Reaction–diffusion–advection approach to spatially localized treadmilling aggregates of molecular motors

• Reaction–diffusion–advection model for the formation of spatially localized molecular-motor aggregates (pulses).
• Analytic trends of pulses properties via model parameters: shape and propagation velocity.

Unconventional myosins belong to a class of molecular motors that walk processively inside cellular protrusions towards the tips, on top of actin filament. Surprisingly, in addition, they also form retrograde moving self-organized aggregates. The qualitative properties of these aggregates are recapitulated by a mass conserving reaction–diffusion–advection model and admit two distinct families of modes: traveling waves and pulse trains. Unlike the traveling waves that are generated by a linear instability, pulses are nonlinear structures that propagate on top of linearly stable uniform backgrounds. Asymptotic analysis of isolated pulses via a simplified reaction–diffusion–advection variant on large periodic domains, allows to draw qualitative trends for pulse properties, such as the amplitude, width, and propagation speed. The results agree well with numerical integrations and are related to available empirical observations.