  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.
