Influence of boundary geometry on active patterns

TL;DR

This paper investigates how the shape and size of a cell's boundary influence the formation of mechanochemical patterns in the actomyosin cortex, using a hydrodynamic model and analytical as well as numerical methods.

Contribution

It provides a general framework for analyzing pattern formation on arbitrary domains and reveals how boundary geometry affects pattern types and transitions.

Findings

Patterns transition from isotropic to anisotropic with active stress changes

Domain curvature influences pattern emergence and shape

Patterns resemble those observed in confined cells

Abstract

Mechanochemical patterns arising in the actomyosin cortex drive many cellular processes. Here we consider a hydrodynamic model for the actomyosin cortex of cells and study the sensitivity of the emergent patterns to both physical parameters and the geometry of the confining domain. We first establish a general framework for the Galerkin analysis of such patterns far from the linear stability regime on an arbitrary two-dimensional domain. In the case of a circular disk, our analytical results predict transitions from isotropic to anisotropic patterns upon changing the strength of the active stress and the turnover rate. We confirm the existence of these genuine nonlinear bifurcations by an explicit numerical analysis of our model. Extending our numerical analysis to harmonic deformations of the circular disk, we show that the emergent patterns are also sensitive to the curvature of the domain. In particular, the actomyosin patterns resulting from our study closely resemble those seen in cells confined to micropatterned substrates. Our study demonstrates the role of geometry in controlling patterns within the context of a simple model for the actomyosin cortex.