Jamming transitions in cancer

Journal of Physics D: Applied Physics

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Jamming transitions in cancer To cite this article before publication: Linda Oswald et al 2017 J. Phys. D: Appl. Phys. in press https://doi.org/10.1088/1361-6463/aa8e83

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Linda Oswald*1 , Steffen Grosser*1 , David M. Smith2 , Josef A. Käs1 1 University

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Jamming transitions in cancer

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of Leipzig, Faculty of Physics and Earth Sciences, Debye Institute, Linnéstr. 5, 04103 Leipzig, Germany 2 Fraunhofer Institute for Cell Therapy and Immunology, Perlickstr. 1, 04103 Leipzig, Germany * These authors contributed equally to this work.

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Abstract The traditional picture of tissues, where they are treated as liquids defined by properties such as surface tension or viscosity has been redefined during the last few decades by the more fundamental question: Under which conditions do tissues display liquid-like or solid-like behaviour? As a result, basic concepts arising from the treatment of tissues as solid matter, such as cellular jamming and glassy tissues, have shifted into the current focus of biophysical research. Here, we review recent works examining the phase states of tissue with an emphasis on jamming transitions in cancer. When metastasis occurs, cells gain the ability to leave the primary tumour and infiltrate other parts of the body. Recent studies have shown that a linkage between an unjamming transition and tumour progression indeed exists, which could be of importance when designing surgery and treatment approaches for cancer patients.

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AUTHOR SUBMITTED MANUSCRIPT - JPhysD-113342.R1

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transition. More plausible triggers for a jamming transition are active motility, interaction forces, cell shape and applied stress. A phase diagram for cellular monolayers similar to that one proposed by Liu and Nagel is shown in figure 4 on the right side [7]. Here, the phase space is spanned by adhesion, motility and density. The role of jamming in multicellular systems especially with respect to tumour development and metastasis will be subject of the next sections.

2 Tissues as liquids

In the last few decades, tissues have often been treated as simple or viscoelastic liquids behaving as elastic solids on short time scales and viscous fluids on long time scales. In this section, we will give an overview of experiments that have led to this picture and present the according models.

2.1 Experiments that have led to the broad consensus that tissues are basically liquid

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In the early 1960s, Steinberg and coworkers published a study on in vitro cell sorting, i.e. the segregation of two mixed cell populations into separated clusters [38]. They showed that one cell population forms an inner sphere (e.g. heart ventricle cells), while the other one forms an outer shell (e.g. liver cells). This behaviour is analogous to the segregation of two immiscible liquids thought to be caused by differences in their surface tensions. This cell sorting demonstration has been repeated several times with different cell lines and primary cells with similar results (see fig. 5 A) [39, 40, 41, 35]. Analogous to the segregation of cells, their aggregation, rounding up and fusion (see fig. 5 B) can also be compared to liquid drops [42, 47, 48]. Mombach et al. found that rounding up of embryo chick multicellular aggregates can be modelled as viscoelastic liquid droplets [47]. The fusion of two liquid drops is governed by their surface tension as the driving force and their viscosity as counteracting force. Particularly for embryonic tissue, the dynamics of fusion are in accordance with hydrodynamics [49, 42, 43]. The tissue surface tension (TST) can be measured with multicellular spheroids in a plate tensiometer (see fig. 5 C) [50, 51]. Most tissue types show an elastic response to tension on short time scales and a viscous response on long time scales [50, 52]. Another liquid property which can also be found in tissues is wetting, which describes the spreading of liquid drops on a substrate. Depending on substrate-cell interfacial tension, substrate-medium interfacial tension and cell-medium interfacial tension, non-wetting, partial wetting or complete wetting can be observed for multicellular spheroids (see fig. 5 D) [46, 53, 45]. For cell aggregates with low cohesion, complete wetting can be followed by the escape of single cells from the monolayer similar to a 2D liquid-gas transition [46]. Cells and cellular monolayers placed on non-wettable substrates (e.g. agarose gel, PEG-PLL) also form 3D aggregates by nucleation and growth, which is called dewetting [54, 55].

