suspension through trypsinization or mechanical removal from their substrate. Trypsinization, however, might result in a disturbance of the usual state of the cell cytoskeleton and finally, without the possibility of reattachment, in cell apoptosis. Microfluidic measurement techniques have become increasingly popular after the invention of low-cost and reproducible micron-scale production methods, for example soft lithography [18]. Moreover, the use of microfluidics increases the measurement throughput dramatically. Instead of < 100 cells/h [41], up to > 2000 cells/s [13] can be measured with a microfluidic technique. Thus, cell mechanical measurements can be applied in a clinical context, for instance for the screening of patient samples. Micropipette aspiration, which was invented in the 1970s, is the oldest measurement technique for cells in suspension and built the foundation of most of the other microfluidic measurement techniques presented in this section. Hereby, a cell is sucked into a glass capillary with a width of 1-10 µm, and its length inside the capillary is monitored in dependence of the applied suction pressure. With Laplace’s law, the cortical tension of the cells can be calculated [42]. The measurement throughput of micropipette aspiration measurements is limited to < 30 cells/h [43–46]. Moreover, the optical stretcher was developed to measure cell mechanics in a contact free way. With an optical stretcher, a cell is trapped between two counter-propagating laser beams. Increasing the laser power leads to a longitudinal cell stretch, which can be measured as an increase in the cell aspect ratio of typically 1-4 %. By deforming the cell optically, cell activation through the contact to a measurement device can be avoided, which might finally result in cell stiffening for long measurement durations. If the forces generated by the laser are known, cell mechanical properties can be quantified through power-law rheology, for example [14]. The optical stretcher reaches a medium throughput of up to 60 cells/h [7, 47]. Disadvantagely, recent studies reported that cells are considerably heated up by the laser light during measurements with the optical stretcher. An increase in temperature can change cell mechanical properties and thus bias the measurement results [48]. Another field of new microfluidic measurement techniques is shear-flow-stretchers. With these techniques, cells are either trapped and stretched at crossroads of diverging flows [49, 50] or sheared while traveling through channels which have a slightly larger diameter than the cells themselves [13]. Shear flow stretching techniques reach a very high throughput of up to 2000 cells/s [13] and create unknown possibilities for whole blood screening of cancer patients. There they might detect at an early stage rare circulating tumor cells, because they differ from normal blood cells concerning their size and deformability [51]. So far, only a few linear, (visco-) elastic material models in combination with finite element simulations were used to extract quantitative mechanical parameters from shear flow stretcher measurements, whereas non-linear material properties have not yet been considered [52, 53]. However, these properties, termed stress and strain stiffening, 6

1.3 Historical development of microconstriction setups

are likely to influence the resulting measurement parameters, as the cells are subject to very high stress and strain rates in shear flow stretchers. Cells are for example stretched by up to 200 % in 0.5 ms [49]. Additionally, microfiltration assays have been used since the 1970s for indirect measurements of cell mechanical properties. Cells are flushed through a mesh of micronscaled pores and the retention rate of the cell suspension in dependence of the applied pressure is measured. With microfiltration assays, a very high measurement throughput can be reached (> 100,000 cells/h), since many samples can be measured in parallel (> 30 samples/h). Moreover, its easy applicability and non-expensive setup allow for a wide application for screening purposes. However, it is difficult to control the exact stress that works on the cells, because the short-term clogging of the pore meshwork by passing cells cannot be monitored during the measurements. Moreover, the pore size must be finely adapted to the median cell diameter of the investigated cell populations in order to measure under comparable strain conditions [19, 54, 55]. The last set of measurement techniques to be investigated in this context are microconstriction setups. In a microconstriction setup, suspended cells are pumped through one or several micron-scaled constrictions by means of a hydrostatic pressure. For evaluation, cell deformation into the constrictions is monitored and quantified. Microconstrictions enable a high measurement throughput of > 10,000 cells/h, because the deformation of many cells can be investigated in parallel. In contrast to other microfluidic measurement techniques, cells experience comparatively physiological stresses and strains. The employed microfluidic channels are adapted to the sizes of blood capillaries in the human body and the applied pressure induces fluid flow speeds on the same order as in our blood vessels [19, 56–58]. Previous studies on microconstriction setups are evaluated in the next section.

1.3

Historical development of microconstriction setups

As early as in the 1970s, researchers used narrow glass capillaries to observe in-vitro the shape and motion of red blood cells [59]. Furthermore, they performed experiments with sieves and Millipore filters to mimic blood circulation and especially the retention of cells at constrictions in the human body. Thus the clogging of narrow pulmonary blood vessels by activated leukocytes could be correlated with cell deformability for the first time [60]. These findings evoked systematic and controlled studies on cell deformations in micronscaled channels in the laboratory, which were additionally facilitated through the invention of new production processes of micron-scaled channels, such as soft-lithography [18]. A microfluidic microconstriction device typically consists of several parallel or serial micronscaled constrictions. During measurements, a cell suspension is flushed into the device at the cell inlet through a hydrodynamic pressure, which can be applied by a pressure pump. Subsequently, the cells are pushed through one or several constrictions of variable widths, heights and lengths (2 µm < width/height < 15 µm, 10 µm < length < 200 µm), and their

7

1. INTRODUCTION

deformation is observed and evaluated. After deformation, they leave the device at the cell outlet and might be recollected for further experiments. In the following, a summary of studies on microconstriction setups from the last 14 years is given (comp. to Tab. 1.1). In most studies, the cell stress, which is the applied pressure, is kept constant, and the cell transit through the constrictions is quantified. Therefore, several measures can be applied. First, entry time into the constriction can be used [56, 62, 68]. Enty time is usually defined as the period of time a cell needs to deform itself to the geometry of the constriction entry. Secondly, cell sliding time within the constriction channel can be measured [10, 62, 70]. This is the period of time, the cell travels inside a constriction channel. Finally, transit time through the constriction, which combines both entry and sliding time [19, 20, 58], can be evaluated. Transit time is also termed passage time. For the application of these three measures, the length and width of the evaluated constriction channel have to be considered and compared to the cell size and the time resolution of the camera. If the constriction channel is too short, the sliding time cannot be temporally resolved. The cell deformation into a microconstriction is most often monitored through bright-field imaging [58, 61, 62]. To define the duration of cell transit, the standard deviation of the pixel intensities of a region of interest (ROI) in front or on top of a constriction is evaluated. This signal is elevated as long as the cell remains in the ROI, and drops back to the background level, when the cell passes the constriction (comp. to Sec. 2.3.2.1). Cell deformation can alternatively be observed by measuring the electrical resistance of a channel segment, which is correlated to its hydrodynamic resistance. Both resistances are thus increased when a cell is currently located in the investigated channel segment [63, 66]. Lastly, suspended microchannel resonators were constructed. By monitoring the eigenfrequency of a cantilever, which simultaneously functions as one wall of the constriction channel, the position of a cell inside this constriction channel can be measured [57, 70]. Next to measuring the deformation time of the cells, the passing pressure can be investigated alternatively. The passing pressure is the pressure required to push a cell through a constriction channel of short length. Thus it is identical to the pressure which is required to deform the cell to the geometry of the constriction entry. For the measurement, the applied pressure is slowly increased, until the cell can pass through the constriction [64, 67]. In several publications, the developed setups were calibrated through proof of principle measurements. This means that the researchers compared their results from microconstriction measurements to the outcome of previous studies performed with other measurement techniques. Most often, chemicals were employed, which are known to stabilize or soften the cell cytoskeleton. For example, a decrease in entry or transit time after treatment with cytochalasin D or latrunculin A [10, 62, 65], which destabilize the actin cytoskeleton, or after treatment with taxol [56], which depolymerizes microtubules, was connected with earlier findings on a decrease in cell stiffness found with AFM measurements [71]. In 8

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x

x

Chen et al.. [63]

2011

B,R

x

x

Guo et al. [64]

2012

B

Adamo et al. [65]

2012

B

x

Rowat et al. [58]

2013

B

x

Khan et al. [66]

2013

B,R

Preira et al. [67]

2013

B

x

x

x

Mak et al. [56]

2013

B

x

x

x

Byun et al. [57]

2013

SMR

x

x

x

Tsai et al. [68]

2014

B

x

x

x

Vasquez et al. [69]

2015

B

Bagnall et al. [70]

2016

SMR

x

Nyberg et al. [19]

2016

B

x

x

x

x

malaria, RBCs

x

cyto D, fMLP

hematologic disease, pathology in leukostasis

x

jasplakinolide lat. A

capillary leukocyte traveling osteoblast vs. osteocyte

cortical tension x

malaria, RBCs

x

lat. A lamin A overexpression

x x

brain cancer cells x

cell viscosity x

taxol lat. B PEG coating dimensionless stiffness index comparison with opt. stretcher

x

metastatic potential of breast cancer cells whole blood of prostate cancer patients

x

x

metastatic potential of cancer cells RBCs of diabetes patients

x

x

Biol. applications

Gabriele et al. [10]

Proof of principle

x

Fluorescence

x

Mech. properties

B

Parallelization

2008

Passing pressure

Rosenbluth et al. [62]

Sliding velocity

B

Sliding time

2003

Entry time

Detection mode

Shelby et al. [61]

Author

Year

1.3 Historical development of microconstriction setups

elastic and viscous particles of known prop.

Table 1.1: Historical development of microconstriction setups. Publications since 2003 using microconstrictions to investigate cell mechanical properties. Abbreviations: B = bright-field, cyto D = cytochalasin D, fMLP = N-formylmethionine-leucyl-phenylalanine, lat. A/B = latrunculin A/B, R = electrical resistance, parallelization = use of more than one parallel constriction, PEG = polyethylene glycol, RBC = red blood cell, SMR = suspended microchannel resonator.

9

1. INTRODUCTION

summary, all studies concluded that cell entry or transit time is positively correlated with cell elastic stiffness and viscosity. In some studies, a quantitative mechanical evaluation was developed, using viscous material models to extract cell viscosity [67] or cortical tension [63, 64] from the acquired deformation data. Moreover, a dimensionless stiffness index was developed. This measure for cell stiffness takes into account both the influences of the cell size compared to the constriction size, and of the cell velocity before entering the constriction compared to the fluid velocity [68]. It was found that cell entry time is mostly governed by cell elastic stiffness, whereas cell viscosity influences the cell sliding time and velocity inside a microchannel [57, 68]. Microconstriction setups were moreover applied in some biomedical studies, for example to elucidate the mechanical influence of malaria on erythrocytes [61, 64]. Moreover, they were employed to study mechanical changes during cancer cell progression, for example with benign and malign brain cancer cell lines [66], breast cancer cell lines [69], or primary prostate cancer samples from patients [70]. So far, only one group of researchers extended their mechanical measurements with the detection of fluorescently tagged intracellular proteins. After measuring the cell transit time through a microconstriction, they investigated the fluorescence intensity of proteins for each cell, which provides the possibility to correlate cell mechanics with protein expression and possibly use the setup to sort cells according to their expression levels [70]. In summary, many studies successfully used microconstriction devices to compare the deformation behavior of different cell populations on a qualitative basis. However, a calibration of the measurement results with comparisons to previous studies, as well as a quantification of cell deformation through visco-elastic material models is mostly missing. Moreover, microconstriction setups have not been employed on a large scale in biomedical studies so far.

10

2

Methods and methodological evaluations As depicted in Sec. 1.3, there already exist first approaches to develop microconstrictions into a measurement technique for cell mechanical properties. Only few of these approaches, however, led to quantified measurements, and even less led to wide-range biological applications or screening studies. The high potential of microconstriction setups concerning their measurement throughput motivated me to develop existing layouts further and use them for the quantification of passive cell mechanical properties through a visco-elastic material theory. This chapter describes the materials and techniques, and the theoretical framework underlying the calculations of quantitative cell mechanical properties from measurements with a microconstriction setup. It includes first tests and calibrations concerning the setup construction and evaluation.

2.1

Development of a microconstriction setup

Microconstriction measurements take place in a microfluidic measurement device. One of the most common production techniques for microfluidic devices is soft lithography. Through soft lithography, photoresist masters of a device layout can be produced in a clean room to mold on a large scale identical measurement devices using PDMS (polydimethylsiloxane), which is an optically transparent polymeric organosilicon compound (comp. to Sec. 2.1.2). First, however, a suitable measurement layout had to be designed.

11

2. METHODS AND METHODOLOGICAL EVALUATIONS

a

b

c

Inlet

Filter

Bypass

Outlet

w50 w50

w50

w50 w40 w50

d

w50

w50

e

f

Constriction region

200 μm

w50 w50

w50

w50 w50

w50 w50

w50

w50

w50

w50

w50

Figure 2.1: History of device development. Earliest devices a+b) contain 32 microconstrictions. Devices c+e) contain eight constrictions, d) contains four, device f) only one constriction. Except for device a), all devices have a filter, which holds back PDMS debris and cell agglomerates. Except for devices a) and e), all devices are equipped with a circular bypass, which simplifies declogging the constrictions through reverse flushing. A bright-field image of a constriction is shown in Fig. 2.10. The flow in all layouts was applied from top (inlet) to bottom (outlet). Scale bar is 200 µm. Scale bar of zooms is 50 µm. Layout scheme adapted from [20].

12

2.1 Development of a microconstriction setup

2.1.1

Design

General layout A microconstriction device has to meet certain basic requirements. First of all, all measurement areas have to be connected through an inlet, where cells can be pumped in from the outside through tubings, and an outlet, where cells can leave the device after measurements (Fig. 2.1 a-f). The exact design of structures inside the circular inlet and outlet region is irrelevant for measurements with a microconstriction setup, as these structures are cut away through the punch holes, into which the tubing is inserted. In this thesis, the geometry of the punch hole regions was therefore simply adapted from previous studies [58]. After the inlet, the cells encounter a filter. In previous studies, this meshwork of thinning channel branches was proven to be highly valuable to hold back cell agglomerates and PDMS waste from the constriction area [58]. In all layouts, the filter channels gradually decrease in width from typically 40 µm to 15 µm. However, their widths are adapted to the median size of the currently investigated cell population. Having passed the filter system, the cells reach the constriction region, which is in most designs surrounded by a circular bypass. This large channel bypasses the majority of the fluid around the constriction branches, and thus clamps the pressure working on the constriction region after the filter and before the outlet. When large cells or debris clog one or more constrictions, the flow can now be turned around, freeing the constrictions. Flushing forward again, there is a high probability that debris and large cells now enter the bypass instead of the constriction region and just leave the device for good. Aiming for high-throughput measurements, not only one single constriction is created for observing cell deformations, but several in parallel. Since all constrictions should experience the same flow and thereby pressure drop in the system, an exactly symmetrical branching network has to be placed between the filter and each constriction. This branching network is then horizontally mirrored and reunites the flow after the constrictions back into the outlet (Fig. 2.1 a-f). Constriction sizes between 2-10 µm in width were built. In one and the same device, however, only constrictions of one size were implemented. Logically, constrictions have to be smaller than the cell diameter to induce cell deformation. In principal, constrictions of different sizes could be used to measure different cellular components. A wider constriction only deforms and thereby measures the mechanical properties of the cytoskeleton. Small constrictions, however, might produce measurement results, which are dominated by the cell nucleus and do not probe cytoskeletal mechanics. Moreover, the constriction dimensions have to be adapted to the median size of the currently investigated cell population. Finally, an empirically found compromise between high measurement throughput and sensitivity to all cell components, was chosen for each cell type. All setup designs were equipped with the smallest possible constriction width, which still produced medium 13


cell entry times between 0.01-0.5 s and thereby ensured a high cell throughput. For all devices, a constriction length of 10 µm was implemented, which is for most cell types smaller than the median cell diameter. With this length, cell sliding in the channel could not be resolved with the employed camera and was therefore not investigated. The height of all layouts was chosen to be slightly higher than the mean cell diameter. This channel height allows the cells to float freely to the constriction area, but ensures the complete filling of the constriction during cell deformation and avoids fluid leaking between the cell and the channel walls. Historical design development in this thesis The first microconstriction layout of this thesis contains 32 parallel constrictions (Fig. 2.1 a). However, setup a) has neither a filter, nor a bypass system, which proved to be very disadvantageous. First, PDMS debris and large cells were flushed into the constrictions and could not pass with the usually applied range of pressures. Furthermore, clogged constrictions could not be freed again by the bypass, and the PDMS debris just reentered the constriction by flushing forwards and backwards. Thus, the measurement time was limited to < 5 min. From layout b) on, a filter system was incorporated into every device. In the filter, the majority of large cells, which often contain several nuclei, and PDMS debris are stopped permanently and thus cannot reach the constrictions. Furthermore, a pressure-equalizing bypass surrounding the whole constriction region was included (Fig. 2.1 b-d, f). Several bypass designs were tested, for instance bypass channels positioned in parallel to the constriction branches. These straight bypasses tend to take up almost all cells, which makes a high measurement throughput impossible. Only a circular bypass, which diverges from the main feeder channel in front of the constriction branches perpendicularly, allows many cells to enter the constriction branches due to inertia. The bypass channel of setup b) is 120 µm wide and it is supported by pillars of 10 µm in width to ensure the stability of the channel ceiling. However, the use of a bypass was accompanied by a disadvantage. Sometimes, an unsymmetric flow formed in the filter. Then, after leaving the filter system, cells only traveled along one wall of the feeding channel, and they very likely entered the bypass instead of reaching the constriction region, which decreased the measurement throughput. Unsymmetric flows can be caused by un-centered positioning of the inlet or outlet punch holes, and also just by arbitrary, unsymmetrical clogging of the filter system over time. Still, with the implementation of a bypass in design b), long-time measurements > 30 min were possible. Transits of several thousands of cells can be measured and qualitatively compared. However, after measuring for one hour at most, the filter system of every tested device layout became gradually clogged by large cells and PDMS debris, which finally terminated the measurements.

14


Aiming for a quantitative evaluation of cell mechanical properties the number of constrictions in a 32-constriction device (comp. to Fig. 2.1 a+b) had to be decreased. With a 10x magnification, only ten of 32 constrictions are visible in the field of view of the recording camera, and thus the pressure working on the cells during transit cannot be computed. For such a computation, the clogging configurations of all constrictions of the device need to be monitored over time, as explained in Sec. 2.3.3.1. To ensure a symmetrical branching network, the device was shrunk to only eight parallel constrictions, which resulted in device layout c) (Fig. 2.1 c). The bypass was kept in its original form, but its size was adapted to closely surround the remaining constriction region. Most of the quantitative measurements presented in Chap. 3 and Chap. 4 were conducted with a design of type c). For cells of differing sizes, the dimensions of the feeding channels, the constriction width, and the device height had to be adapted to avoid clogging of the feeding channels, but at the same time to ensure a complete clogging of the constrictions by each transiting cell. The most commonly used dimensions, mainly for design layout c), can be found in Tab. 2.1. All dimensions were confirmed by confocal microscopy (comp. to Sec. 2.1.3). For primary cells and mouse embryonic fibroblasts, which had a mean diameter of up to 22 µm, devices with constriction widths of 5-8 µm and feeding channel widths of 25-32 µm were developed. Measuring cells of much smaller diameter, for example erythrocytes, lymphocites or lymphocytic leukemia cells, required the use of a downscaled device, shrunk by 25-50 %. Additionally, a higher magnification had to be used to monitor the cell transit through the constrictions and perform cell tracking. Therefore, the number of constrictions had to be limited to four, when shrinking the device by 25 % (Fig. 2.1 d). Because of their asymmetric shape, erythrocytes could not be measured with this device design. During measurements, they aligned perfectly with the constriction when passing. A constriction width of w < 2 µm would be needed to deform the cell, which could not be manufactured with the available mask aligner (see Sec. 2.1.2). Moreover, layouts c-e) were found not to be suitable for heights below 7 µm. By lowering the device height, the hydrodynamic resistance of the devices becomes too high for flushing cells from the cell vial into the device in a reasonable amount of time, which was set to be < 20 min. To enable measurements of patient samples only containing few cells per volume, a shrunk design without a bypass was tried again (Fig. 2.1 e). Thereby, the measurement throughput should be increased. In this study, the cells also had a very small diameter of approx. 5 µm. With device layout e), no successful measurements could be achieved. First, permanent clogging of the constrictions by debris limited the measurement time to at most < 10 min. Moreover, the pressure could not be adjusted to a suitable level. Using a high pressure, cell entry time was too small and could not be resolved by the high-speed camera. Using a lower pressure did not bring the cells into the constriction region at all, because they settled down in the inlet punch hole. Lastly, a single constriction device was designed to investigate the influence of a multiconstriction setup on the transit time distribution (Fig. 2.1 f). The throughput of such a 15


setup is obviously eight times lower than for devices of design c). This limitation makes measurements difficult to achieve, as, after at most one hour, filters and constriction channels always clog due to accumulating PDMS debris and overly big cells in the filter. Two other device adaptations of design f), which are not shown in Fig. 2.1, were produced to perform observations of single cell deformations. First, a single long channel with a width of 20 µm was designed to measure and correlate cell speed to flow speed by the simultaneous tracking of cells and small beads, as explained in detail in Sec. 2.3.3.1. Secondly, a device with a single constriction with a width of 7 µm, equipped with a cavity after the constriction channel, was produced to observe single cell deformation and relaxation and validate power-law deformation on a single cell basis, as outlined in Sec. 3.2.1 and Fig. 3.3.

2.1.2

Soft lithography process

The microfluidic devices presented in Sec. 2.1.1 were produced using standard soft lithography [18] in the clean room facility of ECAP (Erlangen Center for Astroparticle Physics) at the University of Erlangen-N¨ urnberg. The procedure is summarized in the following (comp. to Fig. 2.2), and all production parameters and numbers can be found in App. 6.1. As a first step, a photoresist, for example SU8-2025, was applied to a silicon wafer through spin coating. The spinning speed (∼ 4000 rpm) in combination with the viscosity of the photoresist defined the height of the whole device. Before resist application, the adhesive properties of the silicon wafer were increased by preheating the wafer to 200◦ C, in order to reduce the wafer humidity. Cleaning unused wafers further, for example through Piranhacleaning [18], was not found to improve the adhesiveness of the wafer. After spin coating, the wafer was brebaked to harden the photoresist. With the help of a mask aligner, the wafer was then illuminated by ultraviolet (UV) light through a chrome mask, which carried the pattern of the device design. Thereby, the negative of the channel structure was crosslinked inside the photoresist. A following baking step eliminated all remaining solvents from the photoresist. Then, the the channel structures were developed with the dissolving chemical PGMEA (propylenglycolmonomethyletheracetat), which removed all non-illuminated and thereby un-hardened photoresist from the wafer. Through a final hard-baking step at 200◦ C the channel patterns on the wafer were mechanically strengthened. All protocol parameters were found through empirical trial and error procedures, gradually changing the free parameters of the system until a stable channel structure was reproducibly manufactured. This was necessary since no quantitative values for UV illumination and only manufacturer suggestions for baking times were available. Before the actual production of measurement devices, the dimensions of each master had to be remeasured because an exact reproduction of channel dimensions following one and the same protocol was not possible. First, the room temperature and aging of the photoresist

16


change its viscosity and thereby the device height achieved through spin coating. Secondly, through micro-impurities on the photoresist surface (mostly dust), the distance between chrome mask and photoresist varied slightly during UV exposure. This led to changing resist hardening along the edges of the channels. Thus, it varied the width and the straightness of the channel walls in an unpredictable way. For measurements, a µ-surf confocal microscope was used. All results are shown in Sec. 2.1.3. Now, measurement devices could be molded from the photoresist masters us-

I

Wafer cleaning

II

Spin coating of photoresist

III

Prebake

IV

Exposure with UV light

V

Post exposure bake

VI

Development (Hardbake)

VII

PDMS molding

VIII

Plasma bonding

ing silicone PDMS (Sylgard 184, Dow Corning) [72]. The stiffness of PDMS can be adjusted by mixing the silicone base with different amounts of its crosslinker. To achieve undeformable channel walls, a mixing ratio of 1:7 was chosen, which resulted in a Young’s modulus of the PDMS of ≥ 2.2 MPa [73]. After baking for approx. 2 h, the PDMS was stripped off of the silicon master and inlet and outlet holes were punched with a biopsy punch (diameter of 0.75 mm).

Then,

the punched devices were bonded to a thin glass slide (18x24 mm), in order to seal the channel structure. Therefore, a plasma bonder was used to produce nitrogen plasma and to chemically activate both the PDMS and glass surface, in order to irreversably connect them [74]. Devices were produced at least 48 h before the beginning of a measurement se-

Figure 2.2: Soft lithography production of microconstriction devices. Temporal sequence (top to bottom) of baking, UV illumination and development steps. All production parameters can be found in App. 6.1.

ries. This time gap was chosen to assure that the channels reached constant surface properties after plasma bonding [19].

2.1.3

Characterization of channel dimensions

For the measurements of channel dimensions, confocal fluorescence microscopy was used (TCS SP5, Leica). At the beginning of this thesis, FITC-labeled dextran (fluorescein isothiocyanate dextran, mol wt. = 70,000, 30 µM) was filled into the channels, and they were imaged through confocal stacks (pixel size x-y-z: 84.9 nm x 84.9 nm x 250 nm) under continuous flow to avoid bleaching of the dye. Dextran as a carrier for the fluorescent dye was thereby employed to prevent the dye from leaking into the PDMS walls.

17


Unfortunately, the z-profiles of all channels were found to be systematically biased at the edges, both at the surface PDMS-water and at the surface water-glass slide. Additionally, all intensities were damped with increasing imaging depth, especially when imaging very high channels, or channels of small widths. A reason for this imaging bias could be that the channels were imaged with an oil-immersion objective. This objective was not optimized for imaging at the interface of water and PDMS. Moreover, the high-weight molecule dextran could have damped the fluorescence intensity to a bigger extent than the fluorescent dye alone. Due to the damping, the evaluation of the confocal image data through global thresholding (full-width-half-maximum) gave significantly tilted channel walls (for instance tilted for 2 µm over a height of 10 µm), and the constrictions were measured to be about 40 % less high than the feeding channels. However, with this method, the change of channel width and height, for example under application of increasing pressures, can be monitored at a constant imaging depth, when these changes are small (comp. to Sec. 2.1.4).

a

b 15 22 µm 10 me

an

hei

ght

=13

5 .6µ

m

5.1 µm Height [µm]

6 µm

21 µm

me

an

hei

ght

=16

.6µ

m

0

Figure 2.3: Confocal measurement of device geometry. 3-dimensional surface plots of constriction area of a) device type O3 and b) device type S7, showing four constrictions and feeding channels. Height is color coded. Figure adapted from [22].

As an alternative to fluorescence confocal microscopy, unsealed PDMS devices were cut manually with a scalpel, and the cross-sections were observed via bright-field microscopy. Therefore, the cut edges were oriented perpendicularly to the microscopic focus plane and the height of the devices was measured using a 40 x objective with a pixel size in x-y of 0.185 µm. Still, this method only allowed a limited resolution, because manual cutting of devices is accompanied by a high uncertainty of the cutting angle of the channel cross-sections. Finally, all dimensional measurements were performed with a µ-surf confocal microscope (Nanofocus, Oberhausen, Germany) at the Lehrstuhl f¨ ur Fertigungstechnologie at the University of Erlangen-N¨ urnberg. This confocal microscope uses a multi-pinhole disc to acquire a confocal stack of bright-field images with a pixel size in z of 0.18 µm at 20x magnification. A 3-dimensional height profile can be calculated from the region of interest,

18


Design name

# Constrictions

Bypass

Constriction width [µm]

Channel width [µm]

Height [µm]

O3 S5 S7 X4W5scaled X3W6scaled U1 W1 O3 single

8 8 8 8 8 8 0 1

x x x x x x x x

6.02 ± 0.20 5.51 ± 0.24 5.10 ± 0.12 7.69 ± 0.27 7.46 ± 0.43 6.09 ± 0.16 5

21.95 ± 0.19 21.25 ± 0.06 20.96 ± 0.10 27.28 ± 0.09 28.98 ± 0.09 22.66 ± 0.18 21.25 ± 0.09 21.72 ± 0.09

13.57 ± 0.02 14.64 ± 0.02 16.62 ± 0.02 18.89 ± 0.02 18.89 ± 0.02 19.88 ± 0.02 15.73 ± 0.02 13.56 ± 0.02

Table 2.1: Summary of microconstriction masters, giving production names, layout specifications and measurements of constriction width, feeding channel width and device height. Errors are standard deviations computed from multiple measurements of molds from one device master and from repeated measurements of the same device mold at different positions.

having a pixel resolution in x-y of 0.625 µm. The constrictions were imaged without the glass cover seal, the channels facing up towards the objective lens. This turned position caused a global lopsidedness of the PDMS-block, due to the concavely-formed upper side of the blocks from the capillary effect of fluid PDMS before baking. It was corrected by the built-in µ-surf software and the manual definition of regions of equal heights in the image stacks. Channel height, width and length were extracted from the 4 x-interpolated 3-dimensional height profiles, which had a final x-y-resolution of 0.156 µm (Fig. 2.3). The measurements provided results in accordance with the perpendicular-cut-technique described above. They showed very straight channel walls, which are tilted by less than 0.5 µm over a height of 17 µm. Moreover, they confirmed that the constrictions were not lower or only slightly less high than the rest of the device. From the 3-dimensional height profiles, the median channel height was defined as the height measured at the middle of each channel. The average channel height of all channels of the device was used for theoretical pressure calculations of a channel segment (comp. to Sec. 2.3.3.1). The channel width was evaluated from the same height profiles at a distance of 2 µm from the floor of the channels. Dimensional data for all given devices are listed in Tab. 2.1. The table also gives the production names of the series. Letters correspond to wafer numbers (chronologically rising), numbers correspond to wafer sections which were UV illuminated independently from each other.

2.1.4

Stability of channel geometry

Before quantifying cell mechanical properties with a microconstriction device, the stability of the channel geometry during pressure application was tested. Applying high amounts of hydrodynamic pressure could possibly dilate the channels. Thus, deformation and pressure could not be tuned independently from each other. To test for a possible channel dilation with increasing pressures, the channels were flooded

19


5.9

5.8

Width [µm]

Width of constriction [µm]

Figure 2.4: Stability of microconstriction geometry during pressure application. The constriction width (mean ± sd) increases linearly for an increase in pressure application from 0-150 kPa. Inset: Constriction dilation observed for the range of pressure applied during measurements (0-10 kPa) is unsignificant. Figure adapted from [20].

5.7

5.6 0

5.8 5.75 5.7 0

10 5 Pressure [kPa]

50 100 External pressure [kPa]

150

with FITC bound to high-weight dextran (comp. to Sec. 2.1.3) and the constriction diameter was fluorescently imaged with a confocal microscope (TCS SP5, Leica). Confocal fluorescence microscopy could be used in this case, as only differences in channel width at the same z-position of the channel were compared, and the quantitative values were of minor importance (comp. to Sec. 2.1.3). For a wide range of applied pressures, ranging from 1-150 kPa, a small but gradual linear dilation of the constriction width was observed (Fig. 2.4). However, the constriction width remained constant over the complete range of pressures applied during microconstriction measurements (0-10 kPa) (Fig. 2.4 inset). Pressures higher than 10 kPa are not relevant for the used microconstriction layouts. A falsification of the resulting cell mechanical properties caused by a dilation of the constrictions during pressure application can thereby be excluded.

2.1.5

Setup

Microconstriction measurements took place on a Leica DM-IL bright-field microscope. A sketch of the measurement setup is shown in Fig. 2.5. All materials used to prepare the setup can be found in App. 6.1. Prior to measurements, microconstriction devices were glued to a thick glass slide, which was in turn glued to the microscope stage with adhesive tape. Attaching the devices to the stage was necessary to avoid drift during measurements. An adjustable, pressure-equalizing pump (Bellofram, Special Instruments) was used to apply air pressure to custom-manufactured cell vials. Pressure application could be stopped through valves without changing the pressure level at the pump. The pump worked at a pressure range of 20 mbar to 1.75 bar. Depending on the used device layout, pressures between 20-90 mbar were used during measurements. For devices with large channel diameters, which have an overall smaller hydrodynamic resistance, an additional resistance was introduced into the tube circuit between pump and cell vial. Thereby, the pressure applied at the constriction device could be decreased below the working range of the pump

20


Pressure pump Ø 2.00 mm Ø 0.75 mm control wheel

lamp cell tube

waste tube

0.010 bar valve

device

Image recording

0

0 cell vial

waste vial

computer objective

camera

Microscope Figure 2.5: Sketch of microconstriction setup. Right: Installment of microconstriction device on microscope stage, showing inlet vial with cells and waste vial. Inlet and waste vial are connected to the device via PEEK-tubing. Left top: Pressure-equalizing pump with adjustable pressure range, connected to cell vial. Left bottom: Image acquisition through CCD camera, and connection to computer, where images are stored in video files.

to < 5 mbar. In principle, a water column could be used to apply pressure in the range of 1-30 mbar. The handling of a water column in combination with several valves, however, proved to be difficult and gave an unstable pressure output. To apply the pressure to the cell vial, the lid of the cell vial was equipped with a needle (outer diameter of 0.75 mm), which was in turn connected to the pressure pump by a tube with an inner diameter of 2 mm. The lid also contained a PEEK-tube (polyether-etherketone) with an outer diameter of 0.75 mm, which transported the cell suspension from the cell vial into the measurement device. During measurements, images were continuously taken by a high-speed charge-coupled device (CCD) camera (GE680, Allied Vision). All videos were stored by a quadcore computer (Fujitsu, Siemens) for further image evaluation.

21


2.2

Measurement process

In the following section, the measurement process for observing cell deformation into a micron-scaled constriction is outlined. A detailed protocol is given in App. 6.2.

2.2.1

Measurement preparation and clean-up

Prior to measurements, devices were precoated with 1 % pluronic (F-127, BASF, #P2443, Sigma-Aldrich) dissolved in PBS (phosphate-buffered saline) for 30 min. Pluronic coats the channel walls and thereby decreases non-specific adhesion of cells and cellular proteins to the channel walls. After coating, stable channel surface characteristics were guaranteed, which could otherwise change during the time of measurement [75, 76]. Prior to measurements, cells were harvested from the cell culture flasks at a culture density of normally 80 %. Therefore, adherent cells had to be trypsinized for typically 4 min with trypsin-EDTA (ethylenediaminetetraacetic acid, 0.25 %). Naturally adherent and naturally suspended cells were then centrifuged for 4 min at 1200 rpm (405 × g) to increase cell density in the suspension and at the same time clear the cells from waste and debris in the medium. Afterwards, the cells were resuspended in 0.5-1 ml PBS to increase image quality compared to medium. Moreover, cells were prefiltered through a 20 µm cell strainer to get rid of cell agglomerates or giant multinuclear cells. Cells finally reached a density of approx. 5·106 cells/ml. Details on the influence of the measurement preparation procedure on resulting cell mechanical parameters can be found in Sec. 3.8. Next, the cells were placed into the cell vial and flushed into the device applying a hydrodynamic pressure of approx. 200 mbar, depending on the device layout and its hydrodynamic resistance. As soon as the cells reached the device after 1-5 min, the pressure was reduced to the measurement pressure (5-90 mbar), which was empirically adjusted to provide a medium entry time (0.01-0.5 s) of cells into the constrictions. Cell speed had to be low enough to enable cell tracking in front of the constrictions at a camera frame rate of 750 fps. At the same time, a high measurement throughput was important. Both requirements were usually fulfilled by a cell speed of approx. 5 · 10−3 m s. During one measurement, usually 20-30 videos with a length of 1 min were recorded, depending on the mean cell transit times and clogging frequency of the constrictions. After each video, the flow was reversed to free permanently clogged constrictions and assure a high measurement throughput at all times. The overall measurement time was limited to roughly 40 min. For longer measurement durations, cytoskeletal changes and even apoptosis of the investigated cells, which might be induced by their detachment from the substrate or by room temperature, could not be excluded. In this time span, around 3000-5000 cell transits were recorded. To acquire enough data for a quantitative evaluation of cell mechanical properties and ensure good statistics, 2-3 individual measurements were combined and results were pooled before quantitative evaluation.

22

2.2 Measurement process

For a quantitative comparison of different cell lines or chemical treatments, up to nine measurements were conducted on one and the same day to avoid that changing measurement or culture parameters, for example the age of the devices, changing room temperatures, cell passage numbers etc., bias measurement results. Between all measurements, care was taken to flush the used tubes thoroughly with PBS to remove remaining cells. Devices, and predominantly the filter region, could unfortunately not be freed from stuck cells after a measurement. Flushing with aggressive chemicals would have been necessary to get rid of all cell remains. As only one pressure pump was available for flushing during the time of this thesis, this procedure was not performed due to time limitations. A repeated use of one and the same device was therefore not possible and a fresh device was used for each experiment. After measurements, cell tubes were additionally flushed with distilled water. Flushing with PBS only led to calcification and thereby clogging of the tubes.

2.2.2

Video recording

Figure 2.6: Tool chain of image acquisition system. Camera GE680 communicates with a streamer, viewer and video recorder. The streamer handles acquisition and bidirectional communication with the camera. Recorded images are displayed live and stored in a h264 compressed video file. Configuration files (file ending = .cfg) provide camera and recording parameters. Figure adapted from [77].

During measurements, a CCD camera (GE680, Allied Vision) recorded bright-field images of the constriction region for further offline image processing. The exposure time was approx. 60 µs and the gain was kept at zero for all measurements to ensure a high signal-tonoise ratio. Instead of imaging the maximum field of view of 640 x 480 px, the field of view

23


was restricted to 520 x 90 px. Thereby, the feeding channels in front of the constrictions and the constriction entries were monitored for evaluation (comp. to Fig. 2.18), and a frame rate of 750 fps could be reached. Video recording was conducted with C++-programs, custom-written and designed by Sebastian Richter and implemented by Christian Heidorn [77]. The program consisted of several subtools, like GigEStreamer, which worked as interface between camera and computer, and Videorec, which read acquired images from a ring buffer. The images were encoded utilizing h264 compression and stored in an avi container. The interprocess communication (IPC) was based on memory mapped files. The program architecture is depicted in Fig. 2.6 [77]. Through a graphical user interface (GUI), which will be presented in Sec. 2.4.2, the user starts and stops the recording, and adjusts the storage location, the file name, the exposure time and the camera gain. The frame rate was limited by the maximal frame rate possible for the exposure time and for the image processing capacity of the connected computer. During recording, a display provided continuous information about the number of processed images, and logged if frames were dropped due to system interferences or too high CPU (central processing unit) load caused by other processes.

2.3 2.3.1

Evaluation of cell mechanical properties Theoretical background

In this thesis, cell mechanical properties are described through continuum mechanics and the concept of stress and strain, which are introduced in the following sections. Therefore, background knowledge on theoretical hydrodynamics in microfluidic channels is required in order to calculate the stress working on a cell in a microconstriction. 2.3.1.1

Continuum mechanics

Cells are heterogeneous structures consisting of a filamentous cytoskeleton of actin, microtubuli, and intermediate filaments (comp. to Sec. 3.6). Moreover, they contain various cell organelles, like the cell nucleus. All components are embedded in the aqueous cell cytoplasm and the whole cell is surrounded by a lipid-bilayer membrane, which forms its boundary to the environment. All cellular components are crosslinked with each other through linker proteins. The transmembrane proteins integrins, for example, connect the cell cytoskeleton to the cell surroundings [78] (comp. to Sec. 4.4), and LINC-complexes attach the nucleus to the cytoskeleton [79] (comp. to Sec. 4.9). So far, there is no theoretical model which would take into account all known cell components for a description of cell mechanical properties. Moreover, lots of interactions between cell components are still poorly understood or completely unknown, and can thus not be incorporated into a model.

24

2.3 Evaluation of cell mechanical properties

a

cells as a homogeneous material. Even though this is a clear oversimplification, this concept at least allows for a quantification of cell deformation, for example through the engineering concepts of

b

stress and strain. Stress σ is thereby defined as the force F per area A: F σ= A

(2.1)

c

Shear: Shear modulus G

Strain describes the relative change in length or width of a body in response to the applied stress, and is explained in detail in Sec. 2.3.3.2. In a first approximation, cells can be depicted as a homogeneous, linearly elastic material, which reacts to a force step through an instant deformation (Fig. 2.8 left). The reaction of such a material to a uniaxial tensile or compressive stress is de-

dy

Tension: Young’s modulus E

continuum approach and characterize

σ

Compression: Young’s modulus E

This is why researchers often apply a

y

dy y

σ σ

α

Figure 2.7: Types of mechanical deformations. a) Tension, b) compression and c) shear, with according material constants Young’s modulus E and shear modulus G, undeformed lengths y and displacements dy, and shearing angle α, respectively. Arrows indicate direction of stress. Figure layout adapted from [80].

scribed by Hooke’s law, which connects the applied stress σ with the experienced strain ǫ through the elastic material constant E, which is called Young’s modulus: σ =E·ǫ

(2.2)

The Young’s modulus thereby predicts how much a material extends under stretch or shortens under compression (Fig. 2.7 a+b). The response of a material which is sheared with a stress τs by an angle α is characterized by the shear modulus G (Fig. 2.7 c): τs = G · tan(α)

(2.3)

Due to geometrical reasons, E and G are linked through the Poisson ratio ν of the investigated material: E = 2G(1 + ν)

(2.4)

ν describes the response of a material in the transverse direction to the stress. For example, ν = −dǫx /dǫy characterizes the relative decrease in width dǫx in x-direction induced by

25


the elongation of the material under stretch dǫy in y-direction [42]. Alternatively, cells can be described as a viscous fluid, reacting to a force step through yielding according to Newton’s law of viscosity [42] (Fig. 2.8 second from left): τs = µ ·

du dy

(2.5)

with τs as the shear stress, µ being the coefficient of viscosity and

du dy

the uniform velocity

gradient of the fluid. In numerous studies, cells have been found to show at the same time both elastic behavior, like a solid material, and viscous behavior, like a fluid [11, 26, 41]. In engineering, material properties are often illustrated through equivalent mechanical components, which poses a further simplification from 3-dimensional continuum mechanics to only one remaining dimension. In the following, this description is used to introduce visco-elastic material behavior. In terms of macroscopic mechanical components, the equivalent description of an elastic material is a spring, which is called a Hook element. A viscous material is represented by a dashpot, termed Newton element. Visco-elastic material properties can thus be reached through a serial or parallel combination of Hookean elastic springs and Newtonian viscous dashpots. Different structural components of a body can thus often be attributed to individual elements of the equivalent circuit. Fig. 2.8 shows the development of three visco-elastic material models from the combinations of elastic and viscous material components. ε

F

elastic

ε

F

t

ε viscous

F

t

Maxwell

ε

F

t

Voigt

ε

F

Power-law

t

t

Figure 2.8: Continuum mechanical material description of cells. A cell is described as a homogeneous material, either showing an elastic, viscous, or visco-elastic material response to an applied force. Top: Relative cell deformation ǫ (black lines) in response to a force step (grey dashed lines). Bottom: Mechanical equivalent description through Hook and Newton elements. Figure layout adapted from [80].

