Performance of a population of independent filaments in lamellipodial protrusion.

Actin polymerization is responsible for moving a wide variety of loads, from the protrusion of membrane-bound filopodia and lamellipodia of immune, cancer, and other motile cells, to the propulsion of some intracellular pathogens. A universal explanation of the forces and velocities generated by these systems has been hampered by a lack of understanding in how a population of independent filaments pushes these loads. Protrusion of a lamellipodium by the very filaments supporting the membrane load is thought to operate by the Brownian ratchet mechanism, with overall organization governed by the dendritic-nucleation/array-treadmilling model. We have incorporated these two models into a two-dimensional, stochastic computer model of lamellipodial protrusion, and studied how force and velocity generation varied under different assumptions. Performance is very sensitive to the extent to which the work of protrusion is shared among individual polymerization events within the filament population. Three identified mechanisms promote this "work-sharing": 1), Most systems, including lamellipodia, utilize a self-organizing distribution of filament-load distances which serves to decrease the effective size of a monomer and dramatically improve performance. 2), A flexible membrane allows for consistent performance over wide leading edges. 3), Finally, very flexible filaments are capable of sharing work very uniformly, and therefore, of near-perfect theoretical performance. Transient tethering to the lamellipodial membrane limits their efficacy, however, and mandates a minimum filament stiffness. Overall, we estimate lamellipodia to operate with 40-nm bending-length filaments and low characteristic tether forces. Modeled lamellipodia exhibit sigmoidal force-velocity relationships and share the work of protrusion only moderately well among filaments, performing at approximately one-half of theoretical force and velocity maximums. At this level of work-sharing, the natural monomer size is optimal for generating velocity.