Journal of Biomechanics 47 (2014) 2598–2605
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Dissecting the contribution of actin and vimentin intermediate filaments to mechanical phenotype of suspended cells using high-throughput deformability measurements and computational modeling Evgeny Gladilin a,n, Paula Gonzalez a, Roland Eils a,b a b
German Cancer Research Center, Division of Theoretical Bioinformatics, Im Neuenheimer Feld 580, 69120 Heidelberg, Germany University Heidelberg, BioQuant and IPMB, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany
art ic l e i nf o
a b s t r a c t
Article history: Accepted 28 May 2014
Mechanical cell properties play an important role in many basic biological functions, including motility, adhesion, proliferation and differentiation. There is a growing body of evidence that the mechanical cell phenotype can be used for detection and, possibly, treatment of various diseases, including cancer. Understanding of pathological mechanisms requires investigation of the relationship between constitutive properties and major structural components of cells, i.e., the nucleus and cytoskeleton. While the contribution of actin und microtubules to cellular rheology has been extensively studied in the past, the role of intermediate filaments has been scarcely investigated up to now. Here, for the first time we compare the effects of drug-induced disruption of actin and vimentin intermediate filaments on mechanical properties of suspended NK cells using high-throughput deformability measurements and computational modeling. Although, molecular mechanisms of actin and vimentin disruption by the applied cytoskeletal drugs, Cytochalasin-D and Withaferin-A, are different, cell softening in both cases can be attributed to reduction of the effective density and stiffness of filament networks. Our experimental data suggest that actin and vimentin deficient cells exhibit, in average, 41% and 20% higher deformability in comparison to untreated control. 3D Finite Element simulation is performed to quantify the contribution of cortical actin and perinuclear vimentin to mechanical phenotype of the whole cell. Our simulation provides quantitative estimates for decreased filament stiffness in drugtreated cells and predicts more than two-fold increase of the strain magnitude in the perinuclear vimentin layer of actin deficient cells relatively to untreated control. Thus, the mechanical function of vimentin becomes particularly essential in motile and proliferating cells that have to dynamically remodel the cortical actin network. These insights add functional cues to frequently observed overexpression of vimentin in diverse types of cancer and underline the role of vimentin targeting drugs, such as Withaferin-A, as a potent cancerostatic supplement. & 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
Keywords: Mechanical cell properties Actin filaments (AF) Vimentin intermediate filaments (VIF) Cytoskeletal drugs Cytochalasin-D Withaferin-A High-throughput measurements Microfluidic optical stretcher (MOS) Finite Element Method (FEM) Parameter estimation Cancer Epithelial–mesenchymal transition (EMT)
1. Introduction
1.1. Overview of cytoskeletal filaments
The structural and molecular organization of cells is highly dynamic and undergoes permanent adaptive changes as a result of integration of environmental signals and evolutionary conserved molecular-genetic clues. To dissect the contribution of one particular molecular component to the constitutive phenotype of the whole cell, a number of biological and technical factors have to be considered. Below, we give an overview over the key aspects that played a role by motivation, design and implementation of the present study.
Three major groups of cytoskeletal filaments, i.e., actin filaments (AF), microtubules (MT) and intermediate filaments (IF), are known to maintain mechanical cellular integrity. Besides differences in molecular structure and function, each group of cytoskeletal filaments has its particular intracellular location, topological organization and material properties. In non-adherent cell lines, AF build a cortical layer beneath the cell membrane which serves as major mechanical barrier between the cellular exterior and interior (Alberts et al., 2007). In adherent cells, AF together with myosin and interlinking proteins form a dynamic scaffold providing the cell with mechanical stability and flexibility on variable substrates (Stamenovic and Ingber, 2002). Intermediate
n
Corresponding author. Tel.: þ 49 6221 54 51299; fax: þ 49 6221 54 51488. E-mail address:
[email protected] (E. Gladilin).