The Maxwell model (Fig. 2.8 middle), for example, is comprised of the serial combination of a spring and dashpot, which leads to the total strain ǫ = ǫe +ǫv . ǫe and ǫv are the strains applied to the elastic and viscous equivalent elements, respectively. It is mathematically

26


described by the differential equation ǫ˙ =

σ σ˙ + E η

(2.6)

The elastic spring thereby has the stiffness E and the viscous dashpot the viscosity η. The material strain over time t in response to a sudden stress is ǫ(t) =

σ σ +t· E η

(2.7)

For t → ∞ the deformation is unlimited and irreversible [42]. The (Kelvin-)Voigt-body (Fig. 2.8 second from right), contrastingly, consists of a parallel combination of a spring and a dashpot [81, 82]. It is mathematically described by the differential equation σ = σe + σv = E · ǫ + η · ǫ˙

(2.8)

with σ being the sum of the stress working on the elastic (σe ) and viscous (σv ) equivalent components. The Kelvin-Voigt body is solved through σ ǫ(t) = E

E 1 − exp(− t) η

For t → ∞ the deformation is limited to ǫ →

σ E,

(2.9)

which reduces the body to a Hook

element. Both models characterize the material through the time-constant τ =

η E.

It either de-

scribes the time when a typical amount of stress has decayed after the application of a sudden strain, or the time after a typical amount of strain has decayed after the application of a sudden stress, depending on the conducted experiment [83]. At the beginning of the 20th century, researchers improved the time resolution of their experiments and studied cell mechanical behavior for a variety of different time and length scales. Surprisingly, they found that, when applying the Maxwell- or Voigt-model to fit for instance the pulmonary pressure after a step decrease of lung volume, the decaying constant τ only depends on the measurement duration [84]. The same is true for measurements on bulk single cells. This result suggests that the decaying constants τ do not describe the mechanical behavior of single cell components, such as the cell cortex, the cytoskeleton or the nucleus, in a physically meaningful way, nor do they provide further physical insight into their functioning [11]. This shortcoming of the mentioned models led to the development of power-law rheology, which is described in Sec. 2.3.4.

27


2.3.1.2

Theoretical hydrodynamics

Moreover, theoretical knowledge of the fluid velocity profile in a rectangular microfluidic channel is required, to finally calculate the pressure drop over a channel segment from fluid velocity. In mechanics, Newton’s second law of motion describes the motion of a body with mass m, which is accelerated by the acceleration ~a through the sum of forces F~i : m · ~a =

n X

F~i

(2.10)

i=1

In fluid dynamics, Newton’s second law of motion is given through the Navier-Stokes equation, which thus builds the constitutive equation for the motion of an incompressible fluid by means of continuum mechanics [85]: ρ (δt~v + (~v · ∇)~v ) = −∇p + η∇2~v

(2.11)

g with ρ being the fluid density (ρwater = 1 cm v (~r, t) the Eulerian velocity field of the 3 ), ~

fluid, p the pressure and η = 1.002 mP a · s the dynamic viscosity of water. The left side of this non-linear, inhomogeneous differential equation describes the acceleration of a fluid volume through the total time derivative of its speed. The right side summarizes the forces working on the body. The forces considered here and in the following are the divergence of the pressure p, and the viscous friction force between two fluid volumes. For a rectangular channel, as produced through standard soft-lithography, no analytical solution of the Navier-Stokes equation is available. However, considering the stationary case (δt~v = 0), a solution for a rectangular channel can be approximated by expansion of the equation through Fourier-sums. Thereby, the boundary conditions vx (−w/2, z) = vx (+w/2, z) = vx (w, 0) = vx (w, h) = 0 are taken into account [85]. Here, h is the height of the channel in z-direction, w its width in y-direction. The flow speed is only non-zero in x-direction due to the boundary conditions in y and z, and it is translationally invariant in x. For an incompressible, Newtonian fluid with laminar, pressure-driven flow, the solution is called (Hagen-) Poiseuille flow, yielding the fluid velocity field [85]: ∞ cosh(nπ hy ) z 4h2 ∆p X 1 1− vx (y, z) = w sin(nπ ) ηπ 3 l n3 cosh(nπ 2h h )

(2.12)

n, odd

l is the length of the channel segment (x-direction), and ∆p = p(l) − p(0) the pressure drop over the channel segment. From this solution, the maximum fluid speed can be calculated by inserting vmax = vx y = 0, z = h2 . The volume flow I is subsequently given through integration over the channel cross-section:

28


I=2

Z

1 w 2

0

dy

Z

h 0



 ∞ X 1 192 h ∆p  w  1− tanh nπ dz vx (y, z) = 12η l n5 π 5 w 2h h3 w

(2.13)

n,odd

As I can also be represented through I = vavg · h · w

(2.14)

the average fluid speed vavg is given by

vavg

  ∞ w X h2 ∆p  1 192 h  1− = tanh nπ 12η l n5 π 5 w 2h

(2.15)

n,odd

Rearranging the components of I and extracting ∆p leads to an alternative, and more commonly known representation of Hagen-Poiseuille’s law [85]: I=

∆p R

(2.16)

with R being the hydrodynamic resistance of the channel segment: R=

12 · η · l h3 · w · M

(2.17)

Here, M is a constant depending on the ratio between w and h [85]: M =1−

∞ w X 1 192 h tanh nπ n5 π 5 w 2h

(2.18)

n,odd

For the case of h/w ∼ 2/3, which represents a typical ratio of height to width of a microfluidic channel, M is approx. 0.6. If the height h and width w change along a channel segment according to h(x) and w(x), Eq. 2.17 must be integrated along the length x of the channel. Moreover, M transforms into M (x). If w < h in the investigated channel segment, both w and h have to be interchanged in all equations, which corresponds to turning the coordinate system by 90◦ .

2.3.2

Measurement parameters

For the evaluation of quantitative cell mechanical properties, the time series recorded during cell deformation through a microconstriction was evaluated through image analysis. All necessary measurement parameters were extracted from the bright-field videos with custom-written Matlab (The Mathworks) programs. The evaluation of cell entry time into the constriction, cell size, which can be transformed into cell strain, and cell speed, from which cell stress can be calculated, are explained in the following (comp. to Fig. 2.9).

29


Measurement parameters

Mechanical description

Cell entry time tentry

Deformation time tentry

Cell size rcell

Strain ε

Cell speed vcell

Stress ∆p

Figure 2.9: Overview over measurement evaluation. Transformation of measurement parameters into a mechanical description of cell deformation through deformation time, cell strain and cell stress.

2.3.2.1

Entry time analysis

Entry time into a constriction principally differs from transit time through a constriction. The latter combines both entry and sliding time of the cell inside the constriction channel. For the devices used in this study, however, entry time is equivalent to transit time, because the time the cell slides inside of the constriction channel is below the camera resolution limit of 1.4 ms. The measure is still called entry time and not transit time, since physically only the time the cell takes to enter into the constriction is measured. Entry times were measured through ROIs in front of each constriction. When a cell reaches the area in front of a constriction at high speed, the standard deviation of the pixel intensities of a ROI rises abruptly, as shown in Fig. 2.10. During the cell deformation into the constriction (a+b: II-IV), the standard deviation signal remains high, until it falls dramatically when the cell slides through the constriction channel and travels on through the channel network (a+b: V). The brightness standard deviation of the ROIs was then thresholded by an empirically defined threshold (threshold value = 0.035), which was kept constant for all evaluations (Fig. 2.10 b, red line). Principally, cell debris and cell vesicles passing a constriction can produce brightness intensity deviations of the same intensity as cells. These false detections were eliminated in further evaluation steps, when the cell size is measured. For each experiment, the ROIs were positioned manually by defining the center of each constriction entry. The center of the ROI was then chosen to be as close to the constriction entry as possible, but constrained to not overlap with the channel walls. The size of the ROIs was 12 x 12 px, which corresponded to approx. 65 µm2 for a pixel size of 0.74 µm. 2.3.2.2

Cell size detection

The entry time of a cell into a micron-scaled constriction depends on constriction size (comp. to Sec. 2.1), but also on cell size. Larger cells take more time to deform to the

30


a

Figure 2.10: Calculation of entry time. a) Time series of a cell passing a microconstriction. Cell cytoskeleton was stained with calcein (green, #C0875, SigmaAldrich), cell DNA (deoxyribonucleic acid) with DRAQ5 (red, #ab108410, Abcam) for better visibility. Brightness intensity deviation of ROIs (white squares) is monitored continuously. b) Brightness intensity deviation of cell transit from a) over time. Entry time (II-IV) is determined by thresholding (red line). Roman numbers in a) and b) are corresponding. Figure adapted from [20].

flow

I Outlet

time

II

III

+250ms

IV V

Intensity deviation

b

C

III IV

II

V

I Time

constriction width and height than smaller ones. For each cell entry, cell size was therefore measured from the bright-field videos to finally compute the cell strain. When the brightness standard deviation signal of a ROI rose above the given threshold (image number # = n) during a measurement, the preceding image (# = n − 1) was investigated to detect the cell boundaries. In this image, the cell of interest approaches the constriction, and has not made contact with the constriction walls yet. The cell is therefore undeformed and has a circular outline. To measure the cell diameter, image # = n − 1 was background subtracted, where care was taken not to subtract a background image which already contained a floating cell. Then, a sobel-filter in combination with filling-algorithms was used to mark the cell edges. Finally, the cell body was filled and a circle was fitted to its boundary to give the area and radius for each measured cell. For all filter thresholds, the current image brightness was taken into account.

31


2.3.2.3

Cell speed detection

For further quantitative evaluation of cell deformation, it was of high interest to know the stress applied on each cell during its transit. In this case, this is the pressure drop over the constriction. Evidently, a cell which experiences a high pressure during its transit has a shorter entry time into a constriction than a cell which experiences a small pressure. Due to the gradual clogging of the whole microfluidic network during the time of measurement, however, the externally applied pressure could not be taken as a stable indicator for the internally working pressure drop over each constriction branch. Therefore, the pressure working currently on a cell during its transit was extracted from the cell speed in front of the channel. For the calculation of cell speed from the recorded bright-field images, the position of each cell approaching the constriction was determined in images # = n − 1 and # = n − 2 before the beginning of cell entry (# = n). The extraction of the cell positions was done by the same cell detection algorithm as described in the previous section (Sec. 2.3.2.2). Cell speed was calculated with v =

x ∆t

, with x being the traveled cell path between images # = n − 2

and # = n − 1, and ∆t the time difference between the two recorded images, as illustrated in Fig. 2.11 a.

2.3.3

Calculation of stress and strain

After the extraction of cell size and cell speed from the recorded videos, these measures were processed further for the quantification of cell mechanical properties. Cell size was translated into a dimensionless strain measure. The stress, which is the pressure drop working on each cell during its entry into a constriction, was calculated from cell speed. 2.3.3.1

Calculation of stress: Mean pressure drop ∆p

For a constriction device with just one constriction, the pressure, which is externally applied to the device by a pressure pump, is correlated to the pressure drop over the constriction through a constant factor. The pressure drop over this constriction can thereby be computed theoretically, or it might be deducted from calibration measurements of particles with known mechanical properties [19]. In the constriction setup of this work, however, large fluctuations of the pressure drop over a constriction arise over the whole time of a measurement through changes of the hydrodynamic resistance of the system. Intermediate time pressure fluctuations are caused by gradual clogging or declogging of the filter, and the in- and outlet. Really fast pressure fluctuations are caused by clogging and declogging of the neighboring constrictions. Moreover, it was not possible to position the punch holes of the in- and outlets at exactly the same position for all used devices, as punching was done manually. Differences in the in- and outlet punch hole position were found to change the overall pressure drop over

32


the system significantly. Resistance calculations according to Eq. 2.17 gave a difference in pressure drop over the constrictions of more than 20 Pa for a combined shift of in- and outlet by 100 µm (50 µm each). The punch hole diameter was assumed to be 750 µm. Due to all these reasons, a continuous pressure monitoring at each constriction over the time of measurement was necessary. Therefore, flow speed was measured from cell speed, and Hagen-Poisseuille’s law was used to calculate the pressure drop. The single steps of this procedure are outlined in the following. Calculation of average flow speed and volume flow from cell speed

c

b

vbead [m/s]

Time

0.02

y

1.5 data binned data fit

vmax 1.25 vcell/vavg

a

0.01

1

+6 ms

0.75 0 -10 Way x +30 µm

0 Channel section [µm]

10

0.9

1 1.1 rcell/rhyd(channel)

1.2

1.3

Figure 2.11: Calculation of flow speed from cell speed. a) Calculation of cell speed from cell tracking in front of constrictions. Scale-bar is 10 µm. b) Flow profile in a rectangular channel, measured by tracking of micron-sized beads, with vmax at its peak. Channel width, and thus channel section, is oriented in y-direction, channel height in z-direction. c) Dependence of cell speed vcell on average flow speed vavg , with rcell normalized by the hydrodynamic radius of the channel r(hyd)channel . Orthogonal fitting yields vcell /vavg = 2.65 − 1.59 · rcell /r(hyd)channel . Figure adapted from [20] and [22].

To measure the relationship between cell speed and flow speed, both K562 leukemia cells (Fig. 2.11 a) and small beads (diameter of 1 µm) were tracked simultaneously while flowing under a constant pressure in a channel of width w = 21 µm and height h = 15.5 µm. The fluid velocity profile was reconstructed from the tracking of beads which travel with the fluid at a median height of the channel (z-direction). The maximum fluid velocity vmax was recorded, which occurs at the center of the channel in y- and z-direction (Fig. 2.11 b). To extract the average flow velocity vavg from the measurement values of vmax , Eqs. 2.12 and 2.15 can be rearranged, which yields: vavg = 0.48 · vmax

(2.19)

for a rectangular channel of width w = 21 µm and height h = 15.5 µm. In general, the conversion factor 0.48 only depends on the ratio between h and w and only slightly changes with changing channel aspect ratio, for example 2 % for ± 15 %. Next, the relationship between cell speed vcell and average flow speed vavg was evaluated

33


in dependence of the radius rcell of each cell. The cell radius was therefore normalized by the hydrodynamic radius of the channel rhyd(channel) , which describes the equivalent radius of a circular channel [86, 87]: rhyd(channel) =

h·w h+w

(2.20)

Cells in the experiments had sizes of rcell /r(hyd)channel ≥ 0.7 and traveled at a slightly higher speed than the average flow speed. Moreover, cell speed decreased linearly with increasing cell radius (Fig. 2.11 c). The relationship was then fitted by linear orthogonal regression, giving

vcell rcell = 2.65 − 1.59 · vavg r(hyd)channel

(2.21)

Principally, cell speed is also influenced by the position of the cell in the channel perpendicular to the flow direction. Since cells in this thesis occupied most of the channel cross section (rcell /r(hyd)channel ∼ 0.9), they predominantly moved along the center of the channel with a standard deviation of only ∼ 1.49 µm. The error induced by de-centered cells was therefore neglected in all evaluations. Next, the volume flow I in a microfluidic branch was calculated from vavg according to Eq. 2.14. Calculation of pressure drop from flow speed The pressure drop ∆pi−j for the channel segment between the two nodes ni and nj was then calculated according to Hagen-Poiseuille’s law (comp. to Eq. 2.16): ∆pi−j = Ri−j · Ii−j

(2.22)

with Ii−j being the volume flow between the two nodes, and Ri−j the resistance of the channel, which was calculated through Eq. 2.17. Ri−j can also consist of the resistances of two parallel microfluidic branches (comp. to Fig. 2.12), for example Rg−h = 1/Rg + 1/Rh

(2.23)

Calculation of pressure drop over constriction region In the following, the term microconstriction region refers to the branching channel network leading to and from the constrictions, which is surrounded and clamped by the bypass. All nodes and resistances of this region are shown in Fig. 2.12. Before calculating a pressure drop over a constriction, the global pressure ∆P1−14 working on the whole constriction region was calculated to create a continuous global pressure over time. Therefore, the pressure psim,i at each node ni of the microconstriction region was

34


Figure 2.12: Resistances and nodes of microconstriction region. All resistances Rz are connected by nodes (bifurcations) ni . Nodes n1 and n14 function as source and sink.

n1 Ra

Rb

Rd

Re

n2 Rc

n3

n4

Rg

n5

Rh

n8

n6

Rj

Ri

n9

Rk

n7

Rl

Rq

n12

Rm

Rn

n11

n10

Rp

Ro

Rf

Rr n13

Rs

Rt n14

first calculated theoretically by using Kirchhoff’s current law, also called nodal equation: m X

Ii = 0

(2.24)

i=1

with Ii being one of the m flows arriving at a considered node ni of the network. In this work, an arbitrary theoretical global pressure drop of 1 Pa was assumed. The source pressure n1 was thus set to 1 Pa, and n14 was set to 0 Pa. For a mathematically efficient solution, a matrix representation of the nodal equations was chosen, representing the flows Inet through resistances Rinv and pressures Psim : Rinv · Psim = Inet

(2.25)

Here, Inet contained the net flows at the source and drain nodes n1 and n14 , and was zero at all other entries. Psim contained all pressures psim,i at the nodes. Rinv was the inverse resistance matrix. At all diagonal entries (nz1 = nz2 ), it contained the sum of inverse resistances connected to node nz1 . At non-diagonal entries (nz1 6= nz2 ), it contained −1/Rz , which is the negative inverse resistance between the nodes nz1 and nz2 . The rows of Rinv corresponding to all source and drain nodes were set to 0, except for their diagonal entries, which were set to 1. In the case of the microconstriction region, this gives for example for source node n1 : Rinv (nz1 = 1, nz2 = 2...nmax ) = 0 Rinv (nz1 = 1, nz2 = 1) = 1

35


With the inverse resistance matrix Rinv and the source flow vector Inet , the equation system was solved for the theoretical pressure psim,i at each node ni by matrix inversion. The measured pressure drop ∆pi−j over a constriction between the nodes ni and nj can now be used to calculate the global pressure drop ∆P1−14 by rescaling the simulated values: ∆P1−14 = ∆Psim,1−14 ·

∆pi−j ∆psim,i−j

(2.26)

using the linear dependencies between all pressure drops of the microconstriction region. For all calculations, the clogging configuration at the time of flow measurement was taken into account, because changing clogging directly results in changing hydrodynamic resistances of the channel network (comp. to Fig. 2.13). Thereby, a clogged constriction branch was approximated with a hydrodynamic resistance of infinity.

flow

0.4

0 kPa Figure 2.13: Dependence of pressure drop on clogging configuration. From left to right, an increasing number of cells clogs neighboring constrictions. The externally applied pressure remains constant. The pressure drop over the observed constriction (left-most in each device) increases by 79 %. The right branch of the microconstriction region, here containing four empty constrictions, is unaffected by the cloggings of the four constrictions of the left branch. Figure adapted from [20].

In the 8-constriction device, the two major branches, which bifurcate closely after the bypass, built a parallel resistance. Therefore, changing clogging configurations in one of the major branches do not influence the resistances in the second major branch. In the two branches, many clogging configurations are axially symmetric and can be further reduced to identical configurations. Thus, initially 256 different clogging configurations of the whole device give rise to six possible clogging combinations which result in different pressure drops over a constriction (Tab. 2.2). Compared to only one clogged constriction, the pressure drop increases for up to 79 %, when all neighboring constrictions of the observed constriction are clogged. From each new cell approaching a constriction, the external pressure drop ∆P1−14 was updated. Then, a continuous external pressure ∆P1−14 (t) was calculated from these discrete pressure measurements through linear interpolation.

36


# Clogged constrictions 1 2 2 3 3 4

Clogging configuration [1000] [1010]/[1001] [1100] [1110]/[1101] [1011] [1111]

Relative pressure 1.00 1.12 1.29 1.32 1.47 1.79

Table 2.2: Clogging configurations which result in different pressure drops over left most constriction (position # 1 in brackets). Only one of the two main branches, containing four constrictions, is considered due to the symmetry of the system. Left: Number of clogged constrictions. Middle: Clogging configurations. A clogged constriction is symbolized by the number 1, an empty constriction by the number 0. Right: Pressure drop over constriction # 1, normalized by the pressure value of one clogged channel.

Calculation of mean pressure drop during cell entry Finally, from the linearly interpolated pressure drop ∆P1−14 (t) over the whole constriction region, the continuous pressure drop ∆pt (t) over each constriction during cell entry was calculated according to Eq. 2.26, using again the linear dependence of all pressures in the network. The mean pressure drop during each cell entry into a constriction was finally calculated as ∆p =

1 tentry

·

Z

tentry

∆pt (t)dt

(2.27)

t=0

with ∆pt (t) being the temporarily changing pressure drop over a constriction during a cell’s transit, and tentry the cell entry time into a constriction. A mean pressure drop working on each cell during entry simplified the calculations, compared to considering the stepwise-changing pressure induced by different clogging configurations. In the following, the error induced by the mean pressure approximation is evaluated. Errors from mean pressure approximation For the quantification of cell mechanical properties, the mean pressure of the pressure series working during a cell entry was computed and used for further calculations, instead of the accurate series of pressures. Using the mean pressure instead of the exact time course of the pressure, as shown in Fig. 2.14 a+b for an exemplary cell, can introduce an error into the calculation of cell mechanical properties. To estimate the error on the resulting cell mechanical properties induced by this approximation, power-law exponents from deformations of 2984 K562 leukemia cells under a series of pressures (termed full pressures) and under the mean of this pressure series (termed mean pressure) were calculated through power-law rheology (Eq. 2.34), which will be introduced in Sec. 2.3.4, and through soft glassy rheology (Eq. 3.5), which will be introduced in Sec. 3.7. Finally, the power-law distributions of cells for both approaches were compared (Fig. 2.14 c). Then,

37


a

b 240 200

ε

∆p [Pa]

220

Full pressure Mean pressure

180 160 140 0

1 1.5 Time [s]

10

2

00

2.5

d

8 6 4


0.5

20


1 1.5 Time [s]

(β

full

Error [%]

Relative prob.

c

0.5

0.7 0.6 0.5 0.4 0.3 0.2 0.1

2

−β

mean

2.5

) /β

full

10 0

−10

2 0 0

0.2 0.4 0.6 Power−law exponent

0.8

−20 0

1000 2000 Cell no.

3000

Figure 2.14: Mean pressure approximation. a) Mean pressure (black) compared to step-wise changing full pressure (red) during cell transit. b) Simulated development of cell deformation ǫ(t) during cell transit, comparing full pressure (red) to mean pressure (black). c) Calculation of single cell fluidity (= power-law exponent) of 2984 cells for step-wise changing full pressure and for mean pressure. No systematic differences are visible in the distributions. d) Relative error of cell fluidity β induced by mean pressure approximation. Red line shows mean relative error. Figure taken from [20].

the relative error δβ = 100 % ·

βfull −βmean βfull

was computed. The mean relative error is al-

most zero (-0.15 %) with a standard deviation of 2.2 % (Fig. 2.14 d). In conclusion, the mean pressure approximation introduces a negligibly small error into the calculation of the pressure drop over the microconstrictions. 2.3.3.2

Calculation of strain: Maximum compression

From cell size, a dimensionless cell strain was computed for the calculation of cell mechanical properties with a continuum approach according to Sec. 2.3.1.1. The most general description of the deformation of a body in response to an applied stress is a 3-dimensional strain tensor. This tensor describes the change in distance between two points of an arbitrary body after application of an arbitrary transformation. Often, the Seth-Hill family of strain measures is used: ǫ(m) =

1 (U2m − I) 2m

(2.28)

with U including the coordinates of the deformed material, and I of the original, undeformed material [42]. With different values of m, all known strain measures can be

38


developed. An alternative representation of strain is given through the observation of the distance between two points before (x1 , x2 , x3 vs. x1 + ∆x1 , x2 + ∆x2 , x3 + ∆x3 ) and after transformation (a1 , a2 , a3 vs. a1 + ∆a1 , a2 + ∆a2 , a3 + ∆a3 ): 1 δaα δaβ eij = (δij − δαβ ) 2 δxi δxj

(2.29)

with δij being the Kronecker-Delta. The Kronecker-Delta gives the number one for i = j and zero for all other cases [42]. In the following, only the normal components, representing stretch or compression, are considered. This reduces the tensors to one dimension, for example to relative changes in length or area. Relative changes in length or area are most commonly represented through the so-called stretch ratio, or compressive ratio: λ=

l + ∆l l

(2.30)

which compares for example the diameter of the cell l + ∆l after the deformation to the diameter of the undeformed cell l. The diameter l of a cell can either be stretched, when ∆l > 0 or compressed, when ∆l < 0. When considering the surface of a body, the diameter l of a cell is replaced by its surface A. Measures based on an increase in area during compression or elongation of a normally spherical body are called area expansion moduli. Four of the most widely used strain measures are listed in Tab. 2.3. Cauchy strain, developed from Eq. 2.28 with m = 0, also called engineering strain, and True strain (also m = 0), describe materials which experience infinitesimal strain. True strain thereby takes into account the spacial path of the strain, because it integrates over each strain increment. Green (-Lagrangian) strain (using m = 1) and (Euler-) Almansi strain (using m = −1) describe finite strains, instead [42]. Mechanical term

Mathematical expression

Cauchy strain True strain Green strain Almansi strain

ǫ=λ−1 ǫ = ln(λ) ǫ = 21 (λ2 − 1) ǫ = 21 (1 − λ12 )

Table 2.3: Four commonly used strain measures. λ symbolizes stretch or compressive ratio from Eq. 2.30.

In this thesis, cell strain was defined as the maximum relative deformation ( = compression) a cell reaches when it fully deforms to the size of the constriction, which is equivalent to a Cauchy strain: ǫmax =

rcell − rcon rcell

(2.31)

39


Figure 2.15: Definition of cell strain as maximum cell compression. A NIH 3T3 cell is maximally compressed inside a microconstriction ac−rcon . The decrease of its cording to ǫmax = rcellrcell diameter 2rcell to the width of the constriction 2rcon (red lines) is illustrated through black arrows. Scale bar is 10 µm.

2rcell

2rcon

with rcell being the radius of the undeformed cell measured in front of the constriction and rcon half of the width of the constriction (comp. to Fig. 2.15). The width thereby represents the smallest dimension of the constrictions used in this thesis, because the height of the constrictions is the same as the height of the rest of the device. ǫmax logically ranges between 0 and 1, and is between 0.4 ≤ ǫmax ≤ 0.8 for most investigated cell lines. Its advantages compared to the application of stretch strain measures or area expansion moduli are investigated in Sec. 3.4.

2.3.4 2.3.4.1

Power-law rheology Background

In the 1960s, a satisfactory description of cell mechanics was found by Hildebrandt in the form of power-laws [88]. In a simple experiment, he compared the stress-strain curves of a cat lung with a visco-elastic balloon, and thus demonstrated the applicability of power-law rheology to animal tissue. In the following years, the suitability of power-law rheology to all sorts of single cell and tissue deformations was more and more established, for example by measuring the deformation of cells through atomic force microscopy or magnetic twisting cytometry [41, 89](comp. to Sec. 1.2). Power-law theory describes the relative deformation ǫ(t) of a material in response to a sudden pressure step ∆p at t = 0 as a creep-response J(t) over time t: ǫ(t) 1 t = J(t) = · ( )β ∆p E τ E is the elastic stiffness of the material, which can also be expressed as

(2.32) 1 j0 ,

with j0 being

the cell compliance or deformability. The power-law exponent β is a measure for cell fluidity, which is the inverse of viscosity. A power-law exponent of β = 0 is indicative of a purely elastic solid, as Eq. 2.32 collapses to the description of Hooke’s law: ǫ(t) =

∆p E

(comp. to Eq. 2.2). β = 1 stands for a purely viscous fluid, which is equivalent to Newton’s law of viscous deformations: ǫ(t) =

∆p η

· t, with η being the viscosity of the body (comp. to

Eq. 2.5). In cells, β mostly falls in the range between 0.05-0.4. τ is an arbitrarily defined time constant. Its choice does not change the value of the power-law exponent, which is called timescale-invariance. Throughout this thesis, Eq. 2.32 was consistently evaluated at

40


τ = 1 s. For a description of the power-law through an equivalent of springs and dashpots, an unlimited series of springs and dashpots would be needed. This is illustrated through the connection of an unlimited amount of Voigt-bodies in Fig. 2.8 (right side). Power-law rheology can also be Fourier-transformed to describe the frequency-dependent cell response to sinusoidally varying forces: G(ω) = E · (iωτ )β Γ(1 − β)

(2.33)

with ω being the radian frequency, and Γ the Gamma-function. Note that power-law rheology according to Eq. 2.32, similar to a purely elastic or purely viscous description, predicts a linear material response, and yields constant values for E and β independent of the stress or strain applied in the measurement. During the last years, however, studies indicated more and more that cells show a non-linear response to finite stresses and strains [90–92]. This behavior is termed stress and/or strain stiffening. Its impact on microconstriction measurements is evaluated in Sec. 3.3. 2.3.4.2

Power-law fitting

For the reasons outlined above, power-law theory was applied to extract quantitative mechanical cell properties from microconstriction measurements. Power-law fitting gives two free fit parameters, cell elastic stiffness E and the power-law exponent β, which is proportional to cell fluidity. The theory was fitted to the scatters of deformation time tentry , strain ǫmax and stress ∆p, measured from several thousand cells per measurement. In each scatter plot, the local bivariate kernel density of data points is indicated by the marker color. The fitting gave thus population averages for the fit parameters E and β. With the current setup, the evaluation of single cell mechanical properties was not performed, except for the application of soft glassy rheology (comp. to 3.7). Before fitting, the power-law equation (Eq. 2.32) was rearranged to tentry = (

ǫmax E β1 ) ∆p

(2.34)

Moreover the data and the power-law equation were transformed by the logarithm to the power of 10: log(tentry ) =

1 β

log(

ǫmax ) + log(E) ∆p

(2.35)

max With x = log( ǫ∆p ), y = log(tentry ), the power-law resulted in a linear fit function y = ax+b

with the two fit parameters β =

1 a

b

and E = 10 a .

Since both the transformed x- and y-data carry errors, orthogonal regression was applied. Moreover, transformed x- an y-data have differing standard deviations, which requires the

41


use of weighted total least squares fitting, which minimizes: m q X (wx (xi − x ¯))2 + (wy (yi − y¯))2

(2.36)

i=1

x ¯ and y¯ are the mean x and y-values, wx =

1 std(x) ,

and wy =

1 std(y)

the weights.

For the comparison of two cell populations, a combined dataset of the two measurements was formed. Then, the standard deviations std(x) and std(y) of the combined dataset were calculated and finally used as weights for fitting the power-law to both populations. Unequal weights easily led to biased fit results, because the range of measured pressures was not necessarily correlated with the resulting cell mechanical properties. 2.3.4.3

Statistical analysis

Bootstrapping For the quantitative comparison of the cell mechanical properties of two or more cell populations, mostly 2-3 individual measurements per condition were pooled to get a sufficient amount of data points per fit. Standard errors for E and β were calculated by bootstrapping, where the fitting was repeated 100 times on ensembles of randomly selected cells. With bootstrapping, the standard error (se) of the sample is the standard deviation (sd) of the sampling distribution [93]. Statistics evaluation To test for significant differences when comparing experiments, the area of overlap between the probability density distributions of the fit parameters was computed. Differences were considered statistically significant for an overlap < 5% (p < 0.05) for all cases of this work.

2.4

Correlation of cell mechanical properties with protein expression

Cell populations, which are extracted from biopsies or even grow under controlled conditions in a laboratory, are often highly heterogeneous, even though all cells belong to the same lineage or carry the same DNA. This variety in biochemical and mechanical cell properties is mainly caused by differences in gene expression, which is in turn highly influenced by the cell cycle and the cell metabolism. For investigating the influence of protein expression on cell mechanical properties, cell lines are often genetically modified through transfection with viruses. Transfections induce foreign DNA-vectors into the cell DNA and thereby trigger for instance the overexpression of a protein corresponding to the transfected gene. Transfection efficiency, i.e. the percentage of cells which are positively infected by a virus and overexpress a protein, differs greatly

42

2.4 Correlation of cell mechanical properties with protein expression

between between 10-90 % between different transfection techniques and cell lines [94]. Cell transfections therefore even increase the heterogeneity of cell populations. In these cases, the investigation of cell mechanical properties through a population average of cell stiffness and fluidity, as conducted with the microconstrction assay (comp. to Sec. 2.3.4), reaches its limit. Given the case that differing protein expression levels change cell mechanical properties, the population averages of stiffness and fluidity depend dramatically on the transfection efficiency and on the mean protein expression level of the investigated cell population. Quantitative cell mechanical properties can thus no longer be compared between different experiments, even less so when they stem from different transfections. To resolve this problem, the microconstriction setup was extended by a fluorescence detection, which allows for the correlation of cell mechanics with protein expression levels of subpopulations of cells.

2.4.1

Fluorescence setup extension

lamp

filter T: λ > 590 nm

camera 2 specimen

objective

camera 1

dichroitic mirror T: λ > 510 nm beam splitter

filter T: λ < 550 nm

eyepiece

beam splitter/ mirror

filter T: λ > 515 nm

cylindrical lenses

laser

mirror

Figure 2.16: Optical path of fluorescence extension in microconstriction setup. Laser and bright-field illumination excite sample. The laser illumination is constrained to the field of view by a combination of cylindrical lenses. Later, both bright-field reflection and fluorescence emission are seperated by a 70:30 beam splitter and a lowpass filter before they enter the two synchronized cameras. Figure taken from [22].

For a parallel mechanical evaluation and protein expression analysis, a diode-pumped solid-state laser (wavelength 473 nm; VA-I-N-473, Viasho, Beijing, China) with a max43


imum power of 100 mW was coupled to the epifluorescence port of the microscope to observe GFP (green fluorescent protein)-tagged proteins during the mechanical measurements. A sketch of the optical path is shown in Fig. 2.16. First, the laser light passed two cylindrical lenses, which were oriented perpendicularly to each other, and a normal spherical lens (f1 = -50 mm, f2 = 50 mm, f3 = 50 mm). This configuration reduced the Gaussian beam profile to a highly rectangular illumination field which had an aspect ratio of approx. 1:10 and overlapped with the field of view normally observed for mechanical measurements. Through a dichroitic mirror and a normal 10x objective (Leica, numerical aperture = 0.2), the laser was focused on the sample. For bright-field illumination, only light with λ > 590 nm was used. The emission light of GFP-tagged proteins (∼ 515-550 nm), together with the bright-field light, could then pass the dichroitic mirror (λ > 515 nm), where the laser light was held back. It was finally divided between the eyepiece or the camera region. In front of the cameras, a 70:30 beam splitter transported both fluorescence and bright-field light into the bright-field camera. In front of the fluorescence camera, which received 70% of the light, a short-pass filter (transmission for λ > 590 nm) split the GFP-emission wavelengths from the bright-field light. A summary of all excitation and emission wavelengths is given in Fig. 2.17. Both cameras were placed on a camera port with a custom-made coupler (C-port to SM1), so that they had the same distance from the sample to ensure the same magnification factor. GFP signal

bright-field signal

450

500

550

590nm longpass

20

550nm shortpass

40

515nm longpass

60

510nm dichroitic mirror

80 473nm laser

Transmission [%]

100

600

λ [nm]

Figure 2.17: Wavelength distribution of fluorescence extension of microconstriction setup. The laser excites the fluorescent sample at 473 nm. The bright-field excitation is restricted to wavelengths λ > 590 nm by a longpass filter. A dichroitic mirror splits the laser excitation light from the fluorescence and bright-field emission at 510 nm. The GFP signal recording is limited to 515-550 nm by the combination of a longpass and a shortpass filter.

2.4.2

Image recording with synchronized cameras

Synchronized image acquisition was realized with an addition to the C++-recordingprogram, adapted by Sebastian Richter and implemented by Christian Heidorn [77]. In brief, the usually used CCD camera (G680, Allied Vision) in the bright-field channel,

44

2.4 Correlation of cell mechanical properties with protein expression

Figure 2.18: GUI for synchronized image recording. Display of live images of camera 2 (bright-field) and camera 1 (fluorescence channel) with approx. 60 fps. Exposure, gain and thereby frame rate can be set independently for both cameras (top right). Synchronized image recording can be started with the START-button (top left). The log window (bottom) shows the log history of all recordings of this imaging session.

which ran at a frame rate of 750 fps with an exposure time of 60 µs, triggered a second, synchronized camera (also G680, Allied Vision) in the GFP-channel. The fluorescence camera recorded the GFP-emission light at a framerate of 125-375 fps with an exposure time of 2-4 ms. The frame rate was limited by the maximum frame rate reached for the given fluorescence exposure time (Fig. 2.18 top right). For bright-field images, the gain was set to zero, with fluorescence imaging, instead, a gain between 8-16 dB was used. With an Allied Vision camera, the gain is defined as gdB = 20 log

Vout Vin

, with Vout being the

outgoing and Vin the incoming sensor voltage.

Through an extended GUI, the user could start and stop the recording of both cameras at the same time (Fig. 2.18 top left). Moreover, bright-field and fluorescence images were shown continuously for the user at a frame rate of 60 fps to enable an adjustment of bright-field or laser illumination, or image parameters, like exposure time and gain.

2.4.3

Image analysis

Only fluorescence images of cells that were immobilized at the constriction entrance were evaluated to avoid motion blurring. For computing the fluorescence intensity of a cell,

45


a region of interest corresponding to the channel area in front of the constriction was considered (approx. 20 x 60 µm). Pixel intensities were background-subtracted with the median pixel intensity of the ROI to counterbalance brightness fluctuations induced by instable bright-field or laser illumination. Subsequently, the sum over all positive pixel intensities in the ROI was formed. The intensity sum of all pixels was then normalized by the cell area extracted from bright-field images. Thereby, a cell-size independent average fluorescence intensity of the cell in units of counts per cell pixel was achieved.

2.5

Cell systems

In this work, various cell lines were investigated and compared. Two of the most often used lines, plus the advantages of their usage, are characterized in detail in the following.

2.5.1

K562 leukemia cells

K562 leukemia cells were used as a model system for various measurements of this work. This cell line was derived from precursor granulocytes of a leukemia patient in 1973 [95] and has been investigated thoroughly since then concerning its differentiation. It was also widely used as a model system for countless overexpressions or knockouts of intracellular proteins [96, 97]. The cells used in this study were bought from ATCC (#CCL243; American Type Culture Collection) and cultured according to App. 6.3. K562 cells combine several advantageous cell properties, which simplify stable and long-time measurements with a microfluidic setup. All of them stem from the fact that K562 cells are naturally non-adherent cells, meaning that they live in suspension without adhering to a substrate. As trypsinization was not necessary for K562 cells before microconstriction measurements, they do not suffer from changes in the cell cytoskeleton after lift off of the substrate. Therefore, temporally stable intrinsic cell mechanical properties could be assumed. Moreover, in contrast to trypsinized cells, which sometimes take over 2 h to reach a perfectly spherical morphology after detachment from the substrate, K562 cells show a stable sphericity with an axis aspect ratio of < 1.05 at all times of the measurement. Furthermore, suspended cells do not tend to adhere to the channel walls or coaggulate during the measurement, because their cell-cell-cohesion and cell-matrix-adhesion is extremely week, if not non-existent. A gradual clogging of the feeding channels or the filter system due to cell-cell-sticking or cell-cell-channel-wall-sticking, which could in the worst case terminate measurements prematurely, is therefore excluded. Furthermore, K562 cells have shorter transit times through microconstrictions than all other investigated cell lines. This is probably due to their lack of a highly contractile actin cytoskeleton. Shorter transit times enable a higher measurement throughput and a better statistical evaluation of all measurements. Finally, a big amount of K562 cells can be successively harvested from one and the same culture flask (flask area A = 175 cm2 ). Thus, up to 12 independent measure-

46

2.5 Cell systems

ments from cells cultured under identical cell culture parameters can be conducted.

2.5.2

DLD-1 colon carcinoma cells

The second cell sytem used for many technical measurements of this work is called DLD1. This colon carcinoma cell line was derived from a white man who suffered from an adenocarcinoma of the sigmoid colon in 1981 [98]. The cells were kindly provided by Prof. Michael St¨ urzl’s lab (Division of Molecular and Experimental Surgery, University Clinics of Erlangen). DLD-1 cells had been transfected with an empty backbone vector (pMVC) and subsequently colony-picked for the research project detailed in Sec. 4.6. This procedure led to a monoclonal, highly homogeneous cell line in terms of cell size and mechanical properties. Even though DLD-1 cells are a naturally adherent cell line, they do not coaggulate after trypsinization, which enables long-time measurements free of clogging. For measurements, the cells were cultured according to App. 6.3.

47


48

3

Investigations of cell mechanics After the construction of the microconstriction assay, some technical evaluations were performed to test the stability of experimental procedures, and the influence of microconstriction measurements on cell morphology and viability (Sec. 3.1). Among other things, the applicability of power-law rheology for the description of cell deformation in a constriction was verified (Sec. 3.2) and the influence of the measurement parameters strain and stress on the resulting cell mechanical properties was investigated (Sec. 3.3 and Sec. 3.4). The sensitivity of the setup, concerning the detection of changes in cell mechanical properties, like the cytoskeleton or the nucleus (Sec. 3.6), and to changes in cell culture and measurement parameters, like cell culture density, was studied (Sec. 3.8). Finally, the correlation of fluorescently labeled proteins with cell mechanics was validated and the impact of high-power laser illumination on cell mechanics was tested (Sec. 3.9).

3.1

Influence of microconstriction measurements on cell morphology, viability, and proliferation

During the measurement of cell mechanical properties with a microconstriction setup, cells are subjected to unphysiological environmental conditions. Firstly, measurements do not take place at body temperature (37◦ C), but at room temperature, which is approx. 22◦ C. Secondly, naturally adherent cells must be trypsinized before measurements, which changes their metabolism and induces reorganization processes of the cytoskeleton. The actin stress fibers of cells, for example, are depolymerized over a time period of less than 10 min after detachment [99]. Moreover, microconstriction measurements apply high stresses and strains on cells. Cells are flushed at high speeds through the feeding channels and are sheared at crossroads. Furthermore, they possibly collide with channel walls and with other cells during their approach to the microconstrictions. During cell deformation into the microconstrictions, the cell diameter is compressed by 50% on time scales of only 0.01-1 s on average. All these processes might potentially change cell morphology and induce cell inflation,

49

3. INVESTIGATIONS OF CELL MECHANICS

shrinkage, or membrane rupture. Furthermore, they could damage the cell through DNAbreakages, which could even result in apoptosis. In previous studies, cell apoptosis, in turn, was already linked to changes in cell deformability [25]. Cell apoptosis might therefore lead to biased measurements or a lack of measurement reproducibility. Moreover, for the case that cells are recollected after the measurements for further investigations, it is interesting to observe if the cells suffer from long-term damage after the measurements, for instance if their proliferation is stopped or decreased. Due to these considerations, the influence of cell mechanical measurements with a microconstriction setup on cell morphology, viability and proliferation was checked.

