Segregation of co-cultured multicellular systems: review and modeling consideration.

Cell segregation caused by collective cell migration (CCM) is crucial for morphogenesis, functional development of tissue parts, and is an important aspect in other diseases such as cancer and its metastasis process. Efficiency of the cell segregation depends on the interplay between: (1) biochemical processes such as cell signaling and gene expression and (2) physical interactions between cells. Despite extensive research devoted to study the segregation of various co-cultured systems, we still do not understand the role of physical interactions in cell segregation. Cumulative effects of these physical interactions appear in the form of physical parameters such as: (1) tissue surface tension, (2) viscoelasticity caused by CCM, and (3) solid stress accumulated in multicellular systems. These parameters primarily depend on the interplay between the state of cell-cell adhesion contacts and cell contractility. The role of these physical parameters on the segregation efficiency is discussed on model systems such as co-cultured breast cell spheroids consisting of two subpopulations that are in contact. This review study aims to: (1) summarize biological aspects related to cell segregation, mechanical properties of cell collectives, effects along the biointerface between cell subpopulations and (2) describe from a biophysical/mathematical perspective the same biological aspects summarized before. So that overall it can illustrate the complexity of the biological systems that translate into very complex biophysical/mathematical equations. Moreover, by presenting in parallel these two seemingly different parts (biology vs. equations), this review aims to emphasize the need for experiments to estimate the variety of parameters entering the resulting complex biophysical/mathematical models.

The rearrangement of co-cultured cellular model systems via collective cell migration.

Cancer invasion through the surrounding epithelium and extracellular matrix (ECM) is the one of the main characteristics of cancer progression. While significant effort has been made to predict cancer cells response under various drug therapies, much less attention has been paid to understand the physical interactions between cancer cells and their microenvironment, which are essential for cancer invasion. Considering these physical interactions on various co-cultured in vitro model systems by emphasizing the role of viscoelasticity, the tissue surface tension, solid stress, and their inter-relations is a prerequisite for establishing the main factors that influence cancer cell spread and develop an efficient strategy to suppress it. This review focuses on the role of viscoelasticity caused by collective cell migration (CCM) in the context of mono-cultured and co-cultured cancer systems, and on the modeling approaches aimed at reproducing and understanding these biological systems. In this context, we do not only review previously-published biophysics models for collective cell migration, but also propose new extensions of those models to include solid stress accumulated within the spheroid core region and cell residual stress accumulation caused by CCM.

The dynamics along the biointerface between the epithelial and cancer mesenchymal cells: Modeling consideration.

Epithelial cancer is the one of most lethal cancer type worldwide. Targeting the early stage of disease would allow dramatic improvements in the survival of cancer patients. The early stage of the disease is related to cancer cell spreading across surrounding healthy epithelium. Consequently, deeper insight into cell dynamics along the biointerface between epithelial and cancer (mesenchymal) cells is necessary in order to control the disease as soon as possible. Cell dynamics along this epithelial-cancer biointerface is the result of the interplay between various biological and physical mechanisms. Despite extensive research devoted to study cancer cell spreading across the epithelium, we still do not understand the physical mechanisms which influences the dynamics along the biointerface. These physical mechanisms are related to the interplay between physical parameters such as: (1) interfacial tension between cancer and epithelial subpopulations, (2) established interfacial tension gradients, (3) the bending rigidity of the biointerface and its impact on the interfacial tension, (4) surface tension of the subpopulations, (5) viscoelasticity caused by collective cell migration, and (6) cell residual stress accumulation. The main goal of this study is to review some of these physical parameters in the context of the epithelial/cancer biointerface elaborated on the model system such as the biointerface between breast epithelial MCF-10A cells and cancer MDA-MB-231 cells and then to incorporate these parameters into a new biophysical model that could describe the dynamics of the biointerface. We conclude by discussing three biophysical scenarios for cell dynamics along the biointerface, which can occur depending on the magnitude of the generated shear stress: a smooth biointerface, a slightly-perturbed biointerface and an intensively-perturbed biointerface in the context of the Kelvin-Helmholtz instability. These scenarios are related to the probability of cancer invasion.

