Modelling the effect of cell motility on mixing and invasion in epithelial monolayers

Collective cell invasion underlies several biological processes such as wound healing, embryonic development, and cancerous invasion. Here, we investigate the impact of cell motility on invasion in epithelial monolayers and its coupling to cellular mechanical properties, such as cell-cell adhesion and cortex contractility. We develop a two-dimensional computational model for cells with active motility based on the cellular Potts model, which predicts that the cellular invasion speed is mainly determined by active cell motility and is independent of the biological and mechanical properties of the cells. We also find that, in general, motile cells out-compete and invade non-motile cells, however, this can be reversed by differential cell proliferation. Stable coexistence of motile and static cell types is also possible for certain parameter regimes.

A shape-driven reentrant jamming transition in confluent monolayers of synthetic cell-mimics

Many critical biological processes, like wound healing, require densely packed cell monolayers/tissues to transition from a jammed solid-like to a fluid-like state. Although numerical studies anticipate changes in the cell shape alone can lead to unjamming, experimental support for this prediction is not definitive because, in living systems, fluidization due to density changes cannot be ruled out. Additionally, a cell's ability to modulate its motility only compounds difficulties since even in assemblies of rigid active particles, changing the nature of self-propulsion has non-trivial effects on the dynamics. Here, we design and assemble a monolayer of synthetic cell-mimics and examine their collective behaviour. By systematically increasing the persistence time of self-propulsion, we discovered a cell shape-driven, density-independent, re-entrant jamming transition. Notably, we observed cell shape and shape variability were mutually constrained in the confluent limit and followed the same universal scaling as that observed in confluent epithelia. Dynamical heterogeneities, however, did not conform to this scaling, with the fast cells showing suppressed shape variability, which our simulations revealed is due to a transient confinement effect of these cells by their slower neighbors. Our experiments unequivocally establish a morphodynamic link, demonstrating that geometric constraints alone can dictate epithelial jamming/unjamming.

Forced back into shape: Mechanics of epithelial wound repair

Wound repair, the closing of a hole, is inherently a physical process that requires the change of shape of materials, in this case, cells and tissues. Not only is efficient and accurate wound repair critical for restoring barrier function and reducing infection, but it is also critical for restoring the complex three-dimensional architecture of an organ. This re-sculpting of tissues requires the complex coordination of cell behaviours in multiple dimensions, in space and time, to ensure that the repaired structure can continue functioning optimally. Recent evidence highlights the importance of cell and tissue mechanics in 2D and 3D to achieve such seamless wound repair.

Modelling of Tissue Invasion in Epithelial Monolayers

Mathematical and computational models are used to describe biomechanical processes in multicellular systems. Here, we develop a model to analyse how two types of epithelial cell layers interact during tissue invasion depending on their cellular properties, i.e., simulating cancer cells expanding into a region of normal cells. We model the tissue invasion process using the cellular Potts model and implement our two-dimensional computational simulations in the software package CompuCell3D. The model predicts that differences in mechanical properties of cells can lead to tissue invasion, even if the division rates and death rates of the two cell types are the same. We also show how the invasion speed varies depending on the cell division and death rates and the mechanical properties of the cells.

Modelling the Collective Mechanical Regulation of the Structure and Morphology of Epithelial Cell Layers

The morphology and function of epithelial sheets play an important role in healthy tissue development and cancer progression. The maintenance of structure of closely packed epithelial layers requires the coordination of various mechanical forces due to intracellular activities and interactions with other cells and tissues. However, a general model for the combination of mechanical properties which determine the cell shape and the overall structure of epithelial layers remains elusive. Here, we propose a computational model, based on the Cellular Potts Model, to analyse the interplay between mechanical properties of cells and dynamical transitions in epithelial cell shapes and structures. We map out phase diagrams as functions of cellular properties and the orientation of cell division. Results show that monolayers of squamous, cuboidal, and columnar cells are formed when the axis of cell proliferation is perpendicular to the substrate or along the major axis of the cells. Monolayer-to-multilayer transition is promoted via cell extrusion, depending on the mechanical properties of cells and the orientation of cell division. The results and model predictions are discussed in the context of experimental observations.

A mesoscale mechanical model of cellular interactions

Computational models of cell mechanics allow the precise interrogation of cell shape change. These morphological changes are required for cells to survive in diverse tissue environments. Here, we present a mesoscale mechanical model of cell-substrate interactions using the level set method based on experimentally measured parameters. By implementing a viscoelastic mechanical equivalent circuit, we accurately model whole-cell deformations that are important for a variety of cellular processes. To effectively model shape changes as a cell interacts with a substrate, we have included receptor-mediated adhesion, which is governed by catch-slip bond behavior. The effect of adhesion was explored by subjecting cells to a variety of different substrates including flat, curved, and deformable surfaces. Finally, we increased the accuracy of our simulations by including a deformable nucleus in our cells. This model sets the foundation for further exploration into computational analyses of multicellular interactions.

