A simple model of Keratocyte membrane dynamics

TL;DR

This paper analytically investigates keratocyte membrane dynamics using a minimal phase field model, deriving integro-differential equations that describe cell interface behavior and conditions for stationary shapes.

Contribution

It introduces a simplified mathematical model for cell membrane dynamics, deriving a key integro-differential equation and analyzing conditions for stable cell shapes.

Findings

Derived a closed-form integro-differential equation for membrane dynamics

Identified conditions for stationary cell shapes

Simplified the model to a Burgers-like equation

Abstract

We perform an analytical investigation of the cell interface dynamics in the framework of a minimal phase field model of cell motility suggested in [1], which consists of two coupled evolution equations for the order parameter and a two-dimensional vector field describing the actin network polarization (orientation). We derive a closed evolutionary integro-differential equation governing the cell interface dynamics. The equation includes the normal velocity of the membrane, curvature, volume relaxation, and a parameter that is determined by the non-equilibrium effects in the cytoskeleton. This equation can be simplified to obtain a Burgers-like equation. A condition on the system parameters for the existence of a stationary cell shape is obtained.