Modeling Cell Protrusion by a Population of Actin FilamentsPublic Deposited
Actin polymerization is responsible for the protrusion of filopodia and lamellipodia in immune, cancer, and other motile cells, as well as for propulsion of some intra cellular pathogens. Protrusion of a lamellipodium by the very filaments supporting the membrane load operates by the Brownian ratchet mechanism, with overall organization governed by the dendritic-nucleation / array-treadmilling model. We have incorporated both models into a 2-D, stochastic computer model of lamellipodial protrusion and studied the self-organization of filament orientations and the energetics of protrusion. Essential dendritic-nucleation sub-models were incorporated, including discretized actin monomer diffusion, Monte-Carlo filament kinetics, and flexible filament and plasma membrane mechanics. Certain parameter values and assumptions led to the experimentally-observed ± 35 deg orientation pattern, from which estimates of the auto-catalytic filament branch rate and extent of the leading edge branching / capping protective zone were made. The model required ≈ 12 generations of successive branching to adapt to a 15 deg change in protrusion direction, suggesting that few parent filaments have long lifetimes. The pattern was robust with respect to membrane surface and bending energies and to actin concentrations, but required leading edge protection from capping and branching angles greater than 60 deg. A +70/0/−70 deg pattern was formed with flexible filaments ≈ 100 nm or longer and velocities less than ≈ 20% of free polymerization. Protrusion performance is dependent on the extent to which the work of polymerization is shared among filaments. Three mechanisms of work-sharing were identified and analyzed: A distribution of filament-load distances allows for polymerization events to protrude the load by less than one monomer length. A flexible membrane does not improve performance of 150 nm sections of lamellipodia significantly, but allows for consistent performance over much larger lengths. Filament flexibility is the most effective mechanism in un-tethered systems, but tethering limits efficacy. We estimate lamellipodia to operate with relatively short, ≈ 40 nm bending length filaments and low characteristic tether forces. Modeled lamellipodia exhibit sigmoidal force velocity relationships and perform at approximately onehalf of maximal stall force and velocity. At this level of work-sharing, the natural monomer size is optimal for maximum protrusion rate.