Coupling mechanical tension and GTPase signaling to generate cell and tissue dynamics

A multiscale theory for spreading and migration of adhesion-reinforced mesenchymal cells

We present a chemomechanical whole-cell theory for the spreading and migration dynamics of mesenchymal cells that can actively reinforce their adhesion to an underlying viscoelastic substrate as a function of its stiffness. Our multiscale model couples the adhesion reinforcement effect at the subcellular scale with the nonlinear mechanics of the nucleus-cytoskeletal network complex at the cellular scale to explain the concurrent monotonic area-stiffness and non-monotonic speed-stiffness relationships observed in experiments: we consider that large cell spreading on stiff substrates flattens the nucleus, increasing the viscous drag force on it. The resulting force balance dictates a reduction in the migration speed on stiff substrates. We also reproduce the experimental influence of the substrate viscosity on the cell spreading area and migration speed by elucidating how the viscosity may either maintain adhesion reinforcement or prevent it depending on the substrate stiffness. Additionally, our model captures the experimental directed migration behaviour of the adhesion-reinforced cells along a stiffness gradient, known as durotaxis, as well as up or down a viscosity gradient (viscotaxis or anti-viscotaxis), the cell moving towards an optimal viscosity in either case. Overall, our theory explains the intertwined mechanics of the cell spreading, migration speed and direction in the presence of the molecular adhesion reinforcement mechanism.

From actin waves to mechanism and back: How theory aids biological understanding

Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.

A multiscale whole-cell theory for mechanosensitive migration on viscoelastic substrates

Increasing experimental evidence validates that both the elastic stiffness and viscosity of the extracellular matrix regulate mesenchymal cell behavior, such as the rational switch between durotaxis (cell migration to stiffer regions), anti-durotaxis (migration to softer regions), and adurotaxis (stiffness-insensitive migration). To reveal the mechanisms underlying the crossover between these motility regimes, we have developed a multiscale chemomechanical whole-cell theory for mesenchymal migration. Our framework couples the subcellular focal adhesion dynamics at the cell-substrate interface with the cellular cytoskeletal mechanics and the chemical signaling pathways involving Rho GTPase proteins. Upon polarization by the Rho GTPase gradients, our simulated cell migrates by concerted peripheral protrusions and contractions, a hallmark of the mesenchymal mode. The resulting cell dynamics quantitatively reproduces the experimental migration speed as a function of the uniform substrate stiffness and explains the influence of viscosity on the migration efficiency. In the presence of stiffness gradients and absence of chemical polarization, our simulated cell can exhibit durotaxis, anti-durotaxis, and adurotaxis respectively with increasing substrate stiffness or viscosity. The cell moves toward an optimally stiff region from softer regions during durotaxis and from stiffer regions during anti-durotaxis. We show that cell polarization through steep Rho GTPase gradients can reverse the migration direction dictated by the mechanical cues. Overall, our theory demonstrates that opposing durotactic behaviors emerge via the interplay between intracellular signaling and cell-medium mechanical interactions in agreement with experiments, thereby elucidating complex mechanosensing at the single-cell level.

Effect of Static and Dynamic Stretching on Corneal Fibroblast Cell

A strain gradient was created by punching a hole in the center of a stretched elastic polydimethylsiloxane membrane to determine the effect of different strains on cultured human keratocytes (HK). In this study, two stretching methods were used: continuous stretching and cyclic stretching. Continuous stretching is relatively static, while acyclic stretching is relatively dynamic. These methods, respectively, represented the effects of high intraocular pressure and rubbing of the eyes on corneal cells. Image processing codes were developed to observe the effects of stress concentration, shear stress, continuous stretching, and cyclic stretching on HKs. The results demonstrate that stretching and shear stress are not conducive to the proliferation of corneal cells and instead cause cell death. A 10% strain had greater inhibitory effects than a 3% strain on cell proliferation. Cell survival rates for continuous stretching (static) were higher than those for cyclic stretching (dynamic). The stretching experiment revealed that cyclic stretching has a greater inhibitory effect on the growth and proliferation of corneal cells than continuous stretching. Accordingly, it shows that cyclic loading is more harmful than high intraocular pressure (static loading) to corneal cells.