http://dx.doi.org/10.1016/j.jbiomech.2014.05.020 0021-9290/& 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
E. Gladilin et al. / Journal of Biomechanics 47 (2014) 2598–2605
filaments represent a large group of polymers with 9–11 nm in diameter which lays between 7 nm of AF and 25 nm of MT. In this study, we focus on vimentin intermediate filaments (VIF) that belong to the type III out of six different IF families. VIF are known to assemble a protective network of fibers around the chromatinbearing cell nucleus (Aubin et al., 1980) and also serve a substrate for a number of cancer-relevant kinases (Satelli and Li, 2011). Upregulation of vimentin is observed in cells undergoing epithelial–mesenchymal transition (Lee et al., 2006) in a wide range of cancer types and seems to correlate with tumor aggressiveness and poor prognosis (Yamashita et al., 2013). Furthermore, all three groups of cytoskeletal filaments can form tight interconnections, especially, in adherent, motile and mechanosensitive cells (Fuchs and Karakesisoglou, 2001). 1.2. Mechanical properties of cytoskeletal filaments Rheological measurements of actin, tubulin and vimentin polymers indicate that AF and VIF have the largest contribution to the cellular stiffness at low and high strain rates, respectively (Janmey et al., 1991). AF have the highest stiffness among all cytoskeletal filaments and determine the elastic cell response at the relatively low strain rates of up to 20%. In contrast, VIF begin to stiffen at significantly higher strain rates and continue to exhibit intact elastic response even under surprisingly high deformation rates of more than 50%. The remarkable vimentin elasticity is ascribed to the multi-scale hierarchical structure of VIF which enables a cascaded activation of different deformation mechanisms over several orders of spatial magnitude (Qin et al., 2009) as well as to the effective density (Bertaud et al., 2010) and the mesh size (Köster et al., 2010) of the VIF network. The contribution of cytoskeletal filaments to mechanical properties of living cells is typically studied using drugs (Cooper, 1987; Yamada et al., 2000). While a number of selective AF- and MT-drugs is known, the choice of a suitable drug for selective inhibition of intermediate filaments is much more limited. In previous works, VIF disruption was induced by acrylamide (Eckes et al., 1998; Haudenschild et al., 2011) which is known to show multiple cytotoxic effects (Aggeler and Seely, 1990; Arocena; 2006). More recently, the vimentin disrupting effect of the ayuverdic medicine constituent, Withaferin-A (WfA), is reported by several authors on the basis of microscopic imaging or western blots (Thaiparambil et al., 2011; Grin et al., 2012). WfA treatment leads to dose-dependent reduction of soluble vimentin forms as well as inhibition of several VIFrelated pathways (Bargagna-Mohan et al., 2013). However, detailed molecular mechanism of VIF disruption by WfA is not yet well understood. To our knowledge, effects of WfA on mechanical cell properties have not been investigated up to now.
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non-adherent cells. While combination of adhesive and gravitational forces promotes formation of complex cytoskeletal structures in adherent cells, topology of cytoskeleton in suspended cells reflects the intrinsic spherical symmetry of liquid environment with different groups of filaments forming shell-like layers around the nucleus (Zhelev et al., 2001). From this perspective, nonadherent cells represent a more suitable system for studying the relationship between material properties the whole cell and a particular group of cytoskeletal filaments. 1.5. Computational modeling of cell mechanics Experimental techniques for probing of cellular mechanics typically enable measurement of the whole cell properties (i.e. cell stiffness). In order to dissect the contribution of subcellular structures to mechanical phenotype of the whole cell, an appropriate computational model of constitutive and structural cell organization is required. Depending on the scale and the goal of the problem, molecular-, filament- or continuum-based models are employed to study mechanics of the whole cell or subcellular components. Because of the general complexity and heterogeneity of structural cell organization, consistent meso–macro transitions are usually applied to simplified problems, such as 3D simulation of mono-component network (Kim et al., 2009) or low-dimensional modeling of cellular geometry (Bertaud et al., 2010). In contrast, continuum models allow an efficient representation of 3D cell shape and subcellular structures, but require a simplified description of the constitutive relationships (Milner et al., 2012; Pachenari et al., 2014). In this work, we apply our previously developed numerical framework for estimation of constitutive parameters of subcellular structures by fitting a multi-component continuum model of 3D cell mechanics to experimental image data using the Finite Element Method (Gladilin et al., 2007; González et al., 2011). 1.6. Summary Summarizing the above, here we focus on comparative investigation of the contribution of actin and vimentin intermediate filaments to mechanical properties of suspended, non-adherent Natural Killer (NK) cells. For selective disruption of AF and VIF, cytoskeletal drugs, Cytochalasin-D (CcD) and Withaferin-A (WfA), are used. High-throughput population measurements of drugtreated cells vs. untreated control are performed using microfluidic optical stretcher (MOS). Subsequent statistical analysis and 3D Finite Element simulation is performed to gain quantitative insights into subcellular mechanisms of cell softening induced by deficiency of cortical AF and perinuclear VIF layers.
