A Unified Term for Directed and Undirected Motility in Collective Cell Invasion

TL;DR

This paper introduces mathematical models to unify the description of directed and undirected collective cell motility, aiding in classification and understanding of tumor invasion without chemotaxis or haptotaxis influences.

Contribution

The paper develops a nonlinear diffusion model that unifies directed and undirected cell motility, extending previous linear models and applying it to tumor invasion scenarios.

Findings

Linear model classifies cell motility assay results.

Nonlinear model captures both directed and undirected motility.

Application to tumor invasion without chemotaxis or haptotaxis.

Abstract

In this paper we develop mathematical models for collective cell motility. Initially we develop a model using a linear diffusion-advection type equation and fit the parameters to data from cell motility assays. This approach is helpful in classifying the results of cell motility assay experiments. In particular, this model can determine degrees of directed versus undirected collective cell motility. Next we develop a model using a nonlinear diffusion term that is able capture in a unified way directed and undirected collective cell motility. Finally we apply the nonlinear diffusion approach to a problem in tumor cell invasion, noting that neither chemotaxis or haptotaxis are present in the system under consideration in this article.