Fingering instability in spreading epithelial monolayers: roles of cell polarisation, substrate friction and contractile stresses.

Collective cell migration plays a crucial role in many developmental processes that underlie morphogenesis, wound healing, or cancer progression. In such coordinated behaviours, cells are organised in coherent structures and actively migrate to serve different biological purposes. In some contexts, namely during epithelial wound healing, it is well known that a migrating free-edge monolayer develops finger-like instabilities, yet the onset is still under debate. Here, by means of theory and numerical simulations, we shed light on the main mechanisms driving the instability process, analysing the linear and nonlinear dynamics of a continuum compressible polar fluid. In particular, we assess the role of cell polarisation, substrate friction, and contractile stresses. Linear theory shows that it is crucial to analyse the perturbation transient dynamics, since we unravel a plethora of crossovers between different exponential growth rates during the linear regime. Numerical simulations suggest that cell-substrate friction could be the mechanism responsible for the formation of complex finger-like structures at the edge, since it triggers secondary fingering instabilities and tip-splitting phenomena. Finally, we obtain a critical contractile stress that depends on cell-substrate friction and the initial-to-nematic length ratio, characterising an active wetting-dewetting transition. In the dewetting scenario, the monolayer retracts and becomes stable without developing finger-like structures.

Tracking collective cell motion by topological data analysis.

By modifying and calibrating an active vertex model to experiments, we have simulated numerically a confluent cellular monolayer spreading on an empty space and the collision of two monolayers of different cells in an antagonistic migration assay. Cells are subject to inertial forces and to active forces that try to align their velocities with those of neighboring ones. In agreement with experiments in the literature, the spreading test exhibits formation of fingers in the moving interfaces, there appear swirls in the velocity field, and the polar order parameter and the correlation and swirl lengths increase with time. Numerical simulations show that cells inside the tissue have smaller area than those at the interface, which has been observed in recent experiments. In the antagonistic migration assay, a population of fluidlike Ras cells invades a population of wild type solidlike cells having shape parameters above and below the geometric critical value, respectively. Cell mixing or segregation depends on the junction tensions between different cells. We reproduce the experimentally observed antagonistic migration assays by assuming that a fraction of cells favor mixing, the others segregation, and that these cells are randomly distributed in space. To characterize and compare the structure of interfaces between cell types or of interfaces of spreading cellular monolayers in an automatic manner, we apply topological data analysis to experimental data and to results of our numerical simulations. We use time series of data generated by numerical simulations to automatically group, track and classify the advancing interfaces of cellular aggregates by means of bottleneck or Wasserstein distances of persistent homologies. These techniques of topological data analysis are scalable and could be used in studies involving large amounts of data. Besides applications to wound healing and metastatic cancer, these studies are relevant for tissue engineering, biological effects of materials, tissue and organ regeneration.