1.3. Single cell vs. high-throughput population measurements 2. Material and methods
Population measurements of rheological cell properties indicate a high degree of cell-to-cell variability (Cai et al., 2013) suggesting that measurement of a low number of cells may not be sufficient for statistically consistent characterization on the population phenotype. Most conventional techniques such as micropipetting, microplate stretching or atomic force microscopy are conceptualized for single cell probing and have a limited throughput capabilities. In this study, we rely on high-throughput microfluidic optical stretching (Guck et al., 2001) which allows probing of up to 150 cells per hour. 1.4. Cytoskeleton organization in adherent vs. non-adherent cells Topological and physical boundary conditions have a determining influence on organization of cytoskeleton in adherent and
2.1. Cell preparation and drug treatment NK-92-C1 cells are kindly provided by Prof. Carsten Watzl (University Darmstadt, Germany) and cultured in Alpha medium supplemented with 12.5% FCS, 12.5% horse serum, 1% L-glutamine and 1% Penicillin/Streptomycin. For cytoskeleton disruption experiments, cells are incubated with 4 mM Withaferin-A in DMSO for 3 h or 1 mM Cytochalasin-D for half an hour prior to the measurement of cellular compliance using an optical stretcher. DMSO treatment is used as control. For measurements with MOS, 10E þ5 cells are transferred into 2 ml cryotubes (Neo Screw-Micro Tube 2 ml, Neolab, Heidelberg, Germany). 2.2. Cell staining and fluorescence imaging For microscopic screening of cytoskeletal filaments, cells are fixed, permeabilized, incubated with primary anti-vimentin antibody (kindly provided by Prof. Harald Herrmann, DKFZ Heidelberg, Germany) and finally stained with Alexa-
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Fluor-488 conjugated secondary antibody, Rhodamine-Phalloidin and Hoechst (both purchased from Sigma-Aldrich, St. Louis, USA). Fixes and stained cells are kept in PBS for microscopy evaluation. All images are acquired at room temperature with a Leica SP5 laser scanning confocal microscope with a 63 objective and the LAS software (Leica, Wetzlar, Germany). XYZ image acquisition in sequential scan mode is used to avoid spectral bleed-through between fluorophores. Contrast enhanced maximal intensity projections for the different image channels are generated and subsequently analyzed with ImageJ v1.44 (National Institute of Health, Bethesda, USA).
2.3. High-throughput deformability measurement using MOS Measurements of cellular deformability are performed using the microfluidic optical stretcher (MOS) system provided from the Lab of Prof. Josef Kaes (University Leipzig, Germany). For a detailed description of MOS we refer to Guck et al. (2001). In brief, the MOS is based on exposing cells to two opposing rays of infrared laser light (wavelength¼ 1060 nm) which generates stretching forces on the boundaries between optically different media. As a result, the cell is continuously stretched along the laser axis. The successive deformation of the cell is captured in time series of 2D phase contrast images for subsequent computational image analysis. The magnitude of the relative cell stretching in MOS is essentially determined by the laser power which is typically chosen in the range of 400–1000 mW. To avoid cellular overheating and phototoxicity (Wetzel et al., 2011), a moderate laser power of 800 mW is used in our experiments to induce sudden cell deformation. Every cell is monitored 1 s before and after the 2 s rectangle laser pulse which results in a sequence of totally 120 images. For every time step t¼ 0–119 of the image sequence, the outer cell contour is segmented and the diameter of the largest cell axis d(t) is determined. On the basis of smoothed time series ds(t), the relative stretch of the cell εðtÞ is computed
εðtÞ ¼ ds ðtÞ=d0 1;
ð1Þ
where d0 denotes the diameter of the largest axis of unloaded cells.