Active wetting of epithelial tissues: modeling considerations.

Morphogenesis, tissue regeneration, and cancer invasion involve transitions in tissue morphology. These transitions, caused by collective cell migration (CCM), have been interpreted as active wetting/de-wetting transitions. This phenomenon is considered based on a model system as wetting of a cell aggregate on a rigid substrate, which includes cell aggregate movement and isotropic/anisotropic spreading of a cell monolayer around the aggregate depending on the substrate rigidity and aggregate size. This model system accounts for the transition between 3D epithelial aggregate and 2D cell monolayer as a product of: (1) tissue surface tension, (2) surface tension of substrate matrix, (3) cell-matrix interfacial tension, (4) interfacial tension gradient, (5) viscoelasticity caused by CCM, and (6) viscoelasticity of substrate matrix. These physical parameters depend on the cell contractility and state of cell-cell and cell-matrix adhesion contacts, as well as the stretching/compression of cellular systems caused by CCM. Despite extensive research devoted to study cell wetting, we still do not understand the interplay among these physical parameters which induces an oscillatory trend of cell rearrangement. This review focuses on these physical parameters in governing the cell rearrangement in the context of epithelial aggregate wetting/de-wetting, and on modeling approaches aimed at reproducing and understanding these biological systems. In this context, we not only review previously published biophysical models for cell rearrangement caused by CCM, but also propose new extensions of those models to point out the interrelation between cell-matrix interfacial tension and epithelial viscoelasticity and the role of the interfacial tension gradient in cell spreading.

Tissue segregation in the early vertebrate embryo.

This chapter discusses our current knowledge on the major segregation events that lead to the individualization of the building blocks of vertebrate organisms, starting with the segregation between "outer" and "inner" cells, the separation of the germ layers and the maintenance of their boundaries during gastrulation, and finally the emergence of the primary axial structure, the notochord. The amphibian embryo is used as the prototypical model, to which fish and mouse development are compared. This comparison highlights a striking conservation of the basic processes. It suggests that simple principles may account for the formation of divergent structures. One of them is based on the non-adhesive nature of the apical domain of epithelial cells, exploited to segregate superficial and deep cell populations as a result of asymmetric division. The other principle involves differential expression of contact cues, such as ephrins and protocadherins, to build up high tension along adhesive interfaces, which efficiently creates sharp boundaries.

Interstitial fluid osmolarity modulates the action of differential tissue surface tension in progenitor cell segregation during gastrulation.

The segregation of different cell types into distinct tissues is a fundamental process in metazoan development. Differences in cell adhesion and cortex tension are commonly thought to drive cell sorting by regulating tissue surface tension (TST). However, the role that differential TST plays in cell segregation within the developing embryo is as yet unclear. Here, we have analyzed the role of differential TST for germ layer progenitor cell segregation during zebrafish gastrulation. Contrary to previous observations that differential TST drives germ layer progenitor cell segregation in vitro, we show that germ layers display indistinguishable TST within the gastrulating embryo, arguing against differential TST driving germ layer progenitor cell segregation in vivo We further show that the osmolarity of the interstitial fluid (IF) is an important factor that influences germ layer TST in vivo, and that lower osmolarity of the IF compared with standard cell culture medium can explain why germ layers display differential TST in culture but not in vivo Finally, we show that directed migration of mesendoderm progenitors is required for germ layer progenitor cell segregation and germ layer formation.

Cell adhesion strength from cortical tension - an integration of concepts.

