Transformation from spots to waves in a model of actin pattern formation

Actin networks in certain single-celled organisms exhibit a complex pattern-forming dynamics that starts with the appearance of static spots of actin on the cell cortex. Spots soon become mobile, executing persistent random walks, and eventually give rise to traveling waves of actin. Here we describe a possible physical mechanism for this distinctive set of dynamic transformations, by equipping an excitable reaction-diffusion model with a field describing the spatial orientation of its chief constituent (which we consider to be actin). The interplay of anisotropic actin growth and spatial inhibition drives a transformation at fixed parameter values from static spots to moving spots to waves.