A viscous active shell theory of the cell cortex

TL;DR

This paper develops a mathematical shell theory for the cell cortex, modeling it as a viscous active layer that captures shape changes in cells, with numerical simulations of osmotic shocks and cell division.

Contribution

It introduces a new viscous active shell model for the cell cortex, incorporating turnover and active stresses, with numerical implementation for biological shape changes.

Findings

The model captures tension and moment dependencies on deformation rate and activity.

Numerical simulations demonstrate the theory's ability to replicate cell shape changes.

The framework integrates active turnover effects into shell mechanics.

Abstract

The cell cortex is a thin layer beneath the plasma membrane that gives animal cells mechanical resistance and drives most of their shape changes, from migration, division to multicellular morphogenesis. It is mainly composed of actin filaments, actin binding proteins, and myosin molecular motors. Constantly stirred by myosin motors and under fast renewal, this material may be well described by viscous and contractile active-gel theories. Here, we assume that the cortex is a thin viscous shell with non-negligible curvature and use asymptotic expansions to find the leading-order equations describing its shape dynamics, starting from constitutive equations for an incompressible viscous active gel. Reducing the three-dimensional equations leads to a Koiter-like shell theory, where both resistance to stretching and bending rates are present. Constitutive equations are completed by a kinematical equation describing the evolution of the cortex thickness with turnover. We show that tension and moment resultants depend not only on the shell deformation rate and motor activity but also on the active turnover of the material, which may also exert either contractile or extensile stress. Using the finite-element method, we implement our theory numerically to study two biological examples of drastic cell shape changes: osmotic shocks and cell division. Our work provides a numerical implementation of thin active viscous layers and a generic theoretical framework to develop shell theories for slender active biological structures.