Cellular Tango: how extracellular matrix adhesion choreographs Rac-Rho signaling and cell movement

The small GTPases Rac and Rho are known to regulate eukaryotic cell shape, promoting front protrusion (Rac) or rear retraction (Rho) of the cell edge. Such cell deformation changes the contact and adhesion of cell to the extracellular matrix (ECM), while ECM signaling through integrin receptors also affects GTPase activity. We develop and investigate a model for this three-way feedback loop in 1D and 2D spatial domains, as well as in a fully deforming 2D cell shapes with detailed adhesion-bond biophysics. The model consists of reaction-diffusion equations solved numerically with open-source software, Morpheus, and with custom-built cellular Potts model simulations. We find a variety of patterns and cell behaviors, including persistent polarity, flipped front-back cell polarity oscillations, spiral waves, and random protrusion-retraction. We show that the observed spatial patterns depend on the cell shape, and vice versa.

Mechanical Pressure Driving Proteoglycan Expression in Mammographic Density: a Self-perpetuating Cycle?

Regions of high mammographic density (MD) in the breast are characterised by a proteoglycan (PG)-rich fibrous stroma, where PGs mediate aligned collagen fibrils to control tissue stiffness and hence the response to mechanical forces. Literature is accumulating to support the notion that mechanical stiffness may drive PG synthesis in the breast contributing to MD. We review emerging patterns in MD and other biological settings, of a positive feedback cycle of force promoting PG synthesis, such as in articular cartilage, due to increased pressure on weight bearing joints. Furthermore, we present evidence to suggest a pro-tumorigenic effect of increased mechanical force on epithelial cells in contexts where PG-mediated, aligned collagen fibrous tissue abounds, with implications for breast cancer development attributable to high MD. Finally, we summarise means through which this positive feedback mechanism of PG synthesis may be intercepted to reduce mechanical force within tissues and thus reduce disease burden.

A three-dimensional vertex model forDrosophilasalivary gland invagination

During epithelial morphogenesis, force generation at the cellular level not only causes cell deformation, but may also produce coordinated cell movement and rearrangement on the tissue level. In this paper, we use a novel three-dimensional vertex model to explore the roles of cellular forces during the formation of the salivary gland in theDrosophilaembryo. Representing the placode as an epithelial sheet of initially columnar cells, we focus on the spatial and temporal patterning of contractile forces due to three actomyosin pools: the apicomedial actomyosin in the pit of the placode, junctional actomyosin arcs outside the pit, and a supracellular actomyosin cable along the circumference of the placode. In anin silico'wild type' model, these pools are activated at different times according to experimental data. To identify the role of each myosin pool, we have also simulated variousin silico'mutants' in which only one or two of the myosin pools are activated. We find that the apicomedial myosin initiates a small dimple in the pit, but this is not essential for the overall invagination of the placode. The myosin arcs are the main driver of invagination and are responsible for the internalization of the apical surface. The circumferential actomyosin cable acts to constrict the opening of the developing tube, and is responsible for forming a properly shaped lumen. Cell intercalation tends to facilitate the invagination, but the geometric constraints of our model only allow a small number of intercalations, and their effect is minor. The placode invagination predicted by the model is in general agreement with experimental observations. It confirms some features of the current 'belt-and-braces' model for the process, and provides new insights on the separate roles of the various myosin pools and their spatio-temporal coordination.

The role of mechanical interactions in EMT

The detachment of cells from the boundary of an epithelial tissue and the subsequent invasion of these cells into surrounding tissues is important for cancer development and wound healing, and is strongly associated with the epithelial-mesenchymal transition (EMT). Chemical signals, such as TGF-β, produced by surrounding tissue can be uptaken by cells and induce EMT. In this work, we present a novel cell-based discrete mathematical model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by chemically-dependent EMT in an epithelial tissue. A continuum description of the model is then derived in the form of a novel nonlinear free boundary problem. Using the discrete and continuum models we explore how the coupling of chemical transport and mechanical interactions influences EMT, and postulate how this could be used to help control EMT in pathological situations.

