Forced and spontaneous symmetry breaking in cell polarization

Pearson W. Miller, Daniel Fortunato, Cyrill Muratov, Leslie Greengard, Stanislav Shvartsman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)504-511
Number of pages8
JournalNature Computational Science
Volume2
Issue number8
DOIs
StatePublished - Aug 2022

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Computer Science Applications
  • Computer Networks and Communications

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