Theory and simulation for equilibrium glassy dynamics in cellular Potts model of confluent biological tissue

Glassy dynamics in a confluent monolayer is indispensable in morphogenesis, wound healing, bronchial asthma, and many others; a detailed theoretical framework for such a system is, therefore, important. Vertex-model (VM) simulations have provided crucial insights into the dynamics of such systems, but their nonequilibrium nature makes theoretical development difficult. The cellular Potts model (CPM) of confluent monolayers provides an alternative model for such systems with a well-defined equilibrium limit. We combine numerical simulations of the CPM and an analytical study based on one of the most successful theories of equilibrium glass, the random first-order transition theory, and develop a comprehensive theoretical framework for a confluent glassy system. We find that the glassy dynamics within the CPM is qualitatively similar to that in the VM. Our study elucidates the crucial role of geometric constraints in bringing about two distinct regimes in the dynamics, as the target perimeter P_{0} is varied. The unusual sub-Arrhenius relaxation results from the distinctive interaction potential arising from the perimeter constraint in such systems. The fragility of the system decreases with increasing P_{0} in the low-P_{0} regime, whereas the dynamics is independent of P_{0} in the other regime. The rigidity transition, found in the VM, is absent within the CPM; this difference seems to come from the nonequilibrium nature of the former. We show that the CPM captures the basic phenomenology of glassy dynamics in a confluent biological system via comparison of our numerical results with existing experiments on different systems.

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.

Role of contact inhibition of locomotion and junctional mechanics in epithelial collective responses to injury

Epithelial tissues form physically integrated barriers against the external environment protecting organs from infection and invasion. Within each tissue, epithelial cells respond to different challenges that can potentially compromise tissue integrity. In particular, cells collectively respond to injuries by reorganizing their cell-cell junctions and migrating directionally towards the sites of damage. Notwithstanding, the mechanisms that drive collective responses in epithelial aggregates remain poorly understood. In this work, we develop a minimal mechanistic model that is able to capture the essential features of epithelial collective responses to injuries. We show that a model that integrates the mechanics of cells at the cell-cell and cell-substrate interfaces as well as contact inhibition of locomotion (CIL) correctly predicts two key properties of epithelial response to injury as: (1) local relaxation of the tissue and (2) collective reorganization involving the extension of cryptic lamellipodia that extend, on average, up to 3 cell diameters from the site of injury and morphometric changes in the basal regions. Our model also suggests that active responses (like the actomyosin purse string and softening of cell-cell junctions) are needed to drive morphometric changes in the apical region. Therefore, our results highlight the importance of the crosstalk between junctional biomechanics, cell substrate adhesion, and CIL, as well as active responses, in guiding the collective rearrangements that are required to preserve the epithelial barrier in response to injury.

Modelling apical columnar epithelium mechanics from circumferential contractile fibres

Simple columnar epithelia are formed by individual epithelial cells connecting together to form single cell high sheets. They are a main component of many important body tissues and are heavily involved in both normal and cancerous cell activities. Prior experimental observations have identified a series of contractile fibres around the circumference of a cross section located in the upper (apical) region of each cell. While other potential mechanisms have been identified in both the experimental and theoretical literature, these circumferential fibres are considered to be the most likely mechanism controlling movement of this cross section. Here, we investigated the impact of circumferential contractile fibres on movement of the cross section by creating an alternate model where movement is driven from circumferential contractile fibres, without any other potential mechanisms. In this model, we utilised a circumferential contractile fibre representation based on investigations into the movement of contractile fibres as an individual system, treated circumferential fibres as a series of units, and matched our model simulation to experimental geometries. By testing against laser ablation datasets sourced from existing literature, we found that circumferential fibres can reproduce the majority of cross-sectional movements. We also investigated model predictions related to various aspects of cross-sectional movement, providing insights into epithelium mechanics and demonstrating the usefulness of our modelling approach.

Contact inhibition of locomotion and mechanical cross-talk between cell-cell and cell-substrate adhesion determine the pattern of junctional tension in epithelial cell aggregates

A computational approach is used to analyze the biomechanics of epithelial cells based on their capacity to adhere to one another and to the substrate and exhibit contact inhibition of locomotion. This approach reproduces emergent properties of epithelial cell aggregates and makes predictions for experimental validation.

We used a computational approach to analyze the biomechanics of epithelial cell aggregates—islands, stripes, or entire monolayers—that combines both vertex and contact-inhibition-of-locomotion models to include cell–cell and cell–substrate adhesion. Examination of the distribution of cell protrusions (adhesion to the substrate) in the model predicted high-order profiles of cell organization that agree with those previously seen experimentally. Cells acquired an asymmetric distribution of basal protrusions, traction forces, and apical aspect ratios that decreased when moving from the edge to the island center. Our in silico analysis also showed that tension on cell–cell junctions and apical stress is not homogeneous across the island. Instead, these parameters are higher at the island center and scale up with island size, which we confirmed experimentally using laser ablation assays and immunofluorescence. Without formally being a three-dimensional model, our approach has the minimal elements necessary to reproduce the distribution of cellular forces and mechanical cross-talk, as well as the distribution of principal stress in cells within epithelial cell aggregates. By making experimentally testable predictions, our approach can aid in mechanical analysis of epithelial tissues, especially when local changes in cell–cell and/or cell–substrate adhesion drive collective cell behavior.

The mechanical properties of a cell-based numerical model of epithelium

In this work we use a computational cell-based model to study the influence of the mechanical properties of cells on the mechanics of epithelial tissues. We analyze the effect of the model parameters on the elasticity and the mechanical response of tissues subjected to stress loading application. We compare our numerical results with experimental measurements of epithelial cell monolayer mechanics. Unlike previous studies, we have been able to estimate in physical units the parameter values that match the experimental results. A key observation is that the model parameters must vary with the tissue strain. In particular, it was found that, while the perimeter contractility and the area elasticity of cells remain constant at lower strains (<20%), they must increase to respond to larger strains (>20%). However, above a threshold of 50% extension, the cells stop counteracting the tissue strain and reduce both their perimeter contractility and area elasticity.