Cellular mitosis predicts vessel stability in a mechanochemical model of sprouting angiogenesis

Angiogenesis, the formation of new vessels, occurs in both developmental and pathological contexts. Prior research has investigated vessel formation to identify cellular phenotypes and dynamics associated with angiogenic disease. One major family of proteins involved in angiogenesis are the Rho GTPases, which govern function related to cellular elongation, migration, and proliferation. Using a mechanochemical model coupling Rho GTPase activity and cellular and intercellular mechanics, we investigate the role of cellular mitosis on sprouting angiogenesis. Mitosis-GTPase synchronization was not a strong predictor of GTPase and thus vessel signaling instability, whereas the location of mitotic events was predicted to alter GTPase cycling instabilities. Our model predicts that middle stalk cells undergoing mitosis introduce irregular dynamics in GTPase cycling and may provide a source of aberrant angiogenesis. We also find that cellular and junctional tension exhibit spatial heterogeneity through the vessel, and that tension feedback, specifically in stalk cells, tends to increase the maximum forces generated in the vessel.

Spots, stripes, and spiral waves in models for static and motile cells : GTPase patterns in cells

The polarization and motility of eukaryotic cells depends on assembly and contraction of the actin cytoskeleton and its regulation by proteins called GTPases. The activity of GTPases causes assembly of filamentous actin (by GTPases Cdc42, Rac), resulting in protrusion of the cell edge. Mathematical models for GTPase dynamics address the spontaneous formation of patterns and nonuniform spatial distributions of such proteins in the cell. Here we revisit the wave-pinning model for GTPase-induced cell polarization, together with a number of extensions proposed in the literature. These include introduction of sources and sinks of active and inactive GTPase (by the group of A. Champneys), and negative feedback from F-actin to GTPase activity. We discuss these extensions singly and in combination, in 1D, and 2D static domains. We then show how the patterns that form (spots, waves, and spirals) interact with cell boundaries to create a variety of interesting and dynamic cell shapes and motion.

Bridging from single to collective cell migration: A review of models and links to experiments

Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.

A free boundary mechanobiological model of epithelial tissues

In this study, we couple intracellular signalling and cell-based mechanical properties to develop a novel free boundary mechanobiological model of epithelial tissue dynamics. Mechanobiological coupling is introduced at the cell level in a discrete modelling framework, and new reaction-diffusion equations are derived to describe tissue-level outcomes. The free boundary evolves as a result of the underlying biological mechanisms included in the discrete model. To demonstrate the accuracy of the continuum model, we compare numerical solutions of the discrete and continuum models for two different signalling pathways. First, we study the Rac-Rho pathway where cell- and tissue-level mechanics are directly related to intracellular signalling. Second, we study an activator-inhibitor system which gives rise to spatial and temporal patterning related to Turing patterns. In all cases, the continuum model and free boundary condition accurately reflect the cell-level processes included in the discrete model.

Membrane Tension Can Enhance Adaptation to Maintain Polarity of Migrating Cells

Migratory cells are known to adapt to environments that contain wide-ranging levels of chemoattractant. Although biochemical models of adaptation have been previously proposed, here, we discuss a different mechanism based on mechanosensing, in which the interaction between biochemical signaling and cell tension facilitates adaptation. We describe and analyze a model of mechanochemical-based adaptation coupling a mechanics-based physical model of cell tension coupled with the wave-pinning reaction-diffusion model for Rac GTPase activity. The mathematical analysis of this model, simulations of a simplified one-dimensional cell geometry, and two-dimensional finite element simulations of deforming cells reveal that as a cell protrudes under the influence of high stimulation levels, tension-mediated inhibition of Rac signaling causes the cell to polarize even when initially overstimulated. Specifically, tension-mediated inhibition of Rac activation, which has been experimentally observed in recent years, facilitates this adaptation by countering the high levels of environmental stimulation. These results demonstrate how tension-related mechanosensing may provide an alternative (and potentially complementary) mechanism for cell adaptation.