3.1.1

Influence on cell morphology

Investigations of the cell shape during deformation revealed that cells often form blebs at the rear and leading edge during transit through narrow constrictions with a width w < 6 µm, as visible in Fig. 2.10 and 3.9. The occurrence of cell blebbing and its and correlation with cell entry time and cell size was subsequently investigated to shed light on the origins of blebbing. As exemplary cell population, K562 leukemia cells were monitored during deformation through a constriction with a width of 5.1 µm (device type S7, comp. to Sec. 2.1). Cells were cultured as usual according to App. 6.3. Cell and device preparation were conducted according to Tab. 3.2. In this experiment, the field of view showed the region in front of the constriction, but it also included the whole constriction channel, and not only its entry, in order to capture the full cell transit.

b

c

0.6 0.4 0.2

9 *

8 7 6

0 no bleb

bleb

no bleb

1.5

εmax(nobleb) = εmax(bleb)

n=669 0.8

tentry(nobleb) = tentry(bleb)

10

Entry time [s]

1 Cell radius [µm]

Relative frequency

a

*

1 0.5 0

bleb

no bleb

bleb

Figure 3.1: Bleb formation during K562 cell deformation into a microconstriction with width of 5.1 µm. a) Percentage of blebbing cells in constriction (n = 669 cells). b) Correlation of cell blebbing with cell size for two cell populations with the same median entry time. c) Correlation of cell blebbing with cell entry time for two cell populations with the same median cell size. Significant differences (p < 0.05) are indicated by asterisks. Figure adapted from [22].

For a total of 25 % of K562 cells, blebs with a diameter between 1-3 µm were found at either the rear or the leading edge, or on both edges (Fig. 3.1 a). Cell blebbing probability was positively correlated with cell size. To show this, the blebbing occurrence for two cell populations with the same mean entry time into the constrictions

50

3.1 Influence of microconstriction measurements on cell morphology, viability, and proliferation was compared (Fig. 3.1 b). It can be concluded that larger cells, which experience a higher strain during transit, are more likely to suffer from membrane rupture. Furthermore, cell blebbing was positively correlated with cell entry time, which was investigated by comparing two cell populations with the same mean cell size, but with largely differing entry times (Fig. 3.1 c). The longer the strain acts on the cell cortex, the more likely the membrane ruptures and decrease the internal pressure by rupture. These data suggest that both cell size and entry time independently increase membrane rupture and blebbing occurrence [22]. Moreover, cell relaxation was investigated to check if changes in cell morphology were permanent. Therefore, cells were stopped after transiting the constrictions by manually stopping the applied pressure. After compression in the constrictions, the cells showed a complete restoration of their initially approximately circular shape during only few minutes. Cell blebs usually kept their size longer, but were finally also completely retracted by the cells after transit during a time period of at most 10 min (data not shown). As a conclusion, changes in cell morphology are not permanent. The phenomenon of cell blebbing might be relevant considering natural strategies of cells to decrease strain and stress during passage through small constrictions in the human body. Membrane blebbing could increase the passing rate and also decrease the passing time of blood cells in the capillary network. For future studies, a correlation of cell blebbing with cell type, for instance comparing differentiated and undifferentiated blood cells or activated and unactivated leukocytes, would be highly interesting. Moreover, the expression of specific membrane proteins might then be correlated with an in- or decrease of cell blebbing occurrence.

3.1.2

Influence on cell viability and proliferation

In the previous section, cells were demonstrated to restore their morphology completely after measurements with a microconstriction setup. Still, the question arises if cells, after restoring their deformation or retracting blebs, show an increased rate of apoptosis on a long-term basis. As outlined above, a possible increase in apoptosis might not only be caused by the application of high stresses or strains, but also by highly unphysiological environmental conditions during measurements. The influence of microconstriction measurements on cell viability and proliferation of K562 leukemia cells was checked at three measurement steps. After conducting each step independently, cell proliferation, and thereby cell survival, was measured by manual cell counting with a Neubauer hemocytometer over four consecutive days. Before counting, cell survival was checked through trypan blue staining (#T8154, Sigma-Aldrich), and dead cells were excluded. Firstly, cells were counted for four days under continuous incubation with 0.5 % pluronic. The PEG-compound pluronic was usually used to reduce non-specific cell adhesion to the channel walls during microconstriction measurements [75, 76]. Cells

51


5 44

Proliferation rate

Proliferation rate

Figure 3.2: Impact of measurement process on cell viability and proliferation of K562 leukemia cells. Proliferation rate measured over four days after treatment with 0.5 % pluronic, after application of shear flow, and after a measurement with 6 µm-wide constrictions, compared to untreated control group. n = 8 experiments. Figure adapted from [20].

Control 0.5% pluronic Shear flow Constrictions

33 22 11 00

Day 1 Day 2 Day 3 Day 4 Day1 Day2 Day3 Day4

were usually incubated with pluronic for 30-40 min. Secondly, cell proliferation was measured for four days after experiencing shear flow in a shear flow stretcher device for 30 min on day 1. This device only consisted of a cell inlet and outlet, a filter system and a long straight channel with a width of 20 µm, where the cell shearing takes place (comp. to Sec.1.2). Thirdly, cell proliferation was studied for four days after experiencing a full microconstriction measurement with a constriction width of 6 µm for a duration of 30 min on day 1. The last two conditions included the normal measurement preparation, i.e. 4 min centrifugation at 1400 rpm (405 × g), and were conducted at room temperature. The device used for the microconstriction measurement did not contain a bypass, to avoid that cells leave the device without experiencing a compression in a constriction. As a control group, cell numbers were counted for a population which was cultured as usual in an incubator. All populations were initially seeded at the same cell density of 250,000 cells/ml in a 96 well plate. For this study, naturally suspended K562 leukemia cells were used again. Therefore, influences of trypsinization were not investigated. Before the experiment, the cells were cultured and harvested according to App. 6.3. As depicted in Fig. 3.2, there is no systematic difference between the proliferation rates of the four groups. K562 cell proliferation was not impaired by neither a culture with pluronic for four days, nor by shear flow, nor by a full microconstriction measurement including cell deformation in the constrictions. The cells do supposedly not suffer from pluronic incubation, and are able to repair cell membrane damage and possibly nuclear damage induced by shear flow or by passage through the microconstrictions, without compromising their normal cell cycle. All in all, it can be concluded that microconstriction measurements do not permanently damage K562 leukemia cells [20]. These results are in accordance with a previous study, showing that only a constriction size of < 3 µm was likely to increase apoptosis in lamin A-deficient cells [100].

52

3.2 Validation of power-law behavior

200 μm

Figure 3.3: Microconstriction layout for investigations of temporal development of cell shape during deformation. The device contains only one constriction. The constriction is followed by an enlarged cavity to enable the observation of cell relaxation after transit. Inset: Zoom of constriction region. Scale bar of zoom is 50 µm. A bright-field image of the constriction can be found in Fig. 2.15.

w50 w50

w50

w50

3.2

Validation of power-law behavior

As previous studies widely demonstrated the validity of power-law description for the mechanical response of adherent cells [11], power-law theory was also checked for its applicability concerning the deformation of suspended cells through a micron-scaled constriction. Therefore, single cell deformation into a constriction was monitored over time and fitted by power-law rheology. Moreover, the dependence of the scatters of entry times tentry of thousands of cells on both maximum deformations ǫmax and working pressures ∆p was analyzed.

3.2.1

Analysis of single cell deformation

First, it was tested if single cell deformation through a micron-scaled constriction behaves according to power-law theory. This is why the cell shape, and thus the cell strain during cell transit was monitored and evaluated over time. For this study, a special microconstriction layout was developed (comp. to Fig. 3.3). In a system containing two or more constrictions, a constant pressure applied to a constriction from the outside is disturbed by alternating clogging configurations in neighboring constrictions, which cause sudden pressure fluctuations. Therefore, a design containing only a single constriction was built. Moreover, the design contained a cavity placed after the constriction channel. The big increase in channel width automatically decelerates the cell after transit through the constriction. This deceleration gives the researcher the time to react and manually stop the cell after transit by deactivating the pump. The relaxation

53


1 Norm. deformation

Figure 3.4: Development of cell strain over time during cell entry into a constriction. Master curve of cell deformations ǫ(t) = l+∆l(t) of 59 NIH 3T3 l cells (black circles) during their entry into a constriction and power-law fit (orange line). Time t and deformation ǫ(t) were normalized by entry time tentry and maximum deformation ǫmax before averaging. Background curves show deformations of individual cells. Figure adapted from [22].

0.8 0.6 0.4 Power-law fit Mean values

0.2 0

0

0.2

0.4 0.6 Norm. time

0.8

1

of the almost motionless cell could then be observed in the cavity. Moreover, the cell could not collide with channel walls during the relaxation process, which simplified image evaluation. As exemplary cell system, NIH 3T3 fibroblasts were used for measurements. The cells were cultured in DMEM medium (Dulbecco’s Modified Eagle’s Medium, #11965092, gibco), including 10 % FCS (fetal calf serum, #16000036, gibco) and 1 % PSG (penicillinstreptomycin-glutamin, #10378016, gibco). Cells were as usual harvested at a culture confluency of 80 %. For the observation of cell deformation, NIH 3T3 cells were pumped through a constriction with a width of approx. 8 µm in a device with a height of approx. 22 µm. Slightly wider constrictions than usual were chosen, so that an overall smaller pressure could be applied on cells. When applying too high pressures, the resolution of the camera (750 fps) was not sufficient to resolve the whole cell transit properly. Moreover, it was impossible to stop the cell after transit to investigate cell relaxation. Cell and device preparation before measurements were conducted according to Tab. 3.2. The usually applied strain measure ǫmax , which describes the relative compression of the cell inside the constriction (comp. to Sec. 2.3.3.2), could not be applied for measurements of continuous cell deformations. The channel walls massively blur the cell shape inside a microconstriction and the cell width cannot be measured with a high accuracy. This is why the long axis of the cells was used as an alternative measure of deformation: ǫ(t) =

l+∆l(t) , l

with l being the long axis of the undeformed cell, and ∆l(t) the increase in length during compression (comp. to Sec. 3.4.2). The long axis of 59 NIH 3T3 cells was tracked manually during cell transit through the constriction to exclude tracking errors from an automated analysis. The deformation curves of the cells were normalized to ǫmax = 1, and t = 1 was the time point when the cell left the constriction (tentry = 1). Then, an averaged master curve from all transits was formed, as shown in Fig. 3.4. The fit goodness of power-law rheology was tested for the master curve. For comparison, a linear, purely viscous material according to ǫ(t) =

54

∆p η

· t was fitted, which provides the free

3.2 Validation of power-law behavior

fit parameter a =

∆p η ,

with η being the viscosity. Moreover, the cells were approximated as

a visco-elastic Kelvin-Voigt material, fitting ǫ(t) =

∆p E

· (1 − e

−E ·t η

). Here, E represents the

elastic stiffness of the cells, η their viscosity. Finally, the data were fitted by a power-law: t β . The power-law gives the two fit parameters elastic stiffness E and the ǫ(t) = ∆p E · τ

power-law exponent β, which is a measure for cell fluidity. τ was as usual set to 1 (comp.

to Sec. 2.3.4). Other more complicated models, consisting of multiple elastic and viscous components, were not fitted due to the reasons outlined in Sec. 2.3.1.1. The power-law fit gave an excellent fit goodness of R2 = 0.97 , followed by the KelvinVoigt fit with R2 = 0.92 and by the linear fit with R2 = 0.87. This result supports the validity of power-law rheology as a description for cell deformation in a microconstriction [22].

Power-law behavior of tentry vs. ǫmax /∆p of a cell population

3.2.2

The current usage of the microconstriction setup gives measures for entry time tentry , maximum deformation ǫmax and the working pressure ∆p of several thousand cells per measurement. Through power-law fitting, the population average for stiffness E and power-law exponent β were then calculated. Single cell properties could not be extracted with the current use of the setup, because for each cell ǫ(t) was not evaluated over time, but only one measurement of the maximum deformation ǫmax =

rcell −rcon rcell

was conducted. This

is why the dependence of the scatters of entry time tentry on the scatters of deformation ǫmax and pressure ∆p of a cell population was investigated. a

b Δp =244 ± 15 Pa 101 Entry time [s]

Entry time [s]

101 100 10-1 10-2 100

100 10-1 10-2

200 400 Pressure [Pa]

600

0.4

0.5 εmax

0.6 0.7

Figure 3.5: Power-law dependence of population scatters of entry times on stress and strain for K562 cells. a) Scatter plot of tentry vs. ∆p. The local bivariate kernel density of data points is indicated by the marker color. Black squares: Geometric mean of 300 binned cells. Black line: Power-law fit to non-binned data. b) Scatter plot of tentry vs. ǫmax . Pressure range is limited to 244 ± 15 Pa (mean ± sd). Black squares: Geometric means of 70 cells. Black line: Power-law fit to unbinned data. Figure adapted from [20].

To test the applicability of power-law rheology to population averages, K562 leukemia cells were chosen as an exemplary cell system and measured with devices containing constrictions with a width of 6.0 µm and a device height of 13.6 µm (device type O3, see Sec. 2.1).

55


Cells were as usual cultured according to App. 6.3. Cell and device preparation before measurements were conducted according to Tab. 3.2. After the measurements, a power-law was fitted to the scatter data of entry time versus pressure of approx. 3000 cells (Fig. 3.5 a) in a double logarithmic representation. Powerlaw theory predicts the dependence of entry time on working pressure according to tentry ∼ 1 1 β 1 β . The fit was in perfect , and on maximum deformation according to t ∼ (ǫ ) entry max ∆p

agreement with the scatter of the data and its geometric means (∼ 300 cells per bin), which showed a linear decrease in this representation, which means a power-law dependency in a linear representation. To check the dependence of entry time on maximum deformation, only cells from plot a) which have experienced the same pressure range (244 ± 15 Pa, mean ± sd) were chosen. Again, the power-law fit agreed perfectly with the data and its geometric means (∼ 70 cells per bin), this time showing a linear increase (Fig. 3.5 b). The power-law exponents were similar, but not equal for both fits due to stress and strain stiffening [20]. Stress and strain stiffening will be explained in detail in the following section (Sec. 3.3). Confirming the power-law dependency of entry times on both maximum cell deformation and pressure drop highlights the validity of power-law application for the evaluation of population averages of stiffness and power-law exponent. To this date, no other theoretical framework was found to match the linear dependence of entry time on the ratio of strain and stress in a double logarithmic representation better than a power-law. The testing of alternative theoretical frameworks, however, was difficult to achieve, because the big amount of scatter in entry time measured for each cell population made the fitting of highly non-linear functions unstable.

3.3

Investigations of stress and strain stiffening

During the last decades, it has become more and more evident that cell mechanics can only approximately be described by a linear visco-elastic material model. In reality, cells exhibit non-linear mechanical properties, which are often termed stress and strain stiffening [90–92]. The most famous example for macroscopic strain stiffening is human skin. Skin stretches easily under small deformations, but becomes increasingly stiffer with higher strains to protect the body from injuries, such as skin rupture. In many previous studies, the material properties of cells, for instance elastic stiffness, could also be positively correlated with the amounts of stress or strain applied in the measurement [90–92]. Power-law theory describes a linear visco-elastic material with constant stiffness E = E0 and fluidity β = β0 for all values of applied stress and strain (comp. to Sec. 2.3.4). However, considering a typical scatter of entry times tentry , the data do not simply follow a line in the double logarithmic presentation. Instead, they deviate from the power-law dependency of entry time on strain and stress and form a huge scatter cloud. As depicted in Fig. 3.6,

56

3.3 Investigations of stress and strain stiffening

10-1

250 Pa

300 Pa

450 Pa 400 Pa 350 Pa

Entry time [s]

100

Figure 3.6: Stress and strain stiffening. Scatter plot of tentry vs. ǫmax /∆p for 19,991 K562 cells. Black squares (connected by red lines): Median values of tentry vs. ǫmax /∆p for different pressure ∆pj and strain ǫmaxi bins containing at least 250 cells. Strain bin width is 0.03, pressure bin width is 50 Pa. Numbers next to iso-stress and iso-strain lines show median pressure and strain values. Black grid: Fit of extended power-law to the binned data, with stress stiffening according to E = E0 + c1 ∆p. Fit parameters are E0 = 58 Pa, c1 = 1.11 Pa−1 , β = 0.07. Figure adapted from [22].

ε=0.68 ε=0.65 ε=0.62

10-2

ε=0.59

1

2 3 εmax/∆p [x10-3 1/Pa]

4

entry times tentry of K562 cells from six experiments, measured with constrictions with a width of 6.0 µm (device type O3, comp. to Sec. 2.1), scatter over more than 3 orders of magnitude for the same ratio of ǫmax /∆p. A big portion of the scatter can be explained by the fact that cells experience different stresses and strains during microconstriction measurements. To demonstrate that these cells also exhibit stress and strain stiffening, the data were sorted into bins according to ǫmaxi /∆pj for cells which experienced similar strains ǫmaxi and stresses ∆pj . Therefore, a strain bin width of 0.03 and a pressure bin width of 50 Pa was chosen. The median entry time tentry of these bins formed a highly regular grid (black squares in Fig. 3.6). Iso-strain lines, meaning lines that connect data points of equal strain, are aligned more horizontally and are shifted towards larger entry times as the strain increases. Lines that connect points of equal pressure, i.e. iso-stress lines, are aligned more vertically, and are also shifted towards larger entry times as the pressure increases (red connecting lines in Fig. 3.6). This behavior implicates stiffening of the cells with increasing stress and increasing strain. From the extent of stress and strain stiffening shown in Fig. 3.6, it becomes clear that stress and strain stiffening influence the resulting cell stiffness and the power-law exponent to a big extent. Stress and strain stiffening might therefore critically bias the comparison of cell mechanical properties from two or more measurements, when cells in these measurements experienced different pressures or different strains. First, considerations of including stress and strain stiffening into power-law theory are presented. Later, 2-dimensional histogram matching is outlined, which enables the comparison of cell mechanical data from two measurements without bias from stress and strain stiffening.

57


3.3.1

Extension of power-law rheology with stress and strain stiffening

Non-linear cell mechanical properties could best be taken into account by including an explicit stress and strain dependency of the resulting fit parameters in the power-law equation, for example through a linear approximation [11]: E = E0 + c1 ∆p + c2 ǫmax

(3.1)

Here, the impact of stress and strain on stiffness E is given by the two independent fit parameters c1 and c2 . To test this approach, power-law theory extended with stress and strain stiffening of E was fitted to the scatter of tentry vs. ǫmax /∆p of the data shown in Fig. 3.6. The additional fit parameters c1 and c2 could nearly fully account for the spread of the data grid. The best fit for the stress stiffening coefficient c1 was approx. 1, indicating an increase of the cell elastic modulus of 1 Pa for a pressure increase of 1 Pa. The resulting strain stiffening coefficient c2 was approx. 200 Pa. This means that for a strain increase of 100 %, the cell elastic modulus increased by 200 Pa. However, the grid-like systematic scatter of the binned data points could equally well be accounted for by considering only stress stiffening according to E = E0 + c1 ∆p (black grid in Fig. 3.6) or only strain stiffening according to E = E0 + c2 ǫmax (not shown). This implies that there was a considerable covariance between the fit parameters c1 and c2 . The situation became even more inextricable when including the influence of stress and strain on the power-law exponent β, which is termed fluidization [11], for example according to: β = β0 + c3 ∆p + c4 ǫmax .

(3.2)

Again, fitting with two more free parameters could reproduce the grid-like structure of the scatter of entry data equally well. In summary, the fit goodness of all approaches ranged in the same region, and variations of fit errors between arbitrary subsets of the data were higher than systematic advantages of one approach over the other. Therefore, it was not possible to disentangle the influence of stress and strain on stiffness or fluidity with the available scatter of the data. A meaningful extension of power-law theory through Eq. 3.1 or Eq. 3.2 could not be achieved. In the following, linear power-law theory was thus fitted to the data with only two free fit parameters E and β [22].

3.3.2

2-dimensional histogram matching

2-dimensional histogram matching was developed to prevent stress and strain stiffening from biasing comparisons of measurements, where cells experienced differing stresses and strains. Histogram matching chooses cells from two or more different experiments for comparison that have experienced both the same maximum strain ǫmax and the same 58

3.3 Investigations of stress and strain stiffening

pressure drop ∆p. Therefore, 2-dimensional histograms of distributions for ǫmax with a bin width of 0.05, and for ∆p with a bin width of 50 Pa were computed (Fig. 3.7 left+right). For every ǫmaxi /∆pj bin, cells from the measurement population with the larger number of cells were randomly excluded until the number of cells in each histogram bin matched. Thus, also the histograms of the ratios of ǫmax /∆p for each cell population approximately matched (Fig. 3.7 right). During power-law fitting, the random exclusion of cells was repeated in every bootstrap repetition (i.e. 100 times). So all data points were considered with the same probability. Measurement 1

freq.

200 100 0 100 300 ∆p 500

Merged histogram 0.6

0.4 0.2 ε max

freq.

200 100

Measurement 2

freq.

200 100 0 100 300 ∆p 500

0 100 300 ∆p 500

0.6 0.4 0.2 ε max

0.6 0.4 0.2 ε max

Figure 3.7: Principle of 2-dimensional histogram matching. Before comparing two measurements, cells from each histogram bin ǫmaxi /∆pj are randomly excluded, until the number of cells in each bin match (termed merged histogram). This procedure is repeated for every bootstrap repetition, so that all cells per bin are considered with the same probability.

The application of the histogram matching method is shown by comparing the mechanical parameters of cells from the same K562 leukemia population conducted with two devices of differing constriction sizes. Half of the cells were measured with wide constrictions (6.0 µm, device type O3), the other half was measured with narrower constrictions (5.1 µm, device type S7, comp. to Sec. 2.1). Cells were cultured according to App. 6.3 and harvested from the same culture flask (area A = 175 cm2 ), to ensure identical intrinsic cell mechanical properties. Cell and device preparation before measurements were conducted according to Tab. 3.2. Three independent measurements from each of the two devices were pooled after evaluation for power-law fitting. From the scatter plots of tentry vs. ǫmax /∆p (Fig. 3.8 a) and from the histograms of measured ǫmax and ∆p (Fig. 3.8 b left and right), systematic differences concerning the 59


experienced stress and strain are visible. Cells measured with the smaller constrictions experienced a higher maximum deformation than cells measured with the wider constrictions (Fig. 3.8 b left). Moreover, cells measured with the smaller constrictions experienced a higher pressure drop ∆p, because the researcher compensated for the increased cell entry times into the constrictions by increasing the applied pressure (Fig. 3.8 b right). The combined effect of stress and strain stiffening resulted in a significantly increased elastic modulus for measurements with smaller constrictions (Fig. 3.8 c left). The power-law exponent, however, remained similar (Fig. 3.8 c right).

d

100

2 1 0.4

εmax

El. mod. [Pa]

4

0.3

400 800 ∆p [Pa] ns

0.2

200

0.1

100 6.0µm 5.1µm

0

2

4 1 2 εmax/∆p [x10-3 1/Pa]

e overlap 5.1µm 6.0µm

0.4

*

1

1 00

0.8

400

0

2

2

6.0µm 5.1µm

2 1 00

f

#Cells [x103]

#Cells [x103]

3

PL- exponent

#Cells [x103]

b

4 1 εmax/∆p [x10-3 1/Pa]

#Cells [x103]

2

El. mod. [Pa]

1

300

100

10-2

10-2

c

5.1µm

10-1

10-1

00

101 6.0µm

5.1µm Entry time [s]

Entry time [s]

101 6.0µm

*

200 100 0

1

00

0.4 0.8 εmax

400 300

4

0.5

6.0µm 5.1µm

PL- exponent

a

400 800 ∆p [Pa]

0.4 0.3

ns

0.2 0.1 0

6.0µm 5.1µm

Figure 3.8: Histogram matching for measurements with wide (6.0 µm) and narrower (5.1 µm) constrictions. a) Unmatched scatter plots tentry vs. ǫmax /∆p for two K562 leukemia cell populations. Black lines show power-law fit to the data. n > 18859 cells per condition. b) Strain (left) and stress (right) of the two populations is increased for cells in narrow constrictions (blue) compared to cells in wider constrictions (yellow). Histogram overlaps are marked in green. c) Left: Unmatched cell stiffness is significantly increased for cells measured in the narrower constrictions. Right: Power-law exponent is similar. d) Exemplary histogram matched scatter plots and power-law fits of the same measurements as a). n = 10924 cells per condition. e) Exemplary strain histograms (left) and pressure histograms (right) after histogram matching now overlap. f) After histogram matching, cell stiffness (left) and fluidity (right) are now similar between cells measured in the narrow (blue) and wider (yellow) constrictions. Significant differences (p < 0.05) are indicated by asterisks. Figure adapted from [22].

After ∆p and ǫmax histogram matching (exemplary scatters and fits shown in Fig. 3.8 d+e), the cell elastic moduli for the two measurement conditions are now almost identical (Fig. 3.8 f left). After histogram matching, the already matching power-law exponents remained unchanged (Fig. 3.8 f right). The remaining mismatch of the elastic modulus of

60

3.4 Comparison of different strain measures

7 Pa (3 %) is probably caused by inaccuracies of the measurement of the channel geometries (± 0.25 µm) between the different devices, as outlined in detail in Sec. 3.5 [22].

Conclusion In summary, including stress and strain stiffening into the power-law description of cells was not possible to this date. However, 2-dimensional histogram matching was developed to avoid a bias through stress and strain stiffening when comparing different measurements. Thereby, only subpopulations of cells, which experienced both the same range of stress and strain, are compared during power-law fitting. The cell mechanical parameters given in all chapters of this thesis, which result from an unextended power-law fit and 2-dimensional histogram matching, must therefore be interpreted as an effective cell elastic modulus and an effective fluidity. They only apply for the specific range of pressure and strain that the cells experienced in the investigated measurement.

3.4

Comparison of different strain measures

As outlined in Sec. 2.3.3.2, there are multiple possibilities of describing deformations of a body in reaction to an applied force. The choice of a strain depends on the applied stress, the geometry of the deformed body, and on the geometrical parameters that are measured. Cells deforming into a microconstriction experience a highly complex mixture of normal and shear stresses, as well as friction caused by cell sliding inside the constriction channel. Moreover, the deformation systematics differ slightly between cells of different sizes. In Fig. 3.9, the shape development of a small, medium-sized and a big K562 leukemia cell is shown during their transit through a constriction with a width of 6 µm (device type O3, comp. to Sec. 2.1). Cells of all sizes deformed into the constriction by first quickly, then slowly adapting their width to the size of the constriction. After maximum compression, the cells slid through the only 10 µm long channel before exit. The bigger the cell was, (Fig. 3.9 left to right), the more the constriction acted as a steam roller, deforming not the whole cell at the same time, but serially compressing it in the longitudinal direction. After the transit, all cells traveled on in a bullet-like shape and their membranes often kept a ruffled shaped. The occurrence of membrane ruffling increased with increasing cell size. The largest cell in Fig. 3.9 formed a membrane bleb during transit. As explained in detail in Sec. 3.1.1, cell blebbing is positively correlated with both cell size and entry time into the constrictions. Considering the cell shape developments in Fig. 3.9, it is not possible to name one simple strain measure which describes the deformation process of a cell into a microconstriction. The only way to describe the strain correctly would be a complex finite element simulation of the cell deformation into the constriction, which resulted in a strain value for each

61

Time [ms]


0

0

0

15

100

1000

22

150

2000

33

250

4500

39

299

4999

40

300

5000

16

18 Cell diameter [µm]

22

Figure 3.9: Cell shape analysis during transit through a microconstriction. Time series of cell shape for a small (diameter of 16 µm), medium-sized (diameter of 18 µm) and large (diameter of 22 µm) cell. The large cell forms a bleb at its leading edge. In contrast to the approximately simultaneous deformation of the small cell, the constriction works as a steamroller for the large cell and compresses it sequentially. Deformation time is indicated by red numbers. Scale bar is 10 µm. Figure adapted from [22].

element on the cell surface for each time point. Such a simulation, dealing with largescale deformations on a micron-scale is difficult to achieve. Moreover, the description of cell mechanics by power-law theory requires a 1-dimensional strain value. Tensoric representations, containing normal and shear components, are not applicable in the used form of Eq. 2.34. Hence, a simple, but knowingly oversimplifying 1-dimensional strain measure was searched to compare cell transits through a microconstriction taking into account different cell sizes. The strain measure of choice was supposed to fulfill the two following requirements: • Two measurements, which were conducted on the same cell type with devices of differing dimensions, give the same resulting values for cell stiffness and the powerlaw exponent. • The scatter cloud formed by thousands of measurements of entry times tentry vs. 62


ǫmax /∆p can be explained by binning according to different combinations of ǫmaxi /∆pj for different combinations of i and j. The first requirement incorporates the fact that, after correcting for stress and strain stiffening, only intrinsic cell mechanical properties should determine the resulting cell mechanical parameters. Therefore, two measurements should give the same values, even though they are conducted with devices of slightly different dimensions (comp. also to Sec. 3.3). If the difference in constriction dimensions between two measurements is too big, however, this requirement must be dropped. A large constriction width might lead to a measurement only probing the cell membrane. Very narrow constrictions might probe the whole cell, including the cell nucleus. Differing cell mechanical measurements could thereby arise from heterogeneous material properties of the cells. The second requirement indicates that a linear material description with constant values for stiffness E and the power-law exponent β only approximately describes cell mechanics. In reality, stress and strain stiffening influence cell mechanics to a high degree, as outlined in Sec. 3.3). Therefore, the huge scatter of entry time data tentry is caused by cells which experience different amounts of strain ǫmaxi and different amounts of ∆pj . This phenomenon should be visible for a sensible strain measure. Some of the most common ways of strain description are area expansion moduli, stretch measures and compression measures. Their application to microconstriction measurements, and their advantages and disadvantages are shown in the following. For calibration purposes, measurements with two device types, containing a constriction width of 6.0 µm (O3) and 5.1 µm (S7), were conducted. Devices O3 and S7 did not only differ concerning their constriction width, but also concerning the overall device height, giving a height of 13.6 µm for O3, and a height of 16.6 µm for S7 devices (comp. to Tab. 2.1). Cell deformation into the constrictions was analyzed from videos through image segmentation (comp. to Sec. 2.3.2.2). As exemplary cell system, K562 leukemia cells were used and cultured according to App. 6.3 for all measurements. Moreover, they were harvested from the same flask (area A = 175 cm2 ) to ensure identical intrinsic cell mechanical properties. Besides, cell and device preparation before measurements were conducted according to Tab. 3.2. During video recording, the field of view was chosen to be placed symmetrically around the constriction to monitor both cell entry and whole cell deformation during the measurements, as shown in Fig. 3.9.

3.4.1

2- and 3-dimensional area expansion moduli

The area expansion modulus describes relative changes of the surface of a body in the course of deformation. For microconstriction measurements, it can either be measured from bright-field videos through image segmentation, or deducted purely theoretically from knowledge of the undeformed cell size and the constriction geometry.

63


First, the 2-dimensional area expansion modulus (x-y-direction in image plane) was measured from bright-field videos. Therefore, the cell area A of K562 cells was calculated for the whole time series showing the cell transit through a microconstriction (n > 328). For both device types, containing constrictions with a width of 6.0 µm and 5.1 µm, the maximum area expansion strain was calculated according to ǫmax =

Adef Aundef

− 1. Adef is

thereby the area of the cell at its maximum deformation inside the constriction, Aundef is the area of the undeformed cell. As visible in Fig. 3.10 a), the 2-dimensional areas did not differ significantly between the two setup types. They did not lead to a sufficient difference in strain, and did thereby not lead to a matching elastic stiffness measured with both constriction geometries. Even after histogram matching, the remaining mismatch in stiffness was approx. 25 %. From the 2-dimensional cell area during deformation, measures comparing the circumference of cells in a relaxed and compressed state might be applied, according to ǫmax = Udef Uundef

− 1. This strain was tested with regard to the two requirements detailed above,

but with negative outcome. The mismatch in stiffness between the two constriction sizes remained at 10-15 %. Moreover, it was impossible to explain the scatter of data with a 2dimensional grid, as all bins collapsed onto a single line, corresponding to the unextended power-law fit with constant stiffness and fluidity. Moreover, a 3-dimensional area expansion strain was calculated from the 2-dimensional measurement data. In principle, it more accurately describes cell deformation into a constriction. First, a 3-dimensional measure can be calculated by using the 2-dimensional shape and extrapolating it to the 3-dimensional cell area with theoretical knowledge. Thereby, it was assumed that the cells fill the channel in z-direction (perpendicular to the image plane) up to the limit that cell volume before and during the deformation process was conserved. Still, it was unclear during this calculation what the correct cell expansion in z really was. In a channel system which is higher than the cell diameter, the cell could principally first fully fill up the channel before elongating along the channel. The application of the 3-dimensional area expansion strain finally showed that the scatter in entry time according to a 2-dimensional grid could not be explained. Secondly, a 3-dimensional area expansion modulus was calculated from purely theoretical considerations. Each cell was modeled as filling the complete channel, except for its caps at the front and the rear. For the caps, simplified models were used. True values for cell cortical tension and the resulting cell curvature were too complex to calculate for a deformation in a microconstriction. Moreover, they mainly depended on cell mechanical properties themselves, which are unknown before the measurements. Cell curvature was approximated by LaPlace’s law ∆p =

2γ r ,

with ∆p being the pressure in the cell, γ the

cortical tension of the cell membrane, and r the radius of the cell [42]. It was furthermore assumed that

2 rundef

=

1 ra

+

1 rb .

Thus, the radius of the undeformed

cell rundef equals the inverse sum of the cell radii ra and rb in both principle spacial directions, assuming that the pressure and the cortical tension of the cell remain constant 64


a

b

0.5

0.8

εmax

0.25

εmax

1

0 O3 orth. fit S7 orth. fit

−0.25

0.6

O3 orth. fit S7 orth. fit

0.4 0.2 0

−0.5 7

8 9 10 Cell radius [µm]

11

4

6 8 Cell radius [µm]

10

Figure 3.10: Applicability of area expansion moduli as strain measures. a) 2-dimensional area expansion modulus for n > 328 K562 cells from measurements of device types O3 and S7 (constriction widths w = 6.0 µm and w = 5.1 µm, respectively). Dashed lines show orthogonal linear fits to the data. There is no significant difference between the strains resulting from the two device geometries. b) Theoretical 3-dimensional area expansion strain for O3 and S7 device types. Dashed lines show orthogonal exponential fits to the data. Perpendicular lines at abscissa show constriction radii (half the constriction widths) for both devices, where cells should experience zero strain.

during compression. For each cell size, suitable cap sizes were calculated numerically, using a voxel resolution of 0.05 µm, and volume conservation was considered during the deformation process. From the resulting shape of the cell, the surface was numerically calculated. The area expansion strain was then formed according to ǫmax =

Adef Aundef

− 1.

With this procedure, a highly non-linear behavior of the strain function could be gained (Fig. 3.10 b). However, huge errors were made for small cell radii, when the cell does not fully fill the channel geometry. This is why the theoretical 3-dimensional strain did not meet the abscissa at half the size of the constriction (crossing point for cell radius at 3 µm and 2.55 µm), even though a cell of the size of the constriction should pass it undeformed. Moreover, fitting with an exponential function y = exp(−bx) + c yielded high fit errors, and led to an approach of both fit functions for larger cell sizes (Fig. 3.10 b). Due to these reasons, the 3-dimensional expansion modulus did not lead to a matching cell elastic stiffness while comparing the measurements with the two setup types with constriction widths w = 6.0 µm and w = 5.1 µm, leaving a mismatch of over 15 %.

3.4.2

1-dimensional stretch measures

In principle, a 1-dimensional strain measure is desirable for quantification of strain during cell transit through a microconstriction. 1-dimensional measures are easy to calculate and do not require theoretical assumptions of the 3-dimensional cell shape during deformation. First, 1-dimensional stretch measures, also called elongation measures, were investigated. As in the case of area expansion moduli, the cell shape and thereby the cell long axis was extracted during cell transits through image segmentation. Subsequently, four widely used strain measures, introduced in Sec. 2.3.3.2 were calculated from the cell long axes, termed

65


Cauchy, True, Green and Almansi strain (comp. to Tab. 2.3).

1

a


b

0.8

εmax

0.6 0.4 O3 orth. fit S7 orth. fit

0.2

Cauchy

True

0

c


d

εmax

0.8 0.6 0.4 O3 orth. fit S7 orth. fit

0.2 0

Green 7


Almansi 7


11

Figure 3.11: Dependence of four different stretch strain measures on cell size. Data from measurements of long axis of n > 328 K562 cells with constrictions with a width of 6.0 µm (device type O3) and a width of 5.1 µm (device type S7). Panels a-d) show Cauchy strain, Green strain, True strain, and Almansi strain data with according orthogonal line fits.

All elongation strain measures grew linearly with increasing cell radius, as demonstrated by the excellent fit goodness of an orthogonal linear regression to the data (Fig. 3.11 a-d, dashed lines). They all gave different absolute values and numerically different but similar relative differences between the strains of the wide (device type O3, constriction width w = 6 µm) and narrower (device type S7, constriction width w = 5.1 µm) constriction. All stretch measures provided a good match of the elastic stiffnesses of the two measurements performed with two different device types, leaving a mismatch of at most 10 % in the case of Almansi strain (Fig. 3.11 d). However, a grid-like fan of the bins of different ǫmaxi /∆pj combinations was not achieved due to the linear behavior of the strain measures over cell size. All data collapsed onto the central fitting line (data not shown). Moreover, stretch strain measures based solely on the measurement of the long axis of all cells could be biased by cell blebbing, which is explained in detail in Sec. 3.1.1. Cell blebs thereby increase the cell long axis by possibly 50 %. This might lead to a falsification of stretch strain measures depending on cell treatment or even cell type.

66


3.4.3

1-dimensional compressive measures

The most intuitive and reproducible, but nevertheless oversimplified measure of strain applicable for a cell deformation through a microconstriction is defined by one- or twodimensional cell compression. Obviously, a cell has to be compressed to the width of the microconstriction to pass through. Area expansion and cell elongation, in turn, are only a passive byproduct of this active compression. Compressive measures carry the big advantage that they are only defined by the

1

values of constriction size and cell size. 0.8

No further additional measurements of cell shape during entry into a constric-

0.6

εmax

tion are necessary. Furthermore, compression measures can be applied to all

0.4

cell types and treatments, as they are

0.2

O3: 6.0 µm S7: 5.1 µm

independent of cell blebbing (comp. to Sec. 3.1.1).

0

A compression measure could principally describe an average compression of two dimensions, comparing the uncom2 pressed cell area Aundef = rundef π to the

6

8

10 12 Cell radius [µm]

14

Figure 3.12: Theoretical 1-dimensional compressive strain measure according to Cauchy, as shown in Fig. 2.15. The dependence of strain on cell size is non-linear.

area of the constriction Acon = hcon ·wcon . Here, rundef is the radius of the undeformed cell, and hcon and wcon the height and width of the constriction. Alternatively, in one dimension, the cell radius could be compared to the minimum width, or 1-dimensional radius of the constriction rcon = wcon /2. Comparing measurements with device types O3 and S7, the height of the device with the narrower constriction was higher than the height of the device with the wider constriction (6 µm and 13.6 µm vs. 5.1 µm and 16.6 µm, respectively). The definition of a 2-dimensional compressive strain measure qdid not make sense, because the thus resulting effective radii of the constrictions reff = hconπ·wcon were almost identical. This implies that their appli-

cation did not compensate for the big difference of entry times measured between the two device types. Therefore, a 1-dimensional compression ratio was formed according to λmax =

rcon rcell

(3.3)

In analogy to the four commonly used elongation measures described in Tab. 2.3, this compressive ratio can again be transformed into four compressive strains. All four of these measures led to almost matching elastic stiffnesses of the investigated K562 cells extracted from measurements with devices O3 and S7, and left a mismatch of

67


at most 5 %. At the same time, they enabled the description of the scatter of entry times tentry vs. ǫmax /∆p data through ǫmaxi /∆pj for combinations of i and j. Both requirements for a strain measure are therefore met. Finally, measure I according to ǫmax = 1 − λmax , equivalent to a Cauchy-compression measure (comp. to Eq. 2.31), was employed, since its matching performance slightly outcompeted the rest of the measures. The dependence of measure I on cell size is shown in Fig. 3.12. Despite its incorrect application to finite strains, the mathematical simplicity of measure I was in this case valued higher than the application of a Green or Almansi strain, which consider finite strains. The application of the chosen Cauchy-compression measure for the comparison of cell mechanical properties between setup type O3 (constriction width w = 6 µm) and S7 (constriction width w = 5.1 µm) is shown in Sec. 3.3.

3.5

Systematic error of cell mechanical properties

Especially for comparisons with other measurement techniques, it was of great interest how accurately cell mechanical properties can be measured with a microconstriction assay. Two types of errors, which influence measurement accuracy, had to be considered. First, random errors of the measurements of stress and strain could occur. Random errors arise from random wrong measurements of cell entry time, cell size, which was transformed into cell strain, or cell speed, which gave the pressure drop. Secondly, a systematic measurement error could occur, which was caused by uniformly biased calculations of, for example, the channel geometry of the devices, and thus systematically influenced the resulting cell strain or cell stress. Random errors were mainly induced by resolution limits of the microscopy system used for cell tracking and cell size evaluation. During measurements, the high-speed CCD camera recorded images with a maximum framerate of 750 fps. Cells traveling at very high velocities through the channels could not accurately be tracked while approaching the microconstrictions, which led to inaccuracies in cell speed and thus pressure drop. Average entry times into a constriction ranged between 0.05-0.3 s, and were high above the resolution limit. However, very short entry times could not be resolved with a sufficient resolution. Videos were recorded with a pixel size of only 0.74 µm (camera GE680, Allied Vision), which roughly corresponds to 10 % of a typical cell radius. Cell size could thus be over- or underestimated by 10 %. Concerning the measurement accuracy of the confocal microscope used for the measurements of channel geometries, the manufacturer, Nanofocus, reports a z-error of only few nanometers. The x-y-scanning resolution of the measurements, though, was only 0.62 µm, which equals to an approximate random error. Random errors are generally taken into account for by the bootstrapping routine during power-law fitting. Cells are excluded randomly from the evaluation to statistically in-

68

3.5 Systematic error of cell mechanical properties

vestigate the spread of the data and thereby the spread of the resulting cell mechanical properties (comp. to Sec. 2.3.4.3). Systematic, uniform deviations of the most important measurement parameters cell size and pressure drop, however, can bias the resulting cell mechanical properties and cannot be easily eliminated. Case name Case I Case II Case III Case IV

Cell size + + -

Channel dimensions + + -

Table 3.1: Systematic in- (+) or decrease (-) of measured cell sizes and channel dimensions by ± 0.25 µm, leading to datasets I-IV.