Morphogenetic mechanisms such as cell movement or tissue separation depend on cell attachment and detachment processes, which involve adhesion receptors as well as the cortical cytoskeleton. The interplay between the two components is of stunning complexity. Most strikingly, the binding energy of adhesion molecules is usually too small for substantial cell-cell attachment, pointing to a main deficit in our present understanding of adhesion. In this Opinion article, I integrate recent findings and conceptual advances in the field into a coherent framework for cell adhesion. I argue that active cortical tension is best viewed as an integral part of adhesion, and propose on this basis a non-arbitrary measure of adhesion strength - the tissue surface tension of cell aggregates. This concept of adhesion integrates heterogeneous molecular inputs into a single mechanical property and simplifies the analysis of attachment-detachment processes. It draws attention to the enormous variation of adhesion strengths among tissues, whose origin and function is little understood.

Tissue cohesion and the mechanics of cell rearrangement.

Morphogenetic processes often involve the rapid rearrangement of cells held together by mutual adhesion. The dynamic nature of this adhesion endows tissues with liquid-like properties, such that large-scale shape changes appear as tissue flows. Generally, the resistance to flow (tissue viscosity) is expected to depend on the cohesion of a tissue (how strongly its cells adhere to each other), but the exact relationship between these parameters is not known. Here, we analyse the link between cohesion and viscosity to uncover basic mechanical principles of cell rearrangement. We show that for vertebrate and invertebrate tissues, viscosity varies in proportion to cohesion over a 200-fold range of values. We demonstrate that this proportionality is predicted by a cell-based model of tissue viscosity. To do so, we analyse cell adhesion in Xenopus embryonic tissues and determine a number of parameters, including tissue surface tension (as a measure of cohesion), cell contact fluctuation and cortical tension. In the tissues studied, the ratio of surface tension to viscosity, which has the dimension of a velocity, is 1.8 µm/min. This characteristic velocity reflects the rate of cell-cell boundary contraction during rearrangement, and sets a limit to rearrangement rates. Moreover, we propose that, in these tissues, cell movement is maximally efficient. Our approach to cell rearrangement mechanics links adhesion to the resistance of a tissue to plastic deformation, identifies the characteristic velocity of the process, and provides a basis for the comparison of tissues with mechanical properties that may vary by orders of magnitude.

Multi-scale nature of the tissue surface tension: Theoretical consideration on tissue model systems.

Tissue surface tension is one of the key parameters that govern tissue rearrangement, shaping, and segregation within various compartments during organogenesis, wound healing, and cancer diseases. Deeper insight into the relationship between tissue surface tension and cell residual stress accumulation caused by collective cell migration can help us to understand the multi-scale nature of cell rearrangement with pronounced oscillatory trend. Oscillatory change of cell velocity that caused strain and generated cell residual stress were discussed in the context of mechanical waves. The tissue surface tension also showed oscillatory behaviour. The main goal of this theoretical consideration is to emphasize an inter-relation between various scenarios of cell rearrangement and tissue surface tension by distinguishing liquid-like and solid-like surfaces. This complex phenomenon is discussed in the context of an artificial tissue model system, namely cell aggregate rounding after uni-axial compression between parallel plates. Experimentally obtained oscillatory changes in the cell aggregate shape during the aggregate rounding, which is accompanied by oscillatory decrease in the aggregate surface area, points to oscillatory changes in the tissue surface tension. Besides long-time oscillations, cell surface tension can perform short time relaxation cycles. This behaviour of the tissue surface tension distinguishes living matter from other soft matter systems. This complex phenomenon is discussed based on dilatational viscoelasticity and thermodynamic approach.

Cell jamming-to-unjamming transitions and vice versa in development: Physical aspects.

Collective cell migration is essential for a wide range of biological processes such as: morphogenesis, wound healing, and cancer spreading. However, it is well known that migrating epithelial collectives frequently undergo jamming, stay trapped some period of time, and then start migration again. Consequently, only a part of epithelial cells actively contributes to the tissue development. In contrast to epithelial cells, migrating mesenchymal collectives successfully avoid the jamming. It has been confirmed that the epithelial unjamming cannot be treated as the epithelial-to-mesenchymal transition. Some other mechanism is responsible for the epithelial jamming/unjamming. Despite extensive research devoted to study the cell jamming/unjamming, we still do not understand the origin of this phenomenon. The origin is connected to physical factors such as: the cell compressive residual stress accumulation and surface characteristics of migrating (unjamming) and resting (jamming) epithelial clusters which depend primarily on the strength of cell-cell adhesion contacts and cell contractility. The main goal of this theoretical consideration is to clarify these cause-consequence relations.

