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.

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.

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.

Assessment of heterogeneity in collective endothelial cell behavior with multicolor clonal cell tracking to predict arteriovenous remodeling.

Arteries and veins form in a stepwise process that combines vasculogenesis and sprouting angiogenesis. Despite extensive data on the mechanisms governing blood vessel assembly at the single-cell level, little is known about how collective cell migration contributes to the organization of the balanced distribution between arteries and veins. Here, we use an endothelial-specific zebrafish reporter, arteriobow, to label small cohorts of arterial cells and trace their progeny from early vasculogenesis throughout arteriovenous remodeling. We reveal that the genesis of arteries and veins relies on the coordination of 10 types of collective cell dynamics. Within these behavioral categories, we identify a heterogeneity of collective cell motion specific to either arterial or venous remodeling. Using pharmacological blockade, we further show that cell-intrinsic Notch signaling and cell-extrinsic blood flow act as regulators in maintaining the heterogeneity of collective endothelial cell behavior, which, in turn, instructs the future territory of arteriovenous remodeling.

Transition from growth to decay of an epidemic due to lockdown.

We study the transition of an epidemic from growth phase to decay of the active infections in a population when lockdown health measures are introduced to reduce the probability of disease transmission. Although in the case of uniform lockdown, a simple compartmental model would indicate instantaneous transition to decay of the epidemic, this is not the case when partially isolated active clusters remain with the potential to create a series of small outbreaks. We model this using the Gillespie stochastic simulation algorithm based on a connected set of stochastic susceptible-infected-removed/recovered networks representing the locked-down majority population (in which the reproduction number is less than 1) weakly coupled to a large set of small clusters in which the infection may propagate. We find that the presence of such active clusters can lead to slower than expected decay of the epidemic and significantly delayed onset of the decay phase. We study the relative contributions of these changes, caused by the active clusters within the population, to the additional total infected population. We also demonstrate that limiting the size of the inevitable active clusters can be efficient in reducing their impact on the overall size of the epidemic outbreak. The deceleration of the decay phase becomes apparent when the active clusters form at least 5% of the population.

Effects of social distancing on the spreading of COVID-19 inferred from mobile phone data.

A better understanding of how the COVID-19 pandemic responds to social distancing efforts is required for the control of future outbreaks and to calibrate partial lock-downs. We present quantitative relationships between key parameters characterizing the COVID-19 epidemiology and social distancing efforts of nine selected European countries. Epidemiological parameters were extracted from the number of daily deaths data, while mitigation efforts are estimated from mobile phone tracking data. The decrease of the basic reproductive number ([Formula: see text]) as well as the duration of the initial exponential expansion phase of the epidemic strongly correlates with the magnitude of mobility reduction. Utilizing these relationships we decipher the relative impact of the timing and the extent of social distancing on the total death burden of the pandemic.

Multicellular contractility contributes to the emergence of mesothelioma nodules.

Malignant pleural mesothelioma (MPM) has an overall poor prognosis and unsatisfactory treatment options. MPM nodules, protruding into the pleural cavity may have growth and spreading dynamics distinct that of other solid tumors. We demonstrate that multicellular aggregates can develop spontaneously in the majority of tested MPM cell lines when cultured at high cell density. Surprisingly, the nodule-like aggregates do not arise by excessive local cell proliferation, but by myosin II-driven cell contractility. Prominent actin cables, spanning several cells, are abundant both in cultured aggregates and in MPM surgical specimens. We propose a computational model for in vitro MPM nodule development. Such a self-tensioned Maxwell fluid exhibits a pattern-forming instability that was studied by analytical tools and computer simulations. Altogether, our findings may underline a rational for targeting the actomyosin system in MPM.

Processivity of molecular motors under vectorial loads.

Molecular motors are cellular machines that drive the spatial organization of the cells by transporting cargos along intracellular filaments. Although the mechanical properties of single molecular motors are relatively well characterized, it remains elusive how the geometry of a load imposed on a motor affects its processivity, i.e., the average distance that a motor moves per interaction with a filament. Here, we theoretically explore this question for a single-kinesin molecular motor by analyzing the load dependence of the stepping and detachment processes. We find that the processivity of the kinesin increases with lowering the load angle between the kinesin and the microtubule filament, due to the deceleration of the detachment rate. When the load angle is large, the processivity is predicted to enhance with accelerating the stepping rate through an optimal distribution of the load over the kinetic transition rates underlying a mechanical step of the motor. These results provide new insights into understanding of the design of potential synthetic biomolecular machines that can travel long distances with high velocities.

