A continuum model for the growth of dendritic actin networks

Polymerization of dendritic actin networks underlies important mechanical processes in cell biology such as the protrusion of lamellipodia, propulsion of growth cones in dendrites of neurons, intracellular transport of organelles and pathogens, among others. The forces required for these mechanical functions have been deduced from mechano-chemical models of actin polymerization; most models are focused on single growing filaments, and only a few address polymerization of filament networks through simulations. Here, we propose a continuum model of surface growth and filament nucleation to describe polymerization of dendritic actin networks. The model describes growth and elasticity in terms of macroscopic stresses, strains and filament density rather than focusing on individual filaments. The microscopic processes underlying polymerization are subsumed into kinetic laws characterizing the change of filament density and the propagation of growing surfaces. This continuum model can predict the evolution of actin networks in disparate experiments. A key conclusion of the analysis is that existing laws relating force to polymerization speed of single filaments cannot predict the response of growing networks. Therefore, a new kinetic law, consistent with the dissipation inequality, is proposed to capture the evolution of dendritic actin networks under different loading conditions. This model may be extended to other settings involving a more complex interplay between mechanical stresses and polymerization kinetics, such as the growth of networks of microtubules, collagen filaments, intermediate filaments and carbon nanotubes.