2.4. Statistical analysis of cellular deformability measurements Measurement of the relative stretch in N cells results in a statistical distribution
εi ¼ 1…N ðtÞ. Since cell-to-cell variability in population measurements of cellular deformability is relatively high and the exact type of statistical distribution is unknown, the parameter-free bootstrap approach is applied for computation of the empirical distribution of sample means and corresponding confident intervals (Efron and Tibshirani, 1993).
2.5. Cell shape analysis To assess statistical changes in patterns of cellular deformation due to disruption of AF/VIF layers, average shape models are generated from 2D cell contours. First, the contour of each cell is normalized by rescaling the bounding box of the undeformed cell to the square and translating the mass center to (0,0). Then, contours are uniformly resampled in canonic polar coordinates rðφÞ with 360 sampling points which correspond to 11-stepping of the polar angle φ ¼1–3601. Finally, the average cell shape is computed by constructing the mean of N normalized contours r avg ðφÞ ¼
∑ r i ðφÞ=N:
i ¼ 1…N
ð2Þ
2.6. Constitutive cell modeling and parameter estimation In this study, our focus is on analysis of mechanical cell response during the force-driven creep phase, i.e., time steps t¼ 30–89. In the first approximation, the experimental stretch curves (Eq. (1)) can be fit by the viscoelastic Kelvin–Voigt model
εðtÞ ¼ ε0 ð1 e t=τ Þ;
ð3Þ
where ε0 ¼ FðkL0 Þ 1 is the pure elastic stretch of a 1D Hookean spring with the initial length L0 and the stiffness k due to application of the force F, and τ is the characteristic delay (retardation time) of viscoelastic material response to sudden stress. To account for three-dimensional structure of AF/VIF layers and the whole cell, the elastic component of cellular deformation is described by the generalized Hook's law (Ciarlet, 1988)
s ¼ CðE; νÞε;
ð4Þ
where s denotes the Cauchy stress tensor, ε is the Green–St. Venant strain tensor and CðE; νÞ is the tensor of elastic constants which in the case of a piecewise homogeneous material contains only two independent constants, i.e., Young's modulus (E) and Poisson's ratio (ν). The forces that arise on the cellular boundaries and trigger the cellular deformation in MOS are approximated by a simplified stress
profile suggested in Guck et al. (2001)
sr ¼ s0 cos 2 ðϑÞ;
ð5Þ
where s0 denotes the maximum stress along the main stretching axis and ϑ is the canonical polar angle. The unknown parameter s0 is estimated iteratively by fitting the simulated cell stretch to the experimentally observed magnitude of the relative cellular elongation. Poisson's ratio of the cell is set to ν ¼ 0:49. In accordance with the literature (Guilak et al., 2000), the relative stiffness (RS) of the nucleus is set five times higher in comparison to the remaining cytoplasm. To quantify changes of the relative stiffness of cortical AF and perinuclear VIF layers due to application of cytoskeletal drugs, simulation of the cellular deformation is performed iteratively for the range of successfully reduced stiffness values 0 o α o 1 8 5:1:1 > < RS of the nucleus : VIF : AF ðuntreated cellsÞ : RS of the nucleus : VIF : AF ðCcD treated cellsÞ : 5 : 1 : αAF ; 0 o αAF o 1 > : RS of the nucleus : VIF : AF ðWfA treated cellsÞ : 5 : α 0 o αVIF o 1: VIF : 1; ð6Þ The sought value of the relative stiffness is determined from the best fit between the experimentally observed and simulated cellular deformation. For the detailed description of the FEM-based parameter estimation scheme, we refer to our previous publications (Gladilin et al., 2007).