Targeted adaptive isolation strategy for COVID-19 pandemic.

We investigate the effects of social distancing in controlling the impact of the COVID-19 epidemic using a simple susceptible-infected-removed epidemic model. We show that an alternative or complementary approach based on targeted isolation of the vulnerable sub-population may provide a more efficient and robust strategy at a lower economic and social cost within a shorter timeframe resulting in a collectively immune population.

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.

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.

The role of Allee effect in modelling post resection recurrence of glioblastoma.

Resection of the bulk of a tumour often cannot eliminate all cancer cells, due to their infiltration into the surrounding healthy tissue. This may lead to recurrence of the tumour at a later time. We use a reaction-diffusion equation based model of tumour growth to investigate how the invasion front is delayed by resection, and how this depends on the density and behaviour of the remaining cancer cells. We show that the delay time is highly sensitive to qualitative details of the proliferation dynamics of the cancer cell population. The typically assumed logistic type proliferation leads to unrealistic results, predicting immediate recurrence. We find that in glioblastoma cell cultures the cell proliferation rate is an increasing function of the density at small cell densities. Our analysis suggests that cooperative behaviour of cancer cells, analogous to the Allee effect in ecology, can play a critical role in determining the time until tumour recurrence.

Optical-flow based non-invasive analysis of cardiomyocyte contractility.

Characterization of cardiomyocyte beat patterns is needed for quality control of cells intended for surgical injection as well as to establish phenotypes in disease modeling or toxicity studies. Optical-flow based analysis of videomicroscopic recordings offer a manipulation-free and efficient characterization of contractile cycles, an important characteristics of cardiomyocyte phenotype. We demonstrate that by appropriate computational analysis of optical flow data one can identify distinct contractile centers and distinguish active cell contractility from passive elastic tissue deformations. Our proposed convergence measure correlates with myosin IIa immuno-localization and is capable to resolve contractile waves and their synchronization within maturing, unlabeled induced pluripotent stem cell-derived cardiomyocyte cultures.

Bistable front dynamics in a contractile medium: Travelling wave fronts and cortical advection define stable zones of RhoA signaling at epithelial adherens junctions.

Mechanical coherence of cell layers is essential for epithelia to function as tissue barriers and to control active tissue dynamics during morphogenesis. RhoA signaling at adherens junctions plays a key role in this process by coupling cadherin-based cell-cell adhesion together with actomyosin contractility. Here we propose and analyze a mathematical model representing core interactions involved in the spatial localization of junctional RhoA signaling. We demonstrate how the interplay between biochemical signaling through positive feedback, combined with diffusion on the cell membrane and mechanical forces generated in the cortex, can determine the spatial distribution of RhoA signaling at cell-cell junctions. This dynamical mechanism relies on the balance between a propagating bistable signal that is opposed by an advective flow generated by an actomyosin stress gradient. Experimental observations on the behavior of the system when contractility is inhibited are in qualitative agreement with the predictions of the model.

Functional Definition of Progenitors Versus Mature Endothelial Cells Reveals Key SoxF-Dependent Differentiation Process.

BACKGROUND: During adult life, blood vessel formation is thought to occur via angiogenic processes involving branching from existing vessels. An alternate proposal suggests that neovessels form from endothelial progenitors able to assemble the intimal layers. We here aimed to define vessel-resident endothelial progenitors in vivo in a variety of tissues in physiological and pathological situations such as normal aorta, lungs, and wound healing, tumors, and placenta, as well. METHODS: Based on protein expression levels of common endothelial markers using flow cytometry, 3 subpopulations of endothelial cells could be identified among VE-Cadherin+ and CD45- cells. RESULTS: Lineage tracing by using Cdh5creERt2/Rosa-YFP reporter strategy demonstrated that the CD31-/loVEGFR2lo/intracellular endothelial population was indeed an endovascular progenitor (EVP) of an intermediate CD31intVEGFR2lo/intracellular transit amplifying (TA) and a definitive differentiated (D) CD31hiVEGFR2hi/extracellular population. EVP cells arose from vascular-resident beds that could not be transferred by bone marrow transplantation. Furthermore, EVP displayed progenitor-like status with a high proportion of cells in a quiescent cell cycle phase as assessed in wounds, tumors, and aorta. Only EVP cells and not TA and D cells had self-renewal capacity as demonstrated by colony-forming capacity in limiting dilution and by transplantation in Matrigel plugs in recipient mice. RNA sequencing revealed prominent gene expression differences between EVP and D cells. In particular, EVP cells highly expressed genes related to progenitor function including Sox9, Il33, Egfr, and Pdfgrα. Conversely, D cells highly expressed genes related to differentiated endothelium including Ets1&2, Gata2, Cd31, Vwf, and Notch. The RNA sequencing also pointed to an essential role of the Sox18 transcription factor. The role of SOX18 in the differentiation process was validated by using lineage-tracing experiments based on Sox18CreERt2/Rosa-YFP mice. Besides, in the absence of functional SOX18/SOXF, EVP progenitors were still present, but TA and D populations were significantly reduced. CONCLUSIONS: Our findings support an entirely novel endothelial hierarchy, from EVP to TA to D, as defined by self-renewal, differentiation, and molecular profiling of an endothelial progenitor. This paradigm shift in our understanding of vascular-resident endothelial progenitors in tissue regeneration opens new avenues for better understanding of cardiovascular biology.