2.2 Liquid tissue models

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To account for the liquid properties tissues shown in experiments, different models have been developed. As mentioned above, cell sorting is proposed to be the result of differing tissue surface tensions between the two cell populations. Steinberg and coworkers suggested that these differences arise from varying cell-cell adhesion forces mediated by cadherins [38, 41]. This hypothesis is called the differential adhesion hypothesis (DAH) and seems to hold true for certain cell types [41]. However, other explanations for the origin of TST have been suggested. The differential surface contraction hypothesis (DSCH) proposed by Harris states that TST arises from cell contractility rather than adhesion [56]. Brodland and coworkers proposed an extension of this hypothesis, the differential interfacial tension hypothesis (DITH), which includes both contractility and adhesion but neglects the influence of adhesion strength [57]. Experimental evidence for this hypothesis was found for gastrulating zebrafish embryos [58]. Another extension of the DAH was proposed by Manning and coworkers [59, 60, 35], which states

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5.4 Continuum descriptions

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Another approach for modeling tissue dynamics utilises continuum descriptions [61, 63, 88, 89, 90]. Ranft et al. calculated macroscopic variables such as large-scale stress distributions and flow fields of cells, both with and without cell division as well as apoptosis as sources of anisotropic stress [62]. Without division and apoptosis, the isotropic tissue behaves as elastic solid, while otherwise it behaves as viscoelastic fluid with a relaxation time set by the rates of cell division and death. If the tissue is confined in a fixed volume, it reaches a homeostatic state in which cells undergo diffusive motion. The authors make use of dissipative particle dynamics simulations to verify the analytical results for viscosities and diffusion constants as a function of cell division rate in the homeostatic state. Cells are represented as point particles in a repulsive potential, where two cells interact repulsively on short distances and attractively on long distances. Similar to results from analytical approaches, saturating mean-squared displacements indicative of caging behaviour were found without division and apoptosis while diffusive behaviour was found if division and apoptosis are included. Other sources of noise, such as cell shape fluctuations, were not included in the model. [62] Recently, a minimal particle based model including cell-cell adhesion, cell division and apoptosis made similar predictions about the fluidisation of tissue due to cell division and death [91]. The authors produce a complex phase diagram with a gaseous, a gel-like and a self-melting liquid-like phase, where the tissue fails to show a glassy phase due to internal activity. However, glassy features were also found for embryonic tissue with normal cell division rates [43]. Thus, it seems not clear that division and apoptosis always inhibit glassy behaviour.

6 Falsification of pure fluidity and observation of jamming in 3D systems

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6.1 Breakdown of DAH in 3D tumour models

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Recent studies have shown that some cell types do not only behave as fluids on long time scales in 2D, but also in 3D systems. Pawlizak et al. [35] published a study on sorting behaviour of 3D aggregates from three different cell lines with varying metastatic potential (MCF-10A, MDA-MB-436 and MDA-MB-231, see fig. 16) .

Figure 16: Confocal images through one plane of a 3D aggregate of metastatic MDA-MB-231 cells (a), normal MCF-10A cells (b) and cancerous MDA-MB-436 cells (c). Reprinted from [35].

Different methods were used to test DAH, DITH and extended DAH (see section 2). Cell-cell adhesion was directly measured via atomic force microscopy and indirectly by counting cadherins on the cell surface. The angles between surface cells and the aggregate were measured to test the extended DAH and whole-cell deformabilites determined by the Optical Stretcher were used as a measure for cell cortical tension. The resulting predictions from the different hypotheses are summarised in figure 17 and compared to the actual sorting hierarchy shown in fig 5 A.

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been observed in in vitro experiments, however, conclusively demonstrating that unjamming transitions can accompany the formation of metastasis in 3D tissue particularly in vivo, is still pending. However, real tumours do not only consist of a collective mass of dense cells. Hence, it is also important to experimentally and theoretically investigate the general phenomena leading to and arising from single-cell jamming in the extracellular matrix or under external constrictions, and use this information to infer its influence on tumour progression. For example, jamming in the ECM might not only be influenced by jamming of the whole cell but also by nuclear blocking, which might be connected to the shape and mechanics of the nucleus. If the formation of metastasis is indeed linked to an unjamming transition, this could be of significant importance for clinical applications. Determining the fluid and non-fluid areas in a tumour by magnet resonance elastography [96, 8] could be used as a predictive marker for cancer progression. Moreover, if cellular jamming is linked to cell shape as predicted by the SPV model, thin sections of tumours could be used to gain information on cellular dynamics from the shapes of cells within the biopsy, thus yielding a map for potential directions of metastatic invasion.

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Acknowledgements This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 668039/FORCE). We thank Cristina Marchetti and Lisa Manning for helpful discussions and comments.

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