Before revision:  Here we describe a possible physical mechanism for this distinctive set of dynamic transformations . Starting from the observation that excitable reaction-diffusion models of chemical systems can describe both localized spots and traveling waves, we augment one such model with a variable describing the spatial orientation of its chief constituent . We consider this constituent to be a caricature of polymerized actin, and regard its orientation as a measure of local actin fiber alignment. This spatial anisotropy, which is not possessed by conventional chemical species, profoundly affects localized structures to drive a transformation at fixed parameter values from static spots to moving spots to waves.
After revision:  Here we describe a possible physical mechanism for this distinctive set of dynamic transformations . Starting from the observation that excitable reaction-diffusion models of chemical systems can describe both localized spots and traveling waves, we augment one such model with a variable 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.