3. Results 3.1. Microscopic evaluation of cytoskeletal drug effects In control conditions, NK cells are characterized by a large nucleus which takes almost half of the cell volume. The cytoplasmic layer around the nucleus forms a cage of intertwined VIF. A rim of cortical AF can be observed at the cell edge (Fig. 1A, upper panel). CcD treatment leads to visible dissolution of cortical AF while perinuclear VIF stay widely unaffected (Fig. 1A, lower panel). Upon treatment with WfA, the VIF network is disrupted forming differently shaped aggregates while the layer of cortical AF still remains visible (Fig. 1A, middle panel). Notably, a similar nucleation of VIF has been observed by treatment of cells with body's own chemokines (Brown et al., 2001; Qi et al., 2006) which indicates that WfA effects may originate from natural mechanisms of VIF reorganization. The degree of filament disruption in comparison to controls is quantified by measuring the decrease of AF intensity in CcD treated cells (Fig. 1B) and the accumulation of VIF aggregates in WfA treated cells (Fig. 1C). Our image analysis suggests that CcD and WfA induce selective disruption of AF and VIF in NK cells without statistically significant crosseffects. 3.2. Statistical analysis of deformability measurements Deformability measurement of NK cells is performed using the microfluidic optical stretcher as described above for totally 420 untreated control, 371 CcD- and 477 WfA-treated cells. To obtain a statistically significant fingerprint of untreated and drugtreated cell populations, bootstrap mean-values and 95%-confidence intervals of the relative cell stretch are calculated from the entity εi ¼ 1…N ðtÞ of N measured cells. As one can see in Fig. 2, application of CcD and WfA results in statistically significant softening of NK cells in comparison to untreated control. By the end of the creep phase (t ¼89), the relative stretch of untreated, 1 mM WfA- and 4 mM CcD-treated probes amounts to 7.3%, 8.8% and 10.3%, respectively, which means that AF and VIF deficient NK cells are, in average, 41% and 20% softer than untreated control. Remarkably, the creep curves of all three conditions exhibit similar time-patterns of cellular elongation. The fit of creep curves with the Kelvin–Voigt model (Eq. (3)) confirms that drug-treated cells do not significantly differ from untreated control with respect to the retardation time, which lays by
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Fig. 1. Changes in vimentin and actin organization upon drug-treatment. A. Maximal intensity projections of exemplary images showing the nuclear, VIF and AF in stained NK cells. In control conditions (upper panel) VIF form a network caging the nuclei of NK cells while a cortical actin rim is observed along the cell edge. Treatment with Withaferin-A (middle panel) causes aggregation of vimentin while the cortical actin remains visible. Incubation with Cytochalasin-D, on the other hand, results in disruption of the rim of cortical actin (lower panel). Scale bar ¼5 mm. B. Quantification of AF disruption upon drug treatment. The average intensity of the summed maximal projection of actin stained cells is quantified for 10 cells of each condition. The strongest decrease in AF intensity is measured in the CcD treated cells. C. Quantification of VIF disruption upon drug treatment. Treatment with Withaferin-A does not have an effect on the total fluorescent intensity of VIF, but it is quantified on the average filaments size in the 2D image slices of the vimentin stained cells. Only the WfA treated cells show that strong accumulation of VIF to dot- and stripe-like structures (yellow) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
τ ¼3.4 s. In the recovery phase (t ¼ 90–119), CcD-treated cells show more rapid recovery rate of 50% than untreated and WfA-treated cells that recover only 30% of their maximum
relative elongation within the same time frame. Similar to Guo et al. (2013), we observe that WfA softens the cellular interior while CcD causes destabilization of outer cellular contours and,
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Fig. 2. Average creep-and-recovery curves depict mechanical fingerprints of drug-treated and untreated NK cells in MOS. Mean values of the relative cell stretch and confidence intervals are computed using the bootstrap simulation. At the end of the creep-phase (t¼ 89), the relative elongation of untreated, WfA- and CcD-treated NK cells amounts, in population average, to 7.3%, 8.8% and 10.3%, respectively. Thus, CcD-treated (red) and WfA-treated NK cells (green) show 41% and 20% larger stretch in comparison to untreated control (blue). In the recovery phase (t ¼ 90–119), WfA-treated cells show no significant difference to untreated control, while CcD-treated cells exhibit faster recovery than untreated control (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
Fig. 3. From left to right: examples of phase contrast images acquired with MOS show undeformed configuration (time step t¼ 0), maximum deformation (time step t ¼89) and 1 s relaxation (time step t ¼ 119) of CcD-treated (top row) and WfA-treated (bottom row) NK cells. Yellow arrows indicate the main stretching axis. AF deficient cells (upper row) exhibit larger deformation and more irregular contours in comparison to VIF deficient cells due destabilization of the cortical filaments network (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
consequently, higher cytotoxicity, see Fig. 3. To generalize isolated observations, statistical shape models of drug-treated and untreated cells are generated, see Fig. 4. The differences in
statistical shape changes confirm our microscopic findings that CcD and WfA selectively disrupt cortical AF and perinuclear VIF in NK cells.
