Pattern formation in polymerising actin flocks: spirals, spots and waves without nonlinear chemistry

We propose a model solely based on actin treadmilling and polymerisation which describes many characteristic states of actin wave formation: spots, spirals and travelling waves. In our model, as in experiments on cell recovering motility following actin depolymerisation, we choose an isotropic low density initial condition; polymerisation of actin filaments then raises the density towards the Onsager threshold where they align. We show that this alignment, in turn, destabilizes the isotropic phase and generically induces transient actin spots or spirals as part of the dynamical pathway towards a polarized phase which can either be uniform or consist of a series of actin-wave trains (flocks). Our results uncover a universal route to actin wave formation in the absence of any system specific nonlinear biochemistry, and it may help understand the mechanism underlying the observation of actin spots and waves in vivo. They also suggest a minimal setup to design similar patterns in vitro.