Effects of cell elasticity on the migration behavior of a monolayer of motile cells: Sharp Interface Model

Abstract

In order to study the effect of cell elastic properties on the behavior of assemblies of motile cells, this paper describes an alternative to the cell phase field (CPF) \cite{Palmieri2015} we have previously proposed. The CPF is a multi-scale approach to simulating many cells which tracked individual cells and allowed for large deformations. Though results were largely in agreement with experiment that focus on the migration of a soft cancer cell in a confluent layer of normal cells \cite{Lee2012}, simulations required large computing resources, making more detailed study unfeasible. In this work we derive a sharp interface limit of CPF, including all interactions and parameters. This new model offers over $200$ fold speedup when compared to our original CPF implementation. We demonstrate that this model captures similar behavior and allows us to obtain new results that were previously intractable. We obtain the full velocity distribution for a large range of degrees of confluence, $\rho$, and show regimes where its tail is heavier and lighter than a normal distribution. Furthermore, we fully characterize the velocity distribution with a single parameter, and its dependence on $\rho$ is fully determined. Finally, cell motility is shown to linearly decrease with increasing $\rho$, consistent with previous theoretical results