During cell size detection, the image segmentation algorithm was influenced by image brightness. Therefore, varying image brightness between different video recordings was compensated for by the sobel-filtering routine with automatically adapted thresholds. Still, there is no objective knowledge about the true cell size of the measured cells. Hence, the algorithm was likely to induce a global error for all cell size measurements. Systematically biased calculations of cell size rcell did not only influence the resulting cell mechanical properties through strain, according to ǫmax ∼ 1/rcell , but also through the calibration of the dependence of cell speed vcell on cell size and its subsequent calculations of flow speed vavg in the channels, according to vavg ∼ 1/rcell (comp. to Sec. 2.3.3.1). Furthermore, the measured channel dimensions influenced the value for cell strain through the width of the constriction wcon according to ǫmax ∼ rcon , with rcon = wcon /2. Additionally, the channel dimensions also governed the empirically found dependence of cell speed on cell size and therefore flow speed, as vavg ∼ rhyd(channel) (comp. to Sec. 2.3.3.1). The calculation of the average fluid volume flow I also required direct, linear knowledge of h and w: I ∼ h · w. Thereby, h is the height and w the width of the channel. Moreover, all channel dimensions played a role in the calculations of the fluidic resistances through Hagen-Poiseuille’s law. At each channel position, the smaller channel dimension (either width w or height h) was incorporated into the calculations with a cubic dependence: ∆p ∼ 1/ min(h, w)3 , the bigger channel dimension with a linear dependence: ∆p ∼ 1/ max(h, w). Both resistance and fluid flow finally determine the pressure drop over the constriction (comp. to Sec. 2.3.3.1). The list of all these dependencies highlights that the influence of errors of channel dimensions and cell size/speed on the calculation of mechanical cell properties with a microconstriction assay is highly complicated. Therefore, a systematic investigation of maximum errors concerning cell size and channel geometries was conducted. After performing a measurement of several thousand K562 cells (device type S7, constriction width w = 5.1 µm, device height h = 16.6 µm, comp. to Sec. 2.1), the measured cell

69


2500 2000 1500 1000 500

1000 500

0

1500

CASE 1 +/+

original data

Entry time [s]

100

1000 ∆p [Pa]

0

0.2

0.4

0.6 εmax

CASE 3 −/+

0

c 101

3000

CASE 2 +/−

0

5000

0.8

1

CASE 4 −/−

Counts

b 7000

original data CASE 1 +/+ CASE 2 +/− CASE 3 −/+ CASE 4 −/−

Counts

a

10-1 10-2

0

e

0.1

ns

ns

ns CASE 4 −/−

0.2

ns

CASE 3 −/+

0.3

CASE 2 +/−

0.4

CASE 1 +/+

*

1 2 4

1 2 4

1 2 4 εmax/∆p [x10-3 1/Pa]

original data

ns

CASE 4 −/−

100

ns

CASE 3 −/+

200

original data

Stiffness [Pa]

300

CASE 1 +/+

*

CASE 2 +/−

d

1 2 4

Power−law exponent

1 2 4

0

Figure 3.13: Systematic error of cell mechanical properties. Influence of systematic change of calculated cell sizes (± 0.25 µm) and channel dimensions (± 0.25 µm) on cell stiffness and power-law exponent of K562 cells. Cases listed in Tab. 3.1. a) Histogram of calculated pressure drops ∆p for all cases. b) Histograms of calculated strains ǫmax . Colors correspond to panel a). c) Exemplary scatters of entry time tentry vs. ǫmax /∆p with power-law fits (black lines). Histogram matching was not performed for this study. d) Resulting cell stiffness. e) Resulting power-law exponents. n = 19559 cells per population. Asterisks indicate significant differences to original data calculated from bootstrapping with p < 0.05.

70

3.5 Systematic error of cell mechanical properties

diameters were artificially and systematically either increased or decreased by ± 0.25 µm. Moreover, all channel dimensions, including height, width and length, were either in- or decreased by ± 0.25 µm. A combination of the two independent changes finally formed the datasets I-IV, as shown in Tab. 3.1. Then, power-law theory was applied to calculate the resulting mechanical properties elastic stiffness and power-law exponent from the changed datasets. The resulting cell mechanical properties of cases I-IV are shown in Fig. 3.13. For comparison, the unchanged measurement data, termed original data, is shown. For decreased channel dimensions (case II and case IV), an increase in the average pressure drop, which works on the cells during transit through a microconstriction, was observed. For cases I and III, which correspond to an increase in channel dimensions, a decrease in average pressure drop was found (Fig. 3.13 a). Changes of cell size induced no change in the resulting cell strain for cases I and IV, where cell size and channel dimensions changed in the same direction. A highly increased strain was produced for case II, and a highly decreased strain for case III, where cell size and channel dimensions changed in opposite directions (Fig. 3.13 b). Bootstrapping and power-law fitting was conducted to all five datasets independently, as histogram-matching was not intended for this comparison (Fig. 3.13 c). The combined change of increase of cell size and channel dimensions (case I) led to a significant decrease in the resulting cell stiffness, but no significant change in the power-law exponent. For cases II and III, no significant change in cell stiffness or power-law exponent was observed. Case IV led to a significantly stiffer, but equally fluid cell population (Fig. 3.13 d+e). All in all, only the same change of ± 0.25 µm in both cell size and channel dimensions, either positively or negatively, led to a significant in- or decrease of the resulting cell mechanical properties. Since there is no correlation between the measurements of cell size and channel geometry, all error scenarios are equally probable. For the definition of a measurement accuracy of cell stiffness and fluidity, the standard deviation between all cases of systematic variation was used, and calculated to be 281 ± 10 Pa, which corresponds to a relative error of 3.6 %. This error investigation only applies for the comparison of measurements between different device geometries. For comparisons of measurements conducted with one and the same device type under identical measurement conditions (for example image brightness), only errors from the spread of data, calculated through bootstrapping, must be considered.

71


3.6

Sensitivity of microconstriction measurements to mechanical changes of cell cytoskeleton and nucleus

Biological background One of the fundamental questions in cell mechanics is to which extent bulk cell stiffness and viscosity are determined through the different cell components. With a microconstriction measurement, principally, constrictions of differing widths can be employed to measure the bulk cell mechanics. While big constrictions (width w > 10 µm) supposedly probe the mechanical properties of the outer cell membrane and the cell cytoskeleton, the mechanical properties determined by small constrictions (width w < 5 µm) should be dominated by the mechanics of the cell nucleus. Medium-sized constrictions should measure the mechanics of both the cytoskeleton and the nucleus. However, the range of possible constriction sizes which can be used to investigate a cell population is small (comp. to Sec. 2.1.1). If the employed constrictions are too small, the measurement throughput decreases dramatically. When too wide constrictions are used, the cells do not fully clog the constrictions during transit and a pressure drop cannot be calculated (comp. to Sec. 2.3.3.1). This is why mostly medium-sized constrictions were used for studies in this thesis. To answer the question if cell mechanical measurements with medium-sized constrictions are really sensitive to both cytoskeletal and nuclear components, these cell components were stiffened and softened with pharmacological substances, and the resulting cell stiffness and fluidity were measured. First, the distribution and arrangement of the most important cell-stabilizing components is shown in Fig. 3.14 and their basic characteristics are shortly summarized below. The major stabilizers of the cell are cytoskeletal filaments, such as actin, microtubules and intermediate filaments, and the cell nucleus. Actin is either present in the form of globular actin (G-actin) molecules, or forms polymeric microfilaments, which are called Factin. These F-actin filaments are about 7-9 nm in diameter and are mostly non-symmetric (Fig. 3.14). This non-symmetry contributes to a filament polarity, where actin polymerization dominates at the barbed (plus) end and actin disassembly at the pointed (minus) end. The Young’s modulus of F-actin filaments is approx. 1-2 GPa [101]. In a cell, branched actin networks build the cell cortex, which stabilizes the cell membrane against compression. Morevoer, actin filaments together with non-muscle myosin-II motor proteins form stress fibers. Through actomyosin contraction of these fibers, the cell can exert forces and migrate actively [11]. Microtubules are formed by tubulin heterodimers, which consist of α- and β-subunits. Several dimers form a protofilament, which in turn assemble into a single microtubule of 25 nm in diameter (Fig. 3.14). The stiffness of microtubules is reported to be between 6 MPa and 7 GPa [102]. Microtubules span through the whole cell and thereby function as

72

3.6 Sensitivity of microconstriction measurements to mechanical changes of cell cytoskeleton and nucleus

road ways for vesicle and organelle transport through microtubule-bound motors. They are organized by microtubule organization centers, where all minus ends (the side of a microtubule ending with an α-tubulin subunit) colocalize. Moreover, microtubules are involved in mitosis, where they govern chromosome separation. In mechanical terms, microtubules supposedly support cell polarity and directionality of movement [103]. Intermediate filaments form a family of related cytoplasmic and nuclear proteins, which are on average 10 nm in diameter (Fig. 3.14). They are categorized into six subfamilies according to similarities in amino acid sequences and protein structures, and thus function. Prominent examples are keratins (I and II), desmin and vimentin (III), neurofilaments (IV), lamins (V) and nestin (VI) [103]. The existence and amount of a certain intermediate filament in cells is highly depending on the cell type and cell function [104]. The stiffness of intermediate filaments is around 2 GPa (Young’s modulus) [105, 106]. Intermediate filaments fulfill versatile functions in cells. For example, the intermediate filament lamin A was reported to stabilize the nuclear lamina and thus protects the cell against DNA damage through mechanical compression or shear of the nucleus [100, 107, 108]. All mentioned proteins are continuously de- and repolymerized inside a cell. Moreover, they are all interconnected through linker proteins and can interact with each other. The composition and structure of the cell nucleus is discussed in detail in Sec. 4.9. actin + membrane

7-9 nm

cortical network

stress fibers

nucleus centromer

intermediate filaments

10 nm

microtubuli 25 nm +

-

Figure 3.14: Cytoskeletal components. The major cell stabilizers are the cytoskeletal proteins actin, microtubuli and intermediate filaments. They span through the whole cell, are closely interconnected and linked to the cell membrane (comp. to Fig. 4.5) and the cell the nucleus (comp. to Fig. 4.17). Image adapted from [103] and [109].

73


Results For all measurements, K562 leukemia cells were used. Cells were cultured according to App. 6.3. As explained in Sec. 2.5, the use of suspended cells allows for the harvesting of all measurement populations from one and the same cell flask (area A = 175 cm2 ), which diminishes flask-to-flask variability of cell mechanical properties caused by differing culture conditions. In previous studies, cell nuclear mechanics were changed by manipulating chromatin condensation. Condensed chromatin was thereby shown to increase cell nucluear stiffness, and vice versa [12, 110]. Also in this study, the chromatin was condensed through the administration of Mg2+ Ca2+ -ions (mgca, 2 mM each, 30 min, #2444-05, J. T. Baker and #C8106, Sigma-Aldrich), and decondensed by 5-AZA-2’-deoxycytidine (AZA, 5 µM, 3 h, #A3656, Sigma-Aldrich) to change cell nuclear properties. To change cell cytoskeletal properties, actin polymerization was inhibited by cytochalasin D (cyto D, 10 µM, 30 min, #C8273, Sigma-Aldrich), which was reported to increase the deformability of the cytoskeleton in previous studies [10, 14, 111]. Moreover, the whole cytoskeleton was unspecifically crosslinked with glutaraldehyde (ga, 500 µM, 30 min, #G5882, Sigma-Aldrich) to stiffen the cell [111]. A similar change in cytoskeletal properties was expected by changing the microtubular network of the cells [26, 112]. To inhibit microtubule polymerization, cells were treated with nocodazole (noc, 500 nM, 3 h, #M1404, Sigma-Aldrich). For observing the opposite changes, microtubule depolymerization was stopped with paclitaxel (pax, 5 µM, 1 h, #T7191, Sigma-Aldrich). To agglomerate the intermediate filaments vimentin and keratin, cells were treated with acrylamide (acry, 5 mM, 3 h, #A8887, Sigma-Aldrich), which was also reported to decrease cell deformability [26, 113–115]. After the measurements and evaluation of tentry , cell strain ǫmax and ∆p, histogram matching was not performed due to historical reasons. This is why the cell radius after measurement preparation and after the administration of the used chemicals was carefully checked to rule out a possible bias on cell mechanics induced by cell shrinking or swelling. Therefore, cells were stained with calcein (500 nM, 30 min, #C0875, Sigma-Aldrich) and imaged with an epifluorescence microscope (DM4, Leica Microsystems). There are no significant differences between the average radii of cell populations after the washing procedure, which includes a centrifugation step (4 min at 1400 rpm, 405 × g) and resuspension with PBS, nor after a 3 h cell culture at room temperature, which extends the measurement time of approx. 2 h (Fig. 3.15 a). For investigating the influence of chemicals on cell size, the measurements were conducted after the incubation of the chemicals plus an additional time period of 2 h. There was no significant difference in cell radius after administration of the investigated chemicals in this study, namely Mg2+ Ca2+ -ions, 5-AZA-20-deoxycytidine, cytochalasin D, glutaraldehyde, nocodazole, paclitaxel, and acrylamide [20] (Fig. 3.15 a).

74

3.6 Sensitivity of microconstriction measurements to mechanical changes of cell cytoskeleton and nucleus

a

b

105

14

100 100

Viability [%] Viability [%]

Cell radius [µm] Cell radius [ µm]

12 10 8 6 4

95 95

90 90

ga

noc pax acry

cyto D

mgca AZA

00

control washing 3h roomt.

ga

noc pax acry

cyto D

mgca AZA

0

control washing 3h roomt.

2

Figure 3.15: Influence of pharmacological treatments on cell size and cell viability. a) Mean cell radius of control cells, cells after washing procedure, cell stored for 3 h at room temperature, and cells after administration of all chemicals used in this study. b) Viability of control cells, cells after washing procedure, cell stored for 3 h at room temperature, and cells after administration of all chemicals used in this study. Measurements were conducted after incubation time of chemicals plus 2 h. Abbreviations are explained in the text. Error bars in a) and b) are standard deviations of 25 field-of-views with a total of n > 10,000 cells for each condition. Figure adapted from [20].

Moreover, cell viability was checked with propidium iodide (100 µg/ml, #P4864, SigmaAldrich) for the same conditions as cell size. Dead cells, or cells under apoptosis were shown to stiffen and might therefore bias the measurement results (comp. to Sec. 3.1). Cell viability was found to range between 95-100 % for all conditions, except for glutaraldehyde treatment (Fig. 3.15 b). Glutaraldehyde-treated cells were tested positively for apoptosis less than 10 min after chemical administration. The chemical supposedly disrupts the cell membrane instantly, and cell staining is not a result of a gradual apoptosis process [20]. For mechanical measurements, a microconstriction device with a constriction width of 6.0 µm and a channel height of 13.6 µm (device type O3, comp. to Sec. 2.1) was chosen. Cell and device preparation before measurements were conducted according to Tab. 3.2. During the measurements, all drug concentrations were kept constant. All measurements were conducted on one and the same day while applying the same pressure range with the pressure pump. Significant changes in cell mechanical properties compared to the control population could be observed for all pharmacological treatments, except for acrylamide (Fig. 3.16 b+c). The biggest influence on mechanical properties was measured for actin disruption with cytochalasin D, which decreases stiffness by over 50 %. Simultaneously, fluidity decreased by 29 %. Moreover, cells stiffened dramatically under glutaraldehyde treatment by 135%, and fluidity decreased by ∼ 40 %. Microtubule depolymerization with nocodazole decreased cell stiffness by 10 %, and decreased fluidity slightly but not signicantly (p = 0.22). After stabilizing the microtubule network with paclitaxel, cell stiffness increased by 18 %, whereas cell fluidity decreased by 29%. These changes of cell mechanics, however, were small compared

75


a 10

Entry time [s]

10

control

mgca

AZA

cyto D

ga

noc

pax

acry

1 0

10-1

101 10

0

-1

10

200

400

800

200

400 800 200 Pressure [Pa]

b

800

200

400

800

*

*

*

0.3

600

* *

*

*

ns

*

*

*

x 0.17

c 0.23

0.14

ry 0.21

ac

pa

no

0.31

0.29

0.19

0.24

0

nt ro m l gc a AZ A cy to D ga

c 265 pa x ac 348 ry 300

703

no

nt ro m l 296 gc a AZ 335 A 206 cy to D 134 ga

co

*

0.2 0.1

*

200

ns

co

400

0


c 800

Stiffness [Pa]

400

Figure 3.16: Change in stiffness and fluidity of K562 leukemia cells after drug treatments. a) Scatter plots of tentry vs. applied pressure ∆p for control cells and cells after drug treatments (see main text). n > 2000 cells for each condition. Geometric means of ∼ 200-400 cells binned according to pressure are given by solid markers. Power-law fit to the binned data is given by solid line. The dashed lines show fit to control data in all other plots for comparison. b) Cell stiffness and c) cell fluidity for populations after drug treatments. Abbreviations are explained in the text. Error bars represent standard errors calculated by bootstrapping. Significant differences with p < 0.05 are indicated by asterisks. Figure adapted from [20].

to the influence of actin depolymerization. Hence, for strains between 0.3 > ǫmax > 0.7 and on timescales between 5 ms and 10 s, the deformability of K562 leukemia cells was not mainly governed by their microtubule network. Chromatin condensation through Mg2+ Ca2+ -ions resulted in an increase of cell stiffness by 13 % and a decrease of fluidity by 21 %. In contrast to that, after treating the cells with 5-AZA-20-deoxycytodine to decondense the nucleus, cell stiffness decreased by 30 % and fluidity increased by 21 %. Acrylamide treatment, as mentioned above, did not result in changes of cell stiffness and only slightly decreased cell fluidity. This underlines that the vimentin/keratin network of K562 cells is only of minor importance under the stress and strain circumstances investigated in this study [20].

76

3.7 Soft glassy rheology

Conclusion In summary, the investigation of the influence of nuclear and cytoskeletal cell components on the resulting bulk mechanical properties revealed that both nuclear and cytoskeletal cell changes are measurable with the microconstriction assay using medium-sized constrictions with a width of 6 µm. The influence of actin was shown to dominate the deformability of K562 cells under the given stress and strain application. Still, smaller influences of the microtubular network were detectable. No detectable changes in bulk cell mechanics could be induced by interconnecting the intermediate filament network of K562 cells. Here, keratin and vimentin only influence cell mechanics to a non-significant degree. At the same time, an important influence of the nucleus on the bulk cell deformability was found by changing chromatin condensation.

3.7

Soft glassy rheology

Theory Cell mechanics is described by power-law rheology in this thesis. Fitting a power-law to the scatter data tentry vs. ǫmax /∆p for a population of several thousand cells gives population averages of cell elastic stiffness E and cell fluidity β ( = power-law exponent). Both are in principle two independent fit parameters. However, previous studies showed that the fit parameters E and β are closely correlated to each other for many cell systems, for example after changing cell mechanical properties through a variety of pharmacological treatments. The increase in elastic stiffening of the cells thereby resulted in a decrease of their powerlaw exponent, and vice versa [41, 116]. Through this correlation, the description of cell mechanics can be limited to only one single parameter. An interpretation of this systematic reduction of mechanics is given by the theory of soft glassy materials, termed soft glassy rheology (SGR) [11]. SGR theory describes the mechanical behavior of various substances, including emulsions, colloids and foams, by neglecting their individual molecular interplay. All molecules are considered being part of a simplified energy landscape, which consists of energy wells of varying depths formed by molecule-molecule interactions. Thermal fluctuations alone cannot enable the molecules to hop out of the wells. Instead, the molecules have to be excited to change their position or configuration. The source of excitation can either be physical temperature (kinetic energy), or active cell conformational changes induced by molecular motors via adenosine triphosphate (ATP). The level of excitation is called effective temperature, or noise level x, which corresponds to the power-law exponent β. When x increases (β > 0), all elements can hop randomly between the wells, and the system fluidizes when β approaches 1. When the minimum value of x is approached (β = 0), the system increases its order and finally freezes, which is called glass transition. Chemicals that disrupt the cell cytoskeleton, for example cytochalasin D, were shown to 77


fluidize the cell, since they increase disorder. Chemicals that stabilize or interconnect the cell cytoskeleton, for instance glutaraldehyde, order the cytoskeleton and shift β towards the glass transition point [29, 35, 117]. The applicability of SGR theory on adherent cells was proven with many different measurement techniques [29, 35, 117]. Therefore, it should be checked with microconstriction measurements if SGR theory also applies to suspended cells.

Results

a

b 6

800

200

100 0

control mgca AZA cytoD ga noc pax acry

Prob. density

Stiffness [Pa]

400

control cytoD ga

5

600

4 3 2 1

0.1 0.2 0.3 Power−law exponent

0.4

0 0

0.2 0.4 0.6 0.8 Power−law exponent

1

Figure 3.17: Soft glassy rheology of pharmacologically treated K562 leukemia cells, as shown in Fig. 3.16. a) Inverse relationship between stiffness E and power-law exponent β can be fitted by a function of form E = E0 · exp(a · β). Abbreviations are given in Sec. 3.6. b) Distribution of single cell power-law exponents for cell populations under control conditions, and after treatment with cytochalasin D and glutaraldehyde, respectively. Shaded areas show Gaussian fit to data. Figure adapted from [20].

To investigate the applicability of SGR theory on cells in suspension, naturally suspended K562 leukemia cells were investigated. From the measurements of Sec. 3.6, which showed the changes in bulk cell mechanical properties in reaction to pharmacological treatments of the cell cytoskeleton or cell nucleus, the correlation between the values for elastic stiffness and power-law exponent β was now evaluated. For all treatments, an inverse correlation between cell stiffness E and the power-law exponent β was found (Fig. 3.17 a). Substances that decrease cell fluidity caused the stiffness to increase, and vice versa. Plotting the logarithm of E for different treatment conditions versus the power-law exponent β, all data points collapsed onto a line, according to E = E0 · exp(a · β)

(3.4)

with the best fit parameters a = −2.51 and E0 = 1189 Pa. Changing cell cytoskeletal or cell nuclear mechanical properties thus only in- or decreased one single parameter, β, which shows that SGR theory can be applied to suspended cells.

78

3.8 Influence of measurement and culture parameters on measurements of cell mechanics

Through atomic force microscopy, it was shown for adherent cells that the master relationship between stiffness and viscosity does not only apply to population averages of these measures, but also to single cells mechanical properties [117]. Thus, SGR theory provides the possibility to evaluate single cell mechanical properties from measurements of tentry , ǫmax and ∆p, according to β=

ln( E0∆p ·ǫmax ) a − ln(tentry )

(3.5)

inserting the relation between E and β from Eq. 3.4 into the usual power-law equation (Eq. 2.34). Through Eq. 3.5, the distribution of mechanical properties in a cell population (Fig. 3.17 b) could then be analyzed. Under control conditions, the fluidity of individual K562 cells was found to follow a normal distribution with mean and standard deviation β = 0.31 ± 0.12. After treatment with glutaraldehyde, the distribution shifted to β = 0.17 ± 0.04, corresponding to a freezing of the cell caused by a higher connectivity of the cell cytoskeleton. Cells treated with cytochalasin D, which destroys their actin cytoskeleton, exhibit a fluidization, and their β-distribution shifted to higher values: β = 0.45 ± 0.15 [22].

Conclusion The current use of the microconstriction array normally only allows for the calculation of populations averages of the mechanical properties stiffness and fluidity. For a specific cell line, however, the mechanical properties of individual cells could be calculated by applying SGR theory. Through a range of pharmacological treatments, the correlation between the two fit parameters E and β, which were normally independently fitted to a scatter of entry times under certain stress and strain conditions for thousands of cells, could be found. Population averages of E and β of K562 leukemia cells in suspension collapse onto a master curve. Fluidity values of suspended single cells were thereby shown to be normally distributed, which is in accordance with previously published data on adherent cells. The quantitative values of β were moreover close to fluidity values from previous studies [41, 117, 118].

3.8

Influence of measurement and culture parameters on measurements of cell mechanics

As in all other biophysical areas, cell mechanical measurements generally suffer from a lack in reproducibility [119, 120], with extremely low reproduction rates around 10 % [121]. In most measurement environments, a neat control over all experimental parameters, like device preparation and cell culture conditions, is difficult to achieve and is thereby often

79


missing. Thus, most of the time, the sources of the lack of reproducibility remain unclear. Against this background, several cell culture and device preparation parameters of the microconstriction setup were analyzed concerning their influence on the resulting cell mechanical properties, to possibly reveal hidden sources of measurement bias. First, a control measurement was conducted. Control measurements, where the reproducibility of a measurement result for measurements on independent, but identically prepared samples, is ensured, are widely lacking in the literature. Here, four cell samples of the same cell population, harvested from four different cell flasks, were investigated with the microconstriction setup. Moreover, different cell culture parameters were investigated. For adherent cells, especially cell culture density before harvesting was of importance, as it might vary widely between different cell lines due to differences in their proliferation rate. Moreover, the detachment time of cells, measured between trypsinization and the beginning of the measurement, was changed to analyze its impact on cell mechanics. Finally, several parameters of the preparation of the measurement setup were evaluated concerning their influence on the measurement results. Here, the measurement medium, and the coating procedure of the measurement device with the surfactant pluronic, which is used to prevent unspecific cell adhesion to the channel walls during measurements, were of great interest.

Standard parameters for all measurements First, the standard parameters of cell culture and device preparation used in all measurements are outlined in Tab. 3.2, to give an overview over usual measurement conditions. Parameter measurement medium cell culture density detachment time pluronic coating time pluronic coating concentration

Standard value PBS 80 % 20 min 30 min 1%

Table 3.2: Standard parameters of cell culture and measurement preparation for mechanical measurements with a microconstriction device.

Cells were usually harvested at a culture density of 80 % before measurements. They were centrifuged after trypsinization and the suspension density was increased by a factor of eight. Finally, at least 250 µl of cell suspension with a concentration of approx. 5 · 106 cells/ml was required for measurements. For certain cell lines (for example HeLa cervix carcinoma), a lower culture density was chosen for all measurements, because these lines showed an increased cell-cell-cohesion after trypsinization for increasing cell culture densities. However, working with lower cell densities prolonged measurement times. Between trypsinization and the beginning of the measurements, the time was minimized

80


as well as possible. Still, cells had to be trypsinized for 4 min, followed by a 4 min centrifugation step (1400 rpm, 405 × g). The cell resuspension and filtering through a 20 µm prefilter, together with the transport to the microscope, required another 5 min. Finally, cells were flushed into the device with PEEK-tubing, which took 1-5 min, depending on the setup design. All in all, up to 20 min passed between the detachment of the cells and the beginning of the measurements. Since the measurement usually took 40 min, the maximum time of cell detachment was 1 h. As measurement medium, PBS (#10010023, gibco) was used during all measurements. Cell medium, for instance DMEM, would provide a more natural environment for the cells. Still, the optical properties of PBS largely beat those of cell medium, which justifies its use for a limited amount of time. Pluronic coating of the devices was usually conducted for 30 min at a pluronic concentration of 1 wt%. Values for pluronic coating from previous studies range from 0.1% [19] to 2 % [122], and coating times are reported to be up to 2 h [19]. The chosen standard values combine a minimization of the preparation time before each measurement to increase measurement flow during a day, and still guarantee a sufficiently high and reproducible coating of the device. Deviations from the standard parameters of cell and device preparation are explicitly mentioned in all chapters.

Reproducibility of measurements on identical cell populations As a control measurement, four independent experiments on DLD-1 colon carcinoma cell populations, harvested from four identically cultured cell flasks, were conducted. Cells were cultured according to App. 6.3. The cells had been seeded into the cell flasks 48 h prior to the measurements and reached a cell density of 80 % at the time of the measurements. Cell and device preparation before measurements were conducted with the standard parameters, according to Tab. 3.2. The resulting scatters of entry time tentry vs. ǫmax /∆p were pooled for two arbitrarily paired measurements (termed control 1) and compared to the remaining two measurements, which were also pooled (termed control 2). Finally, histogram matching was applied to extract quantitative cell mechanical properties through power-law fitting (Fig. 3.19 a). Between the two investigated groups, no significant differences were measurable (Fig. 3.18 a and Fig. 3.19 b). The p-values were p = 0.35 and 0.24 for stiffness and fluidity, respectively. This result highlights that unsignificantly different measurement results are gained when comparing cell mechanical properties from identically cultured and harvested cell populations from the same cell line, when they are measured under identical conditions on one day [22].

81


b

Confluency

d

200

0 PBS

60min 100min 600

Pluronic concentration

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345 ± 3

*

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327 ± 2

*

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40min

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* 200

* 280 ± 2

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*

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*

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421 ± 3

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400

*

485 ± 3

El. mod. [Pa]

El. mod. [Pa]

600

c

600

ns

442 ±2

a

1%

4%

0

0 0min

0.25%

Figure 3.18: Influence of cell culture and measurement parameters on resulting stiffness of DLD-1 colon carcinoma cells. a) Four measurements, arbitrarily split into two groups (control 1 and control 2). b) Cell populations harvested from different cell culture confluency before measurements (20 %, 60 %, 100 %). c) Different detachment times before measurement (20 min, 60 min, 100 min). d) Different measurement media: PBS, HEPES-buffer and DMEM cell culture medium. e) Device coating with 1 wt % pluronic for different periods of time: 0 min, 20 min and 40 min. f) Device coating for 30 min with pluronic concentrations of 0.25 wt %, 1 wt %, and 4 wt %. n > 1203 cells for each condition. Histogram matching was performed separately for each panel (a-e). Significant (p < 0.05) differences to first parameter values (green bars) are indicated by asterisks. Figure adapted from [22].

Results Moreover, several cell culture and measurement preparation parameters were systematically changed for measurements of DLD-1 colon carcinoma cells. Again, cells were cultured according to App. 6.3. Cell and device preparation before measurements was conducted according to Tab. 3.2 except for the parameter investigated in each substudy. First, culture densities of 20 %, 60 % and 100 % confluency were compared. For this measurement, cells were seeded only 24 h before measurements at 10 %, 30 % and 50 % confluency to ensure an identical spreading and growth time of all observed conditions.

82


At least two independent measurements were conducted for each condition. After evaluation, the resulting measurement parameters were pooled for each condition and power-law fitting including histogram matching was conducted (Fig. 3.19 c). Compared to 20 % confluency, both the cell stiffness calculated for 60 % and for 100 % confluency were decreased significantly (Fig. 3.18 b). The power-law exponents did also show a slight, but significant decrease with increasing cell culture density (Fig. 3.19 d). A decrease in cell stiffness induced by a higher culture density can be explained by changing cell environmental parameters. The denser the cell culture grows, the more cell-cellcontacts can be formed between the cells. Therefore, changes in cell-cell-signaling alone could explain the reported changes in cell mechanics. Furthermore, cells come in touch with surrounding cells and feel a softer environment. Previous studies have established that cell mechanical properties are tuned by matrix properties. Stiff substrates allow for the formation of higher prestress and cortical tension in adherent cells, which results in a higher bulk cell stiffness [123, 124]. Cells touching soft neighboring cells, instead of only the infinitely stiff substrate, might therefore have a decreased cell stiffness. Moreover, the detachment time of cells between trypsinization and the beginning of the measurement was varied to analyze its impact on cell mechanics. Mechanical measurements with microconstriction devices can only be conducted on cells brought into suspension. This principally comprises an unnatural state, to which cells finally react with apoptosis. Additionally, cells depolymerize their actin stress fibers shortly after detachment. To investigate the influence of detachment time on cell mechanics, the detachment time of cells before the beginning of the measurement was prolonged from the usual 20 min to 60 min and 100 min. Before measurements, the cell suspension was stored in an incubator, to ensure a temperature 37◦ C and 5 % CO2 as long as possible and to avoid the additional influence of an extended exposure to room temperature. After histogram matching and power-law fitting to the pooled data of 2-3 independent measurements per condition (Fig. 3.19 e), a small, but significant decrease in cell stiffness could be measured for cells detached longer than 20 min before the beginning of the measurements (Fig. 3.18 c). This effect was not further increased for a detachment time of 100 min. The power-law exponent did not show a systematic in- or decrease compared to the control cells (Fig. 3.19 f). This cell behavior is in accordance with the expectations mentioned above. However, it is in contrast to measurements on stem cells from a previous study, which were conducted with an optical stretcher [125]. A gradual cell stiffening was reported after detachment, which lasted for 1 h. Possibly, there are large cell type-to-cell type variations in their reactions on lift-off from the substrate. Some cell types might depolymerize their whole actin cytoskeleton, some other cell types might rather stop actin remodeling totally, which might result in an increase in stiffness. Furthermore, the measurement medium was changed from PBS to HEPES-buffer (4-(283


hydroxyethyl)-1-piperazineethanesulfonic acid, 150 mM NaCl, 10mM glucose) and normal cell medium (DMEM, #11965092, gibco) to investigate its influence on cell mechanical properties. Once more, histogram matching and power-law fitting was conducted to the pooled data of 2-3 independent measurements per condition (Fig. 3.19 g). For experiments with DMEM, an increase in the resulting cell stiffness compared to measurements with PBS could be found (Fig. 3.18 d). For experiments with a HEPES-buffer, even more, a distinct increase of cell stiffness and a big decrease of the power-law exponent was detected (Fig. 3.18 d and Fig. 3.19 h). Again, there are only speculations about the reasons for these mechanical results. The pH values (potential of hydrogen) of the three measurement fluids were found to differ significantly, varying between 7.25, 7.00 and 8.13 for PBS, HEPES and DMEM, respectively. With three measurement points only, a biphasic correlation between pH and cell stiffness cannot be established. In conclusion, this observation highlights the necessity to refrain to the use of only one measurement medium for a series of compared experiments to ensure unbiased results. Considering the preparation process of the device before measurement, plasma treatment and pluronic coating procedures can be varied within certain limitations. Concerning plasma treatment, all parameters were optimized to reach the best-possible adhesion between the glass cover slide and the PDMS mold. A change of these parameters was not possible without loosing bonding efficiency. However, the time between bonding and measurements could be varied. This experiment was already conducted in a previous study. It was reported that the surface properties of the PDMS device change over a time period of up to two days after bonding, and thus influence the transit times of cells through the constrictions. Afterward two days, they remain constant [19]. Therefore, devices were produced at least two days before the measurements to ensure stable channel wall properties. With pluronic coating, first, the duration of coating was systematically varied. Coating the devices with 1 % pluronic solution was abolished completely, or increased to 40 min, compared to the usual coating time of 20 min. Histogram matching and power-law fitting was conducted to the pooled data of 2-3 independent measurements per condition (Fig. 3.19 i). Surprisingly, an increase in cell stiffness with increased coating time was found, which was most pronounced for 40 min coating (Fig. 3.18 e). The power-law exponents also changed systematically within this measurement, rising with increased pluronic coating time (Fig. 3.19 j). This stands against the expectation that cells can pass constrictions faster with increased coating time due to decreased cell friction at the constriction walls. One explanation of this behavior might be that, during a measurement without pluronic pre-coating, many cells got stuck in the filter system or were not able to pass the constrictions at all. The experiment with 0 min pluronic coating might therefore result in a biased investigation, limited to softer cells only, since they are more likely to pass the constrictions under high84


b 0.3 101

control 1

control 2

P-L exponent

Control Entry time [s]

a 100 10-1

ns ns 0.2 0.1

10-2

Confluency Entry time [s]

60%

101 20%

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0.6 1 2 2 εmax/∆p [x10-3 1/Pa]

0.3 100%

ns

*

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control 1 control 2

d P-L exponent

0.6 1

c

0.1

-2

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2

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0

2

20% 60% 100%

f *

*

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-2

2

i 101

0min

0.6 1 2 0.6 1 εmax/∆p [x10-3 1/Pa] 20min

l 2

101 0.25%

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10-2 0.6 1 2 0.6 1 εmax/∆p [x10-3 1/Pa]

PBS HPS DMEM

0.2

*

*

0.1

0min 20min 40min

l 0.3

4%

10-1

2

ns

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*

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20min60min100min

h 0.3

DMEM

P-L exponent

HEPES

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P-L exponent

Medium Entry time [s]

2

100

10

0.2

-2

101 PBS

10

Pluronic concentration Entry time [s]

P-L exponent

10-1

0.6 1

k

100min

100

10

g

60min

P-L exponent

Detachment time Entry time [s]

0.3 101 20min

2

*

*

0

0.2 0.1 0

0.25% 1%

4%

Figure 3.19: Influence of cell culture and measurement conditions on power-law exponents of DLD-1 colon carcinoma cells. Exemplary scatter plots of entry time tentry vs. ǫmax /∆p with power-law fit (left) and power-law exponents (right) from power-law fitting. For a detailed explanation, refer to caption of Fig. 3.18. a+b) Control measurement. c+d) Cell culture confluency. e+f) Detachment times before measurement. g+h) Different measurement media. i+j) Pluronic coating duration. k+l) Pluronic coating concentration. n > 1203 cells for each condition. Histogram matching was performed separately for each panel (a-k). Significant (p < 0.05) differences to first parameter values (green bars) are indicated by asterisks. Figure adapted from [22].

85


friction conditions. Interactions between normally adherent cells and pluronic cannot be ruled out either. However, at least for suspended K562 leukemia cells, an impact of pluronic on cell morphology or viability was excluded (comp. to Sec. 3.1.2). Lastly, pluronic coating concentration was varied from 0.25 wt % to the usual 1 wt %, and increased to 4 wt % to investigate its influence on the resulting cell mechanical properties. Histogram matching and power-law fitting was conducted to the pooled data of 2-3 independent measurements per condition (Fig. 3.19 k). Compared to 0.25 wt % coating concentration, a decrease in cell stiffness was measured for both 1 wt % and 4 wt % coating concentrations. This decrease was not accompanied by a systematic change in the powerlaw exponent (Fig. 3.19 l). For coating with 0.25 wt %, an increase of the retention rate of cells in the filter was not observed. Therefore, these results might stem from the fact that higher pluronic coating concentrations result in a decreased friction between the cells and the channel walls, which in turn decreases cell entry times. A possible interaction between pluronic micelles and the cells at high coating concentrations, however, cannot be excluded [22].

Conclusion Summarizing, all changes in cell culture conditions or measurement parameters resulted in only slightly, but significantly changed cell mechanical properties. Still, a combination of varying cell culture conditions or measurement parameters can easily lead to a significant falsification of mechanical results and must be avoided. Another measurement parameter, which has not been investigated with the microconstriction system yet, is measurement temperature. A previous study found a decrease of cell stiffness with increasing environmental temperature [48]. They thereby highlight the necessity of controlled room temperatures during measurements of cell mechanical properties. So far, during experiments with the microconstriction setup, room temperature was always kept constant at 22◦ C by means of air conditioning.

3.9

Validation of fluorescence setup

Before using the fluorescence setup in biological studies, its functionality and its evaluation software was tested. Therefore, a proof-of-principle measurement with a known correlation of fluorescence signal and cell mechanics was performed. Moreover, the impact of highpower laser illumination on cell mechanics was investigated, to exclude biased measurement results.

3.9.1

Combined calcein staining and cytochalasin D softening

As a proof-of-principle measurement, a heterogeneous population of K562 leukemia cells was used. Cells were cultured according to App. 6.3. Prior to measurements, half of the

86

3.9 Validation of fluorescence setup

c

#Cells

104 10

3

Fluorescence threshold

102 101

10 1 Mean intensity/px

b zero

d

high +cytoD

100 10−1 10

−2

1

2

6 1 2 εmax/∆p [x10−3 1/Pa]

6

* 200 100 0

100

zero

high +cytoD

0.4 PL- exponent

Entry time [s]

101

300 El. mod. [Pa]

a

*

0.3 0.2 0.1 0

zero

high +cytoD

Figure 3.20: Correlation of cell mechanics with expression of fluorescently tagged proteins. Measurement of a K562 leukemia cell population, containing 50 % untreated cells and 50 % cells softened through cytochalasin D (10 µM, 30 min) and stained with calcein (250 nM, 30 min). a) Histogram of average fluorescence intensities per cell pixel. Dashed green line represents the fluorescence threshold for separating cells into a zero and a high fluorescence intensity group. b) Exemplary scatter plots of entry time tentry vs. ǫmax /∆p for cells for the zero fluorescence (non-treated) and high fluorescence (cytoD-treated) group after histogram matching. Black lines indicate the power-law fit to the data. c) Cell elastic modulus for the two groups. d) Cell fluidity (power-law exponent) for the two groups. n = 3134 cells per condition. Significant differences (p < 0.05) are indicated by asterisks. Figure adapted from [22].

cells were treated with the actin-depolymerizing drug cytochalasin D (10 µM, #C8273, Sigma-Aldrich) together with the green fluorescent dye calcein (250 nM, #C0875, SigmaAldrich) for 30 min.

The labeled cells were then mixed with unlabeled control cells

and measured in a microconstriction setup of constriction width w = 5.1 µm and height h = 16.6 µm (device type S7, comp. to Sec. 2.1). Apart from the mentioned staining, cell and device preparation before measurements were conducted according to Tab. 3.2. For the quantification of cell mechanics, the data were split into a fluorescent (≥ 1 count/cell pixel, median = 21 counts/cell pixel) and a non-fluorescent group (≤ 1 count/cell pixel) and ǫmax and ∆p histogram matching was performed between the two groups (Fig. 3.20 a+b). For the green fluorescent, cytochalasin D-treated group a significantly (p < 0.05) decreased cell stiffness (Fig. 3.20 c) and an increased power-law exponent (Fig. 3.20 d) were calculated. A decrease in cell stiffness and an increase in the power-law exponent for cytochalasin D-softened cells is in accordance with previous studies [13, 126]. Thus, the fluorescence extension of the microconstriction setup was able to correlate fluorescence intensities with mechanical properties of subgroups of measured cell populations [22].

87


3.9.2

Impact of laser illumination on cell mechanics

Moreover, the influence of laser illumination on cell mechanics was checked. For measurements with the optical stretcher, previous studies found that illumination with high-power lasers induces cell softening, probably caused by an increase in temperature. For an increase in temperature of 15◦ C, a linear three-fold increase in cell compliance was published, plus a 50 % increase of cell fluidity [48].

a 113 mW

2

p21-/-

4

c

0

p21-/-

1

2

4

0.3 Power−law exponent

113 mW

200

*

225 mW

*

100

control

1 2 4 εmax/∆p [x10−3 1/Pa]

300

2.25 mW

Stiffness [Pa]

control

*

*

225 mW

1

0.1

0

0

10-2

b

400

113 mW

10-1

0.2

0.1

2.25 mW

100

225 mW Power−law exponent

2.25 mW

Stiffness [Pa]

Entry time [s]

101

0

Figure 3.21: Influence of high-power laser illumination on cell mechanics. Measurement of K562 leukemia cell population stained with calcein (100 nM, 30 min) under continuous illumination with different laser powers. a) Exemplary scatter plots of tentry vs. ǫmax /∆p for cells illuminated with 2.25 mW, 113 mW and 225 mW blue laser light. Black lines are power-law fits to the data. b) Cell elastic modulus E for the three groups. c) Cell fluidity (power-law exponent) for the three groups. n = 3904 cells per condition. Significant differences (p < 0.05) are indicated by asterisks.

