Eur. Phys. J. E (2019) 42: 52
https://doi.org/10.1140/epje/i2019-11815-x

Tips and Tricks

Sharp interface model for elastic motile cells

Department of Physics, McGill University, 3600 University Montréal, H3A 2T8, Québec, Canada

^* e-mail: yony.bresler@mail.mcgill.ca

Received: 25 November 2018
Accepted: 20 March 2019
Published online: 3 May 2019

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) 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, simulations required large computing resources, making a more detailed study unfeasible. In this work we derive a sharp interface limit of CPF, including all interactions and parameters. This new model scales linearly with both system and cell size, compared to our original CPF implementation, which is quadratic in cell size, this gives rise to a considerable speedup, which we discuss in the article. We demonstrate that this model captures a 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, , 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 is fully determined. Finally, cell motility is shown to linearly decrease with increasing , consistent with previous theoretical results.