Three-dimensional phase field model for actin-based cell membrane dynamics

TL;DR

This paper introduces a 3D phase field model for simulating actin-driven cell membrane dynamics, extending previous 2D models to better understand 3D cell motility in complex environments.

Contribution

It presents a novel 3D generalization of a 2D phase field model, including coupled equations for membrane and actin network dynamics, with a derived integro-differential equation for interface evolution.

Findings

Derived a 3D interface evolution equation incorporating curvature and cytoskeletal effects.

Extended 2D models to 3D, enabling more realistic simulations of cell motility.

Provided a mathematical framework for future computational studies of cell dynamics.

Abstract

The interface dynamics of a 3D cell immersed in a 3D extracellular matrix is investigated. We suggest a 3D generalization of a known 2D minimal phase field model suggested in [1] for the description of keratocyte motility. Our model consists of two coupled evolution equations for the order parameter and a three-dimensional vector field describing the actin network polarization (orientation). We derive a closed evolutionary integro-differential equation governing the interface dynamics of a 3D cell. The equation includes the normal velocity of the membrane, its curvature, cell volume relaxation, and a parameter that is determined by the non-equilibrium effects in the cytoskeleton. This equation can be considered as a 3D generalization of the 2D case that was derived in [2].