Mechanical measurements with a microconstriction assay, which are accompanied by fluorescence detection performed by a high-power laser, might therefore be biased by energy deposition in the cells, which might lead to cell softening. To exclude this effect, K562 leukemia cells were stained with 100 nM calcein (#C0875, Sigma-Aldrich) for 30 min prior to measurements. Cells were then measured at three different laser intensities in a microconstriction setup of constriction width w = 6.0 µm and height h = 13.6 µm (device type O3, comp. to Sec. 2.1). Apart from staining, cell and device preparation before measurements was conducted according to Tab. 3.2. As a control measurement, a laser intensity of 2.25 mW was chosen. As medium laser intensity, measurements were conducted at an illumination of 113 mW. For high-power laser illumination, a laser intensity of 225 mW was applied. Two individual measurements were

88

3.9 Validation of fluorescence setup

conducted for each condition and pooled for evaluation. Fluorescence intensity measurements were not performed, because all cells were presumably equally stained during measurements. Power-law fitting with a combined histogram matching concerning stress and strain, was performed as usual to extract quantitative cell mechanical data (Fig. 3.21 a). Surprisingly, a significant increase in cell stiffness was found for medium and high laser illuminated cells (Fig. 3.21 b), which was accompanied by an inversely correlated drop of the power-law exponent (Fig. 3.21 c). In summary, the expected cell softening with medium or high laser power could be ruled out by this investigation. Cell heating by a laser illumination at 225 mW does not result in measurable cell softening. A previous study reports cell contraction for extremely high temperatures over 15◦ C above room temperature, which might finally result in a similar cell stiffening [48], as found for medium and high power laser illumination. However, cell stiffening was most pronounced for medium laser illumination and again slightly decreased for high laser power in this study, which makes this interpretation unlikely. Alternatively, results might be biased by differences in cell staining. Calcein staining was shown to significantly stiffen cells at higher doses (250 nM -1 µM), with a clear correlation between staining dose and increase in stiffness (data not shown). Even though cells were stained from the same stock solution in the current study, an influence of slightly varying dye-intensity on cell mechanics cannot be ruled out. The findings of this study can only partially be transferred to measurements of GFPtransfected cells. Phototoxicity and energy deposition might principally vary between calcein staining and transfections with GFP-tagged proteins.

89


90

4

Biomedical applications In this section, biomedical applications of the microconstriction setup are presented. The projects were chosen from different fields of research, correlating cell mechanics with cell motility and invasiveness (Sec. 4.1, Sec. 4.4, Sec. 4.6, and Sec. 4.9), cell contractility (Sec. 4.3), and cell division (Sec. 4.5 and Sec. 4.8). One project was chosen from industrial medicine to study the influence of environmental pollution on cell mechanics (Sec. 4.7).

4.1

Correlation of cell mechanical properties with cell invasiveness

Biological background Cells migrate through the ECM of our bodies during many physiological processes, for example embryogenesis, morphogenesis [3], wound healing [127] and metastasis formation [128]. The migratory ability of cells depends foremost on their active cell mechanical properties, like contractility and force generation [9]. The more force cells can exert on their surroundings, the more easily they can cross small intercellular gaps or pores of the fiber network. However, also passive cell mechanical properties were reported to govern cell migratory abilities in previous studies. Invasive cancer cells were found to be softer than their non-invasive counterparts. Low cell elastic stiffness was suggested to help cancer cells to overcome the steric hindrance of confined spaces during their migration through the ECM [17, 129, 130] (comp. to Sec. 2.3.1.1 and Sec. 3.6). In this study, cell invasiveness, which is defined as the cell migratory capacity into confined 3-dimensional spaces, was correlated with a range of active and passive cell mechanical properties of four cancer cell lines, including one fibrosarcoma, one lung cancer and two epithelial breast cancer lines [21]. Besides cell deformability, cell contractility, cell adhesiveness to the substrate, cell migratory velocity in two dimensions, and cell nuclear volume were investigated. All measurements except for microconstriction measurements were conducted by Dr. Lena

91

4. BIOMEDICAL APPLICATIONS

Lautscham and Christoph K¨ ammerer [21]. Still, these results are presented here to show microconstriction measurements in a context. In the following, the characteristics of the four used cancer cell lines are shortly summarized. Fibroblastic HT1080 fibrosarcoma cells have widely been used in cell research due to their high invasive properties and high proliferation rate. The cells were extracted from the fibrosarcoma of a 35-year old Caucasian male in 1972 [131]. MDA MB 231 cells (MDA) were gained from a patient’s pleural effusion in 1973. They are reported to have undergone epithelial-to-mesenchymal transition (EMT) and to show a clearly mesenchymal phenotype. Moreover, MDA cells migrate fast and independently from each other [132]. A 125 cells were extracted from a patient lung cancer and provided as a kind gift by Prof. Peter Altevogt (DKFZ, Heidelberg). They are reported to show mesenchymal characteristics and to be invasive [133]. IFD (IFDUCI) cells were extracted from a patient inflammatory ductal breast cancer at the University Clinics of Erlangen. To date, they are poorly characterised in terms of their migratory properties [21].

Cell migration on substrate and into channel array As main measurement parameter, cell migration into a stiff 3-dimensional environment was studied. Therefore, a microchannel array similar to the microconstriction setup was used. The microchannel array was formed through PDMS channels with an elastic modulus of approx. 1.77 MPa (mixing ratio 10:1, Sylgard 184, Dow Corning), rendering the channels undeformable by the cells. In contrast to cell mechanical measurements with microconstrictions, the cells were seeded on one side of the constriction array and freely migrated through a serial range of fibronectin-coated channels with a narrowing width from 11.2 µm to 1.7 µm. The height of the array was around 3.7 µm. Cell invasive capacity was characterized by bright-field time-lapse video recording. Through image analysis, cell velocity, the fraction of invaded cells and invasion depth into the microchannels were analyzed. Thereby, the parameter stalling ratio was defined as the relative amount of cells which was detected in front of a channel, compared to the amount of cells detected directly behind a channel. Additionally, 2-dimensional unconfined cell migration on fibronectin-coated tissue culture dishes was tracked and cell velocity and directional persistence were analyzed and compared to invasiveness. As cell and nuclear volume also determine the steric hindrance of cells during cell squeezing through tiny pores, the cell and nuclear volume were measured by fluorescent cell staining. Cell contractility was studied with traction microscopy. Thereby, the deformation of an elastic polyacrylamide gel with a Young’s modulus of 11.3 kPa (mixture of acrylamide (2%) and bis-acrylamide (0.25%)) was used to calculate the traction forces applied by a cell to the substrate. Next, cell invasion into a 3-dimensional collagen matrix, which is widely used to mimic the

92

4.1 Correlation of cell mechanical properties with cell invasiveness

ECM of our bodies [134] was quantified. This alternative platform for the investigation of cell invasiveness was evaluated by seeding cells on top of a collagen gel and by measuring the invasion depth after three days by fluorescence cell staining and imaging. Cell adhesiveness to the substrate was calculated by spinning disk measurements. Thereby, a shear flow is applied to cells seeded on fibronectin-coated tissue culture dishes and the amount of detached cells is evaluated by fluorescence microscopy. Moreover, lamin A-overexpressing fibrosarcoma HT1080 and epithelial breast cancer cells MDA MB 231 were generated by lentiviral transfection. A 3-fold overexpression was confirmed through Western-blotting. In previous studies lamin A overexpression was reported to increase the nuclear stiffness of cells [135, 136] and it was correlated with a decrease in cell invasiveness [21, 124].

Results Finally, to test the correlation of cell invasiveness into confined spaces with whole cell deformability, cell elastic stiffness and viscous fluidity of the four cancer cell lines and the two lines with increased lamin A levels were investigated with the microconstriction assay. For the measurements, medium-sized constrictions were used, because they measure a bulk cell stiffness and fluidity determined by both the cell cytoskeleton and the cell nucleus (comp. to Sec. 3.6).

0.5

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800

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b

1000

HT1080

Stiffness [Pa]

a

0

Figure 4.1: Mechanical properties of four cancer cell lines. a) Stiffness and b) power-law exponent of HT1080, HT1080 overexpressing lamin A (HT1080 LaA+), MDA MB 231 (MDA), MDA MB 231 overexpressing lamin A (MDA LaA+), A125, and IFD cells. n > 1000 per population. Histogram matching was not conducted with the data. For a discussion of significance levels, see the main text. Subfigure a) is adapted from [21].

All six cell lines were cultured as explained in [21] and harvested at a confluency of approx. 80 %. Constrictions of width w = 6.0 µm and a channel height h = 13.6 µm were used (device type O3, comp. to Sec. 2.1.3). Cell and device preparation before measurements was conducted according to Tab 3.2. After measurements, quantitative mechanical properties were evaluated by fitting a powerlaw to the scatter of tentry vs. ǫmax /∆p. Histogram matching was not performed with these

93


Figure 4.2: Correlation of invasion into microchannels and collagen gels with other cell Nucleus Vol. properties. Squared correlation coefficients (r2 ) for nuclear volume, cytoplasmic volume, cell ad- Cytoplasmic Vol. hesiveness, cell contractility, cell stiffness, lamin Adhesiveness A levels, invasion depth into 3-dimensional collaContractility gen gels, and stalling ratio in front of microchanCell Stiffness nels. Significant (p < 0.05) correlations are indiLamin A Level cated by asterisks. Figure adapted from [21].

r2 1

0.8

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LaA

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Invasion

Stiffness

Adh.

Contract.

Cyto Vol.

Nuc Vol.

*

*

*

Invasion Depth Stalling Ratio

0.6

*

measurements, as it was unknown at the beginning of this thesis. However, great care was taken to measure the cells with the same pressure. The mechanical results show that, comparing only the untransfected cell lines, MDA MB 231 cells were the stiffest, and IFD cells the softest (Fig. 4.1 a). The stiffness of HT1080 and A125 cells ranged in between. All stiffness values were significantly different from all others. The power-law exponents were inversely correlated with the stiffness values (Fig. 4.1 b). Differences between the power-law exponents of HT1080 and MDA MB 231 cells and between A125 and IFD cells were not significant. Concerning the overexpression of lamin A, a systematic increase in cell stiffness and a decrease in the power-law exponent could be found for both transfected cell lines HT 1080 and MDA MB 231 (Fig. 4.1 a+b) [21].

Conclusion In the presented study, a statistically significant positive (+/+) or inverse (+/-) correlation between cell characteristics was found for the pairs: stalling ratio vs. invasion depth into collagen (+/-), cytoplasmic volume vs. contractility (+/+), nuclear volume vs. stalling ratio (+/-), and invasion depth into collagen vs. adhesiveness (+/+) (comp. to Fig. 4.2). Cell stiffness was significantly correlated with lamin A overexpression in a positive way (+/+). However, with the other cell characteristics, cell stiffness did not show significant correlations. These results highlight that cell stiffness and fluidity alone cannot determine the invasive capability of the investigated fibrosarcoma, lung cancer and epithelial breast cancer cell lines in 3-dimensional stiff or soft matrices. Cell migration was mostly impeded in cell lines with larger nuclei, lower adhesiveness, and only to a lesser degree also in cells with lower contractility and higher stiffness. Invasion depth into soft 3-dimensional collagen matrices was especially correlated with cell adhesiveness, whereas the stalling ratio during migration into stiff matrices was increased by nuclear volume. All in all, the ability to overcome the steric hindrance of the matrix cannot be attributed

94

4.2 Influence of Hoechst staining on cell mechanics

to a single cell property, but instead arises from a combination of all of them [21].

4.2

Influence of Hoechst staining on cell mechanics

Biological background Fluorescence imaging often provides better image quality than bright-field imaging. For example, it allows for the specific coloring of cell components, like the nucleus, when tracking individual cells in cell cohorts during their migration in the ECM of a laboratory animal. Moreover, cells are often fluorescently stained and imaged to monitor their migration and deformation inside 3-dimensional microchannels in-vitro, as shown in Sec. 4.1. For live cell tracking, cells can be stained with several commercially available dyes, such as cyTRAK Orange (Abcam), nuclear yellow (Abcam), nuclear green (Abcam), draq5 (Abcam) [137], or Hoechst 33342 (Invitrogen), which often stain the cell DNA [138]. All of these dyes are different concerning their excitation and emission wavelenghts and can be chosen either according to microscopic requirements and possibilities, or in combination with other cell dyes for multi-channel imaging. Fluorescence imaging and cell staining, however, have the potential of cell toxicity. First, cells can be damaged by the exposure to the dye itself, which might interact with unwanted protein pathways. Additionally, dyes often intercalate into the DNA, which perturbs gene reading. Moreover, cells can be harmed when energy is deposited in them during fluorescence illumination, because this process enhances radical formation. Usually, the short- and long-term influence of cell staining and fluorescence imaging is not investigated in biomedical studies, either due to a lack of awareness of potentially cell compromising reactions, and/or due to a lack of alternatives. Therefore, the systematic investigation of the influence of Hoechst staining on cell migration and on their mechanical properties was the main goal of this study. First, HT1080 fibrosarcoma cells (comp. to Sec. 4.1) were tracked during 2-dimensional migration in a tissue culture dish, after staining them with a range of Hoechst concentrations up to 25 µg/ml. Additionally, they were irradiated with increasing UV light intensities up to 10 mW/cm2 to mimic fluorescence image recording. Illumination was applied every 5 min with an exposure time of 500 ms. Cell migration experiments were conducted by Dr. Lena Lautscham. HT1080 cells were found to migrate more slowly and with a lower persistence for all Hoechst concentrations, even without UV illumination. Under UV illumination, these effects were increased. In summary, cell speed and persistence decreased with increasing UV intensity and increasing duration of UV irradiation [21]. Next to cell migratory capabilities, cell stiffness and fluidity of Hoechst-stained cells were investigated. For the measurements of this study, medium-sized constrictions were used, which measure a bulk cell stiffness and fluidity determined by both the cell cytoskeleton

95


and the cell nucleus, as shown in Sec. 3.6.

Results a Hoechst

control Entry time [s]

101 100 10-1 10-2 0.5

Stiffness [Pa]

3

c 0.3

500 *

400 300 200 100 0

0.5 1 εmax/∆p [x10−3 1/Pa]

control

Hoechst


b

3

1

*

0.2

0.1

0

control

Hoechst

Figure 4.3: Influence of Hoechst-staining on cell mechanical properties. a) Exemplary histogram matched scatter plots of tentry vs. ǫmax /∆p of K562 cells stained with 1.5 µg/ml Hoechst 33342 for 2 h prior to measurements, compared to control population. Black lines show powerlaw fit to the data. b) Stiffness of Hoechst-dyed cells compared to the control group. c) Power-law exponent of Hoechst-stained cells. n = 3599 cells per condition. Significant differences (p < 0.05) are indicated by asterisks. Figure adapted from [21].

As an exemplary cell system, K562 leukemia cells were used. They were cultured in a flask with an area of 175 cm2 , to provide enough cells for six measurements. Otherwise, they were cultured according to App. 6.3. Half of the cells were stained with a medium dose of Hoechst 33342 (1.5 µg/ml, #H1399, Invitrogen) for 2 h prior to microconstriction measurements. The cells were not exposed to UV light, but kept in a light-shielded incubator before measurements. Fluorescence emission was checked before the measurements under an epifluorescence microscope. The Hoechst concentration was neither kept constant after the washing procedure, nor during the measurement. Cells were measured with a constriction setup containing constrictions of 5.1 µm width and 16.6 µm height (device type S7, comp. to Sec. 2.1.3). Besides staining, cell and device preparation before measurements was conducted according to Tab. 3.2. Three independent measurements were conducted with both control cells and Hoechst-stained cells, and the results were pooled for the two groups after the measurements.

96

4.3 Influence of myosin-II on cell mechanical properties

After the measurements, histogram matching and power-law fitting was applied to calculate the fit parameters cell stiffness E and the power-law exponent β (comp. to Fig. 4.3 a). Cell mechanics were clearly influenced by Hoechst staining. Cell stiffness was significantly increased by more than 15 % (Fig. 4.3 b). At the same time, Hoechst-stained cells became slightly less fluid-like (approx. 2 %), as seen by the decrease of the power-law exponent. This change, however, was only slightly significant (p = 0.04) (Fig. 4.3 c) [21].

Conclusion In this study, both the migration of HT1080 fibrosarcoma cells and the deformability of K562 leukemia cells were found to be influenced by Hoechst-staining. Cells migrated more slowly and less persistently on a 2-dimensional substrate after staining. Moreover, as found by the microconstriction assay, they became stiffer and less fluid-like. Comparing the behavior of stained and unstained cells in different experiments might therefore bias the results. When using Hoechst in invasion experiments, possible changes in cell mechanics should be considered. There can only be speculations about the origin of the mechanical changes. A possible explanation is the intercalation of Hoechst into the DNA of cells. First, Hoechst potentially changes the expression levels of various proteins, as DNA reading and protein production is stopped. Secondly, DNA-intercalation might stiffen the DNA itself and, similar to chromatin condensation, might thereby stiffen the cell nucleus. In summary, this study underlines the importance of minimizing Hoechst-staining and UV illumination to the smallest possible extent in in-vitro cell studies. It furthermore highlights the necessity of improvements of bright-field microscopy techniques, which might make cell staining superfluous at some point in the future.

4.3

Influence of myosin-II on cell mechanical properties

Biological background Many cells, for example fibroblasts, move and exert forces through actomyosin contractility [139, 140] (comp. to Sec. 3.6). Non-muscle myosin-II functionality and thereby cell contraction can be inhibited by chemicals like blebbistatin, which prevents the re-attachment of the myosin head after the power stroke on actin fibers [140]. For a wide range of cell lines and measurement techniques, myosin-II inhibition could be correlated with an increase in cell deformability, which was widely explained by a loss in prestress [141, 142]. In contrast, recently, a study by Chan et al. suggested that myosin-II inhibition increases cell stiffness and decreases cell fluidity in suspended cell lines and cell lines brought into suspension [143]. These novel results were gained through microfluidic measurement methods, like the optical stretcher, a microconstriction-like assay and real-time deformability

97


cytometry. The authors described the role of myosin-II contractility in a suspended cell state as contrary to its role in an adherent state. In a suspended state, where cells lack stress fibers and prestress, the actin reorganizing activity of myosin-II supposedly dominates its cell contracting activity. A decrease in actin reorganization would thus lead to cell stiffening after myosin-II inhibition [143]. As these novel results are still highly debated and since the difference between myosin-II impact on adherent and suspended cell mechanics is poorly understood, the influence of myosin-II inhibition on cell mechanics was reinvestigated with the microconstriction assay.

Results

a

Entry time [s]

101

DMSO

bleb

100

10-1

10-2 1

2

c

Stiffness [Pa]

400

*

300 200 100 0

DMSO

bleb


b

4 1 εmax/∆p [x10-3 1/Pa]

2

4

0.3

*

0.2 0.1 0

DMSO

bleb

Figure 4.4: Influence of cell contractility on mechanical properties. a) Scatter plots of tentry vs. ǫmax /∆p of DLD-1 cells treated with 50 µM blebbistatin for 20 min, compared to control population. Histograms are matched for stress and strain. Black lines show power-law fit to the data. b) Stiffness of blebbistatin-treated cells compared to control group shows significant (p < 0.05), but very slight increase. c) Power-law exponent of blebbistatin-treated cells compared to control group is significantly decreased. n = 6419 cells for each condition.

In this study, blebbistatin (#B0560, Sigma-Aldrich) was employed to inhibit myosin-II activity at the same concentration and for the same incubation period as used by Chan et al., giving 50 µM blebbistatin for 20 min before measurements [143]. The measurements were conducted on DLD-1 colon carcinoma cells, which were cultured according to App. 6.3 and harvested at a cell culture density of approx. 80 %. Cell and device preparation before measurements were conducted according to Tab. 3.2. The cells

98

4.4 Influence of αvβ3 and αIIbβ3 integrin on cell mechanical properties

were brought into suspension by trypsinization before treatment with blebbistatin. The control group was incubated with DMSO (DiMethyl SulfOxide, #D4540, Sigma-Aldrich) for the same period of time as a carrier control. The microconstrictions used in this study had a width of 5.1 µm, and the device had a height of 16.6 µm (device type S7, comp. to Sec. 2.1.3). These medium-sized constrictions probe both the cell cytoskeleton and the cell nucleus (comp. to Sec. 3.6). For both control and blebbistatin-treated cells, three independent measurements were conducted and pooled afterwards. The scatters of tentry vs. ǫmax /∆p were histogram matched and then fitted by power-law theory to extract quantitative cell mechanical properties (Fig. 4.4 a). The stiffness of blebbistatin treated cells was very slightly, but significantly increased compared to the control group (Fig. 4.4 b). This difference in cell stiffness is likely to be irrelevant in any biological context. The power-law exponent was significantly decreased, which means that the cells became more solid-like after myosin-II inhibition (Fig. 4.4 c).

Conclusion These results are partially in accordance with Chan et al., who reported a big increase in cell stiffness and a huge decrease of the power-law exponent through blebbistatin for naturally suspended cells or cells brought into suspension [143]. Importantly, the results disagree with a pronounced softening of adherent cells after myosin-II inhibition, which seemed to be established for adherent cells with multiple adherent measurement techniques. Therefore, the present study confirms a new, underestimated influence of myosin-II activity on the mechanics of suspended cells. On a speculative basis, two effects, one predominant in adherent cells and one predominant in suspended cells, might counter-act each other and thereby produce contradicting experimental results. As suggested by Chan et al., the results of this study also suggest that the loss of prestress observed in adherent cells is only of minor importance for suspended cells. For such an effect, measurement results are likely to depend on the time between cell detachment from the substrate and measurement, and probably also on the temporal sequence of cell detachment and myosin-II inhibition. The presented results thus underline the necessity of future studies on the role of myosin-II in suspended and adherent cells.

4.4

Influence of αvβ3 and αIIbβ3 integrin on cell mechanical properties

Biological background Integrins are transmembrane receptors which are expressed on the surface of most cells in the body. They are α/β-heterodimers, which span the plasma membrane, and form a

99


bi-lobular ECM-protein binding head. Integrins are located in focal adhesions [78, 144], as depicted in Fig. 4.5. These protein complexes link the cytoskeleton to the ECM through linker proteins and signaling partners, for example vinculin, talin, paxillin, and FAK (focal adhesion kinase) [145]. Integrins normally exist in an inactivated state. After activation through chemical and possibly mechanical cues, they undergo conformational changes, which are mediated into the cells and lead to further signaling cascades (outsidein-signaling) [146].

α-actinin

VASP Talin Paxillin

Vinculin FAK

α β

VASP Talin Paxillin

Vinculin FAK

α β Membrane

Integrin Activation

Outside-In-Signaling

actin

Mn2+

Figure 4.5: Integrin location and activation. Integrins are transmembrane proteins which colocalize in focal adhesions with talin, vinculin, and FAK, for example. They link the ECM to the cytoskeleton via actin coupling. Integrins can be activated through manganese ions. Figure adapted from [145] and [146].

αvβ3 integrin and αIIbβ3 form the β3 integrin family [78, 144]. The expression of αvβ3 was shown to govern endothelial neovascularization, and mediate osteoclastic bone resorption. Moreover, αvβ3 is upregulated in solid and diffuse tumors like melanoma and glioblastoma, respectively [147]. αvβ3 binds to the arginine-glycine-aspartate (RGD) tripeptide sequence in many ECM proteins, for instance vitronectin, osteopontin, fibrinogen, and fibronectin [148, 149]. Thus, changing αvβ3 integrin expression could be used as a cancer therapeutics and to prevent osteoporosis and angiogenesis, by changing the adhesiveness of cells to their surroundings [150]. αIIbβ3 integrin is highly homologous to αvβ3 [151]. It is usually only expressed in platelets when they rearrange their cytoskeleton during clot formation [152]. A lack of αIIbβ3 integrin was shown to cause diseases like hemorrhage, osteosclerosis and Glanzmann-thrombasthenia [153]. Moreover, αIIbβ3 integrin expression was reported to be upregulated in cancer cells like mouse melanoma cells, human leukemia cells and human squamous cell carcinoma [151]. In pharmaceutical studies, αIIb or β3 antibodies were successfully used in melanoma models in mice to reduce the metastatic potential of malign cells [154]. The concrete functioning of αvβ3 or

100


αIIbβ3 overexpression in tumor progression, however, is not fully understood, especially concerning changes in cellular mechanical properties. This is why the passive mechanical properties of two cell lines were studied with the microconstriction assay. First, suspended K562 leukemia cells, which express recombinant αvβ3 integrin after stable transfection (termed K562-αvβ3), were investigated [155]. Secondly, adherent human melanoma M21 cells, which do no longer express αvβ3 integrin after knockout (termed M21L) [156] or which now express αIIbβ3 integrin instead of αvβ3 (termed M21-αIIbβ3), were used as model cell lines. Both cell lines still express other integrins, for instance α5β1 integrin. Among others, this study was supposed to shed light on the question if the expression of αvβ3 or αIIbβ3 integrin in K562/M21 cell lines is correlated with changes in passive cell mechanical properties. These could be introduced by linkage of the integrins to the actin cytoskeleton of the cells. This theory was further tested by destroying the actin cytoskeleton of cells through latrunculin A, and then again comparing their passive mechanics. Additionally, integrins were activated through Mn2+ -ions (comp. to Fig. 4.5) and changes in the stiffness and fluidity of all cell lines were monitored. Finally, cell morphology of M21 and M21L cells was analyzed through immunohistochemistry assays and flow cytometry on M21/M21L cells was applied to connect the actin content of cells to a change in αvβ3 or αIIbβ3 expression [23]. This study was a collaboration with Dr. José-Luis Alonso from Harvard Medical School, Boston, Masachusetts, USA, who kindly provided transfected M21 and K562 cells.

Results Influence of αvβ3 integrin Cell mechanical properties of M21 and M21L cells were assessed with a microconstriction array containing constrictions of width of 7.7 µm and a device height of 18.9 µm (device type X4W5scaled, comp. to Sec. 2.1.3). K562 cells were measured with smaller constrictions, being 6 µm in width and a device being 13.6 µm in height (type O3, comp. to Sec. 2.1.3). Both constriction sizes supposedly probe the mechanical properties of both the cell cytoskeleton and the nucleus of the two cell lines (comp. to Sec. 3.6). M21 cells were cultured as explained in [20] and harvested at a confluency of approx. 80 %. K562 cells were cultured according to App. 6.3. Cell and device preparation before measurements was conducted according to Tab. 3.2. At least two independent measurements were conducted for each condition with identically harvested cells and the results were pooled per condition after the evaluation. Power-law fitting of the scatters of tentry vs. ǫmax /∆p yielded a cell stiffness of 1215 ± 17 Pa for M21 melanoma cells, while M21L cells (αvβ3-knockout) showed a significantly reduced stiffness of 1065 ± 17 Pa (Fig. 4.6 a). The power-law exponents were significantly different with 0.07 ± 0.01 for M21 and 0.09 ± 0.01 for M21L (data not shown). Wildtype K562 leukemia cells had a stiffness value

101


of 598 ± 14 Pa, whereas K562-αvβ3 integrins showed an increase of stiffness to 655 ± 10 Pa (Fig. 4.6 b). The power-law exponents were significantly different with 0.25 ± 0.01 for K562 and 0.23 ± 0.01 for K562-αvβ3 cells (p < 0.05, data not shown). The expression of αvβ3 integrin in both cell lines thus shows a correlation with increased stiffness and a decreased power-law exponent.

400

M21L

c

Mn2+

200 0

M21

K562

K562−αvβ3

d 800

* 600

*

800 latA

latA

400 200

Stiffness [Pa]

Stiffness [Pa]

600

*

*

*

Mn2+

Stiffness [Pa]

* Mn2+

1400 1200 1000 800 600 400 200 0

b 800

* * Mn2+

Stiffness [Pa]

a

600

latA

latA Mn2+

M21

M21

400 200

0

0 M21

M21L

Figure 4.6: Stiffness values for M21 melanoma and K562 leukemia cells with and without αvβ3 integrin expression. a) Cell stiffness for M21 cells compared to M21L cells, with/without treatment with 1 mM Mn2+ for 30 min. b) Cell stiffness for K562 cells compared to K562-αvβ3 cells, with/without treatment with 1 mM Mn2+ for 30 min. c) Cell stiffness of M21 and M21L cells after treatment with 1 mM latrunculin A for 30 min. d) Cell stiffness of M21 cells after treatment with 1 mM latrunculin A and after simultaneous treatment with 1 mM latrunculin A plus 1 mM Mn2+ for 30 min. Histogram matching was conducted separately for each subfigure (a-d). n > 1200 for each population. Asterisks mark significant differences with p < 0.05. Figure adapted from [23].

To check the influence of actin on the overall stiffness of cells with/without αvβ3 integrin expression, melanoma M21 and M21L cells were treated with 1 µM latrunculin A (30 min, #L5163, Sigma-Aldrich), which depolymerizes the actin cytoskeleton of cells [157]. Cell stiffness was reduced to 675 ± 9 Pa with M21 cells, and similarly to 604 ± 11 Pa with M21L cells (Fig. 4.6 c) compared to their untreated counterparts (Fig. 4.6 a). The power-law exponents rose to 0.12 ± 0.01 for M21 cells and to 0.15 ± 0.01 (significant difference) for M21L cells (data not shown). These results suggest that a different baseline stiffness remains in both populations after the destruction of the actin cytoskeleton, which cannot be restored. In conclusion, the difference in cell stiffness might also be due to other cell components, such as microtubules, intermediate filaments, or an enhanced cell nuclear

102


membrane, and not only depend on actin reenforcement through integrins. Inside-out activation of integrins was evoked through the addition of 1 mM Mn2+ to the cell medium [158]. Stiffness was increased in both M21 and M21L (Fig. 4.6 a), and in K562 and K562-αvβ3 cell lines significantly after treatment (Fig. 4.6 b), and the power-law exponents were significantly decreased. After chemical disruption of the actin cytoskeleton through latrunculin A and parallel integrin activation through 1 mM Mn2+ , cell stiffness was still significantly increased (Fig. 4.6 d) and a significant decrease in the power-law exponent was still observed (data not shown). Stiffness differences are thus not only induced by increased integrin-actin coupling, which presumably increases the actin content in the cells, but through other mechanisms [23]. Integrin deactivation through 1 mM calcium/magnesiumions, which supposedly keeps α5β1/αvβ3 integrins in an inactive/closed conformation [159], led to a small increase in cell stiffness (data not shown). Calcium/magnesium ions, however, were reported to change the chromatin condensation, which might also in this case have led to increased nuclear stiffness [12]. Under these circumstances, the influence of the cell nucleus seems to dominate over the influence of integrin deactivation and coupling to the actin cytoskeleton [23].

M21L

MFI

M21

4

10x 10 M21 8

M21L

K562αvβ3

αvβ3 β1 αv

c

αvβ3 β1 αv

a

6 4 2

d 25 adherent

1.4 1

*

M21 M21L

0.4

x10

3

20 15 [%]

x10 1.8

3

Cell area [µm2]

Cell area [µm2]

b

αvβ3 β1 αv

0

0.2 0

suspended M21

M21L

10 5 0 −5 Relative difference in actin content (norm. to M21 cells)

Figure 4.7: Influence of αvβ3 expression on morphology of M21 and K562 cells. a) Phalloidinstained M21 and M21L cells, spread on 10 µg/ml fibronectin-coated surfaces for 18 h. Scale bar is 50 µm. b) Mean area of M21 and M21L cells under adherent and non-adherent conditions. Error bars represent standard errors. c) Mean fluorescent intensity (MFI) of integrin cell surface expression level of M21, M21L, and K562-αvβ3 cells, showing αvβ3, β1, and αv integrins. d) Relative difference in actin content [%] between M21 and M21L cells, measured by flow cytometry. Figure adapted from [23].

To shed light on how exactly αvβ3 integrin expression influences cell mechanics, the impact of integrin activation and integrin expression levels on actin, and on cell morphology, cell

103


volume, and cell spreading area of M21 cells expressing α5β1 and αvβ3 integrins compared to M21L cells expressing only α5β1 (Fig. 4.7 a) were compared. Moreover, the cell actin content was measured. First, flow cytometry was employed to investigate the integrin expression level of α5β1 and αvβ3 integrins in M21 and M21L cells. The procedure is in detail elucidated in [23]. As expected, M21L cells do not express αvβ3 integrin. The α5β1 integrin expression was found to be slightly higher in M21L cells compared to M21 cells (Fig. 4.7 c). There was no difference in αvβ3 and β1 integrin expression between K562-αvβ3 and M21 cells. Moreover, cell morphology of M21 and M21L cells was analyzed by phalloidin staining of the actin cytoskeleton. In general, M21L cells were found to be less spread out on fibronectin surfaces (10 µg/ml) and to have a more rounded cell body than M21 cells (Fig. 4.7 a). M21L cells were also found to be smaller in an adherent and a suspended state than M21 cells (Fig. 4.7 b left + right), which shows that M21L cells have a smaller cell volume than M21 cells. Finally, M21 cells had an approx. 15 % higher relative F-actin content than M21L cells, which is given through (actin (M21) – actin (M21L))/ acin (M21) (Fig. 4.7 d) [23]. Influence of αIIbβ3 integrin a

*

1000 800 600 400

1200 1000 800 600

*

*

400 200

200 0

b

Stiffness [Pa]

Stiffness [Pa]

1200

*

M21

M21L M21-αIIbβ3

0

M21

M21L M21-αIIbβ3

Figure 4.8: Influence of αIIbβ3 on cell mechanics. a) Stiffness of M21L and M21-αIIbβ3 cells compared to control population M21. b) Stiffness of M21L cells and M21-αIIbβ3 compared to control cells M21 after treatment with 0.5 µM latrunculin A for 30 min. Histogram matching was conducted separately for all sugfigures. n > 1200 for each population. Asterisks mark significant differences with p < 0.05.

Moreover, the mechanical properties of M21-αIIbβ3 melanoma cells, expressing α5β1, and αIIbβ3 instead of αvβ3 integrins, was calculated in comparison to M21 (α5β1 and αvβ3) and M21L (α5β1 only) cells. It was hypothesized that the replacement of αvβ3 by αIIbβ3 integrin might restore the mechanical properties of M21L cells to the level of M21 cells, since both integrins have a very similar molecular structure. Again, cells were measured with a microconstriction array containing constrictions of width w = 7.7 µm and a device height h = 18.9 µm (device type X4W5scaled, comp. to Sec. 2.1.3). Cells were cultured as explained in [20] and harvested at a confluency of 80 %. Cell and device preparation before measurements was conducted according to Tab. 3.2. After conducting 104


three individual measurements, the results were pooled during evaluation. Power-law fitting was conducted after histogram matching between M21, M21L and M21-αIIbβ3 cell populations. The introduction of αIIbβ3 into M21L cells led to a stark increase in cell mechanical stiffness, which even slightly exerted the stiffness of M21 cells (Fig. 4.8 a). The power-law exponent of M21-αIIbβ3 cells ranged between those of M21 and M21L cells (data not shown). After a treatment with 0.5 µM latrunculin A for 30 min, which disrupted the actin cytoskeleton of the cells, M21-αIIbβ3 cells still showed the highest stiffness of the three compared cell lines (Fig. 4.8 b). In summary, the transfection of αIIbβ3-transfection restored the difference in cell stiffness resulting from αvβ3-knockout. This might suggest that in M21 cells, αIIbβ3 integrins at least partially overtake the tasks of αvβ3 integrins in cell mechanics.

Conclusion In this study, a systematic effect of αvβ3 integrin expression on cellular mechanics was found. For both M21 and K562 cell lines, an increase in cell stiffness and a decrease in cell fluidity could be correlated with the expression of αvβ3 integrin. This effect could be due to the association of αvβ3 integrin with the actin cytoskeleton through focal adhesions. This link could either increase the connectivity of all cell components in terms of crosslinking or even influence actin polymerization directly [160, 161]. Support for this notion comes from a decreased actin content measured by flow cytometry in M21L cells compared to M21 cells and from the finding that αvβ3 integrin expressing M21 cells have a higher cell volume. In the case of M21-αIIbβ3 cells, which expressed αIIbβ3 instead of αvβ3, the stiffness and fluidity of cells could be restored to the level of M21 cells, and even exceeded their stiffness slightly [23]. The disruption of the actin cytoskeleton with latrunculin A decreased the stiffness of M21, M21L and M21-αIIbβ3 cells in the same way. This means that a difference in stiffness is still measurable between M21, M21L and M21-αIIbβ3 cells without the influence of the actin cytoskeleton. From this it can be concluded that other cellular components, such as the nucleus, microtubules, or intermediate filaments might be influenced as well by the expression of αvβ3 and αIIbβ3 integrins. Moreover, after the addition of Mn2+ , which is believed to activate integrins by mimicking outside-in-signaling, an increase in cell stiffness could be measured for all cell lines. Thus, this mechanism seems to be independent of αvβ3 integrin and might be promoted by other integrins, too. Interestingly, after the disruption of the actin cytoskeleton by latrunculin A, an increase in cell stiffness after activation through Mn2+ could still be measured. This supports the notion that the cell nucleus or other cytoskeletal components might also stiffen in the presence of manganese cations [23].

105


In the future, more detailed studies using cell populations expressing different levels of only αvβ3, only αIIbβ3 or only α5β1 will be required to finally assess the differential contribution of these integrins to integrin-mediated cellular stiffness and fluidity. Unfortunately, there is no biophysical method available to date that can measure the mechanical properties of the cytoskeleton totally independent of the mechanics of the nucleus or vice versa, since all cell components are coupled and linked in many ways [111, 162]. The best results in decoupling differential properties of cell components might be achieved by AFM measurements on adherent cells [36], probing the mechanics of different cell areas. Alternatively, isolated cell nuclei could be measured with contact-free microfluidic measurement techniques, such as the optical stretcher, for example [7, 23].

4.5

Influence of p21 on cell mechanical properties

Biological background For many years, p21, also called p21Cip1 or p21WAF1/Cip1 , has been established as an important cell cycle arrester and tumor suppressor. It supposedly works in a p53-dependent and -independent way to arrest cells in G1 phase or induce senescence after detection of genetic damage [163]. In detail, p21 was found to either work through cyclin cdk2/-cdk1 inhibition [164], or through binding with the proliferating nuclear antigen, a subunit of DNA polymerase δ, itself, and it can thereby directly stop DNA replication [165]. In human cancer, increased levels of p21 were found, which promote unlimited cell proliferation [164]. Recently, is has become more and more evident that p21 does not only play a role in cell cycle regulation, gene transcription, and DNA repair, but also in cell differentiation, cell migration and cytoskeletal dynamics [165, 166]. Besides many others, the loss of p21 was reported to induce EMT, where cells lose E-cadherin expression, accumulate β-catenin in the nucleus, and express laminin V. Moreover, well-known EMT markers like Snail-1 are upregulated after p21-knockout [167]. EMT-induction was accompanied by increased single cell migration, 3-dimensional invasion into artificial ECMs, and 2-dimensional wound healing [168]. So far, the influence of p21 on passive cell mechanical properties, like cell stiffness and fluidity, has not been investigated. Still, the understanding of mechanical implications of p21 expression is a valuable tool for advancing in metastasis inhibition and for understanding p21 overexpression during morphogenesis [167]. To investigate how p21-absence affects cell mechanical properties, a stable p21-knockdown (p21-/-) was introduced in HCT116 colon carcinoma cells [169]. On a 2-dimensional substrate, the morphology of p21-knockdown HCT116 cells was visibly changed to a more widespread, elongated cell form. This is in accordance with the previously reported EMT induction in the normally epithelial HCT116 cells [167].

106

4.5 Influence of p21 on cell mechanical properties

After p21-knockdown, a change in cellular and especially nuclear deformability was expected, because p21 supposedly influences the chromatin structure in the cell nucleus [164]. To find the origin of possible changes of cell mechanical properties, cells were first measured without pharmaceutical treatment, and secondly after depolymerizing their actin cytoskeleton through latrunculin A. For the first case, changes in cell mechanics should be determined by both the mechanical properties of the cell cytoskeleton and the nucleus. After latrunculin A treatment, the changes of cell nuclear mechanics should dominate the measurement results. Cells were kindly provided by our collaborator Pablo Lennert from the chair of Experimentelle Tumorpathologie (Prof. Regine Schneider-Stock) from the University Clinics of Erlangen.

Results a control

Entry time [s]

10

p21-/-

1

100

10-1

10-2

b

0.6

1200

1 *

0.4 0.6 εmax/∆p [x10−3 1/Pa]

1

c 0.3 Power−law exponent

0.4

Stiffness [Pa]

*

800

400

0

0.2

0.1

*

0 control

p21-/-

control

p21-/-

Figure 4.9: Influence of p21-knockout on mechanical properties of HCT116 cells. a) Scatter plots of tentry vs. ratio of ǫmax /∆p for cells with stable p21-knockout, compared to control cells. Populations are histogram matched. Black lines show power-law fit to the data. b) Stiffness of p21-/- cells compared to control population, calculated from power-law fitting. c) Power-law exponent of p21-/- cells compared to control population. n = 624 cells per population. Asterisks mark significant differences with p < 0.05.

HCT116 wildtype cells were cultured in RPMI 1640 (#P04-18500, Pan Biotech), including 10 % FBS (fetal bovine serum, #P04-18500, Pan Biotech), 1 % P/S (penicillin-streptomycin, #P06-07100, Pan Biotech). HCT116 p21-/- cells were cultured in DMEM medium 107


(#41965039, gibco), including 10 % FCS (#P30-1502, Pan Biotech), 1 % P/S. They were both harvested at a culture confluency of approx. 80 %. HCT116 cells were mechanically investigated through constrictions of width w = 6 µm and height h = 13.6 µm (device type O3, comp. to Sec. 2.1.3). These medium-sized constrictions probe the mechanical properties of both the cell cytoskeleton and the cell nucleus (comp. to Sec. 3.6). Cell and device preparation before measurements was conducted according to Tab. 3.2. Three independent measurements were performed per condition with identically harvested cells. After analysis, the results were pooled per condition. The scatter plots of tentry vs. ratio of ǫmax /∆p were fitted by power-law theory to extract quantitative mechanical parameters (comp. to Fig. 4.9 a). As usual, only cells that had experienced both the same deformation ( = strain) and the same pressure ( = stress) during the measurements were chosen for a quantitative comparison. Results show a systematic difference in mechanical properties between p21-/- cells compared to a control population. p21-knockdown and thereby EMT led to a significant increase in cell stiffness and to a significant decrease in the power-law exponent (Fig. 4.9 b+c). To test the hypothesis whether this difference in mechanical properties might stem from nuclear mechanical differences, cells were treated with 0.5 µM latrunculin A (#L5163, Sigma-Aldrich) for 30 min to disrupt the actin cytoskeleton and more directly measure the mechanical properties of the cell nucleus. Device type and the rest of cell and device preparation remained unchanged. The same power-law fitting was conducted on the scatter plots of tentry vs. ǫmax /∆p after histogram matching (Fig. 4.10 a). Again, cell stiffness of p21-/- cells was increased significantly by almost 20 %, whereas cell fluidity, indicated by the power-law exponent, was also increased significantly after latrunculin A treatment (Fig. 4.10 b+c).

