Translational instability in actin lamellar fragments: a weakly nonlinear stability analysis

Lamellar fragments of cells with actin filaments exhibit autonomous symmetry-breaking shape transitions and motility. We model such lamellar fragments as a fluid bound by an elastic boundary with bending resistance that is driven continuously by actin polymerization. Weakly-nonlinear stability analysis is applied to investigate the fingering instability at such an interface. We show that the dominant unstable modes can cause the translational mode to become unstable in the nonlinear regime, leading to asymmetric shapes and net motility of the fragment. We further show that a local geometry-based line model of the interface can reproduce the qualitatively similar behaviour.