Collective motion of cells crawling on a substrate: roles of cell shape and contact inhibition

Cell-Level Modelling of Homeostasis in Confined Epithelial Monolayers

Tissue homeostasis, the biological process of maintaining a steady state in tissue via control of cell proliferation and death, is essential for the development, growth, maintenance, and proper function of living organisms. Disruptions to this process can lead to serious diseases and even death. In this study, we use the vertex model for the cell-level description of tissue mechanics to investigate the impact of the tissue environment and local mechanical properties of cells on homeostasis in confined epithelial tissues. We find a dynamic steady state, where the balance between cell divisions and removals sustains homeostasis, and characterise the homeostatic state in terms of cell count, tissue area, homeostatic pressure, and the cells' neighbour count distribution. This work, therefore, sheds light on the mechanisms underlying tissue homeostasis and highlights the importance of mechanics in its control.

Collective motion of cells modeled as ring polymers

In this article, we use a coarse-grained model of disjoint semi-flexible ring polymers to investigate computationally the spatiotemporal collective behavior of cell colonies. A ring polymer in this model is self-propelled by a motility force along the cell's polarity, which depends on its historical kinetics. Despite the repulsive interaction between the cells, a collective behavior sets in as a result of cells pushing against each other. This cooperative motion emerges as the amplitude of the motility force is increased and/or their areal density is increased. The degree of collectivity, characterized by the average cluster size, the velocity field order parameter, and the polarity field nematic order parameter, is found to increase with increasing the amplitude of the motility force and area coverage of the cells. Furthermore, the degree of alignment exhibited by the cell velocity field within a cluster is found to be stronger than that exhibited by the cell polarity. Comparison between the collective behavior of elongated cells and that of circular cells, at the same area coverage and motility force, shows that elongated cells exhibit a stronger collective behavior than circular cells, in agreement with earlier studies of self-propelled anisotropic particles. An investigation of two-cell collisions shows that while two clustered cells move in tandem, their polarities are misaligned. As such the cells push against each other while moving coherently.

Modeling and simulation of cell migration on the basis of force equilibrium

To study cell behavior, we developed a cell model to simulate cell movements and the interacting forces among cells and between cells and obstacles. The developed model simulates several cells simultaneously and examines correlations among characteristic parameters between cells and substrates during migration. We modified Odde's model to develop fundamental model, applied Gillespie's stochastic algorithm to design time during in the migration simulation, and employed Keren's membrane theory to analyze the equilibrium at the leading edges. Thus, the proposed model can analyze stresses due to substrate, the intracellular body, and the external interaction between cells and obstacles. Simulation results indicate that cell-cell interaction depends on the equilibrium between the forces at the leading edge of the membrane, namely the cell-substrate interaction force, cell-cell interaction forces, and the cell membrane force. These results also indicate that the migration direction is dependent on the resultant forces. The membrane force and substrate force directions are "low correlation," and the polymerization rate exhibits "little correlative" with the migration direction. We propose a modified cell migration model for simulating allocation and interaction among multiple cells. This model helps indicate the weightings of characteristic parameters that affect the cell migration direction and velocity.

Combining experiments and in silico modeling to infer the role of adhesion and proliferation on the collective dynamics of cells

The collective dynamics of cells on surfaces and interfaces poses technological and theoretical challenges in the study of morphogenesis, tissue engineering, and cancer. Different mechanisms are at play, including, cell–cell adhesion, cell motility, and proliferation. However, the relative importance of each one is elusive. Here, experiments with a culture of glioblastoma multiforme cells on a substrate are combined with in silico modeling to infer the rate of each mechanism. By parametrizing these rates, the time-dependence of the spatial correlation observed experimentally is reproduced. The obtained results suggest a reduction in cell–cell adhesion with the density of cells. The reason for such reduction and possible implications for the collective dynamics of cancer cells are discussed.

