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

¹ Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel.
² Department of Mathematics, The College of Sakhnin - Academic College for Teacher Education, Sakhnin 30810, Israel.
³ Department of Mathematics, Gordon College of Education, Haifa 3570503, Israel.

^* Corresponding author: mohammad.jaber.a.h@gmail.com

Received: 8 August 2021
Accepted: 27 September 2021

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 Ziebert et al. [J. R. Soc. Interface 9 (2012) 1084–1092] 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 studied in Abu Hamed and Nepomnyashchy [Physica D 408 (2020)].