Mechanobiology in cortical waves and oscillations

Cortical actin waves have emerged as a widely prevalent phenomena and brought pattern formation to many fields of cell biology. Cortical excitabilities, reminiscent of the electric excitability in neurons, are likely fundamental property of the cell cortex. Although they have been mostly considered to be biochemical in nature, accumulating evidence support the role of mechanics in the pattern formation process. Both pattern formation and mechanobiology approach biological phenomena at the collective level, either by looking at the mesoscale dynamical behavior of molecular networks or by using collective physical properties to characterize biological systems. As such they are very different from the traditional reductionist, bottom-up view of biology, which brings new challenges and potential opportunities. In this essay, we aim to provide our perspectives on what the proposed mechanochemical feedbacks are and open questions regarding their role in cortical excitable and oscillatory dynamics.

Mechanical Cell Competition in Heterogeneous Epithelial Tissues

Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimensional mechanical model of heterogeneous epithelial tissue dynamics that includes cell-length-dependent proliferation and death mechanisms. Proliferation and death are incorporated into the discrete model stochastically and arise as source/sink terms in the corresponding continuum model that we derive. Using the new discrete model and continuum description, we explore several applications including the evolution of homogeneous tissues experiencing proliferation and death, and competition in a heterogeneous setting with a cancerous tissue competing for space with an adjacent normal tissue. This framework allows us to postulate new mechanisms that explain the ability of cancer cells to outcompete healthy cells through mechanical differences rather than an intrinsic proliferative advantage. We advise when the continuum model is beneficial and demonstrate why naively adding source/sink terms to a continuum model without considering the underlying discrete model may lead to incorrect results.

Fluid Shear Stress Sensing by the Endothelial Layer

Blood flow produces mechanical frictional forces, parallel to the blood flow exerted on the endothelial wall of the vessel, the so-called wall shear stress (WSS). WSS sensing is associated with several vascular pathologies, but it is first a physiological phenomenon. Endothelial cell sensitivity to WSS is involved in several developmental and physiological vascular processes such as angiogenesis and vascular morphogenesis, vascular remodeling, and vascular tone. Local conditions of blood flow determine the characteristics of WSS, i.e., intensity, direction, pulsatility, sensed by the endothelial cells that, through their effect of the vascular network, impact WSS. All these processes generate a local-global retroactive loop that determines the ability of the vascular system to ensure the perfusion of the tissues. In order to account for the physiological role of WSS, the so-called shear stress set point theory has been proposed, according to which WSS sensing acts locally on vessel remodeling so that WSS is maintained close to a set point value, with local and distant effects of vascular blood flow. The aim of this article is (1) to review the existing literature on WSS sensing involvement on the behavior of endothelial cells and its short-term (vasoreactivity) and long-term (vascular morphogenesis and remodeling) effects on vascular functioning in physiological condition; (2) to present the various hypotheses about WSS sensors and analyze the conceptual background of these representations, in particular the concept of tensional prestress or biotensegrity; and (3) to analyze the relevance, explanatory value, and limitations of the WSS set point theory, that should be viewed as dynamical, and not algorithmic, processes, acting in a self-organized way. We conclude that this dynamic set point theory and the biotensegrity concept provide a relevant explanatory framework to analyze the physiological mechanisms of WSS sensing and their possible shift toward pathological situations.