Conclusion The mechanical measurements conducted on HCT116 colon carcinoma cells with and without actin cytoskeleton showed a systematic increase in cell and nuclear stiffness after p21-knockout. The power-law exponent was decreased for both sets of measurements. This hints to the fact that the increase in overall stiffness measured without latrunculin A treatment might also stem from the increase in cell nuclear stiffness. However, an additional increase in cell cytoskeletal stiffness cannot be ruled out by this study. Explanations for these results are mainly speculative to this date. Stiffening of the cell cytoskeleton does not have to be induced by p21 itself, but could be governed by all its downstream signaling partners. Cells undergoing EMT through p21-knockout were reported to have increased invasive and migratory capabilities. An increase in cytoskeletal stiffness might therefore be caused by an enhanced actin cytoskeleton and increased cell contractility. Moreover, increased vimentin levels were measured after p21 knockout (data

108

4.6 Influence of GBP-1 on cell mechanical properties

a

Entry time [s]

101

p21-/+ latA

control + latA

100

10-1

10-2 1

c

500 400

+ latA

*

300 200 100 0

control

p21-/-

2

0.3 Power−law exponent

Stiffness [Pa]

b

1 4 εmax/∆p [x10−3 1/Pa]

2

+ latA

4

*

0.2 0.1 0

control

p21-/-

Figure 4.10: Influence of p21-knockout on nuclear mechanical properties of HCT116 cells. a) Scatter plots of tentry vs. ratio of ǫmax /∆p for cells with stable p21-knockout, compared to control cells, both after treatment with 0.5 µM latrunculin A for 30 min. Cell populations were histogram matched for stress and strain. Black lines show power-law fit to the data. b) Stiffness of p21-/- cells compared to control population after latrunculin A-treatment. c) Power-law exponent of p21-/- cells compared to control population after latrunculin A-treatment. n = 834 cells per population. Asterisks mark significant differences with p < 0.05.

not shown, private communication with Pablo Lennert). Changes in nuclear stiffness might be based on the interaction of p21 with cell DNA. p21-knockout might for example lead to chromatin condensation, which was reported to stiffness cells [20]. The findings of this study, however, are contradictory with recent measurements on human ovarian cancer cell lines conducted with a microfiltration assay [170]. Inducing EMT through the overexpression of the key transcription factors Snail, Slug and Zeb1 in ovarian cancer cells resulted in a decrease of cell stiffness. This discrepancy might be explained by the difference in investigated cell lines, or by the difference in EMT-induction.

4.6

Influence of GBP-1 on cell mechanical properties

Biological background Guanylate-binding proteins (GBPs) are large GTPases and constitute a family of seven highly homologous proteins in humans. The large GTPase guanylate-binding protein 1 (GBP-1) di- or -tetramerizes in-vitro in presence of GTP, which activates its GTPase ac-

109


tivity [171]. Moreover, it has been shown to heterodimerize with GBP-2 and GBP-5 [172]. GBP-1 expression is induced by interferon-γ (IFN-γ), a cytokine often expressed during inflammation [173]. GBP-1 mediates the cell biological effects of IFN-γ, for example by inhibiting cell proliferation, invasiveness and migration [174, 175]. Immunocytochemical double staining of GBP-1 and actin recently showed that both proteins co-localized, and that disruption of the actin cytoskeleton was dependent on the oligomerization and the GTPase activity of GBP-1. GBP-1 is thus a novel member within the family of actin-remodeling proteins specifically mediating IFN-γ-dependent defense strategies [176]. Moreover, the interaction of purified GBP-1 and actin was sufficient to impair the formation of actin filaments in-vitro, as shown by high resolution STED (stimulated emission depletion) microscopy [176]. Furthermore, impairment of polymerization was dependent on the time point of GBP-1 addition (unpublished data from Isabella Schöpe). Since cell stiffness is crucially influenced by the concentration and mechanical tension of polymerized actin, GBP-1 overexpression was supposed to increase the mechanical deformability of cells. To test this hypothesis the microconstriction array was used to systematically investigate the influence of GBP-1 on cell mechanics. First, the influence of the overexpression of wildtype GBP-1 in stably transfected DLD1 colon carcinoma cells on cell mechanics was studied. Moreover, the wildtype GBP-1 protein was genetically mutated at four different points, which supposedly change GTPaseactivation and actin-binding at the actin binding site of the wildtype GBP-1 protein. The resulting mutants were then transiently transfected into HeLa cervix carcinoma cells. A summary of the GBP-1 mutants is shown in Tab. 4.1. The influence of the four point mutants on HeLa cell mechanics was investigated in comparison to a negative control transfection, where only an empty backbone vector was added, and to wildtype GBP1 overexpressing cells. Moreover, the mechanical influence of the activation of wildtype GBP-1 by IFN-γ was checked with HeLa cells. This study was a collaboration with the Division of Molecular and Experimental Surgery, Department of Surgery (Prof. Michael St¨ urzl), University Clinics of Erlangen. All transfections and biochemical investigations were conducted by Isabella Schöpe. Backbone vector F-pMCV 1.4 (-) F-pMCV 1.4 (-) F-pMCV 1.4 (-) F-pMCV 1.4 (-) F-pMCV 1.4 (-) F-pMCV 1.4 (-)

Point mutations empty empty K51A R227E/K228E L550A/L554A/L561A L550X

Properties control wildtype GBP-1 deactivated GTPase const. activated GTPase little actin binding no actin binding

Abbreviation control GBP OE K51A R227E L550A L550X

Table 4.1: Genetic modifications of GBP-1 GTPase: utilized backbone vector, induced point mutations, assumed influence on GBP-1 function, and used abbreviations.

110


Results Wildtype GBP-1 overexpression in DLD-1 cells

a

Entry time [s]

101

control

GBP OE

100

10-1

10-2 1

c

Stiffness [Pa]

600

*

400

200

0

4 1 εmax/∆p [x10-3 1/Pa]

control

GBP OE


b

2

2

4

0.3

* 0.2

0.1

0

control

GBP OE

Figure 4.11: Influence of GBP-1 overexpression on mechanical properties of DLD-1 colon carcinoma cells. a) Scatter plots of tentry vs. ratio of ǫmax /∆p for DLD-1 pMCV cells (control) and DLD-1 GBP-1 overexpressing (GBP OE) cells. Data are histogram matched for stress and strain. Black lines show power-law fit to the data. b) Stiffness of pMCV cells compared to GBP-1 overexpressing cells. c) Power-law exponent of pMCV cells compared to GBP1 overexpressing cells. n = 3689 cells per condition. Significant differences are indicated by asterisks (p < 0.05).

First, stably transfected DLD-1 colon carcinoma cells overexpressing GBP-1 (GBP OE) were measured and compared to a control group, which were transfected with the empty backbone vector only (F-pMCV 1.4 (-)). Details on the transfection procedure can be found in [177]. The expression of GBP-1 was checked through Western blotting, giving almost zero GBP-1 for the control cells and a pronounced overexpression of GBP-1 in the GBP-1 overexpressing population. For the microconstriction measurements, cells were cultured according to App. 6.3 to a harvesting density of approx. 80 %. During measurements, constrictions with a width of 5.1 µm and a device height of 16.6 µm were employed (device type S7, comp. to Sec. 2.1.3). Constrictions of these dimensions principally probe both the mechanical properties of the cell cytoskeleton and the cell nucleus (comp. to Sec. 3.6). Cell and device preparation before measurements was conducted according to Tab. 3.2. Three independent measurements were performed for each condition with identically harvested cells and the results were pooled per condition after the evaluation. A power-law 111


was fitted to the scatter plots of tentry vs. ǫmax /∆p to extract the quantitative mechanical properties stiffness and fluidity (power-law exponent)(Fig. 4.11 a). A distinct reduction in stiffness and an increase in fluidity were measured (Fig. 4.11 b+c) for GBP-1 overexpressing cells. Both changes were highly significant, which was shown through bootstrapping. Influence of GBP-1 GTPase activation and actin binding on HeLa cells Next, a transient expression of GBP-1 mutants was introduced into HeLa cervix carcinoma cells. Details on the transfection procedure can be found in [178]. Next to the normally functioning GBP-1 protein (termed GBP OE, Tab. 4.1), two point mutations were introduced into GBP-1, leading to a supposedly deactivated GTPase function and a constitutively activated GTPase function, respectively (K51A and R227E). Moreover, two point mutations in the actin binding site of GBP-1 (L550A and L550X) were transfected into HeLa cells to supposedly change the actin binding capability at the actin binding site of GBP-1. RIPA lysates (Radio-ImmunoPrecipitation Assay) of HeLa cells could demonstrate that for K51A transfected cells, the amount of expressed GBP-1 protein was increased by at least two fold. R227E point mutated cells, however, showed a decrease in overall GBP1 expression. L550X point mutated cells also showed a decreased GBP-1 expression of the truncated GBP-1 protein. Co-immuno-precipitation assays with actin suggested that the actin binding capacity of GBP-1 at the actin binding site was decreased dramatically for L550A and L550X point mutants. Wildtype GBP-1, instead, showed the same actin binding as the mutants R227E and K51A (data not shown).

0

L550X

L550A

L550X

L550A

0.1

R227E

0.2

K51A

0.3 GBP OE

R227E

K51A

400

GBP OE

800

0.4

control

1200


b

1600

control

Stiffness [Pa]

a

0

Figure 4.12: Influence of GBP-1 point mutations on mechanical properties of transiently transfected HeLa cervix carcinoma cells. a) Stiffness of four point mutations in the GBP-1 protein compared to negative control (control) and positive control (GBP OE) cells, calculated from power-law fitting to the scatter plots of tentry vs. ǫmax /∆p. b) Power-law exponents corresponding to a). Scatter plots were histogram matched for stress and strain before fitting. n = 918 cells per condition. Differences are not significant.

For the measurements of cell mechanics, HeLa cells were investigated with constrictions of width w = 6.1 µm and a device height h = 19.9 µm (device type U1, comp. to Sec. 2.1.3). These medium-sized constrictions measure a bulk cell stiffness and fluidity determined by

112


both the cell cytoskeleton and the cell nucleus (comp. to Sec. 3.6). Measurements were conducted over a time span of three weeks, leading to 25 independent measurements. On each measurement day, all six cell conditions were measured, to create unbiased measurement results. Cells were cultured in DMEM (#11995065, gibco), including 10 % FCS (#16000036, gibco), 1 % PSG (#10378016, gibco) and were harvested at a culture density of only 60 % to decrease cell-cell-cohesion during experiments. All remaining cell and device preparation steps before measurements were conducted according to Tab. 3.2. Unfortunately, despite all effort, the throughput in each measurement was low. HeLa cells, especially after transfection, exhibited a high overall cell stiffness, which led to long transit times through the microconstrictions. Due to limitations through cell size, a device containing wider constrictions or a higher overall height could not be used. Moreover, HeLa cells showed a high cell-cell-cohesion and often agglomerated, which clogged the whole device after a short measurement time. Cell measurements were pooled for each condition after evaluation and the quantitative mechanical properties were evaluated through power-law fitting. Histogram-matching was simultaneously conducted for all six sets of measurement, which led to an even further reduction of cell counts per condition. Thereby, however, all stiffness and power-law values can be compared to each other in a quantitative way. The fit parameters stiffness and power-law exponent are summarized in Fig. 4.12. Two principal groups of mechanical properties were found: One stiffer group comprised by negative control cells, R227E cells and L550X-expressing cells, and a second, softer group built by wildtype GBP-1 overexpressing cells, K51A and L550A-expressing cells (Fig. 4.12 a). The power-law exponents behaved perfectly inversely correlated to the stiffness results (Fig. 4.12 b). As the histogram matching process contained six cell populations, no significant differences in stiffness or power-law exponent could be found, as the overlap between stress and strain ranges was too small. Stimulation of endogenous GBP-1 expression in HeLa cells through IFN-γ Moreover, wildtype HeLa cells were stimulated by IFN-γ at a concentration of 100 U/ml for 24 h before the measurement. This procedure supposedly activates endogenous GBP-1 expression in the cells. HeLa cells were again investigated with constrictions of width w = 6.1 µm and a device height of 19.9 µm (device type U1, comp. to Sec. 2.1.3). Cell and device preparation before measurements was once more conducted according to Tab. 3.2. However, cells were harvested again at a cell culture density of only 60 % to decrease cell-cell-cohesion during experiments. Three independent measurements were conducted per condition and pooled after evaluation. Again, histogram matching was performed and power-law fitting was conducted to the scatter of tentry vs. ǫmax /∆p (Fig. 4.13 a). HeLa IFN-γ-stimulated cells showed a significant decrease in cell stiffness compared to the un-

113


a untreated

+ IFNγ

Entry time [s]

101 100 10-1 10-2 0.4

0.7

1600 Stiffness [Pa]

0.7

1

c *

1200 800 400 0


b

0.4 1 εmax/∆p [x10−3 1/Pa]

untreated + IFNγ

0.2

0.1

0

untreated + IFNγ

Figure 4.13: Influence of GBP-1 activation through IFN-γ (100 U/ml for 24 h) on mechanical properties of HeLa cervix carcinoma cells. a) Histogram matched scatter plots of tentry vs. ǫmax /∆p for activated HeLa (+IFN-γ) cells compared to control population (untreated). Black lines show power-law fit to the data. b) Stiffness of activated HeLa cells compared to control cells. c) Power-law exponent of activated HeLa cells compared to control cells. n = 479 cells per condition. Significant differences are indicated by asterisks (p < 0.05).

stimulated control group (Fig. 4.13 b). Power-law exponents, in turn, were unsignificantly increased after IFN-γ stimulation (Fig. 4.13 c).

Conclusion As shown in many independent studies, a decrease or loss of the actin cytoskeleton is widely correlated with a decrease in bulk cell stiffness and an increase in cell fluidity [10, 13, 14, 20, 111]. For the case of actin remodeling through GBP-1, an impact on cell stiffness was expected, and this hypothesis was tested with the microconstriction setup. With DLD-1 colon carcinoma cells stably overexpressing wildtype GBP-1, a pronounced decrease in cell stiffness and an increase in the power-law exponent was found compared to control cells (Fig. 4.11). The measurements could thereby confirm the influence of GBP-1 on whole cell deformability. In the case of HeLa cells transiently transfected with four point mutations of GBP-1, no significant differences in stiffness or power-law exponent were found between negative control cells, wildtype GPB-1 expressing cells, or one of the four cell populations expressing GBP-1 mutants (Fig. 4.12). This is possibly due to the difficulties during measurements mentioned above which did not allow to evaluate the

114


mechanics of a sufficient number of cells per condition. The number of cells per condition was even more reduced through histogram matching between the six conditions. The fitting of these small cell numbers finally led to high errors of the fit parameters stiffness and power-law exponent. In the case of histogram matching with groups of only two or three conditions, significant differences could be seen between the two stiffness and powerlaw groups mentioned above (control cells, R227E and L550X vs. GBP-1 OE, K51A and L550A cells, data not shown). A decreased stiffness of GBP-1 OE cells compared to the control population is in accordance with the previous measurements on DLD-1 GBP OE cells. A simultaneous decrease in cell stiffness in K51A point mutated cells can not be explained by biochemical expectations on protein functioning, as K51A is a GBP-1 variant without GTPase activity. Decrease in GTPase activity was supposed to be correlated with a decrease in actin remodeling capability of GBP-1 in HeLa cells, which would therefore not lead to a decrease in cell stiffness. Simultaneously, R227E cells should supposedly show an even more decreased cell stiffness than wildtype GBP-1 OE cells, because the constitutively active GBP-1 variant should participate even more in actin remodeling. Interestingly, the resulting stiffnesses of these two populations are directly correlated with the amount of expressed GBP-1 in the cells detected by RIPA lysates. The transfections did not only lead to the expected change in GBP-1 functioning, but also to a changed overall GBP-1 expression in the cells. A highly overexpressed K51A point mutated GBP1 protein could thereby decrease cell stiffness in spite of its malfunctioning, and vice versa. L550X point mutated cells showed a slight increase in cell stiffness. This is in accordance with chemical interpretations of GBP-1 functioning, since L550X mutants lack the binding capability for actin. L550A mutated cells also have a supposedly decreased capability of actin binding. The measurement data are in accordance with this expectation, as they only show a very slight decrease in stiffness compared to the negative control (control), and a higher stiffness compared to the positive control data (GBP OE). The measurements on IFN-γ activated wildtype HeLa cells showed a significant decrease in cell stiffness and an increase of the power-law exponent after activation (Fig. 4.13). This is in accordance with biochemical expectations on IFN-γ-GBP-1 downstream signaling, resulting in a decrease in cell stiffness through GBP-1 expression. For HeLa cells, the impact of GBP-1 on the cell cytoskeleton was also shown through immunofluorescence images. Thereby, GBP-1 overexpression led to a decrease or even complete destruction of actin stress fibers ([176] and data by Isabella Sch¨ ope). All in all, the measurements of point mutants of GBP-1 transiently transfected into HeLa cells provided mixed results, which leave space for interpretation. Still, they should be seen as guiding the way to future, more detailed evaluations of cell stiffness and viscosity under wildtype GBP-1 and point mutants overexpression. Should the results on K51A and R227E cells be reproduced significantly in further measurements, the theory correlating GTPase activation and GBP-1 actin remodeling ability might have to be revised.

115


4.7

Influence of particulate matter on cell mechanical properties

Biological background During the past 50 years, dangerous health effects of particulate matter on the respiratory system have become more and more evident. It is now clear that the exposure to particulate matter, which is produced by smoking cigarettes, vehicle fumes and industrial emissions, is correlated with an increased risk for lung cancer [179] and cardiovascular diseases [180, 181]. Particulate matter enters the body through the respiratory system. Moreover, some sorts of particulate matter are able to enter the lymph system and all secondary body organs due to their size distribution on the nanometer scale. In previous studies, particulate matter was shown to accumulate in rats and humans over a long period of time (up to 700 days) [182]. On a single cell basis, it was found to increase cell proliferation, change the transcription pattern of various genes, and finally induce inflammation after long-term exposure [183]. In many studies, carbon black particles (CB) function as a model system for one of the most relevant kinds of particulate matter, which is diesel exhaust. For example, Pink et al. showed that the long-term exposure to CB over 14 days disturbed the organization of the cell cytoskeleton of eA.hy926 endothelial cells cultured in-vitro [184]. The protein expression of a high number of proteins linked to the cytoskeletal structure and especially of proteins binding to actin was reported to be changed dramatically. Moreover, the amount of actin and vimentin was shown to be significantly increased by 13 % and 25 % after 14 days of CB exposure. Furthermore, an increase in cell motility by 35 % and invasiveness by 90 % was measured. In contrast to most older studies, which used CB doses of up to 50 µg/ml [185], the study of Pink et al. used low dose CB concentrations (approx. 1 - 1,000 ng/ml) over a longer period of time (between 1-14 days), to better mimic the dose and accumulation of CB found in the human body [184]. In following studies, the influence of short-term and low dose CB exposure was investigated. Therefore, cells were exposed to 1 - 1,000 ng/ml CB for only 24 h. First results indicate that already after 24 h, structural cytoskeletal changes in actin and vimentin took place. Phalloidin-staining of actin fibers revealed, for example, that the actin concentration in treated cells was increased compared to control cells (private communication with Dr. Pink). It was therefore of great interest if these structural changes had already an impact on cell mechanics. In this study, the influence of CB particles on the cell mechanics of the epithelial lungbronchus cell line BEAS-2b (#CRL-9609, ATCC) was investigated. Bronchial lung cells are usually subject to high deformations during the breathing cycle, and their performance is not dominated by cell migration or invasiveness. Cell mechanics were therefore not only investigated by a microconstriction assay, which tests cell stiffness and fluidity, but also

116

4.7 Influence of particulate matter on cell mechanical properties

Figure 4.14: Influence of carbon black exposure on cell vulnerability of BEAS-2b cells. Fraction of attached and living cells after 30 % cyclic stretch with 20 % prestretch at f = 0.17 Hz for 1 h. Before stretching, cells were incubated with no CB (control) and CB-concentrations of 0.5 µg/ml and 2 µg/ml for 24 h. n > 230 cells per condition, pooled from 4-5 experiments. Differences are not significant. Figure adapted from [186].

Fraction of surviving cells

1 0.8 0.6 0.4 0.2 0

n=5 Control

n=4 0.5 µg/ml

n=5 100 µg/ml

by stretcher measurements, which specifically test cell vulnerability against cyclic stresses and strains. With both measurement methods, the influence on cell mechanics of a shortterm (24 h) and low dose (500 ng/ml) CB exposure was compared to the influence of a short-term and high dose (2 µg/ml) CB exposure. Therefore, CB particles were prepared at concentrations of 500 ng/ml and 2 µg/ml by vigorous ultra-sonification and suspension in cell medium, as shown in [184]. Dry CB particles were kindly provided by our collaborator Dr. Mario Pink from the Institut der Arbeitsmedizin (Prof. Simone Schmitz-Spanke), Universität Erlangen-N¨ urnberg. The particle size distribution of the resulting CB suspension was characterized by static light scattering. Both particle distributions in the nano- and micron-range were found in the CB suspension, centered around 100 nm and 1-10µm. Possible changes in cell mechanics presented here were therefore caused by a CB stimulation by both nano- and micron-scaled CB particles, which were taken up by the cells during the 24 h-incubation time before measurements. The high CB dose led to a visible accumulation of CB particles in the cells, which visibly stained them black [186].

Results Stretcher measurements BEAS-2b cells were cultured in DMEM medium (#11885084, gibco), containing 10 % FCS (#16000036, gibco) and 1 % PSG (#10378016, gibco). For stretcher measurements, cells were seeded onto flexible PDMS-membranes 48 h prior to measurements (Sylgard 184, Dow Corning). The membranes were produced with a base to crosslinker ratio of 33:1, which yields a Young's modulus of approx. 500 kPa [187]. 24 h before measurements, the cells were treated with the two CB concentrations. Before measurements, cells were washed 5 times to reduce free CB in the cell medium. For a duration of 1 h, the adherent cells were then sinusoidally stretched by 30 % at a frequency of 0.17 Hz (speed = 3.0 mm/s), pertaining a pre-stretch of 20 % the whole time. After stretching, the amount of detached or dead cells were counted and taken as a measure for cell vulnerability. Dead cells were detected through propidium iodide staining (100 µg/ml, #P4864, Sigma-Aldrich).

117


All stretcher measurements were performed by Beate Hartmannsberger. Details of the measurement preparation and procedure can be found in [186]. After stretching, there was no significant difference in viability between the control cell group (no CB exposure) and the cells exposed to low dose CB (0.5 µg) (Fig. 4.14). Moreover, the viability of the cells exposed to high dose CB (2 µg) was not decreased either. All viabilities ranged between 95-100 %, which means that the cells were not fatally damaged by the high stress and strain of the cyclic stretching and did not go into apoptosis. This indicates that the changes in the cell cytoskeleton induced by exposure to low and high CB concentrations for only 24 h did not make the cells vulnerable to 50 % cyclic stress. Microconstriction measurements

Entry time [s]

a 101

0.5 µg/ml

control

100 µg/ml

100 10-1 10-2 1

2

1 2 4 εmax/∆p [x10-3 1/Pa]

4

2

4

*

*

c

200

*

*

100

0

control 0.5 100 µg/ml µg/ml


Stiffness [Pa]

b

1

0.3 0.2 0.1 0

control 0.5 100 µg/ml µg/ml

Figure 4.15: Influence of CB treatment for 24 h on cell mechanical properties of BEAS-2b cells. a) Histogram matched scatter plots of tentry vs. ratio of ǫmax /∆p for control cells, low dose CB-treated cells (0.5 µg/ml) and high dose CB-treated cells (2 µg/ml) with power-law fits (black lines). b) Stiffness for control cells, low dose CB-treated cells and high dose CB-treated cells. c) Power-law exponents corresponding to a+b). n = 5844 cells per condition. Significant differences (p < 0.05) are indicated by asterisks. Figure adapted from [186].

After 24 h incubation with CB particles, BEAS-2b cells were washed 5 times to decrease the amount of free CB in the cell suspension, which would lead to an enhanced permanent clogging of the constrictions during measurements. Cells were then harvested at a culture density of 80 % and measured with the microconstriction method with devices containing constrictions of width w = 7.7 µm and a device height h = 18.9 µm (type X4W5scaled, comp. to Sec. 2.1.3). These medium-sized constrictions measure a bulk cell stiffness and fluidity determined by both the cell cytoskeleton and the cell nucleus (comp. to Sec. 3.6). Cell and device preparation before measurements were conducted according to Tab. 3.2. 118

4.8 Influence of histone 2B on cell mechanical properties

Nine individual measurements in total were performed for control cells (3x), which had just experienced an exchange of medium 24 h before measurements, cells incubated with 500 ng/ml CB (3x) and cells incubated with 100 µg/ml (3x). Against initial expectations, high dose treatment did not result in cell clumping or device clogging during measurements. The three conditions were histogram matched and power-law fitting was conducted to extract quantitative cell mechanical properties from the scatters of tentry vs. ǫmax /∆p (Fig. 4.15 a). CB-treatment resulted in a significant increase in cell stiffness for low dose and in a further increase for high dose exposed cells (Fig. 4.15 b). The power-law exponent also decreased significantly in a dose-dependent manner after low dose and after high dose CB-treatment (Fig. 4.15 b). Principally, changes induced through high dose incubation could be a combination of cytoskeletal rearrangements and the bulk mass accumulation of macroscopic CB particles (∼ 10 µm) in the cells.

Conclusion In this study, the change in cell mechanics after short-time exposure to low dose (nanogram range) carbon black particles was studied. After treatment with a low and even a high CB dose, cell vulnerability towards cyclic stretching remained unchanged. However, a dose-dependent increase in cell stiffness and decrease of the power-law exopnent could be measured with microconstrictions. This leads to the conclusion that after a low dose incubation with CB over 24 h, despite initial changes in cytoskeletal arrangement of actin and vimentin and an enhancement of cell stiffness and decrease of fluidity, cell vulnerability is not altered to a measurable extent.

4.8

Influence of histone 2B on cell mechanical properties

Biological background Histone 2B belongs to the histone proteins, which also include histone 1, histone 2A, histone 3 and histone 4. It is located in the cell nucleus and mainly responsible for chromatin organization through the formation of the nucleosome (comp. to to Fig. 4.17). In recent years, histone 2B expression levels were found to be closely correlated with the degree of chromatin packing via histone-histone and histone-DNA interaction. This is possible because histones are positively charged, in contrast to the highly negatively charged DNA [188]. Histone 2B consists of 126 amino acids and forms two extended histone tails which point outwards [189]. It was found to have 16 isoforms, which all interact with different positions of the genome at different times during the cell cycle [190]. A histone 2B-GFP overexpressing cell line was produced by transfection of HT1080 fibrosarcoma cells (comp. to Sec. 4.1) by our collaborator Katharina Wolf at Nijmegen

119


University. With these cells, collective cell migration through an artificial ECM (collagen gel) could be performed without the addition of further cell dyes. This study was conducted to check if the overexpression of histone 2B in the nuclei of HT1080 cells influences their bulk cell mechanical properties. After a transfection, the protein expression typically varies widely in the resulting heterogeneous cell population. Therefore, the fluorescence extension of the microconstriction setup was employed to allow for a correlation of protein expression levels and cell mechanics.

Results c

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Figure 4.16: Influence of histone 2B overexpression on cell mechanical properties. Measurement of histone 2B-GFP transfected HT1080 fibrosarcoma cells. a) Average fluorescence intensities per cell pixel. Dashed green lines represent the fluorescence threshold for separating cells into a low, medium, and high fluorescence intensity group at 6.2 and 17.3 counts/cell pixel. b) Exemplary histogram matched scatter plots of for cells with low, medium, and high expression levels of histone 2B-GFP. Black lines indicate the power-law fit to the data. c) Cell elastic modulus and d) cell fluidity for the three groups. n = 3107 cells per condition. Significant (p < 0.05) differences compared to the cell group with low fluorescence intensity are indicated by asterisks.

HT1080 histone 2B-overexpressing cells were cultured in DMEM-F12 advanced medium (#11330032, gibco), with 10 % FCS (#16000036, gibco) and 1 % PSG (#10378016, gibco). They were harvested at a cell culture density of 80 %. Measurements were performed with constrictions of width w = 7.7 µm and a device height of 18.9 µm (device type X4W5scaled, comp. to Sec. 2.1.3). These medium-sized constrictions measure a bulk cell stiffness and fluidity determined by both the cell cytoskeleton and the cell nucleus (comp. to Sec. 3.6). Cell and device preparation before measurements was conducted according to Tab. 3.2. For the evaluation of cell mechanics, data from three individual measurements were pooled. Afterwards, cell fluorescence intensity was analyzed as described in Sec. 2.4.3 and cells were 120

4.9 Influence of lamin A on cell mechanical properties

accordingly grouped into three bins of equal cell number, creating median fluorescent intensities of 2.6, 10.1 and 32.5 counts/cell pixel (Fig. 4.16 a). For each group, combined histogram matching and power-law fitting was performed, balancing possible size and pressure differences in the three groups (Fig. 4.16 b). Fitting resulted in a dose-reponse increase in cell stiffness with increasing fluorescence, meaning increasing histone 2B expression (Fig. 4.16 c). At the same time, the power-law exponent decreased monotoneously (Fig. 4.16 d).

Conclusion To sum up, histone 2B overexpression could be shown to increase cell stiffness and decrease cell fluidity in a dose-dependent manner. These results are in accordance with the hypothesis that histone 2B expression influences chromatin condensation. An increase of histone 2B expression might thus condense the chromatin and thereby stiffen the cell nucleus. Previous studies already showed that a condensed chromatin is linked to decreased cell compliance [12, 20, 110]. Moreover, in the metaphase of cell division, cells have been shown to exhibit an increased stiffness, firstly induced by condensed and doubled chromatin, and possibly also induced by cytoskeletal changes or increased actin-myosin contractility [13, 191].

4.9

Influence of lamin A on cell mechanical properties

Biological background Nuclear lamins are cytoskeletal proteins, belonging to the family of intermediate filaments (comp. to Sec. 3.6), which are located at the inner nuclear membrane (comp. to Fig. 4.17). There exist two main classes of lamin proteins, termed A- and B-type. B-type lamins are further classified into B1-lamins and B2-lamins, encoded through the genes LMNB1 and LMNB2, respectively [192]. Since many mutations and especially the lack of B-type lamins were found to have a lethal impact on cells, no genetically heritable diseases are connected with mutations in the LMNB genes [193]. Contrastingly, LMNA, the gene encoding the A-type lamins A, AD10, C and C2, is one of the most mutated genes in humans. The loss of A-type lamin function, however, can still lead to serious diseases, called laminopathies. Some of the most prominent are Emery-Dreifuss muscular dystrophy [194], cardiomyopathies [195], and premature ageing syndroms like Hutchinson-Gilford progeria syndrom [195]. Many laminopathies could be correlated to point-mutations on the LMNA gene. Still, it is largely unclear how these nano-scale punctual mutations change the functioning of the lamin A protein and finally result in a muscular dystrophy, for example. It has been suggested repeatedly that laminopathies stem from a disturbance of the gene-regulating function of the LMNA gene [196]. Moreover, a decrease in cell

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Euchromatin Nucleolus Heterochromatin

Lamin A/C

Lamin B

SUN1/2 Nuclear Pore Complex

Nesprin

Plectin

Dynein

Microtubule

Perinuclear space

Intermediate filament

Actin

Figure 4.17: Nucleus and nuclear lamina. The cell nucleus containing the cell chromatin is surrounded by a nuclear lamina. Lamins A/C and B are located close to the nuclear membrane. In the cytoplasm, the nuclear lamina is connected to actin, microtubuli, and intermediate filaments through LINC-complexes (Linker of Nucleoskeleton and Cytoskeleton), containing SUN and nesprin proteins. Figure adapted from [79, 109, 136].

stiffness, probably caused by a defective nucleo-cytoskeletal integrity after lamin A-loss, was suggested to cause laminopathies [192]. This is why many studies on cell mechanics of lamina A-mutated in-vitro cell populations were conducted during the last years. First results showed that lamin A expression, in contrast to B-type lamin expression, is correlated to cell mechanosensing. This means that lamin A is upregulated when cells are cultured on a stiffer compared to a softer substrate [124]. Moreover, lamin A was found to hinder cells from migrating into narrow constrictions, but at the same time to protect the cells against stresses during this compression. Thereby, the nuclear lamina was assumed to function as a protection against DNA compression and shear [100, 107, 108]. Still, several questions remain unclear, for example if there is a dose-response of cell mechanical stiffness and fluidity on lamin A expression levels. This is why, in this study, the mechanical properties of K562 leukemia cells overexpressing lamin A were investigated with the microconstriction assay and its fluorescence extension. Averaging the mechanical properties over the whole population would lead to biased results, because they would strongly depend on the transfection efficiency of the LMNA-GFP vector. Therefore, cells were sorted according to their fluorescence and thereby their lamin A expression levels after the measurements.

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4.9 Influence of lamin A on cell mechanical properties

a

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Figure 4.18: Influence of lamin A overexpression on cell mechanics. Measurement of lamin A-GFP transfected K562 leukemia cells. a) Histogram of average fluorescence intensities per cell pixel. Dashed green lines indicate the fluorescence threshold for separating cells into a low, medium, and high fluorescence intensity group. b) Exemplary histogram matched scatter plots of for cells with low, medium, and high expression levels of lamin A-GFP. Black lines indicate the power-law fit to the data. c) Cell elastic modulus and d) cell fluidity for the three groups. n = 1107 cells per condition. Significant (p < 0.05) differences compared to the cell group with low fluorescence intensity are indicated by asterisks. Figure adapted from [22].

Results K562 leukemia cells had been transfected by Dr. Thorsten Kolb to overexpress lamin AGFP as described in detail in [20]. The transfection resulted in a highly heterogeneous cell population, comprised of cells not expressing lamin A to a detectable extent, weakly expressing cells (termed medium expression) and highly expressing cells (termed high expression). The cells were cultured like wildtype K562 cells, shown in App. 6.3. Cells were measured with constrictions of width w = 7.7 µm and a device height of 18.9 µm (device type X4W5scaled, comp. to Sec. 2.1.3), which investigate the mechanical properties of both the cell nucleus and the cell cytoskeleton (comp. to Sec. 3.6). Cell and device preparation before measurements was conducted according to Tab. 3.2. After the measurements, the results from three experiments were pooled. Then, three groups of cells were formed, which were either not expressing lamin A-GFP (mean fluorescent intensity = 1.2 counts/cell pixel), moderately expressing lamin A-GFP (mean fluorescent intensity = 11.2 counts/cell pixel) or highly expressing lamin A-GFP (25.5 counts/cell pixel) (Fig. 4.18 a). After 2-dimensional histogram matching, cell mechanical properties were evaluated for the three groups through power-law fitting (Fig. 4.18 b). Thereby, cell elastic modulus and the power-law exponent were extracted. Cell mechanical stiffness rose in a dose-dependent manner with increasing fluorescence intensity, which means

123


with increasing expression of GFP-tagged lamin A (Fig. 4.18 c). The power-law exponent dropped accordingly (Fig. 4.18 d) [21].

Conclusion Cell mechanical measurements with the microconstriction setup showed that cell stiffness increased significantly in a dose-response manner with lamin A overexpression level. At the same time, cell fluidity decreased significantly. These results support the hypothesis that lamin A mechanically supports the integrity of the nuclear lamina. The nuclear lamina, in turn, is connected to all other cell cytoskeletal components and might therefore also increase the stability of the actin cytoskeleton of the whole cell [79, 135, 136]. The presented results are in accordance with previous measurements on lamin A overexpressing adherent cells and nuclei [21, 124].

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5

Summary and outlook Summary In this work, a microfluidic microconstriction setup for high-throughput quantitative measurements of passive cell mechanical properties was developed, calibrated, and applied in medical and biological studies. With a microconstriction setup, the deformation process of suspended cells, which are pumped through micron-scaled constrictions, is recorded and analyzed (comp. to Sec. 2.1.1). The microconstriction devices of this study were produced through soft lithography. First, a photoresist master was developed, which contained feeding channels and constrictions with a width and height adapted to the currently investigated cell population. Identical measurement devices were subsequently molded from this master with the silicone PDMS. The devices typically had eight parallel constrictions with a width smaller than the cell diameter (2-8 µm), so that many cells could be measured in parallel. The dimensions of the microfluidic channels were characterized with confocal microscopy (comp. to Sec. 2.1.2). In each measurement, the deformations of several thousand cells per population were recorded with a high-speed camera (750 fps) for further image analysis (comp. to Sec. 2.2.2). Cell transits through a microconstriction were quantified by measuring cell entry times into a constriction, cell sizes, and the speed of cells approaching a constriction (comp. to Sec. 2.3.2). Cell entry times was defined through investigating the brightness standard deviation of ROIs placed in front of the constrictions. From cell size, the maximum cell strain ǫmax was calculated as 1-dimensional compression of the cell diameter to the width of the constriction. Cell stress ∆p, which is the current pressure drop over the constriction during cell transit, was calculated for each cell from the fluid flow speed through Hagen-Poiseuille’s law (comp. to Sec. 2.3.3.1). Power-law rheology was found to describe both single cell deformation into a microconstriction, as well as the dependence of the scatters of entry time tentry on ǫmax /∆p of cell populations. Through power-law rheology, population averages of the visco-elastic material properties cell stiffness E (elastic modulus) and cell fluidity β (power-law exponent) could be calculated to quantify cell mechanical properties (comp. to Sec. 3.2).

125

5. SUMMARY AND OUTLOOK

With this theoretical framework, cells were confirmed to exhibit non-linear material properties. This means that cell stiffness increases with increasing amounts of stress and strain, for example, which is called stress and strain stiffening (comp. to Sec. 3.3). An extension of the power-law theory through stress and strain stiffening, however, was not possible due to the intrinsic correlation of the fit parameters. In order to ensure an unbiased comparison of cell mechanical properties from different measurements, 2-dimensional histogram matching was developed. This technique chooses cell populations from two measurements for comparison, which were subjected to the same pressure and the same deformation. The cell mechanical properties resulting from histogram matching are therefore only valid for the distribution of stress and strain that the cells experienced during the investigated measurement (comp. to Sec. 3.3.2). The mechanics of suspended cells was found to behave according to soft glassy rheology. Soft glassy rheology theory states that the two material properties elastic stiffness E and power-law exponent β do not change independently from each other, but are inversely correlated. Through this phenomenon, the material properties of single K562 leukemia cells could be investigated. Therefore, the dependence of E on β was determined, so that power-law fitting was reduced to only one free fit parameter. A normal distribution of the resulting single cell power-law exponents was found, which is in accordance with previous studies on adherent cells (comp. to Sec. 3.7). Furthermore, the sensitivity of the measurement technique to changes of the cell cytoskeleton and the cell nucleus in response to drug treatments was analyzed. Microconstriction measurements with medium-sized constrictions (width = 6 µm) were found to be sensitive to changes of both the cell cytoskeleton (actin, microtubules) and the cell nucleus (comp. to Sec. 3.6). Next, the impact of cell culture and measurement parameters on the resulting cell mechanical properties was studied. Slight, but significant and systematic changes of the resulting cell mechanical parameters of DLD-1 colon carcinoma cells were found for changes of the cell culture density, the detachment time of normally adherent cells before the measurements, the measurement medium, and the device coating with the surfactant pluronic. This study highlights the necessity to control all measurement and cell culture parameters tightly, and keep them constant between different measurements (comp. to Sec. 3.8). Finally, the microconstriction setup was applied in biological and medical studies. The investigation of four cancer cell lines revealed, for example, that cell stiffness is inversely and cell fluidity positively correlated with cell invasion into 3-dimensional channel structures and collagen gels. However, other cell characteristics, like cell adhesion to the substrate and cell nuclear volume, determine cell invasiveness to the same or an even higher extent. Passive cell material properties were thus found to be one, but not the only determining factor governing cell invasiveness (comp. to Sec. 4.1). Moreover, the influence of the integrins αvβ3, α5β1 and αIIbβ3 on cell mechanics was investigated. Integrins are transmembrane proteins with which a cell adheres to the extra126

cellular matrix. The expression of αvβ3 in suspended K562 leukemia cells and adherent M21 melanoma cells led to an increase in cell stiffness and a decrease in cell fluidity. As a possible origin of this correlation, a close coupling between integrins and the actin cytoskeleton, which possibly also influences cell nuclear mechanics, was suggested (comp. to Sec. 4.4). In another study, the overexpression of the cell cycle controller p21 could be correlated with cell stiffness and power-law exponent. The knockout of p21 was thereby found to result in an increase in stiffness and a decrease in fluidity of HCT116 colon carcinoma cells. This stiffening might be induced by an increased actin and vimentin cytoskeleton and changes in chromatin condensation (comp. to Sec. 4.5). Moreover, the GTPase enzyme GBP1 was investigated. Its overexpression was detected to soften DLD-1 colon carcinoma cells and HeLa breast cancer cells and make them more fluid-like, probably through a newly found actin-depolymerizing activity of GBP1 (comp. to Sec. 4.6). Furthermore, myosin-II inhibition was linked to a very small increase in the stiffness of suspended K562 leukemia cells, and to a dramatic decrease of their fluidity. This result is in accordance with recent studies on suspended cells, but stands in contrast to earlier studies on adherent cells, which found that actin-myosin contraction increases cell prestress. The new results therefore strengthen the hypothesis of a second, poorly understood functioning of myosin-II in suspended cells (comp. to Sec. 4.3). Additionally, cell mechanical properties were shown to be altered after exposure to carbon black particles, which mimick diesel exhaust. A dose-dependent increase in the stiffness of bronchial BEAS-2b cells could be measured for increasing concentrations of carbon black, which is in accordance with the increase of cytoskeletal components, like actin and vimentin, measured through mass spectrometry (comp. to Sec. 4.7). Finally, the expression of fluorescently labeled proteins was correlated with cell mechanics through a fluorescence extension of the microconstriction setup. For fluorescence detection, a high-power laser was coupled into the microscope and the emission signal of GFP-tagged proteins was recorded with a second, synchronized camera in parallel to mechanical measurements (comp. to Sec. 2.4). A positive correlation between cell stiffness and a negative correlation with cell fluidity were found for both the overexpression of histone 2B, and the nuclear lamina protein lamin A. In the first case, the increase in stiffness of HT1080 fibrosarcoma cells might be caused by the implication of histone 2B in chromatin condensation during cell division (comp. to Sec. 4.8). For the case of lamin A induced stiffening of K562 leukemia cells, the current findings confirm earlier results, where lamin A overexpression was found to stabilized the nuclear lamina and thereby the whole cytoskeleton [124, 136] (comp. to Sec. 4.9). As a conclusion, this thesis built the foundations for a wide application and a quantitative use of microconstriction setups for measurements of cell mechanics in biophysics and medicine. It will provide an alternative and complementary measurement setup to 127


established techniques, like atomic force microscopy. Thereby, it provides a platform to deepen our understanding of fundamental cell mechanics. Outlook For the future, many more applications and improvements of the microconstriction setup are planned. Predominantly, further biological studies correlating cell mechanics with protein expression will be performed. A first important study will focus on the correlation between lamin B overexpression and cell mechanics. A clear mechanical picture of lamin A has emerged during the last years, showing that lamin A stabilizes the cell nucleus against compression and shear and thus protects the DNA. It is much less understood, however, how its close relative lamin B influences cell mechanics. Initial investigations suggest that lamin B only impacts cell viscosity, and to a much smaller degree cell elasticity [124]. Moreover, the microconstriction devices are planned to be used for measurements on blood cells, for example leukocytes and erythrocytes. The activation of immune cells, for example through fMLP, has previously been shown to impact cell deformability and could thus be easily detected with a microconstriction assay [62]. Therefore, the channel dimensions must be adapted to the size of blood cells, which are usually distinctly smaller than adherent cells, such as mesenchymal or epithelial cells (approx. 5-10 µm instead of 13-20 µm in diameter). A decrease in channel width and height automatically implies an increase of the hydrodynamic resistance of the device, which, in turn, leads to an increase of the initial transportation time of the cells to the constriction region. Instead of the usual 5 min, the initial flushing time of cells to the constrictions is increased to up 30 min. As a solution, the new devices might be produced through a multi-layering process. In soft lithography, the subsequent deposition, baking and UV-illumination of several photoresist layers allows the production of microconstrictions which are lower than the rest of the device [18]. Additionally, when primary cells are directly extracted from mouse models or from patients in a clinical context, further investigations on anti-cell-clustering chemicals are required, which are supposed to decrease cell-cell-cohesion after cell preparation. Up to now, the use of EDTA and dextran sulfate did not stop some cell lines, for example adherent A 549 lung cells, from coagulating after their lift-off of the substrate, neither did they dissolve chronic lymphocytic leukemia cells after centrifugation. Applications on blood cells might also open the door to high-throughput screenings of whole blood to detect, for example, circulating tumor cells. For such an application, however, the cells must be pre-sorted according to their size and then measured with constrictions of different, suitable dimensions. In previous studies, size sorting of cells was performed through their different inertia force in diverging flows or mechanical filtering was implemented through narrowing channels [197].

