  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.
