# Modelling adhesion-independent cell migration

## TL;DR

This paper introduces a mathematical model for cell migration that occurs without adhesion, using an elastic cortex and cortical flow, and demonstrates its ability to replicate experimental behaviors.

## Contribution

It presents a novel nonlinear degenerate parabolic model for adhesion-independent cell motility and provides an existence analysis and numerical simulations.

## Key findings

- Model captures key features of adhesion-independent migration
- Simulations align with experimental observations
- Suggests a mechanical mechanism for cell motility without adhesion

## Abstract

A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net polymerization or depolymerization in the cortex is modelled via local addition or removal of material, driving a cortical flow. The model takes the form of a fully nonlinear degenerate parabolic system. An existence analysis is carried out by adapting ideas from the theory of gradient flows. Numerical simulations show that these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for adhesion-independent motility.