Multiscale modelling of motility wave propagation in cell migration

The collective motion of cell monolayers within a tissue is a fundamental biological process that occurs during tissue formation, wound healing, cancerous invasion, and viral infection. Experiments have shown that at the onset of migration, the motility is self-generated as a polarisation wave starting from the leading edge of the monolayer and progressively propagates into the bulk. However, it is unclear how the propagation of this motility wave is influenced by cellular properties. Here, we investigate this question using a computational model based on the Potts model coupled to the dynamics of intracellular polarisation. The model captures the propagation of the polarisation wave and suggests that the cells cortex can regulate the migration modes: strongly contractile cells may depolarise the monolayer, whereas less contractile cells can form swirling movement. Cortical contractility is further found to limit the cells motility, which (i) decelerates the wave speed and the leading edge progression, and (ii) destabilises the leading edge. Together, our model describes how different mechanical properties of cells can contribute to the regulation of collective cell migration.

Tuning Cell Motility via Cell Tension with a Mechanochemical Cell Migration Model

Cell migration is orchestrated by a complicated mechanochemical system. However, few cell migration models take into account the coupling between the biochemical network and mechanical factors. Here, we construct a mechanochemical cell migration model to study the cell tension effect on cell migration. Our model incorporates the interactions between Rac-GTP, Rac-GDP, F-actin, myosin, and cell tension, and it is very convenient in capturing the change of cell shape by taking the phase field approach. This model captures the characteristic features of cell polarization, cell shape change, and cell migration modes. It shows that cell tension inhibits migration ability monotonically when cells are applied with persistent external stimuli. On the other hand, if random internal noise is significant, the regulation of cell tension exerts a nonmonotonic effect on cell migration. Because the increase of cell tension hinders the formation of multiple protrusions, migration ability could be maximized at intermediate cell tension under random internal noise. These model predictions are consistent with our single-cell experiments and other experimental results.

Gαq-mediated calcium dynamics and membrane tension modulate neurite plasticity

The formation and disruption of synaptic connections during development are a fundamental step in neural circuit formation. Subneuronal structures such as neurites are known to be sensitive to the level of spontaneous neuronal activity, but the specifics of how neurotransmitter-induced calcium activity regulates neurite homeostasis are not yet fully understood. In response to stimulation by neurotransmitters such as acetylcholine, calcium responses in cells are mediated by the Gαq/phospholipase Cβ (PLCβ)/phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2) signaling pathway. Here, we show that prolonged Gαq stimulation results in the retraction of neurites in PC12 cells and the rupture of neuronal synapses by modulating membrane tension. To understand the underlying cause, we dissected the behavior of individual components of the Gαq/PLCβ/PI(4,5)P2 pathway during retraction and correlated these with the retraction of the membrane and cytoskeletal elements impacted by calcium signaling. We developed a mathematical model that combines biochemical signaling with membrane tension and cytoskeletal mechanics to show how signaling events are coupled to retraction velocity, membrane tension, and actin dynamics. The coupling between calcium and neurite retraction is shown to be operative in the Caenorhabditis elegans nervous system. This study uncovers a novel mechanochemical connection between Gαq/PLCβ /PI(4,5)P2 that couples calcium responses with neural plasticity.

The Actin Cytoskeleton as an Active Adaptive Material

Actin is the main protein used by biological cells to adapt their structure and mechanics to their needs. Cellular adaptation is made possible by molecular processes that strongly depend on mechanics. The actin cytoskeleton is also an active material that continuously consumes energy. This allows for dynamical processes that are possible only out of equilibrium and opens up the possibility for multiple layers of control that have evolved around this single protein.Here we discuss the actin cytoskeleton from the viewpoint of physics as an active adaptive material that can build structures superior to man-made soft matter systems. Not only can actin be used to build different network architectures on demand and in an adaptive manner, but it also exhibits the dynamical properties of feedback systems, like excitability, bistability, or oscillations. Therefore, it is a prime example of how biology couples physical structure and information flow and a role model for biology-inspired metamaterials.

