Shape-sensing motility of cell clusters and collective durotaxis

Abstract

Collective cell migration plays a central role in many biological processes, such as embryonic development, wound healing and cancer progression. Recent studies have predicted that non-circular epithelial cell clusters could collectively migrate through a shape-sensing mechanism, independently of any guiding external cues. This phenomenon has been called ‘shape-sensing spontaneous motility’ and has been demonstrated in numerical simulations based on the equations for active polar gels adapted to a free-boundary problem, and partially in experiments. On the other hand, collective durotaxis is a well-established phenomenon that manifests in the migration of cell clusters towards stiffer regions when the environment exhibits a stiffness gradient. In this study, we aim to observe and characterise the behaviour of simulated clusters when these two mechanisms are combined and may compete. To address this problem at a quantitative level and in different parameter regimes, one must rely on numerical simulations. Using a code based on the finite elements method, we have modelled the dynamics of cell clusters of different shapes and sizes with or without the effect of durotaxis. Results can then be analysed to draw meaningful conclusions about the motility of these cell clusters and the interplay between the two guiding effects. We find that most cases are highly non-trivial and we find some unexpected behaviours. In addition, we perform a theoretical analysis of the model for the circular case, where the radial symmetry allows us to obtain explicit expressions for most of the magnitudes in the problem. Finally, we study some particular questions arising from simulations, related to the mixed effect of the shape of the clusters and the durotaxis. After our studies, we see that cell clusters are very complex systems where the balance between forces gives rise to intricate and surprising dynamical behaviours. Many cases are not intuitive, but a certain control over the motility of these clusters seems to be possible.