Forced and spontaneous symmetry breaking in cell polarization

Document Type

Article

Publication Date

8-1-2022

Abstract

How does breaking the symmetry of an equation alter the symmetry of its solutions? Here, we systematically examine how reducing underlying symmetries from spherical to axisymmetric influences the dynamics of an archetypal model of cell polarization, a key process of biological spatial self-organization. Cell polarization is characterized by nonlinear and non-local dynamics, but we overcome the theory challenges these traits pose by introducing a broadly applicable numerical scheme allowing us to efficiently study continuum models in a wide range of geometries. Guided by numerical results, we discover a dynamical hierarchy of timescales that allows us to reduce relaxation to a purely geometric problem of area-preserving geodesic curvature flow. Through application of variational results, we analytically construct steady states on a number of biologically relevant shapes. In doing so, we reveal non-trivial solutions for symmetry breaking.

Identifier

85136838682 (Scopus)

Publication Title

Nature Computational Science

External Full Text Location

https://doi.org/10.1038/s43588-022-00295-0

e-ISSN

26628457

First Page

504

Last Page

511

Issue

8

Volume

2

Grant

R01 GM134204

Fund Ref

National Institutes of Health

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