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Fig. 4. Normalized contours of WfA-treated (left) and CcD-treated (right) NK cells. Statistical shape models of undeformed configuration (green) and maximum deformation (blue) of NK cells are generated by normalizing and averaging of cell contours from each drug-treated or untreated population (gray), respectively (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
Fig. 5. Top, left: three-component FE model of a NK cell including the nucleus (violet), cortical AF (red) and perinuclear VIF (green) layers. Top, right: distribution of the maximum local strain in the perinuclear VIF layer of the stretched untreated cell. The color map (from 0% (dark blue) to 24% (red)) indicates the local magnitude of the maximum Eigenvalue of the strain tensor. Bottom: plots of the error norm between simulated and experimental cell deformation as a function of the relative stiffness of AF (red) and VIF (green) layers. The sought values of the relative stiffness correspond to the minimum error norm (i.e., EN ¼ 0) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
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3.3. Dissecting intracellular mechanics using the 3D FE model To establish a quantitative relationship between softening of AF/ VIF layers and 3D cell deformation, a three-component FE mesh model of the NK cell is generated using Amira 4.1 (Mercury Computer Systems, Chelmsford, USA), see Fig. 5 (top row, left). On the basis of image analysis, we consider the unloaded cell to be spherical with the nucleus taking the half of the cell volume (i.e., the nuclear radius¼ 78% of the cellular radius). Accordingly, perinuclear VIF and cortical AF layers are assumed to be nonoverlapping shells of equal thickness that occupy the remaining cytoplasm in the radial range of 78–89% (VIF) and 89–100% (AF), respectively. The basic idea of our FEM-based parameter estimation scheme consists in finding the set of material cell parameters with the best fit between the simulated and experimentally observed cellular deformation. Here, our focus is on quantification of the relative changes in AF/VIF stiffness upon drug-treatment. Since the time-dependent damping factor ð1 e t=τ Þ in Eq. (3) turns out to be equal for drug-treated and untreated NK cells, it is factored out by calculation of the relative changes in cellular deformability using the pure elastic material approximation. The boundary conditions for the simulation of cellular deformation are given by the simplified stress profile (Eq. (5)). For every combination of the relative stiffness values of the three-component cell model (Eq. (6)), the deviation of the simulated cell elongation from the reference configuration is scored using the following L1 error norm:
Simulation of AF softening: ENðαAF Þ ¼ ‖1:41 maxðεt ðαAF ÞÞ= maxðεu Þ‖; Simulation of VIF softening: ENðαVIF Þ ¼ ‖1:20 maxðεt ðαVIF ÞÞ= maxðεu Þ‖; where εt ðαÞ indicates the maximum relative stretch of the cell computed with the FEM for the variable relative stiffness 0 o α o 1 of AF/VIF layers and εu is the maximum relative stretch of the reference model corresponding to the untreated cell (i.e., α ¼ 1). Fig. 5 (bottom row) shows the plots of the simulated error norm as a function of the variable AF/VIF stiffness. The sought values of the relative stiffness of AF/VIF layers corresponding to the minimum of the error norm between simulated and experimental data are found to be αAF ¼ 0:34 and αV IF ¼ 0:52 which suggest a decrease of the relative AF/VIF stiffness by (0.34–1) 100% ¼ 66% and (0.52 1) 100% ¼ 48%, respectively. To quantify the strain state of the VIF layer, the maximum strain Eigenvalue is computed on
tetrahedrons of the FE mesh, see Fig. 5 (top row, right). As expected, the maximum strain of VIF is generated along the main stretching axis of the cell and amounts to 23.7%, 37.5% and 52.6% in untreated, WfA- and CcD-treated NK cells, respectively.