Characterization of convergent thickening, a major convergence force producing morphogenic movement in amphibians.

The morphogenic process of convergent thickening (CT) was originally described as the mediolateral convergence and radial thickening of the explanted ventral involuting marginal zone (IMZ) of Xenopus gastrulae (Keller and Danilchik, 1988). Here, we show that CT is expressed in all sectors of the pre-involution IMZ, which transitions to expressing convergent extension (CE) after involution. CT occurs without CE and drives symmetric blastopore closure in ventralized embryos. Assays of tissue affinity and tissue surface tension measurements suggest CT is driven by increased interfacial tension between the deep IMZ and the overlying epithelium. The resulting minimization of deep IMZ surface area drives a tendency to shorten the mediolateral (circumblastoporal) aspect of the IMZ, thereby generating tensile force contributing to blastopore closure (Shook et al., 2018). These results establish CT as an independent force-generating process of evolutionary significance and provide the first clear example of an oriented, tensile force generated by an isotropic, Holtfreterian/Steinbergian tissue affinity change.

Jamming state transition and collective cell migration.

Jamming state transition has been used in literature to describe migrating-to-resting cell state transition during collective cell migration without proper rheological confirmation. Yield stress often has been used as an indicator of a jamming state. Yield stress points to the liquid-to-solid state transition, but not a priori to jamming state transition. Various solid states such as elastic solid and viscoelastic solids can be considered in the context of their ability to relax. The relaxation time for (1) an elastic solid tends to zero, (2) Kelvin-Voigt viscoelastic solid is finite, and (3) jamming state tends to infinity. In order to clarify the meaning of jamming state from the rheological standpoint we formulated the constitutive model of this state based on following conditions (1) migration of the system constituents is much damped such that the diffusion coefficient tends to zero, (2) relaxation time tends to infinity, (3) storage and loss moduli satisfy the condition G '(ω)/G "(ω) = const > 1. Jamming state represents the non-linear viscoelastic solid state. The main characteristic of this state is that the system cannot relax. Jamming state transition of multicellular systems caused by collective cell migration is discussed on a model system such as cell aggregate rounding after uni-axial compression between parallel plates based on the data from the literature. Cell aggregate rounding occurs via successive relaxation cycles. Every cycle corresponds to a different scenario of cell migration. Three scenarios were established depending on the magnitude of mechanical and biochemical perturbations (1) ordered scenario with reduced perturbations corresponds to the case that most of the cells migrate, (2) disordered scenario corresponds to the case that some cell groups migrate while the others (at the same time) stay in resting state (corresponds to medium perturbations), and (3) highly suppressed cell migration under large perturbations corresponds to the viscoelastic solid under jamming state. If cells reach the jamming state in one cycle, they are able to overcome this undesirable state and start migrating again in the next cycle by achieving the first or second scenarios again.

Micropipette aspiration: A unique tool for exploring cell and tissue mechanics in vivo.

Cell and tissue mechanical properties are paramount in controlling morphogenesis. Microaspiration techniques allow measuring the absolute values of mechanical properties in space and time in vivo. Here, we explain how to build a microaspiration setup that can be used for both cellular and tissue scale measurements. At the cellular scale, microaspiration allows the mapping in space and time of surface tensions of individual interfaces within a tissue to understand the forces shaping it. At the tissue scale, microaspiration can be used to measure macroscopic mechanical properties such as the viscoelasticity and tissue surface tension that regulate the dynamics of tissue deformation. Based on a simple and cost-effective apparatus, these two complementary microaspiration techniques provide unique tools for exploring cell and tissue mechanics in vivo.