Cell Size, Mechanical Tension, and GTPase Signaling in the Single Cell

Cell polarization requires redistribution of specific proteins to the nascent front and back of a eukaryotic cell. Among these proteins are Rac and Rho, members of the small GTPase family that regulate the actin cytoskeleton. Rac promotes actin assembly and protrusion of the front edge, whereas Rho activates myosin-driven contraction at the back. Mathematical models of cell polarization at many levels of detail have appeared. One of the simplest based on "wave-pinning" consists of a pair of reaction-diffusion equations for a single GTPase. Mathematical analysis of wave-pinning so far is largely restricted to static domains in one spatial dimension. Here, we extend the analysis to cells that change in size, showing that both shrinking and growing cells can lose polarity. We further consider the feedback between mechanical tension, GTPase activation, and cell deformation in both static, growing, shrinking, and moving cells. Special cases (spatially uniform cell chemistry, the absence or presence of mechanical feedback) are analyzed, and the full model is explored by simulations in 1D. We find a variety of novel behaviors, including "dilution-induced" oscillations of Rac activity and cell size, as well as gain or loss of polarization and motility in the model cell.

Heterophilic cell-cell adhesion of atypical cadherins Fat and Dachsous regulate epithelial cell size dynamics during Drosophila thorax morphogenesis

Spatiotemporal changes in epithelial cell sizes-or epithelial cell size dynamics (ECD)-during morphogenesis entail interplay between two opposing forces: cell contraction via actomyosin cytoskeleton and cell expansion via cell-cell adhesion. Cell-cell adhesion-based ECD, however, has not yet been clearly demonstrated. For instance, changing levels of homophilic E-cadherin-based cell-cell adhesion induce cell sorting, but not ECD. Here we show that cell-expansive forces of heterophilic cell-cell adhesion regulate ECD: higher cell-cell adhesion results in cell size enlargement. Thus, ECD during morphogenesis in the heminotal epithelia of Drosophila pupae leading to thorax closure corresponds with spatiotemporal gradients of two heterophilic atypical cadherins-Fat (Ft) and Dachsous (Ds)-and the levels of Ft-Ds heterodimers formed concomitantly. Our mathematical modeling and genetic tests validate this mechanism of dynamic heterophilic cell-cell adhesion-based regulation of ECD. Conservation of these atypical cadherins suggests a wider prevalence of heterophilic cell-cell adhesion-based ECD regulation during animal morphogenesis.

Emerging themes and unifying concepts underlying cell behavior regulation by the pericellular space

Cells reside in a complex three-dimensional (3D) microenvironment where physical, chemical, and architectural features of the pericellular space regulate important cellular functions like migration, differentiation, and morphogenesis. A major goal of tissue engineering is to identify which properties of the pericellular space orchestrate these emergent cell behaviors and how. In this review, we highlight recent studies at the interface of biomaterials and single cell biophysics that are lending deeper insight towards this goal. Advanced methods have enabled the decoupling of architectural and mechanical features of the microenvironment, revealing multiple mechanisms of adhesion and mechanosensing modulation by biomaterials. Such studies are revealing important roles for pericellular space degradability, hydration, and adhesion competition in cell shape, volume, and differentiation regulation. STATEMENT OF SIGNIFICANCE: Cell fate and function are closely regulated by the local extracellular microenvironment. Advanced methods at the interface of single cell biophysics and biomaterials have shed new light on regulators of cell-pericellular space interactions by decoupling more features of the complex pericellular milieu than ever before. These findings lend deeper mechanistic insight into how biomaterials can be designed to fine-tune outcomes like differentiation, migration, and collective morphogenesis.

Polarization wave at the onset of collective cell migration

Collective cell migration underlies morphogenesis, tissue regeneration, and cancer progression. How the biomechanical coupling between epithelial cells triggers and coordinates the collective migration is an open question. Here, we develop a one-dimensional model for an epithelial monolayer which predicts that after the onset of migration at an open boundary, cells in the bulk of the epithelium are gradually recruited into outward-directed motility, exhibiting traveling-wave-like behavior. We find an exact formula for the speed of this motility wave proportional to the square root of the cells' contractility, which accounts for cortex tension and adhesion between adjacent cells.