Contact inhibition of locomotion generates collective cell migration without chemoattractants in an open domain

Neural crest cells are embryonic stem cells that migrate throughout embryos and, at different target locations, give rise to the formation of a variety of tissues and organs. The directional migration of the neural crest cells is experimentally described using a process referred to as contact inhibition of locomotion, by which cells redirect their movement upon the cell-cell contacts. However, it is unclear how the migration alignment is affected by the motility properties of the cells. Here, we theoretically model the migration alignment as a function of the motility dynamics and interaction of the cells in an open domain with a channel geometry. The results indicate that by increasing the influx rate of the cells into the domain a transition takes place from random movement to an organized collective migration, where the migration alignment is maximized and the migration time is minimized. This phase transition demonstrates that the cells can migrate efficiently over long distances without any external chemoattractant information about the direction of migration just based on local interactions with each other. The analysis of the dependence of this transition on the characteristic properties of cellular motility shows that the cell density determines the coordination of collective migration whether the migration domain is open or closed. In the open domain, this density is determined by a feedback mechanism between the flux and order parameter, which characterises the alignment of collective migration. The model also demonstrates that the coattraction mechanism proposed earlier is not necessary for collective migration and a constant flux of cells moving into the channel is sufficient to produce directed movement over arbitrary long distances.

Weakening of resistance force by cell-ECM interactions regulate cell migration directionality and pattern formation

Collective migration of epithelial cells is a fundamental process in multicellular pattern formation. As they expand their territory, cells are exposed to various physical forces generated by cell-cell interactions and the surrounding microenvironment. While the physical stress applied by neighbouring cells has been well studied, little is known about how the niches that surround cells are spatio-temporally remodelled to regulate collective cell migration and pattern formation. Here, we analysed how the spatio-temporally remodelled extracellular matrix (ECM) alters the resistance force exerted on cells so that the cells can expand their territory. Multiple microfabrication techniques, optical tweezers, as well as mathematical models were employed to prove the simultaneous construction and breakage of ECM during cellular movement, and to show that this modification of the surrounding environment can guide cellular movement. Furthermore, by artificially remodelling the microenvironment, we showed that the directionality of collective cell migration, as well as the three-dimensional branch pattern formation of lung epithelial cells, can be controlled. Our results thus confirm that active remodelling of cellular microenvironment modulates the physical forces exerted on cells by the ECM, which contributes to the directionality of collective cell migration and consequently, pattern formation.

Dynamic Self-Organization of Idealized Migrating Cells by Contact Communication

This Letter investigates what forms of cellular dynamic self-organization are caused through intercellular contact communication based on a theoretical model in which migrating cells perform contact following and contact inhibition and attraction of locomotion. Tuning those strengths causes varieties of dynamic patterns. This further includes a novel form of collective migration, snakelike dynamic assembly. Scrutinizing this pattern reveals that cells in this state can accurately respond to an external directional cue but have no spontaneous global polar order.

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.

Control of cell colony growth by contact inhibition

Contact inhibition is a cell property that limits the migration and proliferation of cells in crowded environments. Here we investigate the growth dynamics of a cell colony composed of migrating and proliferating cells on a substrate using a minimal model that incorporates the mechanisms of contact inhibition of locomotion and proliferation. We find two distinct regimes. At early times, when contact inhibition is weak, the colony grows exponentially in time, fully characterised by the proliferation rate. At long times, the colony boundary moves at a constant speed, determined only by the migration speed of a single cell and independent of the proliferation rate. Further, the model demonstrates how cell-cell alignment speeds up colony growth. Our model illuminates how simple local mechanical interactions give rise to contact inhibition, and from this, how cell colony growth is self-organised and controlled on a local level.

Molecular dynamics study of a solvation motor in a Lennard-Jones solvent

The motions of a solvation motor in a Lennard-Jones solvent were calculated by using molecular dynamics simulation. The results were analyzed considering the large spatial scale effects caused by the motion of the solvation motor. A reaction site was located on the surface of the solvation motor and the attraction between the reaction site and the solvent molecules was varied for 100 fs. The motion of the motor was driven by solvation changes near the reaction site on the motor. Two finite-size effects were observed in the motion. One was the hydrodynamic effect and the other was the increase in solvent viscosity caused by heat generation. The latter affected not only the displacement of the motor caused by the reaction but also the wave propagation phenomena. Both effects reduced the motor displacement. Heat generation affects the displacement, in particular for small systems. By contrast, the hydrodynamic effect remained even for large systems. An extrapolation method was proposed for the displacement.