4. Discussion Our experimental results show that under impact of sudden stress induced by 2 s 800 mW laser pulse, untreated, 4 mM WfAtreated (VIF deficient) and 1 mM CcD-treated (AF deficient) NK cells exhibit statistically significant differences in the relative elongation which amounts to 7.3%, 8.8% and 10.3%, respectively. According to our FE simulation, experimentally observed softening of CcD- and WfA-treated NK cells by 41% and 20% relatively to untreated control is associated with the decrease of the relative AF and VIF stiffness by 66% and 48% (see Table 1). Our microscopic imaging and statistical shape analysis suggests that CcD and WfA selectively target cortical AF and perinuclear VIF layers in NK cells without significant cross-effects. While CcD inhibits AF polymerization, the effect of WfA consists presumably in coarsening of the VIF network. Despite the differences in molecular mechanisms of AF and VIF disruption by CcD and WfA, cell softening in both cases can be attributed to reduction of the effective density and, consequently, stiffness of filament networks (Wakatsuki et al., 2001; Bertaud et al., 2010; Köster et al., 2010). Further, our FE model predicts that relatively moderate cell elongation (7–10%) is associated with significantly higher strain rates in the perinuclear VIF layer ranging from 24% in untreated to 38% and 52% in WfA- and CcD-treated cells, respectively (see Table 2). This difference is a direct consequence of the higher stiffness of the relatively large nucleus in NK cells. Consequently, the thin and soft cytoplasm undergoes larger relative deformations as the entire cell. According to molecular simulations of VIF mechanics in Qin et al. (2009), the estimated order of maximum VIF strains in our experiments corresponds to the first two (I and II) linear regimes of VIF deformation that are associated with stretching and unfolding of vimentin alpha-helices. Larger strain rates that would enable probing of higher hierarchical levels of mechanical VIF organization in living cells are not accessible with the MOS because of the severe sideeffects of high-energy laser radiation. More than two-fold increase of the perinuclear VIF strain in AF deficient cells indicates that the mechanical function of VIF as a
Table 1 Summary of the results from MOS measurements and FE simulation: increase of the whole cell deformability vs. decrease of the relative stiffness of AF/VIF layers. Effects of drug-induced deficiency
Increase of the whole cell deformability (MOS measurements)
Decrease of the relative stiffness of AF/VIF layers (FE simulation)
Actin (AF) (1 mM CcD) Vimentin (VIF) (4 mM WfA)
þ 41% w.r.t. untreated control þ 20% w.r.t. untreated control
66% w.r.t. untreated control 48% w.r.t. untreated control
Table 2 Summary of the results from MOS measurements and FE simulation: maximum relative stretch of the whole cell by the end of the creep phase (t¼ 89) vs. maximum strain of the VIF layer. Effects of drug-induced deficiency
Max. relative stretch of the whole cell (MOS measurements) (%)
Max. strain of the VIF layer (FE simulation) (%)
Untreated Vimentin (VIF) (4 mM WfA) Actin (AF) (1 mM CcD)
7.3 8.8 10.3
23.7 37.5 52.6
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protective buffer of the chromatin-bearing nucleus becomes particularly essential in motile and proliferating cells that have to dynamically remodel their cortical AF network. Here, our data adds a functional explanation to frequently observed emergence of vimentin as a marker of epithelial–mesenchymal and metastatic transitions (Willipinski-Stapelfeldt et al., 2005), and underlines the role of VIF targeting drugs, such as WfA, as a low-toxic cancerostatic supplement. Our present experimental and computational framework is designed to combine high-throughput population measurements of cellular compliance with the basic structural analysis of threedimensional cell mechanics at a 1 mm scale which corresponds to the estimated thickness of AF/VIF layers in our FE cell model. Consideration of mechanical properties of cytoskeletal filaments is generally possible within the scope of a continuum model, i.e., by construction of an appropriate mesoscopic tensor of viscoelastic constants. Though, a consistent evaluation of higher-order constitutive models of cellular matter is more feasible in conjunction with controlled mechanical micromanipulation and high-resolution imaging of single cells or synthetic filament samples.
Conflict of interest statement We declare that the authors have no competing interests or other interests that might be perceived to influence the results and/or discussion reported in this article.
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