A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation

Mechanical heterogeneity in biological tissues, in particular stiffness, can be used to distinguish between healthy and diseased states. However, it is often difficult to explore relationships between cellular-level properties and tissue-level outcomes when biological experiments are performed at a single scale only. To overcome this difficulty, we develop a multi-scale mathematical model which provides a clear framework to explore these connections across biological scales. Starting with an individual-based mechanical model of cell movement, we subsequently derive a novel coarse-grained system of partial differential equations governing the evolution of the cell density due to heterogeneous cellular properties. We demonstrate that solutions of the individual-based model converge to numerical solutions of the coarse-grained model, for both slowly-varying-in-space and rapidly-varying-in-space cellular properties. We discuss applications of the model, such as determining relative cellular-level properties and an interpretation of data from a breast cancer detection experiment.

Mechanochemical Coupling and Junctional Forces during Collective Cell Migration

Cell migration, a fundamental physiological process in which cells sense and move through their surrounding physical environment, plays a critical role in development and tissue formation, as well as pathological processes, such as cancer metastasis and wound healing. During cell migration, dynamics are governed by the bidirectional interplay between cell-generated mechanical forces and the activity of Rho GTPases, a family of small GTP-binding proteins that regulate actin cytoskeleton assembly and cellular contractility. These interactions are inherently more complex during the collective migration of mechanically coupled cells because of the additional regulation of cell-cell junctional forces. In this study, we adapted a recent minimal modeling framework to simulate the interactions between mechanochemical signaling in individual cells and interactions with cell-cell junctional forces during collective cell migration. We find that migration of individual cells depends on the feedback between mechanical tension and Rho GTPase activity in a biphasic manner. During collective cell migration, waves of Rho GTPase activity mediate mechanical contraction/extension and thus synchronization throughout the tissue. Further, cell-cell junctional forces exhibit distinct spatial patterns during collective cell migration, with larger forces near the leading edge. Larger junctional force magnitudes are associated with faster collective cell migration and larger tissue size. Simulations of heterogeneous tissue migration exhibit a complex dependence on the properties of both leading and trailing cells. Computational predictions demonstrate that collective cell migration depends on both the emergent dynamics and interactions between cellular-level Rho GTPase activity and contractility and multicellular-level junctional forces.

Signaling pathways in context

The last decade has seen a rise in the development of methods and models to analyze cellular networks on all levels. The applications of this knowledge are, however, often confined to specifics of the network in concrete conditions and leveraging it is hampered by the lack of information about this context and its implications on the system. While not all cellular networks have been deciphered yet, even for well-studied networks their versatility in different contexts is barely considered. Here, we focus on challenges and potentials when integrating signaling networks into their encompassing structures. We highlight three different consequences of this process: a) its fundamental importance for whole-cell and large-scale models, b) significant changes in contextual behavior imposed on entire systems by genetic variations, and c) species-specific conservation or divergence of signaling motifs can give important clues on how to handle cellular context. While important studies have been conducted on these topics to some extent, an increased focus on developing and exploiting solutions for integrative contextualization should turn out as a fruitful path for both theoretical and experimental research.

A free boundary model of epithelial dynamics

In this work we analyse a one-dimensional, cell-based model of an epithelial sheet. In the model, cells interact with their nearest neighbouring cells and move deterministically. Cells also proliferate stochastically, with the rate of proliferation specified as a function of the cell length. This mechanical model of cell dynamics gives rise to a free boundary problem. We construct a corresponding continuum-limit description where the variables in the continuum limit description are expanded in powers of the small parameter 1/N, where N is the number of cells in the population. By carefully constructing the continuum limit description we obtain a free boundary partial differential equation description governing the density of the cells within the evolving domain, as well as a free boundary condition that governs the evolution of the domain. We show that care must be taken to arrive at a free boundary condition that conserves mass. By comparing averaged realisations of the cell-based model with the numerical solution of the free boundary partial differential equation, we show that the new mass-conserving boundary condition enables the coarse-grained partial differential equation model to provide very accurate predictions of the behaviour of the cell-based model, including both evolution of the cell density, and the position of the free boundary, across a range of interaction potentials and proliferation functions in the cell based model.