128

Besides other biomedical applications, our understanding of cell mechanics might be further deepened through ongoing fundamental research. For example, previous studies reported that measurements of cell mechanics on adherent cells are in accordance with measurements on suspended cells to a surprisingly big extent (comp. to Sec. 3.6). Still, a quantified comparison between measurements on adherent and suspended cells, performed on the same cell population in the same laboratory, is missing and would yield great insight into the temporal dynamics of the cell cytoskeleton after lift-off of the substrate. This study would require the parallel measurement of cell mechanics with the microconstriction setup and with, for example, atomic force microscopy, after treating the cells with chemicals that supposedly change the mechanics of the nucleus or the cytoskeleton. Further theoretical advances of the description of cell deformation in a microconstriction device should include a coherent description of stress and strain stiffening. As highlighted in Sec. 3.3, it is a global problem in cell mechanical measurements that quantified data cannot be compared between different studies, since all of them were gained under highly differing stress and strain conditions. Only seldom, functional dependencies of stiffness and viscosity over wide stress and strain ranges could be established. Without these dependencies, a full understanding of cell behavior in the body is difficult, because also in nature, cells are subjected to highly varying amounts of stress and strain and react and act accordingly. Moreover, it might be highly interesting to quantify the mechanical properties of single cells with the microconstriction assay, instead of averaging over cell populations. This might yield valuable information on the spread of cell mechanics within one and the same population. Even though, principally, gene expression, and thereby protein levels, are supposedly the same in a laboratory cell population, huge differences in cell mechanics between single cells have been found with several measurement techniques (for example AFM and shear plate rheometer) [19]. To quantify single cell mechanical properties with microconstrictions without the use of SGR theory (comp. to Sec. 3.7), single cell deformation ǫ(t) would have to be monitored over time.

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Bibliography [1] D. T. Tambe, C. C. Hardin, T. E. Angelini, K. Rajendran, C. Y. Park, X. Serra-Picamal, E. H. Zhou, M. H. Zaman, J. P. Butler, D. A. Weitz, J. J. Fredberg, and X. Trepat, “Collective cell guidance by cooperative intercellular forces,” Nature materials, vol. 10, no. 6, pp. 469–75, 2011. 1 [2] P. Friedl, P. B. Noble, P. A. Walton, D. W. Laird, P. J. Chauvin, R. J. Tabah, M. Black, and K. S. Z¨ anker, “Migration of Coordinated Cell Clusters in Mesenchymal and Epithelial Cancer,” Cancer research, vol. 55, pp. 4557–4560, 1995. 1 [3] P. Friedl and D. Gilmour, “Collective cell migration in morphogenesis, regeneration and cancer,” Nature reviews. Molecular cell biology, vol. 10, no. 7, pp. 445–57, 2009. 1, 91 [4] D. L. Nikoli´ c, A. N. Boettiger, D. Bar-Sagi, J. D. Carbeck, and S. Y. Shvartsman, “Role of boundary conditions in an experimental model of epithelial wound healing,” American journal of physiology. Cell physiology, vol. 291, pp. C68–75, 2006. 1 [5] T. E. Angelini, E. Hannezo, X. Trepat, J. J. Fredberg, and D. A. Weitz, “Cell Migration Driven by Cooperative Substrate Deformation Patterns,” Physical Review Letters, vol. 104, no. 16, p. 168104, 2010. [6] T. E. Angelini, E. Hannezo, X. Trepat, M. Marquez, J. J. Fredberg, and D. A. Weitz, “Glass-like dynamics of collective cell migration,” Proceedings of the National Academy of Sciences of the United States of America, vol. 108, pp. 4714–9, 2011. 1 [7] J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. K¨ as, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophysical Journal, vol. 88, no. 5, pp. 3689– 98, 2005. 1, 6, 106 [8] Y. Hegerfeldt, M. Tusch, E.-B. Br¨ ockner, and P. Friedl, “Collective Cell Movement in Primary Melanoma Explants : Plasticity of Cell-Cell Interaction, b1-Integrin Function and Migration Strategies,” Cancer research, vol. 62, pp. 2125–2130, 2002. 1 [9] J. Steinwachs, C. Metzner, K. Skodzek, N. Lang, I. Thievessen, C. Mark, S. M¨ unster, K. E. Aifantis, and B. Fabry, “Three-dimensional force microscopy of cells in biopolymer networks,” Nature Methods, vol. 13, no. 2, pp. 171–176, 2015. 1, 91 [10] S. Gabriele, A.-M. Benoliel, P. Bongrand, and O. Th´ eodoly, “Microfluidic investigation reveals distinct roles for actin cytoskeleton and myosin II activity in capillary leukocyte trafficking,” Biophysical Journal, vol. 96, no. 10, pp. 4308–18, 2009. 1, 2, 8, 9, 74, 114 [11] P. Kollmannsberger, C. M. Bidan, J. W. C. Dunlop, and P. Fratzl, “The physics of tissue patterning and extracellular matrix organisation: how cells join forces,” Soft Matter, vol. 7, no. 20, p. 9549, 2011. 1, 4, 26, 27, 53, 58, 72, 77 [12] K. J. Chalut, M. H¨ opfler, F. Lautenschl¨ ager, L. Boyde, C. J. Chan, A. Ekpenyong, A. Martinez-Arias, and J. Guck, “Chromatin decondensation and nuclear softening accompany Nanog downregulation in embryonic stem cells,” Biophysical Journal, vol. 103, no. 10, pp. 2060–70, 2012. 2, 74, 103, 121

131

BIBLIOGRAPHY

[13] O. Otto, P. Rosendahl, A. Mietke, S. Golfier, C. Herold, D. Klaue, S. Girardo, S. Pagliara, A. Ekpenyong, A. Jacobi, M. Wobus, N. T¨ opfner, U. F. Keyser, J. Mansfeld, E. Fischer-Friedrich, and J. Guck, “Real-time deformability cytometry: on-the-fly cell mechanical phenotyping,” Nature Methods, vol. 12, no. 3, pp. 199–202, 2015. 2, 6, 87, 114, 121 [14] A. E. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschl¨ ager, C. Fiddler, S. Paschke, U. F. Keyser, E. R. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and functiondependent,” PloS one, vol. 7, no. 9, p. e45237, 2012. 2, 6, 74, 114 [15] S. K. Ballas, “Sickle cell anemia with few painful crises is characterized by decreased red cell deformability and increased number of dense cells,” American journal of hematology, vol. 36, pp. 122–130, 1991. 2 [16] S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, and T. Seufferlein, “Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria,” Acta Biomaterialia, vol. 1, pp. 15–30, 2005. 2 [17] T. W. Remmerbach, F. Wottawah, J. Dietrich, B. Lincoln, C. Wittekind, and J. Guck, “Oral Cancer Diagnosis by Mechanical Phenotyping,” Cancer research, vol. 69, no. 5, pp. 1728–1732, 2009. 2, 91 [18] M. J. Madou, Fundamentals of Soft Lithography: The Science of Miniaturization. Boca Raton, Florida: CRC Press, 2002. 2, 6, 7, 16, 128 [19] K. D. Nyberg, M. B. Scott, S. L. Bruce, A. B. Gopinath, D. Bikos, T. G. Mason, J. W. Kim, H. S. Choi, and A. C. Rowat, “The physical origins of transit time measurements for rapid, single cell mechanotyping,” Lab on a Chip, vol. 16, no. 17, pp. 3330–39, 2016. 2, 7, 8, 9, 17, 32, 81, 84, 129 [20] J. R. Lange, J. Steinwachs, T. Kolb, L. A. Lautscham, I. Harder, G. Whyte, and B. Fabry, “Microconstriction Arrays for High-Throughput Quantitative Measurements of Cell Mechanical Properties,” Biophysical Journal, vol. 109, no. 1, pp. 26–34, 2015. 3, 8, 12, 20, 31, 33, 36, 38, 52, 55, 56, 74, 75, 76, 78, 101, 104, 109, 114, 121, 123 [21] L. A. Lautscham, C. K¨ ammerer, J. R. Lange, T. Kolb, C. Mark, A. Schilling, P. L. Strissel, R. Strick, C. Gluth, A. C. Rowat, C. Metzner, and B. Fabry, “Migration in Confined 3D Environments Is Determined by a Combination of Adhesiveness, Nuclear Volume, Contractility, and Cell Stiffness,” Biophysical Journal, vol. 109, no. 5, pp. 900–913, 2015. 3, 91, 92, 93, 94, 95, 96, 97, 124 [22] J. R. Lange, C. Metzner, S. Richter, W. Schneider, M. Spermann, T. Kolb, G. Whyte, and B. Fabry, “Unbiased High-Precision Cell Mechanical Measurements with Microconstrictions,” Biophysical Journal, vol. 112, no. 7, pp. 1472–1480, 2017. 3, 18, 33, 43, 50, 51, 54, 55, 57, 58, 60, 61, 62, 79, 81, 82, 85, 86, 87, 123 [23] J. R. Lange, J. L. Alonso, and W. H. Goldmann, “Influence of avb3 integrin on the mechanical properties and the morphology of M21 and K562 cells,” Biochemical and biophysical research communications, vol. 478, pp. 1280–5, 2016. 3, 101, 102, 103, 104, 105, 106 [24] M. J. Rosenbluth, W. A. Lam, and D. A. Fletcher, “Force microscopy of nonadherent cells: a comparison of leukemia cell deformability,” Biophysical Journal, vol. 90, no. 2, pp. 2994–3003, 2006. 3 [25] W. A. Lam, M. J. Rosenbluth, and D. A. Fletcher, “Chemotherapy exposure increases leukemia cell stiffness,” Blood, vol. 109, no. 8, pp. 3505–8, 2007. 3, 50 [26] N. Wang, J. P. Butler, and D. E. Ingber, “Mechanotransduction across the cell surface and through the cytoskeleton,” Science, vol. 260, pp. 1124–7, 1993. 5, 26, 74 [27] B. Fabry, G. Maksym, J. Butler, M. Glogauer, D. Navajas, and J. Fredberg, “Scaling the Microrheology of Living Cells,” Physical Review Letters, vol. 87, no. 14, p. 148102, 2001. 5 [28] L. Deng, X. Trepat, J. P. Butler, E. Millet, K. G. Morgan, D. A. Weitz, and J. J. Fredberg, “Fast and slow dynamics of the cytoskeleton,” Nature materials, vol. 5, no. 8, pp. 636–40, 2006. [29] R. E. Laudadio, E. J. Millet, B. Fabry, S. S. An, J. P. Butler, and J. J. Fredberg, “Rat airway smooth muscle cell during actin modulation: rheology and glassy dynamics,” American journal of physiology. Cell physiology, vol. 289, pp. C1388–95, 2005. 5, 78

132

BIBLIOGRAPHY

[30] A. R. Bausch, W. M¨ oller, and E. Sackmann, “Measurement of local viscoelasticity and forces in living cells by magnetic tweezers,” Biophysical Journal, vol. 76, no. 1, pp. 573–9, 1999. 5 [31] P. Kollmannsberger and B. Fabry, “High force magnetic tweezers with force feedback for biological applications,” Review of Scientific Instruments, vol. 78, no. 11, p. 114301, 2007. [32] N. Bonakdar, R. Gerum, M. Kuhn, M. Sp¨ orrer, A. Lippert, W. Schneider, K. E. Aifantis, and B. Fabry, “Mechanical plasticity of cells,” Nature materials, vol. 15, no. 10, pp. 1090–94, 2016. 5 [33] G. Binnig, C. F. Quate, and C. Gerber, “Atomic Force Microscope,” Physical Review Letters, vol. 56, no. 9, pp. 930–34, 1986. 5 [34] J. Alcaraz, L. Buscemi, M. Grabulosa, X. Trepat, B. Fabry, R. Farre, and D. Navajas, “Microrheology of Human Lung Epithelial Cells Measured by Atomic Force Microscopy,” Biophysical Journal, vol. 84, no. 3, pp. 2071–2079, 2003. [35] B. A. Smith, B. Tolloczko, J. G. Martin, and P. Gr¨ utter, “Probing the viscoelastic behavior of cultured airway smooth muscle cells with atomic force microscopy: stiffening induced by contractile agonist,” Biophysical Journal, vol. 88, no. 4, pp. 2994–3007, 2005. 78 [36] P. Roca-Cusachs, I. Almendros, R. Sunyer, N. Gavara, R. Farr´ e, and D. Navajas, “Rheology of Passive and Adhesion-Activated Neutrophils Probed by Atomic Force Microscopy,” Biophysical Journal, vol. 91, no. 9, pp. 3508–3518, 2006. 106 [37] L. I. Mi, L. I. U. Lianqing, X. I. Ning, W. Yuechao, D. Zaili, X. Xiubin, and Z. Weijing, “Atomic force microscopy imaging and mechanical properties measurement of red blood cells and aggressive cancer cells,” Science China, vol. 55, no. 11, pp. 968–973, 2012. 5 [38] O. Thoumine and A. Ott, “Time scale dependent viscoelastic and contractile regimes in fibroblasts probed by microplate manipulation,” Journal of Cell Science, vol. 110, no. 17, pp. 2109–2116, 1997. 5 [39] P. Fernandez, P. A. Pullarkat, and A. Ott, “A Master Relation Defines the Nonlinear Viscoelasticity of Single Fibroblasts,” Biophysical Journal, vol. 90, no. 10, pp. 3796–3805, 2006. [40] N. Desprat, A. Guiroy, and A. Asnacios, “Microplates-based rheometer for a single living cell,” Review of Scientific Instruments, vol. 77, no. 5, p. 055111, 2006. 5 [41] B. Fabry, G. N. Maksym, S. A. Shore, P. E. Moore, R. A. Panettieri, J. P. Butler, and J. J. Fredberg, “Time course and heterogeneity of contractile responses in cultured human airway smooth muscle cells,” Journal of applied physiology, vol. 91, pp. 986–94, 2001. 6, 26, 40, 77, 79 [42] Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues. New York: Springer Science+Business Media, 2 ed., 1993. 6, 26, 27, 38, 39, 64 [43] M. A. Tsai, R. S. Frank, and R. E. Waugh, “Passive mechanical behavior of human neutrophils: power-law fluid,” Biophysical Journal, vol. 65, no. 5, pp. 2078–88, 1993. 6 [44] R. M. Hochmuth, “Micropipette aspiration of living cells,” Journal of Biomechanics, vol. 33, pp. 15–22, 2000. [45] W. R. Trickey, F. P. T. Baaijens, T. A. Laursen, L. G. Alexopoulos, and F. Guilak, “Determination of the Poisson’s ratio of the cell: Recovery properties of chondrocytes after release from complete micropipette aspiration,” Journal of Biomechanics, vol. 39, pp. 78–87, 2006. [46] A. Vaziri and M. R. K. Mofrad, “Mechanics and deformation of the nucleus in micropipette aspiration experiment,” Journal of Biomechanics, vol. 40, pp. 2053–2062, 2007. 6 [47] J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. K¨ as, “The Optical Stretcher : A Novel Laser Tool to Micromanipulate Cells,” Biophysical Journal, vol. 81, no. 2, pp. 767–784, 2001. 6 [48] C. J. Chan, G. Whyte, L. Boyde, G. Salbreux, and J. Guck, “Impact of heating on passive and active biomechanics of suspended cells,” Interface focus, vol. 4, p. 20130069, 2014. 6, 86, 88, 89

133

BIBLIOGRAPHY

[49] D. R. Gossett, H. T. K. Tse, S. A. Lee, Y. Ying, A. G. Lindgren, O. O. Yang, J. Rao, A. T. Clark, and D. Di Carlo, “Hydrodynamic stretching of single cells for large population mechanical phenotyping,” Proceedings of the National Academy of Sciences, vol. 109, no. 20, pp. 7630–5, 2012. 6, 7 [50] H. T. K. Tse, D. R. Gossett, Y. S. Moon, M. Masaeli, M. Sohsman, Y. Ying, K. Mislick, R. P. Adams, J. Rao, and D. Di Carlo, “Quantitative diagnosis of malignant pleural effusions by single-cell mechanophenotyping,” Science translational medicine, vol. 5, no. 212, p. 212ra163, 2013. 6 [51] S. C. Hur, N. K. Henderson-MacLennan, E. R. B. McCabe, and D. Di Carlo, “Deformability-based cell classification and enrichment using inertial microfluidics.,” Lab on a Chip, vol. 11, no. 5, pp. 912–920, 2011. 6 [52] A. Mietke, O. Otto, S. Girardo, P. Rosendahl, A. Taubenberger, S. Golfier, E. Ulbricht, S. Aland, J. Guck, and E. Fischer-Friedrich, “Extracting cell stiffness from real-time deformability cytometry: theory and experiment,” Biophysical Journal, vol. 109, no. 10, pp. 2023–2036, 2015. 6 [53] M. Mokbel, D. Mokbel, A. Mietke, N. Tr¨ aber, S. Girardo, O. Otto, J. Guck, and S. Aland, “Numerical Simulation of Real-Time Deformability Cytometry to Extract Cell Mechanical Properties,” ACS Biomaterials, doi: 10.1021/ascbiomaterials.6b00558, 2017. 6 [54] H. L. Reid, A. J. Barnes, P. J. Lock, J. A. Dormandy, and T. L. Dormandy, “A simple method for measuring erythrocyte deformability,” Journal of clinical pathology, vol. 29, pp. 855–58, 1976. 7 [55] G. S. Worthen, B. Schwab III, E. L. Elson, and G. P. Downeyt, “Mechanics of Stimulated Neutrophils : Cell Stiffening Induces Retention in Capillaries,” Science, vol. 245, pp. 183–86, 1989. 7 [56] M. Mak and D. Erickson, “A serial micropipette microfluidic device with applications to cancer cell repeated deformation studies,” Integrative Biology, vol. 5, pp. 1374–84, 2013. 7, 8, 9 [57] S. Byun, S. Son, D. Amodei, N. Cermak, J. Shaw, J. Ho, V. C. Hecht, M. M. Winslow, T. Jacks, P. Mallick, and S. R. Manalis, “Characterizing deformability and surface friction of cancer cells,” Proceedings of the National Academy of Sciences, vol. 110, no. 19, pp. 7580–7585, 2013. 8, 9, 10 [58] A. C. Rowat, D. E. Jaalouk, M. Zwerger, W. L. Ung, I. A. Eydelnant, D. E. Olins, A. L. Olins, H. Herrmann, D. A. Weitz, and J. Lammerding, “Nuclear envelope composition determines the ability of neutrophil-type cells to passage through micron-scale constrictions,” The Journal of biological chemistry, vol. 288, no. 12, pp. 8610–8, 2013. 7, 8, 9, 13 [59] R. M. Hochmuth, R. N. Marple, and S. P. Sutera, “Capillary Blood flow,” Microvascular research, vol. 2, no. 1970, pp. 409–419, 1970. 7 [60] D. Braasch, “Red Cell Deformability and Capillary Blood Flow,” Physiological Reviews, vol. 51, pp. 679–701, 1971. 7 [61] J. P. Shelby, J. White, K. Ganesan, P. K. Rathod, and D. T. Chiu, “A microfluidic model for single-cell capillary obstruction by Plasmodium falciparum-infected erythrocytes,” Proceedings of the National Academy of Sciences of the United States of America, vol. 100, pp. 14618–22, 2003. 8, 9, 10 [62] M. J. Rosenbluth, W. A. Lam, and D. A. Fletcher, “Analyzing cell mechanics in hematologic diseases with microfluidic biophysical flow cytometry,” Lab on a Chip, vol. 8, no. 7, pp. 1062–70, 2008. 8, 9, 128 [63] J. Chen, Y. Zheng, Q. Tan, E. Shojaei-Baghini, Y. L. Zhang, J. Li, P. Prasad, L. You, X. Y. Wu, and Y. Sun, “Classification of cell types using a microfluidic device for mechanical and electrical measurement on single cells,” Lab on a Chip, vol. 11, no. 18, pp. 3174–81, 2011. 8, 9, 10 [64] Q. Guo, S. J. Reiling, P. Rohrbach, and H. Ma, “Microfluidic biomechanical assay for red blood cells parasitized by Plasmodium falciparum,” Lab on a Chip, vol. 12, no. 6, pp. 1143–50, 2012. 8, 9, 10 [65] A. Adamo, A. Sharei, L. Adamo, B. Lee, S. Mao, and K. F. Jensen, “Microfluidics-Based Assessment of Cell Deformability,” Analytical chemistry, vol. 84, pp. 6438–6443, 2012. 8, 9

134

BIBLIOGRAPHY

[66] Z. S. Khan and S. A. Vanapalli, “Probing the mechanical properties of brain cancer cells using a microfluidic cell squeezer device,” Biomicrofluidics, vol. 7, no. 11806, pp. 1–15, 2013. 8, 9, 10 [67] P. Preira, M.-P. Valignat, J. Bico, and O. Theodoly, “Single cell rheometry with a microfluidic constriction: Quantitative control of friction and fluid leaks between cell and channel walls,” Biomicrofluidics, vol. 7, no. 024111, pp. 1–17, 2013. 8, 9, 10 [68] C.-H. D. Tsai, S. Sakuma, F. Arai, and M. Kaneko, “A new dimensionless index for evaluating cell stiffnessbased deformability in microchannel,” IEEE transactions on bio-medical engineering, vol. 61, no. 4, pp. 1187– 95, 2014. 8, 9, 10 [69] R. Martinez Vazquez, G. Nava, M. Veglione, T. Yang, F. Bragheri, P. Minzioni, E. Bianchi, M. Di Tano, I. Chiodi, R. Osellame, C. Mondello, and I. Cristiani, “An optofluidic constriction chip for monitoring metastatic potential and drug response of cancer cells,” Integrative Biology, vol. 7, pp. 477–484, 2015. 9, 10 [70] J. S. Bagnall, S. Byun, and D. T. Miyamoto, “Deformability-based cell selection with downstream immunofluorescence analysis,” Integrative Biology, vol. 8, pp. 654–664, 2016. 8, 9, 10 [71] Y. Zheng, J. Wen, J. Nguyen, M. A. Cachia, C. Wang, and Y. Sun, “Decreased deformability of lymphocytes in chronic lymphocytic leukemia,” Scientific reports, vol. 5, p. 7613, 2015. 8 [72] B. H. Jo, L. M. Van Lerberghe, K. M. Motsegood, and D. J. Beebe, “Three-dimensional micro-channel fabrication in polydimethylsiloxane (PDMS) elastomer,” Journal of Microelectromechanical Systems, vol. 9, pp. 76–81, 2000. 17 [73] B. Trappmann, J. E. Gautrot, J. T. Connelly, D. G. T. Strange, Y. Li, M. L. Oyen, M. A. Cohen Stuart, H. Boehm, B. Li, V. Vogel, J. P. Spatz, F. M. Watt, and W. T. S. Huck, “Extracellular-matrix tethering regulates stem-cell fate,” Nature materials, vol. 11, no. 7, pp. 642–9, 2012. 17 [74] K. Chau, B. Millare, A. Lin, S. Upadhyayula, V. Nu˜ nez, H. Xu, and V. I. Vullev, “Dependence of the quality of adhesion between poly(dimethylsiloxane) and glass surfaces on the composition of the oxidizing plasma,” Microfluidics and Nanofluidics, vol. 10, no. 4, pp. 907–917, 2010. 17 [75] S. Sharma, R. W. Johnson, and T. A. Desai, “Evaluation of the Stability of Nonfouling Ultrathin Poly ( ethylene glycol ) Films for Silicon-Based Microdevices,” Langmuir, vol. 20, pp. 348–356, 2004. 22, 51 [76] S. Krishnan, J. Weinman, and C. K. Ober, “Advances in polymers for anti-biofouling surfaces,” Journal of Materials Chemistry, vol. 18, pp. 3405–3413, 2008. 22, 51 [77] C. Heidorn, Ansteuerung einer Hochgeschwindigkeits-Kamera zur Messung zellmechanischer Eigenschaften in mikrofluidischen Aufbauten. Bachelor thesis, FAU Erlangen-N¨ urnberg, 2015. 23, 24, 44 [78] R. O. Hynes, “Integrins : Bidirectional, Allosteric Signaling Machines,” Cell, vol. 110, pp. 673–687, 2002. 24, 100 [79] M. Zwerger, C. Y. Ho, and J. Lammerding, “Nuclear mechanics in disease,” Annual review of biomedical engineering, vol. 13, pp. 397–428, 2011. 24, 122, 124 [80] F. Lautenschl¨ ager, Cell Compliance Cytoskeletal Origin and Importance for Cellular Function. PhD thesis, University of Cambridge, 2011. 25, 26 [81] K. Seltmann, A. W. Fritsch, J. A. K¨ as, and T. M. Magin, “Keratins significantly contribute to cell stiffness and impact invasive behavior,” Proceedings of the National Academy of Sciences of the United States of America, vol. 110, no. 46, pp. 18507–12, 2013. 27 [82] M. Tozluoglu, A. L. Tournier, R. P. Jenkins, S. Hooper, P. A. Bates, and E. Sahai, “Matrix geometry determines optimal cancer cell migration strategy and modulates response to interventions,” Nature cell biology, vol. 15, no. 7, pp. 751–62, 2013. 27

135

BIBLIOGRAPHY

[83] J. C. Maxwell, “On the dynamical theory of gases,” Philosophical Transactions of the Royal Society of London, vol. 157, pp. 49–88, 1867. 27 [84] T. A. Wilson, “Time constants may be meaningless in exponentials fit to pressure relaxation data,” Journal of applied physiology, vol. 77, pp. 1569–1571, 1994. 27 [85] H. Bruus, Theoretical microfluidics, vol. 18. Oxford, UK: Oxford University Press, 2008. 28, 29 [86] G. Hetsroni, S. Haber, and E. Wacholder, “The flow fields in and around a droplet moving axially within a tube,” Journal of Fluid Mechanics, vol. 41, p. 689, 1970. 34 [87] M. Belloul, W. Engl, A. Colin, P. Panizza, and A. Ajdari, “Competition between local collisions and collective hydrodynamic feedback controls traffic flows in microfluidic networks,” Physical Review Letters, vol. 102, no. 19, pp. 9–12, 2009. 34 [88] J. Hildebrandt, “Comparison of mathematical models for cat lung and viscoelastic balloon derived by Laplace transform methods from pressure-volume data,” Bulletin of mathematical biophysics, vol. 31, pp. 651–667, 1969. 40 [89] B. D. Hoffman and J. C. Crocker, “Cell mechanics: dissecting the physical responses of cells to force,” Annual review of biomedical engineering, vol. 11, pp. 259–288, 2009. 40 [90] M. Gardel, F. Nakamura, J. Hartwig, J. Crocker, T. Stossel, and D. A. Weitz, “Stress-Dependent Elasticity of Composite Actin Networks as a Model for Cell Behavior,” Physical Review Letters, vol. 96, no. 8, p. 089102, 2006. 41, 56 [91] P. Kollmannsberger and B. Fabry, “Linear and Nonlinear Rheology of Living Cells,” Annual Review of Materials Research, vol. 41, no. 1, pp. 75–97, 2011. [92] I. Levental, P. C. Georges, and P. A. Janmey, “Soft biological materials and their impact on cell function,” Soft Matter, vol. 3, no. 3, pp. 299–306, 2007. 41, 56 [93] B. Efron and R. J. Tibshirani, An introduction to the bootstrap. Dordrecht: Springer Science Business Media, 1993. 42 [94] D. Fischer, T. Bieber, L. Youxin, H.-P. Els¨ asser, and T. Kissel, “A novel non-viral vector for DNA delivery based on low molecular weight, branched polyethylenimine: Effect of molecular weight on transfection efficiency and cytotoxicity,” Pharmaceutical Research, vol. 16, no. 8, pp. 1273–1279, 1999. 43 [95] C. B. Lozzio and B. B. Lozzio, “Human chronic myelogenous leukemia cell-line with positive philadelphia chromosome,” Blood, vol. 45, no. 3, pp. 321–335, 1975. 46 [96] J. B. Konopka, S. M. Watanabe, and O. N. Witte, “An alteration of the human c-abl protein in K562 leukemia cells unmasks associated tyrosine kinase activity,” Cell, vol. 37, pp. 1035–1042, 1984. 46 [97] R. D. Klausner, G. Ashwell, J. van Renswoude, J. B. Harford, and K. R. Bridges, “Binding of apotransferrin to K562 cells: explanation of the transferrin cycle,” Proceedings of the National Academy of Sciences of the United States of America, vol. 80, pp. 2263–2266, 1983. 46 [98] D. L. Dexter, E. N. Spremulli, Z. Fligiel, J. A. Barbosa, R. Vogel, A. VanVoorhees, and P. Calabresi, “Heterogeneity of cancer cells from a single human colon carcinoma,” The American journal of medicine, vol. 71, pp. 949–956, 1981. 47 [99] H.-L. Huang, H.-W. Hsing, T.-C. Lai, Y.-W. Chen, T.-R. Lee, H.-T. Chan, P.-C. Lyu, C.-L. Wu, Y.-C. Lu, S.-T. Lin, C.-W. Lin, C.-H. Lai, H.-T. Chang, H.-C. Chou, and H.-L. Chan, “Trypsin-induced proteome alteration during cell subculture in mammalian cells,” Journal of biomedical science, vol. 17, no. 36, pp. 1–10, 2010. 49 [100] H.-R. Thiam, P. Vargas, N. Carpi, C. L. Crespo, M. Raab, E. Terriac, M. C. King, J. Jacobelli, A. S. Alberts, T. Stradal, and M. Piel, “Perinuclear Arp2/3-driven actin polymerization enables nuclear deformation to facilitate cell migration through complex environments,” Nature Communications, vol. 7, p. 10997, 2016. 52, 73, 122

136

BIBLIOGRAPHY

[101] J. Howard, Mechanics of Motor Proteins and the Cytoskeleton. Sunderland, Massachusetts: Sinauer Associates, Inc., 1st ed., 2001. 72 [102] A. Kis, S. Kasas, B. Babic, A. J. Kulik, W. Benoit, G. A. D. Briggs, C. Sch¨ onenberger, S. Catsicas, and L. Forro, “Nanomechanics of Microtubules,” Physical Review Letters, vol. 89, no. 24, pp. 1–4, 2002. 72 [103] B. Alberts, A. Johnson, J. Lewis, and E. Al., Molecular biology of the cell. New York and London: Garland Science, 2nd ed., 2003. 73 [104] S. K¨ oster, D. A. Weitz, R. D. Goldman, U. Aebi, and H. Herrmann, “Intermediate filament mechanics in vitro and in the cell : from coiled coils to filaments , fibers and networks,” Current Opinion in Cell Biology, vol. 32, pp. 82–91, 2015. 73 [105] D. S. Fudge, K. H. Gardner, V. T. Forsyth, C. Riekel, and J. M. Gosline, “The Mechanical Properties of Hydrated Intermediate Filaments : Insights from Hagfish Slime Threads,” Biophysical Journal, vol. 85, no. 3, pp. 2015–2027, 2001. 73 [106] N. M¨ ucke, L. Kreplak, R. Kirmse, T. Wedig, H. Herrmann, U. Aebi, and J. Langowski, “Assessing the Flexibility of Intermediate Filaments by Atomic Force Microscopy,” Journal of molecular biology, vol. 335, pp. 1241–1250, 2003. 73 [107] A. L. McGregor, C.-R. Hsia, and J. Lammerding, “Squish and squeeze - the nucleus as a physical barrier during migration in confined environments,” Current Opinion in Cell Biology, vol. 40, pp. 32–40, 2016. 73, 122 [108] C. M. Denais, R. M. Gilbert, P. Isermann, A. L. McGregor, M. Lindert, B. Weigelin, P. M. Davidson, P. Friedl, K. Wolf, and J. Lammerding, “Nuclear envelope rupture and repair during cancer cell migration,” Science, vol. 352, no. 6283, pp. 353–358, 2016. 73, 122 [109] P. Meinke, A. A. Makarov, P. L. Thanh, D. Sadurska, and E. C. Schirmer, “Nucleoskeleton dynamics and functions in health and disease,” Cell Health and Cytoskeleton, vol. 7, pp. 55–69, 2015. 73, 122 [110] A. Mazumder, T. Roopa, A. Basu, L. Mahadevan, and G. V. Shivashankar, “Dynamics of chromatin decondensation reveals the structural integrity of a mechanically prestressed nucleus,” Biophysical Journal, vol. 95, no. 6, pp. 3028–35, 2008. 74, 121 [111] Q. Guo, S. P. Duffy, K. Matthews, A. T. Santoso, M. D. Scott, and H. Ma, “Microfluidic analysis of red blood cell deformability,” Journal of Biomechanics, vol. 47, no. 8, pp. 1767–76, 2014. 74, 106, 114 [112] F. Lautenschl¨ ager, S. Paschke, S. Schinkinger, A. Bruel, M. Beil, and J. Guck, “The regulatory role of cell mechanics for migration of differentiating myeloid cells,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 37, pp. 15696–15701, 2009. 74 [113] B. S. Eckert, “Alteration of intermediate filament distribution in PtK1 cells by acrylamide,” European journal of cell biology, vol. 37, pp. 169–74, 1985. 74 [114] P. R. Sager, “Cytoskeletal effects of acrylamide and 2,5-hexanedione: selective aggregation of vimentin filaments,” Toxicology and applied pharmacology, vol. 97, pp. 141–55, 1989. [115] M. Hay and U. De Boni, “Chromatin motion in neuronal interphase nuclei: changes induced by disruption of intermediate filaments,” Cell motility and the cytoskeleton, vol. 18, pp. 63–75, 1991. 74 [116] P. Sollich, “Rheological constitutive equation for a model of soft glassy materials,” Physical Review E, vol. 58, no. 1, pp. 738–759, 1998. 77 [117] P. Cai, Y. Mizutani, M. Tsuchiya, J. M. Maloney, B. Fabry, K. J. Van Vliet, and T. Okajima, “Quantifying cell-to-cell variation in power-law rheology,” Biophysical Journal, vol. 105, no. 5, pp. 1093–102, 2013. 78, 79 [118] N. Desprat, A. Richert, J. Simeon, and A. Asnacios, “Creep function of a single living cell,” Biophysical Journal, vol. 88, no. 3, pp. 2224–33, 2005. 79

137

BIBLIOGRAPHY

[119] F. S. Collins and L. A. Tabak, “NIH plans to enhance reproducibility,” Nature, vol. 505, no. 7485, pp. 612–613, 2014. 79 [120] L. Loew, D. Beckett, E. H. Egelman, and S. Scarlata, “Reproducibility of research in biophysics,” Biophysical Journal, vol. 108, p. E01, 2015. 79 [121] “Reproducibility and reliability of biomedical research: improving research practice,” Academy of Medical Sciences, no. October, 2015. 79 [122] X. Serra-Picamal, V. Conte, R. Vincent, E. Anon, D. T. Tambe, E. Bazellieres, J. P. Butler, J. J. Fredberg, and X. Trepat, “Mechanical waves during tissue expansion,” Nature Physics, vol. 8, no. 7, pp. 1–7, 2012. 81 [123] D. E. Discher, P. Janmey, and Y.-L. Wang, “Tissue cells feel and respond to the stiffness of their substrate,” Science, vol. 310, pp. 1139–43, 2005. 83 [124] L. M. Swift, H. Asfour, N. G. Posnack, A. Arutunyan, M. W. Kay, and N. Sarvazyan, “Properties of blebbistatin for cardiac optical mapping and other imaging applications,” Pflugers Archiv European Journal of Physiology, vol. 464, no. 5, pp. 503–512, 2012. 83, 93, 122, 124, 127, 128 [125] J. M. Maloney, D. Nikova, F. Lautenschl¨ ager, E. Clarke, R. Langer, J. Guck, and K. J. Van Vliet, “Mesenchymal stem cell mechanics from the attached to the suspended state,” Biophysical Journal, vol. 99, no. 8, pp. 2479–2487, 2010. 83 [126] P. Bursac, B. Fabry, X. Trepat, G. Lenormand, J. P. Butler, N. Wang, J. J. Fredberg, and S. S. An, “Cytoskeleton dynamics: fluctuations within the network,” Biochemical and biophysical research communications, vol. 355, no. 2, pp. 324–30, 2007. 87 [127] E. Anon, X. Serra-Picamal, P. Hersen, N. C. Gauthier, M. P. Sheetz, X. Trepat, and B. Ladoux, “Cell crawling mediates collective cell migration to close undamaged epithelial gaps,” Proceedings of the National Academy of Sciences of the United States of America, vol. 109, no. 27, pp. 10891–6, 2012. 91 [128] M. Yilmaz and G. Christofori, “Mechanisms of motility in metastasizing cells,” Molecular cancer research, vol. 8, pp. 629–42, 2010. 91 [129] O. Jonas, C. T. Mierke, and J. a. K¨ as, “Invasive cancer cell lines exhibit biomechanical properties that are distinct from their noninvasive counterparts,” Soft Matter, vol. 7, no. 24, pp. 11488–11495, 2011. 91 [130] K. Wolf, M. Te Lindert, M. Krause, S. Alexander, J. Te Riet, A. L. Willis, R. M. Hoffman, C. G. Figdor, S. J. Weiss, and P. Friedl, “Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force,” The Journal of Cell Biology, vol. 201, no. 7, pp. 1069–84, 2013. 91 [131] S. Rasheed, W. Nelson-Rees, E. M. Toth, P. Arnstein, and M. B. Gardner, “Characterization of a newly derived human sarcoma cell line (HT-1080),” Cancer, vol. 33, no. 4, pp. 1027–33, 1973. 92 [132] K. B. Yin, “The Mesenchymal-Like Phenotype of the MDA-MB-231 Cell Line,” in Breast Cancer, ch. 18, Rijeka, Croatia: Intech d.o.o, 2011. 92 [133] C. T. Mierke, D. P. Zitterbart, P. Kollmannsberger, C. Raupach, U. Schl¨ otzer-Schrehardt, T. W. Goecke, J. Behrens, and B. Fabry, “Breakdown of the endothelial barrier function in tumor cell transmigration,” Biophysical Journal, vol. 94, no. 7, pp. 2832–46, 2008. 92 [134] N. R. Lang, K. Skodzek, S. Hurst, A. Mainka, J. Steinwachs, J. Schneider, K. E. Aifantis, and B. Fabry, “Biphasic response of cell invasion to matrix stiffness in three-dimensional biopolymer networks,” Acta Biomaterialia, vol. 13, pp. 61–67, 2015. 93 [135] M. Zwerger, D. E. Jaalouk, M. L. Lombardi, P. Isermann, M. Mauermann, G. Dialynas, H. Herrmann, L. Wallrath, and J. Lammerding, “Myopathic lamin mutations impair nuclear stability in cells and tissue and disrupt nucleo-cytoskeletal coupling,” Human Molecular Genetics, vol. 22, no. 12, pp. 2335–2349, 2013. 93, 124