Traveling band formation in feedback-driven colloids

Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an additional potential that is a superposition of repulsive potential energies centered around the positions of all the particles a delay time ago. Here we show that such a feedback leads to self-organization of the particles into traveling bands. The width of the bands and their propagation speed can be tuned by the delay time and the range of the imposed repulsive potential. The emerging traveling band behavior is observed in Brownian dynamics computer simulations as well as microscopic dynamic density functional theory. Traveling band formation also persists in systems of finite size leading to rotating traveling waves in the case of circularly confined systems.

Spontaneous spatiotemporal ordering of shape oscillations enhances cell migration

The migration of cells is relevant for processes such as morphogenesis, wound healing, and invasion of cancer cells. In order to move, single cells deform cyclically. However, it is not understood how these shape oscillations influence collective properties. Here we demonstrate, using numerical simulations, that the interplay of directed motion, shape oscillations, and excluded volume enables cells to locally "synchronize" their motion and thus enhance collective migration. Our model captures elongation and contraction of crawling ameboid cells controlled by an internal clock with a fixed period, mimicking the internal cycle of biological cells. We show that shape oscillations are crucial for local rearrangements that induce ordering of neighboring cells according to their internal clocks even in the absence of signaling and regularization. Our findings reveal a novel, purely physical mechanism through which the internal dynamics of cells influences their collective behavior, which is distinct from well known mechanisms like chemotaxis, cell division, and cell-cell adhesion.

Two types of exclusion interactions for self-propelled objects and collective motion induced by their combination

Exclusive interactions between self-driven objects may play crucial roles in their collective behavior, e.g., in collective migration of living cells. Here, such collective behavior is studied based on a simple but sufficient model taking account the exclusion effects, which incorporate the following two distinct kinds of exclusion interactions in two dimensions: The first is the mechanical exclusion wherein two objects mechanically repel each other when they overlap. The second is the scattering exclusion, wherein the directions along which each object tries to move are modulated to avoid overlapping. We propose a theoretical model based on two principles: (1) Each object maintains its own polarity with a fixed strength and attempts to move into the polarity direction and (2) objects interact with each other through the abovementioned exclusions. Based on this model, we look at the difference of consequences and combinatory effects of these two kinds of exclusions. Furthermore, we calculate the polar order of polarity directions without an external directional bias. Our results suggest that the combination of these two kinds of exclusions leads to effectively inelastic scattering of two objects, which eventually gives rise to global polar ordering. We also find that the traveling band can arise by this mechanism of alignment at the intermediate density, as generally seen in collective motion with polar alignment and investigated in various earlier works. Characteristics of transitions among disordered, traveling band, and homogeneously ordered states of the presented model are investigated, and their similarities and differences with those given by the explicit alignment interaction are discussed.

Dexamethasone-Mediated Upregulation of Calreticulin Inhibits Primary Human Glioblastoma Dispersal Ex Vivo

Dispersal of Glioblastoma (GBM) renders localized therapy ineffective and is a major cause of recurrence. Previous studies have demonstrated that Dexamethasone (Dex), a drug currently used to treat brain tumor-related edema, can also significantly reduce dispersal of human primary GBM cells from neurospheres. It does so by triggering α5 integrin activity, leading to restoration of fibronectin matrix assembly (FNMA), increased neurosphere cohesion, and reduction of neurosphere dispersal velocity (DV). How Dex specifically activates α5 integrin in these GBM lines is unknown. Several chaperone proteins are known to activate integrins, including calreticulin (CALR). We explore the role of CALR as a potential mediator of Dex-dependent induction of α5 integrin activity in primary human GBM cells. We use CALR knock-down and knock-in strategies to explore the effects on FNMA, aggregate compaction, and dispersal velocity in vitro, as well as dispersal ex vivo on extirpated mouse retina and brain slices. We show that Dex increases CALR expression and that siRNA knockdown suppresses Dex-mediated FNMA. Overexpression of CALR in GBM cells activates FNMA, increases compaction, and decreases DV in vitro and on explants of mouse retina and brain slices. Our results define a novel interaction between Dex, CALR, and FNMA as inhibitors of GBM dispersal.