Bimodal behaviour of interfollicular epidermal progenitors regulated by hair follicle position and cycling.

Interfollicular epidermal (IFE) homeostasis is a major physiological process allowing maintenance of the skin barrier function. Despite progress in our understanding of stem cell populations in different hair follicle compartments, cellular mechanisms of IFE maintenance, in particular, whether a hierarchy of progenitors exists within this compartment, have remained controversial. We here used multicolour lineage tracing with Brainbow transgenic labels activated in the epidermis to track individual keratinocyte clones. Two modes of clonal progression could be observed in the adult murine dorsal skin. Clones attached to hair follicles showed rapid increase in size during the growth phase of the hair cycle. On the other hand, clones distant from hair follicles were slow cycling, but could be mobilized by a proliferative stimulus. Reinforced by mathematical modelling, these data support a model where progenitor cycling characteristics are differentially regulated in areas surrounding or away from growing hair follicles. Thus, while IFE progenitors follow a non-hierarchical mode of development, spatiotemporal control by their environment can change their potentialities, with far-reaching implications for epidermal homeostasis, wound repair and cancer development.

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.

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.

Modelling wound closure in an epithelial cell sheet using the cellular Potts model.

We use a two-dimensional cellular Potts model to represent the behavior of an epithelial cell layer and describe its dynamics in response to a microscopic wound. Using an energy function to describe properties of the cells, we found that the interaction between contractile tension along cell-cell junctions and cell-cell adhesion plays an important role not only in determining the dynamics and morphology of cells in the monolayer, but also in influencing whether or not a wound in the monolayer will close. Our results suggest that, depending on the balance between cell-cell adhesion and junctional tension, mechanics of the monolayer can either correspond to a hard or a soft regime that determines cell morphology and polygonal organization in the monolayer. Moreover, the presence of a wound in a hard regime, where junctional tension is significant, can lead to two results: (1) wound closure or (2) an initial increase and expansion of the wound area towards an equilibrium value. Theoretical approximations and simulations allowed us to determine the thresholds in the values of cell-cell adhesion and initial wound size that allow the system to lead to wound closure. Overall, our results suggest that around the site of injury, changes in the balance between contraction and adhesion determine whether or not non-monotonous wound closure occurs.

Self-organizing actomyosin patterns on the cell cortex at epithelial cell-cell junctions.

The behavior of actomyosin critically determines morphologically distinct patterns of contractility found at the interface between adherent cells. One such pattern is found at the apical region (zonula adherens) of cell-cell junctions in epithelia, where clusters of the adhesion molecule E-cadherin concentrate in a static pattern. Meanwhile, E-cadherin clusters throughout lateral cell-cell contacts display dynamic movements in the plane of the junctions. To gain insight into the principles that determine the nature and organization of these dynamic structures, we analyze this behavior by modeling the 2D actomyosin cell cortex as an active fluid medium. The numerical simulations show that the stability of the actin filaments influences the spatial structure and dynamics of the system. We find that in addition to static Turing-type patterns, persistent dynamic behavior occurs in a wide range of parameters. In the 2D model, mechanical stress-dependent actin breakdown is shown to produce a continuously changing network of actin bridges, whereas with a constant breakdown rate, more isolated clusters of actomyosin tend to form. The model qualitatively reproduces the dynamic and stable patterns experimentally observed at the junctions between epithelial cells.