138

BIBLIOGRAPHY

[136] M. Zwerger and O. Medalia, “From lamins to lamina: A structural perspective,” Histochemistry and Cell Biology, vol. 140, pp. 3–12, 2013. 93, 122, 124, 127 [137] J. Lange, V. Auernheimer, P. L. Strissel, and W. H. Goldmann, “Influence of focal adhesion kinase on the mechanical behavior of cell populations,” Biochemical and biophysical research communications, vol. 436, no. 2, pp. 246–251, 2013. 95 [138] J. Lammerding, L. G. Fong, J. Y. Ji, K. Reue, C. L. Stewart, S. G. Young, and R. T. Lee, “Lamins A and C but not lamin B1 regulate nuclear mechanics,” The Journal of biological chemistry, vol. 281, no. 35, pp. 25768–80, 2006. 95 [139] M. L. Gardel, J. H. Shin, F. C. MacKintosh, L. Mahadevan, P. Matsudaira, and D. A. Weitz, “Elastic behavior of cross-linked and bundled actin networks,” Science, vol. 304, no. 5675, pp. 1301–5, 2004. 97 [140] K. M. Van Citters, B. D. Hoffman, G. Massiera, and J. C. Crocker, “The role of F-actin and myosin in epithelial cell rheology,” Biophysical Journal, vol. 91, no. 10, pp. 3946–56, 2006. 97 [141] J. C. Martens and M. Radmacher, “Softening of the actin cytoskeleton by inhibition of myosin II,” European Journal of Physiology, vol. 456, pp. 95–100, 2008. 97 [142] N. Nijenhuis, X. Zhao, A. Carisey, C. Ballestrem, and B. Derby, “Combining AFM and acoustic probes to reveal changes in the elastic stiffness tensor of living cells,” Biophysical Journal, vol. 107, no. 7, pp. 1502–1512, 2014. 97 [143] C. J. Chan, A. E. Ekpenyong, S. Golfier, W. Li, K. J. Chalut, O. Otto, J. Elgeti, J. Guck, and F. Lautenschl¨ ager, “Myosin II Activity Softens Cells in Suspension,” Biophysical Journal, vol. 108, no. 8, pp. 1856–1869, 2015. 97, 98, 99 [144] J.-P. Xiong, “Crystal Structure of the Extracellular Segment of Integrin avb3,” Science, vol. 294, pp. 339–345, 2001. 100 [145] P. Kanchanawong, G. Shtengel, A. M. Pasapera, E. B. Ramko, M. W. Davidson, H. F. Hess, and C. M. Waterman, “Nanoscale architecture of integrin-based cell adhesions,” Nature, vol. 468, no. 7323, pp. 580–4, 2010. 100 [146] R. O. Hynes, “The emergence of integrins: a personal and historical perspective,” Matrix biology, vol. 23, pp. 333–40, 2004. 100 [147] J. S. Desgrosellier and D. A. Cheresh, “Integrins in cancer: biological implications and therapeutic opportunities,” Nature Reviews. Cancer, vol. 10, no. 1, pp. 9–22, 2010. 100 [148] F. P. Ross and S. L. Teitelbaum, “Avb3 and Macrophage Colony-Stimulating Factor: Partners in Osteoclast Biology,” Immunological reviews, vol. 208, pp. 88–105, 2005. 100 [149] M. A. Horton, “The alpha v beta 3 integrin ”vitronectin receptor”,” The international journal of biochemistry & cell biology, vol. 29, no. 5, pp. 721–725, 1997. 100 [150] K. Ley, J. Rivera-Nieves, W. J. Sandborn, and S. Shattil, “Integrin-based therapeutics: biological basis, clinical use and new drugs,” Nature Reviews. Drug Discovery, vol. 15, no. 3, pp. 173–183, 2016. 100 [151] Y. Q. Chen, X. Gao, J. Timar, D. Tang, I. M. Grossi, M. Chelladurai, T. J. Kunicki, S. E. G. Fligiel, J. D. Taylor, and K. V. Honn, “Identification of the aIIbb3 Integrin in Murine Tumor Cells,” The Journal of biological chemistry, vol. 267, no. 24, pp. 17314–17320, 1992. 100 [152] D. Bouvard, C. Brakebusch, E. Gustafsson, A. Aszodi, T. Bengtsson, A. Berna, and R. F¨ assler, “Functional consequences of integrin gene mutations in mice,” Circulation research, vol. 89, no. 3, pp. 211–223, 2001. 100 [153] A. Kato, “The biologic and clinical spectrum of Glanzmann’s Thrombasthenia : implications of integrin aIIbb3 for its pathogenesis,” Critical Reviews in Oncology/Hematology, vol. 26, pp. 1–23, 1997. 100

139

BIBLIOGRAPHY

[154] C. Zhang, Y. Liu, Y. Gao, J. Shen, S. Zheng, M. Wei, and X. Zeng, “Modified heparins inhibit integrin aIIbb3 mediated adhesion of melanoma cells to platelets in vitro and in vivo,” International Journal of Cancer, vol. 125, no. 9, pp. 2058–2065, 2009. 100 [155] J. P. Xiong, B. Mahalingham, J. L. Alonso, L. A. Borrelli, X. Rui, S. Anand, B. T. Hyman, T. Rysiok, D. M¨ uller-Pompalla, S. L. Goodman, and M. A. Arnaout, “Crystal structure of the complete integrin avb3 ectodomain plus an a/b transmembrane fragment,” The Journal of Cell Biology, vol. 186, no. 4, pp. 589–600, 2009. 101 [156] F. Mitjans, D. Sander, J. Ad´ an, A. Sutter, J. M. Martinez, C.-S. J¨ aggle, J. M. Moyano, H.-G. Kreysch, J. Piulats, and S. L. Goodman, “An anti-av-integrin antibody that blocks integrin function inhibits the development of a human melanoma in nude mice,” Journal of Cell Science, vol. 108, pp. 2825–2838, 1995. 101 [157] E. G. Yarmola, T. Somasundaram, T. A. Boring, I. Spector, and M. R. Bubb, “Actin-latrunculin a structure and function: Differential modulation of actin-binding protein function by latrunculin A,” Journal of Biological Chemistry, vol. 275, no. 36, pp. 28120–28127, 2000. 102 [158] K. Ajroud, T. Sugimori, W. H. Goldmann, D. M. Fathallah, J. P. Xiong, and M. A. Arnaout, “Binding affinity of metal ions to the CD11b A-domain is regulated by integrin activation and ligands,” Journal of Biological Chemistry, vol. 279, no. 24, pp. 25483–25488, 2004. 103 [159] J. L. Alonso and W. H. Goldmann, “Influence of divalent cations on the cytoskeletal dynamics of K562 cells determined by nano-scale bead tracking,” Biochemical and biophysical research communications, vol. 421, pp. 245–8, 2012. 103 [160] W. H. Goldmann, “Mechanotransduction in cells,” Cell Biology International, vol. 36, no. 6, pp. 567–570, 2012. 105 [161] W. H. Goldmann, “Mechanotransduction and focal adhesions,” Cell Biology International, vol. 36, no. 7, pp. 649–652, 2012. 105 [162] C. Cluzel, F. Saltel, J. Lussi, F. Paulhe, B. A. Imhof, and B. Wehrle-Haller, “The mechanisms and dynamics of αvβ3 integrin clustering in living cells,” The Journal of Cell Biology, vol. 171, no. 2, pp. 383–392, 2005. 106 [163] T. Abbas and A. Dutta, “p21 in cancer : intricate networks and multiple activities,” Nature reviews. Cancer, vol. 9, no. 6, pp. 400–414, 2009. 106 [164] M. Ocker and R. Schneider-Stock, “Histone deacetylase inhibitors: Signalling towards p21cip1/waf1,” International Journal of Biochemistry and Cell Biology, vol. 39, pp. 1367–1374, 2007. 106, 107 [165] G. P. Dotto, “p21(WAF1/Cip1): more than a break to the cell cycle?,” Biochimica et biophysica acta, vol. 1471, pp. 43–56, 2000. 106 [166] N.-N. Kreis, F. Louwen, and J. Yuan, “Less understood issues : p21Cip1 in mitosis and its therapeutic potential,” Oncogene, vol. 34, no. 14, pp. 1758–1767, 2014. 106 [167] Y. Zhang, W. Yan, Y. S. Jung, and X. Chen, “PUMA Cooperates with p21 to Regulate Mammary Epithelial Morphogenesis and Epithelial-To-Mesenchymal Transition,” PLoS ONE, vol. 8, no. 6, p. e66464, 2013. 106 [168] X. L. Li, T. Hara, Y. Choi, M. Subramanian, P. Francis, S. Bilke, R. L. Walker, M. Pineda, Y. Zhu, Y. Yang, J. Luo, L. M. Wakefield, T. Brabletz, B. H. Park, S. Sharma, D. Chowdhury, P. Meltzer, and A. Lal, “A p21-ZEB1 Complex Inhibits Epithelial-Mesenchymal Transition through the MicroRNA 183-96-182 Cluster,” Molecular and cellular biology, vol. 34, no. 3, pp. 533–550, 2014. 106 [169] T. Waldman, K. W. Kinzler, and B. Vogelstein, “p21 is necessary for the p53-mediated G1 arrest in human cancer cells,” Cancer research, vol. 55, pp. 5187–5190, 1995. 106 [170] D. Qi, N. K. Gill, C. Santiskulvong, J. Sifuentes, O. Dorigo, J. Rao, B. Taylor-Harding, W. R. Wiedemeyer, and A. C. Rowat, “Screening cell mechanotype by parallel microfiltration,” Scientific reports, vol. 5, no. 17595, pp. 1–12, 2015. 109

140

BIBLIOGRAPHY

[171] S. Kunzelmann, G. J. K. Praefcke, and C. Herrmann, “Transient kinetic investigation of GTP hydrolysis catalyzed by interferon-gamma-induced hGBP1 (human guanylate binding protein 1),” Journal of Biological Chemistry, vol. 281, no. 39, pp. 28627–28635, 2006. 110 [172] N. Britzen-Laurent, M. Bauer, V. Berton, N. Fischer, A. Syguda, S. Reipschl¨ ager, E. Naschberger, C. Herrmann, and M. St¨ urzl, “Intracellular trafficking of guanylate-binding proteins is regulated by heterodimerization in a hierarchical manner,” PLoS one, vol. 5, no. 12, p. e14246, 2010. 110 [173] Y. S. E. Cheng, R. J. Colonno, and F. H. Yin, “Interferon induction of fibroblast proteins with guanylate binding activity,” Journal of Biological Chemistry, vol. 258, no. 12, pp. 7746–7750, 1983. 110 [174] E. Guenzi, K. T¨ opolt, E. Cornali, C. Lubeseder-Martellato, A. J¨ org, K. Matzen, C. Zietz, E. Kremmer, F. Nappi, M. Schwemmle, C. Hohenadl, G. Barillari, E. Tschachler, P. Monini, B. Ensoli, and M. St¨ urzl, “The helical domain of GBP-1 mediates the inhibition of endothelial cell proliferation by inflammatory cytokines,” EMBO Journal, vol. 20, no. 20, pp. 5568–5577, 2001. 110 [175] K. Weinl¨ ander, E. Naschberger, M. H. Lehmann, P. Tripal, W. Paster, H. Stockinger, C. Hohenadl, and M. St¨ urzl, “Guanylate binding protein-1 inhibits spreading and migration of endothelial cells through induction of integrin alpha4 expression,” The FASEB journal, vol. 22, no. 12, pp. 4168–4178, 2008. 110 [176] N. Ostler, N. Britzen-Laurent, A. Liebl, E. Naschberger, G. Lochnit, M. Ostler, F. Forster, P. Kunzelmann, S. Ince, V. Supper, G. J. K. Praefcke, D. W. Schubert, H. Stockinger, C. Herrmann, and M. St¨ urzl, “Gamma Interferon-Induced Guanylate Binding Protein 1 is a novel Actin Cytoskeleton Remodeling Factor,” Molecular and cellular biology, vol. 34, no. 2, pp. 196–209, 2013. 110, 115 [177] A. S. Lee, “The ER chaperone and signaling regulator GRP78/BiP as a monitor of endoplasmic reticulum stress,” Methods, vol. 35, pp. 373–381, 2005. 111 [178] F. L. Graham and A. J. Van der Eb, “A new technique for the assay of infectivity of human adenovirus 5 DNA,” Virology, vol. 52, pp. 456–467, 1973. 112 [179] C. A. Pope III, R. T. Burnett, M. J. Thun, E. E. Calle, D. Krewski, K. Ito, and G. D. Thurston, “Lung Cancer, Cardiopulmonary Mortality, and Long-term Exposure to Fine Particulate Air Pollution,” Journal of the American Medical Association, vol. 287, no. 9, p. 1132, 2002. 116 [180] B. Hoffmann, S. Moebus, S. M¨ ohlenkamp, A. Stang, N. Lehmann, N. Dragano, A. Schmermund, M. Memmesheimer, K. Mann, R. Erbel, and K. H. J¨ ockel, “Residential exposure to traffic is associated with coronary atherosclerosis,” Circulation, vol. 116, no. 5, pp. 489–496, 2007. 116 [181] J. A. Araujo, B. Barajas, M. Kleinman, X. Wang, B. J. Bennett, K. W. Gong, M. Navab, J. Harkema, C. Sioutas, A. J. Lusis, and A. E. Nel, “Ambient particulate pollutants in the ultrafine range promote early atherosclerosis and systemic oxidative stress,” Circulation Research, vol. 102, no. 5, pp. 589–596, 2008. 116 [182] G. Oberd¨ orster, J. Ferin, and B. E. Lehnert, “Correlation between particle size, in vivo particle persistence, and lung injury,” Environmental Health Perspectives, vol. 102, no. Suppl. 5, pp. 173–179, 1994. 116 [183] G. Oberd¨ orster, E. Oberd¨ orster, and J. Oberd¨ orster, “Nanotoxicology: An emerging discipline evolving from studies of ultrafine particles,” Environmental Health Perspectives, vol. 113, no. 7, pp. 823–839, 2005. 116 [184] M. Pink, N. Verma, A. W. Rettenmeier, and S. Schmitz-Spanke, “Integrated proteomic and metabolomic analysis to assess the effects of pure and benzo[a]pyrene-loaded carbon black particles on energy metabolism and motility in the human endothelial cell line EA.hy926,” Archives of Toxicology, vol. 88, no. 4, pp. 913–934, 2014. 116, 117 [185] K. Peters, R. E. Unger, C. J. Kirkpatrick, A. M. Gatti, and E. Monari, “Effects of nano-scaled particles on endothelial cell function in vitro: Studies on viability, proliferation and inflammation,” Journal of Materials Science: Materials in Medicine, vol. 15, no. 4, pp. 321–325, 2004. 116 [186] B. Hartmannsberger, The influence of diesel-exhaust carbon black particles on the mechanical properties of lung cells. Master thesis, University of Erlangen-N¨ urnberg, 2016. 117, 118

141

BIBLIOGRAPHY

[187] Z. Wang, A. A. Volinsky, and N. D. Gallant, “Crosslinking Effect on Polydimethylsiloxane Elastic Modulus Measured by Custom-Built Compression Instrument,” Journal of applied polymer science, pp. 41050:1–4, 2014. 117 [188] M. Bhasin, E. L. Reinherz, and P. A. Reche, “Recognition and Classification of Histones Using Support Vector Machine,” Journal of computational biology, vol. 13, no. 1, pp. 102–112, 2006. 119 [189] T. Rønningen, A. Shah, A. R. Oldenburg, K. Vekterud, and E. Delbarre, “Pre-patterning of differentiationdriven nuclear lamin A / C-associated chromatin domains by GlcNAcylated histone H2B,” Genome research, vol. 25, pp. 1825–35, 2015. 119 [190] J. Wu, S. Mu, M. Guo, T. Chen, Z. Zhang, Z. Li, Y. Li, and X. Kang, “Histone H2B gene cloning , with implication for its function during nuclear shaping in the Chinese mitten crab, Eriocheir sinensis,” Gene, vol. 575, no. 2, pp. 276–284, 2016. 119 [191] H. K. Matthews, U. Delabre, J. L. Rohn, J. Guck, P. Kunda, and B. Baum, “Changes in Ect2 localization couple actomyosin-dependent cell shape changes to mitotic progression,” Developmental cell, vol. 23, pp. 371– 383, 2012. 121 [192] J. L. V. Broers, E. a. G. Peeters, H. J. H. Kuijpers, J. Endert, C. V. C. Bouten, C. W. J. Oomens, F. P. T. Baaijens, and F. C. S. Ramaekers, “Decreased mechanical stiffness in LMNA-/- cells is caused by defective nucleo-cytoskeletal integrity: implications for the development of laminopathies,” Human molecular genetics, vol. 13, no. 21, pp. 2567–80, 2004. 121, 122 [193] R. D. Moir, T. P. Spann, H. Herrmann, and R. D. Goldman, “Disruption of nuclear lamin organization blocks the elongation phase of DNA replication,” The Journal of Cell Biology, vol. 149, no. 6, pp. 1179–1191, 2000. 121 [194] G. Bonne, M. R. Di Barletta, S. Varnous, H. M. B´ ecane, E. H. Hammouda, L. Merlini, F. Muntoni, C. R. Greenberg, F. Gary, J. a. Urtizberea, D. Duboc, M. Fardeau, D. Toniolo, and K. Schwartz, “Mutations in the gene encoding lamin A/C cause autosomal dominant Emery-Dreifuss muscular dystrophy,” Nature Genetics, vol. 21, no. 3, pp. 285–288, 1999. 121 [195] D. Fatkin, C. MacRae, T. Sasaki, M. R. Wolff, M. Porcu, M. Frenneaux, J. Atherton, H. J. Vidaillet, S. Spudich, U. de Girolami, J. G. Seidman, and C. E. Seidman, “Missense mutations in the rod domain of the lamin A/C gene as causes of dilated cardiomyopathy and conduction-system disease,” The New England Journal of Medicine, vol. 341, no. 23, pp. 1715–1724, 1999. 121 [196] D. J. Lloyd, R. C. Trembath, and S. Shackleton, “A novel interaction between lamin A and SREBP1: implications for partial lipodystrophy and other laminopathies,” Human molecular genetics, vol. 11, no. 7, pp. 769–777, 2002. 121 [197] P. Preira, V. Grandn´ e, J.-M. Forel, S. Gabriele, M. Camara, and O. Theodoly, “Passive circulating cell sorting by deformability using a microfluidic gradual filter.,” Lab on a Chip, vol. 13, pp. 161–70, 2013. 128

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6

Appendix The following section contains all necessary protocols to build and use a microconstriction setup and measure the mechanical properties of cells. All protocols mentioned in the main text are presented here in detail, including product numbers and manufacturers. Furthermore, the most important programs for image evaluation and quantification of cell mechanical properties are summarized.

6.1

Generation of microfluidic setup

Production of device masters through soft lithography The production took place at the clean room facility of ECAP (Erlangen Center for Astroparticle Physics), University of Erlangen-N¨ urnberg. 1. Bake 3 inch wafer (Si , Si-Mat) at 200◦ C for 30 min on hot plate to evaporate moist. Let cool down for 20 s. 2. For devices higher than 12 µm: Pour 3 ml SU8-2025 (michrochem) in the middle of wafer. SU8 should be at room temperature and bubbles from transport should have dissolved for at least 24 h. Spin coat for 5 s at 500 rpm (acceleration = 300 rpm), then for 30 s at speeds listed in Tab. 6.1. Spin coater: Convac 1001 S. 3. For devices lower than 10 µm: Pour 3 ml SU8-5 (michrochem) in the middle of wafer. SU8 should be at room temperature and bubbles from transport should have dissolved for at least 24 h. Spin coat for 5 s at 500 rpm (acceleration = 300 rpm), then for 30 s at 2000 rpm for a device height of approx. 7 µm (comp. to Tab. 6.1). 4. Bake for 2-5-2 min at 65-95-65◦ C on hot plates. 5. Let the coated wafer sit for at least 24 h. 6. Use diamond cutter and steel block to cut wafer up into nine wafer pieces, each about 2 x 1 cm. 7. Insert chrome mask (produced by Dr. Irina Harder, Max-Planck-Institute for the Science of Light, Erlangen) into mask aligner (MP3, Karl S¨ uss), center layout you 143

6. APPENDIX

want to produce. Chrome-coated side has to face down. Apply fixation vacuum to mask. 8. Insert one wafer piece into mask aligner. Apply vaccuum to wafer piece. Expose to UV light for 60 s. 9. Reposition chrome mask if necessary. Expose other wafer pieces. 10. Bake wafer pieces for 1-3-1 min at 65-95-65◦ C. 11. Develop each wafer piece in SU8 developer (PGMEA, #dev-6000, microresist) in a glass bowl for about 2 min, until devices are freed from unpolymerized photoresist and channel structures are clearly visible. Shake glass bowl carefully all the time. 12. Optional: Hardbake masters for 20 min at 200◦ C to strengthen channel structures. 13. Check outcome carefully under reflected-light microscope. Photoresist SU8-2025 SU8-2025 SU8-2025 SU8-5

Speed [rpm] 3000 4000 5000 2000

Approx. height [µm] ∼ 30 µm ∼ 22 µm ∼ 17 µm ∼ 7 µm

Table 6.1: Dependence of photoresist height on spinning speed.

Production of devices through PDMS molding 1. First mold: Embed silicon wafer pieces in a plastic dish with PDMS (base : crosslinker 7:1, SylGard 184, Dow Corning). Cover to a height of 1.5 cm. Bake for > 8 h at 70◦ C to harden PDMS. Using a razor blade, cut out area above each wafer piece including a 3 mm border region around channel structures. Avoid touching the structures with your blade. 2. Future molds: Cover SU8 structures with freshly prepared PDMS. Use one PDMS preparation for molding up to 8 h if continuously stored in the fridge. Bake for 1 h 45 min at 70◦ C in an oven. Keep baking times identical for all device molds of a measurement series. 3. Cut out devices as explained above. 4. Use biopsy punch (diameter of 0.75 mm, #E69036-07, Harris Uni-Core) to punch holes in inlet and outlet area of each mold under a magnification glass. 5. Use scotch tape to clean the channel features on the PDMS block (3 times). 6. Bond each device to a glass cover slide (18 x 24 mm, thickness No. 1, #631-0130, VWR) with a plasma bonder. Parameters for plasma bonder (Diener Electronics) at Institut f¨ ur Biomedizinische Technik, Prof. Bernhard Hensel, Universität ErlangenN¨ urnberg: • Always start with an empty plasma bonding run to warm up pressure pump.

144

6.1 Generation of microfluidic setup

• After insertion of PDMS blocks and cover slides: Evacuate for 6 min to a pressure of 0.6 mbar. Use valve positions 6-4.2-0 for automated pressure regulation. Do not plasma-treat more than eight devices in parallel. • Plasma-bond at a plasma power of 0.35 (70 W) for 15 s. 7. After pressure renormalization, immediately press PDMS devices and glass slides together for 10 s. 8. Bake bonded devices at 70◦ C overnight.

Production of cell vials 1. Use vials with a screwable lid (0.5 ml, #72.730.406, Sarstedt). 2. Into lids, cut one punch hole for cell tubing (1/32 inch x 0.25 µm/0.10 inch, # IRT-5610-M3, VICI Jour, Macherey-Nagel) with needle (21 g x 5/8 inch; 0.8 x 16 mm, TERUMO) and push same needle into lid next to the hole. 3. Insert tube with a length of approx. 10 cm into punched hole, pushing it in to a length of approx. 2 cm. 4. Glue needle and tubing into holes with a two-component epoxy glue (for example UHU plus ENDFEST). 5. Equip glued needle with threaded tubing adapter (#554-1799, VWR) to connect to silicone soft tubing with pressure pump.

Setup preparation 1. Prior to measurements, glue device on additional thick glass slide (microscope slides with cut edges, #631-1550, VWR) with scotch tape. 2. Glue glass slide with device to microscope stage of a bright-field microscope (here Leica DM-IL) with scotch tape to protect against drifting. 3. Flush cell tubing with PBS (#10010023, gibco) at least three times at a high pressure using a syringe (1 ml, luer-lok tip, #309628, BD), equipped with a threaded syringe adapter (#554-1785, VWR). 4. Screw custom-made cell tubing with lid onto cell vials. Place cell vials stably next to device, so that no shear stress is applied on the device during measurements. In this thesis, a custom 3-dimensionally printed holder was used. 5. Connect cell vials to pressure pump (Bellofram Type 10 LR 1/4 inch, pressure range 0.05-1.75 bar, Special Instruments) via silicone soft tubing (inner diameter = 5 mm, outer diameter = 10 mm, #228-0716, VWR). 6. Insert tubes from cell vials into measurement device through punch holes. Before pushing the tubes in, wet the tubes with PBS to decrease friction. 7. Fill custom-made cell vials with 1 % pluronic (F-127, BASF, #P2443, Sigma-Aldrich) dissolved in PBS.

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8. Flush device first slowly, then at 200 mbar, with pluronic solution to eliminate remaining air bubbles and to passivate channel walls. Flush for a fixed amount of time, at least 30 min, before beginning the measurement. 9. Choose 10x magnification. 10. Place region of interest (about 520 x 90 px) of employed camera in front of the constrictions, so that the feeding channel and half of the constriction channel of all of the eight constrictions is covered.

6.2

Measurement process

1. Fill cell suspension into custom-made cell vials. 2. Flush cells into device at high pressure (200 mbar) until they reach the constrictions (approx. 1-5 min, depending on device design). 3. Reduce pressure immediately to a value between 5-90 mbar, where at least 80 % of all cells pass the constrictions on time scales below 2 s. 4. Record at least 25 videos (30 min) of cell transits with high-speed video camera (here G680, Allied Vision). Reverse the flow and flush backwards after approx. 1 min of recording to free constrictions from stuck cells or debris. In the end, you should record the transits about 5000 cells per measurement.

6.3

Cell culture

Cell freezing 1. Use fully confluent cell monolayer of a 75 cm2 -flask to freeze 4-6 cryo tubes of cell suspension. 2. Trypsinize cells as usual for 4 min (trypsin-EDTA, 0.25 %, #T3924, Sigma-Aldrich) and resuspend them in appropriate amount of usual cell medium. 3. For suspension cells: Use them right from the flask and densify them by centrifugation (1400 rpm for 4 min, 405 × g). Also resuspend in cell medium. 4. Add 10 % DMSO (dimethyl sulfoxide, #D12345, Sigma-Aldrich) to resuspended cells and fill cells into cryo tubes immediately (1 ml per tube). 5. Place cryo tubes in cryobox and the box into -80◦ C freezer immediately. 6. After 24 h, store cryo tubes in nitrogen tank.

Cell thawing 1. Thaw cryo tube in water bath for a few minutes. 2. Add tube content to 10 ml suitable cell medium. 3. Centrifuge for 4 min at 1400 rpm (405 × g) to wash cells from DMSO.

146

6.3 Cell culture

4. Resuspend cells from cryo tube in 7 ml new medium and add them to freshly prepared cell culture flask. Use 25 cm2 -flask to assure high cell density during cell recovery.

Splitting procedure Cells were split on Mondays, Wednesdays, and Fridays, three times per week. Split density was adapted to cell growth and cell density required for experiments. Suspension cells: K562 1. Heat up cell medium to 37◦ C. 2. Place 10 ml IMDM (Iscove’s modified Eagle’s medium, #12440053, gibco) including 10 % FCS (fetal calf serum, #16000036, gibco) and 1 % Penicillin-Streptomycin-Glutamine (PSG, #10378016, gibco) in new cell flask. 3. Add 0.5-5 ml of old cell suspension to new flask, depending on density you wish to achieve. Mix and flush old flask thoroughly before taking out the cells. Adherent cells: DLD-1 1. Heat up all used fluids to 37◦ C, except for trypsin-EDTA. 2. Suck off old medium. 3. Wash adherent cells with PBS (phosphate-buffered saline, #10010023, gibco). 4. Add 2 ml trypsin-EDTA (0.25 %, #T3924, Sigma-Aldrich) and cover cells with shaking movements for about 20 s. Remove trypsin and put cell flask into incubator for about 4 min (depending on adhesion strength of cell line). 5. Prepare 20 ml fresh cell medium (RPMI, Roswell Park Memorial Institute medium, #11875093, gibco), including 10 % FCS, 1 % PSG and 1 % G418 (#11811098, gibco). Add 10 ml to new cell flask. 6. Wash cells off of old flask with remaining 10 ml medium and add 0.5-3 ml of cell suspension to fresh flask, depending on density you want to achieve.

Cell preparation for measurements 1. For adherent cells: Trypsinize as usually. Lift them off with 7-10 ml cell medium. 2. For suspension cells: Use right from flask. 3. Centrifuge at 1400 rpm for 4 min (405 × g). 4. Resuspend with 0.5-1 ml PBS to achieve cell density of 5·106 cells/ml. Optional: Use cell strainer (20 µm pore size, #43-50020-03, pluriselect) to remove cell agglomerates. 5. Add pluronic to a final concentration of 1 wt%.

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6. APPENDIX

6.4

Software

In the following, the most important programs for the evaluation of cell mechanical properties from microconstriction measurements are summarized. All programs can be found at Bitbucket, in the account of the Lehrstuhl f¨ ur Biophysik, University of Erlangen-N¨ urnberg. The programming software was Matlab. The superstructure of the programs is given in Fig. 6.1.

ROI generation

Calculation of STDs Time stamps Videos

Calculation of tentry, rcell and vcell (fluorescence intensity) Parameters Calculation of deformation εmax and mean pressure drop ∆p

Histogram matching + power-law fitting

Cell mechanical properties stiffness E and fluidity β

Figure 6.1: Structure of programs for evaluation of cell mechanical properties from bright-field videos.

For the evaluation of cell mechanical properties, each measurement requires a “parameters.txt”-file, which contains all necessary parameters. This file lists, for example, the number of channels which are evaluated, the pixel size, thresholds for image segmentation, and the device geometry for the calculation of pressure drop.

ROI-generation For the evaluation of all measurement parameters, the position of the channels within the field of view has to be known. Therefore, the constriction entries are located by the user through an interface. For a series of 30 videos, the ROIs should be set in every 5th-6th video to compensate for slow drifting of the measurement setup, or sooner if an obvious 148

6.4 Software

change in channel position takes place.

Calculation of standard deviations of ROIs In the next step, the standard deviations of all regions of interest are calculated. This step is time-consuming, as each individual image must be read from the hard drive (approx. 70,000 per video). It was therefore separated from all subsequent evaluation steps.

Evaluation: Entry time, cell size and cell speed Through thresholding of the standard deviation signals of all ROIs, cell entry times into constrictions are determined. Next, cell size is detected in each image prior to cell entry through image segmentation. Moreover, cell speed is detected in the two images prior to entry by tracking the center of mass of the cells in the images. In the case of fluorescence evaluation, for each cell, the pixel intensities of a region of interest in the corresponding fluorescence image are background-subtracted and summed up.

Evaluation of stress and strain Up to now, all evaluations were independent from external parameters like pixel size, the geometry of the employed device, or the definition of cell strain. Now, the measurement values of entry time, cell size and cell speed are transformed into values for deformation time, stress and strain, which partially carry SI-units. All external parameters are gained from the files “parameters.txt”. The cell strain is computed from cell size and the size of the constriction. From cell speed, flow speed is calculated and transformed into the pressure drop over each constriction through Hagen-Poiseuille’s law and Kirchhoff’s current law, considering the geometry of the whole microfluidic network.

Histogram matching, bootstrapping and orthogonal least squares fitting To extract quantitative mechanical properties, a power-law is fitted to the double-logarithmically transformed scatter cloud of tentry vs. ǫmax /∆p, yielding the two fit parameters elastic modulus (= stiffness) E and the power-law exponent β (= fluidity). This is achieved by minimizing the orthogonal error between data and fit function through an orthogonal least squares algorithm. To avoid a measurement bias due to stress or strain stiffening during comparison, the power-law is only fitted to subpopulations from two or more cell populations, which have experienced both the same stress and the same strain. This fitting routine, combined with histogram matching, is repeated 100 times, and mean values of the fit parameters and standard errors are calculated from bootstrapping.

149

6. APPENDIX

150

List of abbreviations acry

acrylamide

AFM

Atomic Force Microscopy

App.

Appendix

ATCC

American Type Culture Collection

ATP

Adenosine TriPhosphate

AZA

5-AZA-2’-deoxycytidine

CCD

Charge-Coupled Device

cfg

configuration

Chap.

Chapter

CB

Carbon Black

CPU

Central Processing Unit

cyto D

cytochalasin D

DMEM

Dulbecco’s Modified Eagle’s Medium

DMSO

DiMethyl SulfOxide

DNA

DeoxyriboNucleic Acid

ECM

ExtraCellular Matrix

EMT

Epithelial-to-Mesenchymal-Transition

EDTA

EthyleneDiamineTetraacetic Acid

Eq.

Equation

FAK

Focal Adhesion Kinase

FBS

Fetal Bovine Serum

FCS

Fetal Calf Serum

Fig.

Figure

FITC

Fluorescein IsoThioCyanate

fMLP

N-formylMethionine-Leucyl-Phenylalanine

ga

glutaraldehyde

GBP

Guanylate-Binding-Protein

GFP

Green Fluorescent Protein

GUI

Graphical User Interface

HEPES

4-(2-HydroxyEthyl)-1-PiperazineEthaneSulfonic acid

IFN

InterFeroN

151

6. APPENDIX

IPC

InterProcess Communication

LINC

LInker of Nucleoskeleton and Cytoskeleton

mgca

magnesium-calcium-ions (Mg2+ Ca2+ -ions)

noc

nocodazole

pax

paclitaxel

PBS

Phosphate-Buffered Saline

PDMS

PolyDiMethylSiloxane

PEEK

PolyEther-Ether-Ketone

PEG

PolyEthylene Glycol

PGMEA

Propylene Glycol Monomethyl Ether Acetate

PSG

Penicillin-Streptomycin-Glutamin

P/S

Penicillin-Streptomycin

RBC

Red Blood Cell

RGD

arginine-glycine-aspartate

RIPA

Radio-ImmunoPrecipitation Assay

ROI

Region Of Interest

sd

standard deviation

se

standard error

Sec.

Section

SGR

Soft Glassy Rheology

STED

Stimulated Emission Depletion (microscopy)

Tab.

Table

UV

UltraViolet (light)

152

List of figures 1.1

Measurement techniques for cell mechanical properties . . . . . . . . . . . .

4

2.1

Device layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2

Soft lithography process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3

Confocal measurement of device geometry . . . . . . . . . . . . . . . . . . . 18

2.4

Stability of microconstriction geometry during pressure application . . . . . 20

2.5

Microconstriction setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.6

Video recording software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.7

Types of mechanical deformations . . . . . . . . . . . . . . . . . . . . . . . 25

2.8

Continuum mechanical material description of cells . . . . . . . . . . . . . . 26

2.9

Overview over measurement evaluation . . . . . . . . . . . . . . . . . . . . . 30

2.10 Calculation of entry time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.11 Calculation of flow speed from cell speed . . . . . . . . . . . . . . . . . . . . 33 2.12 Resistances and nodes of constriction region . . . . . . . . . . . . . . . . . . 35 2.13 Dependence of pressure drop on clogging configuration . . . . . . . . . . . . 36 2.14 Errors from mean pressure approximation . . . . . . . . . . . . . . . . . . . 38 2.15 Definition of cell strain as maximum cell compression . . . . . . . . . . . . . 40 2.16 Optical path of fluorescence extension in microconstriction setup . . . . . . 43 2.17 Wavelengths of fluorescence extension . . . . . . . . . . . . . . . . . . . . . 44 2.18 GUI for synchronized image recording . . . . . . . . . . . . . . . . . . . . . 45 3.1

Bleb formation during cell deformation into a microconstriction . . . . . . . 50

3.2

Cell viability and proliferation after microconstriction measurements . . . . 52

3.3

Microconstriction layout for temporal development of cell shape . . . . . . . 53

3.4

Development of cell strain over time during cell entry into a constriction . . 54

3.5

Power-law dependence of population scatters . . . . . . . . . . . . . . . . . 55

3.6

Stress and strain stiffening . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.7

Principle of 2-dimensional histogram matching . . . . . . . . . . . . . . . . 59

3.8

Application of 2-dimensional histogram matching . . . . . . . . . . . . . . . 60

3.9

Cell shape analysis during transit through a microconstriction . . . . . . . . 62

3.10 Applicability of area expansion moduli as strain measures . . . . . . . . . . 65 3.11 Dependence of stretch strain measures on cell size

. . . . . . . . . . . . . . 66

3.12 Compressive strain measure according to Cauchy . . . . . . . . . . . . . . . 67 3.13 Systematic error of cell mechanical properties . . . . . . . . . . . . . . . . . 70 3.14 Sketch of cytoskeletal components . . . . . . . . . . . . . . . . . . . . . . . 73 3.15 Influence of pharmacological treatments on cell size and viability . . . . . . 75 3.16 Sensitivity of microconstriction measurements to changes in cell cytoskeleton and nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

153

LIST OF FIGURES

3.17 Soft glassy rheology of pharmacologically treated K562 leukemia cells

. . . 78

3.18 Influence of measurement parameters and cell culture conditions on resulting cell stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.19 Influence of measurement parameters and cell culture conditions on resulting power-law exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.20 Correlation of cell mechanics with expression of fluorescently tagged proteins 87 3.21 Influence of high-power laser illumination on cell mechanics . . . . . . . . . 88 4.1

Mechanical properties of four cancer cell lines . . . . . . . . . . . . . . . . . 93

4.2

Correlation of cell stiffness with cell invasiveness . . . . . . . . . . . . . . . 94

4.3

Influence of Hoechst-staining on mechanical properties of K562 cells . . . . 96

4.4

Influence of cell contractility on mechanical properties of DLD-1 cells . . . . 98

4.5

Sketch of integrin location and activation . . . . . . . . . . . . . . . . . . . 100

4.6

Influence of αvβ3 on mechanical properties of M21 and K562 cells . . . . . 102

4.7

Influence of αvβ3 on morphology of M21 and K562 cells . . . . . . . . . . . 103

4.8

Influence of αIIbβ3 on mechanical properties of M21 cells . . . . . . . . . . 104

4.9

Influence of p21 on bulk mechanical properties of HCT116 cells . . . . . . . 107

4.10 Influence of p21 on nuclear mechanical properties of HCT116 cells . . . . . 109 4.11 Influence of GBP-1 on mechanical properties of DLD-1 cells . . . . . . . . . 111 4.12 Influence of GBP-1 mutations on mechanical properties of HeLa cells . . . . 112 4.13 Influence of GBP-1 activation on mechanical properties of HeLa cells . . . . 114 4.14 Influence of CB exposure on vulnerability of BEAS-2b cells . . . . . . . . . 117 4.15 Influence of CB exposure on mechanical properties of BEAS-2b cells . . . . 118 4.16 Influence of histone 2B on mechanical properties of HT1080 cells . . . . . . 120 4.17 Sketch of nucleus and nuclear lamina . . . . . . . . . . . . . . . . . . . . . . 122 4.18 Influence of lamin A on mechanical properties of K562 cells . . . . . . . . . 123 6.1

154

Program structure for evaluation of cell mechanical properties . . . . . . . . 148

List of publications J. R. Lange, C. Metzner, S. Richter, W. Schneider, M. Spermann, T. Kolb, G. Whyte, and B. Fabry, “Unbiased high-precision cell mechanical measurements with microconstrictions,” Biophysical Journal, vol. 112, no. 7, pp. 1472-1480, 2017. J. R. Lange, J. L. Alonso, and W. H. Goldmann, “Influence of avb3 integrin on the mechanical properties and the morphology of M21 and K562 cells,” Biochemical and biophysical research communications, vol. 478, pp. 1280-1285, 2016. T. F. Bartsch, M. D. Kochanczyk, E. N. Lissek, J. R. Lange, and E.-L. Florin, “Nanoscopic imaging of thick, heterogeneous soft-matter structures in aqueous solution,” Nature Communications, vol. 7:12729, 2016. L. A. Lautscham, C. K¨ ammerer, J. R. Lange, T. Kolb, C. Mark, A. Schilling, P. L. Strissel, R. Strick, C. Gluth, A. C. Rowat, C. Metzner, and B. Fabry, “Migration in confined 3D environments is determined by a combination of adhesiveness, nuclear volume, contractility, and cell stiffness,” Biophysical Journal, vol. 109, no. 5, pp. 900-913, 2015. J. R. Lange, J. Steinwachs, T. Kolb, L. A. Lautscham, I. Harder, G. Whyte, and B. Fabry, “Microconstriction arrays for high-throughput quantitative measurements of cell mechanical properties,” Biophysical Journal, vol. 109, no. 1, pp. 26-34, 2015. N. Lang, S. M¨ unster, C. Metzner, P. Krauss, J. R. Lange, S. Sch¨ urmann, K. E. Aifantis, O. Friedrich, and B. Fabry, “Estimating the 3D pore size distribution of biopolymer networks from directionally biased data,” Biophysical Journal, vol. 105, no. 9, 1967-1975, 2013. J. R. Lange, V. Auernheimer, P. L. Strissel, and W. H. Goldmann, “Influence of focal adhesion kinase on the mechanical behavior of cell populations,” Biochemical and biophysical research communications, vol. 436, pp. 246-251, 2013. J. R. Lange, and B. Fabry, “Cell and tissue mechanics in cell migration,” Experimental Cell Research, vol. 319, pp. 2418-2423, 2013. P. Krauss, C. Metzner, J. R. Lange, N. Lang, and B. Fabry, “Parameter-free binarization and skeletonization of fiber networks from confocal image stacks,” PLoS ONE vol. 7: e36575, 2012.

155

Acknowledgements

First of all, I would like to thank my supervisor Prof. Ben Fabry for giving me the opportunity to investigate cell mechanics in his lab. During my bachelor thesis, my master thesis and my PhD, he patiently taught me accuracy, endurance, and optimism. He always tried to make me enjoy research, and at the same time deepen my knowledge and understanding about cell biology and cell physics. I am also grateful for his financial support during productive and informative conferences. I would also like to thank Prof. Wolfgang Goldmann, Dr. Ingo Thievessen and PD Dr. Claus Metzner for their continuous and cordial support and help, either with investigating new biological questions and publishing, or solving programming and physical problems. Moreover, I thank Prof. Graeme Whyte and Dr. Thorsten Kolb for introducing me to microfluidics and soft lithography, and for enthusing me to start the microconstriction project. My office mates Dr. Julian Steinwachs, Dr. Vera Flad and Dr. Lena Lautscham helped me with starting my thesis, taught me countless Matlab lessons, and helped me with cell culture and Adobe Illustrator. We also enjoyed adventurous hikes and special dinners in San Francisco and Obergurgl. With my colleagues and friends Marina Spörrer, Richard Gerum, Christoph Mark, and Sebastian Richter, I spent wonderful work days and barbecues, discussing science and life. Richard and Christoph always supported me with programming and physics challenges. Sebastian programmed fast and easy-tohandle image recording software. Special thanks go to Richard for holding his famous cellar parties and guiding us through the streets of Barcelona, and to Marina and Christoph for surviving the Los Angeles trip with me. Moreover, I thank Alexander Winterl, Delf Kah, Andrea Thomaß, Nina Bauer, Julia Kraxner, and all other bachelor and master students for happy hours during lunch breaks, and much fun in the office. A big thank you goes to Werner Schneider, which whom I spent hours adjusting optical tables, and who always fixed technical problems with me, Astrid Mainka, who reliably managed cell culture and provisions, and Heike Mertin, who helped efficiently with administrative issues.

Furthermore, I thank Isabel Gäßner and Dr. Irina Harder for introducing me to the Erlangen clean room and ceaselessly producing chrome masks for me. Moreover, I’d like to thank Reiner Stadter for showing me how to use µ-surf. Also, thanks go to Prof. Bernhard Hensel and Dr. Alexander Rzany for support with plasma bonding. Many thanks go to my friends, especially Alexander Stuhl, Eva Zolnhofer and Carola Weber, who never stopped listening to my dreams and worries, and who all helped me finishing my thesis with their unique support and care. Lastly, I would like to thank Thorsten Brand and his family, and especially my parents, who encouraged and supported me throughout my physics studies and my thesis and always made me believe in my capabilities.