Self-organization of actin filament orientation in the dendritic-nucleation/array-treadmilling model

The dendritic-nucleation/array-treadmilling model provides a conceptual framework for the generation of the actin network driving motile cells. We have incorporated it into a 2D, stochastic computer model to study lamellipodia via the self-organization of filament orientation patterns. Essential dendritic-nucleation submodels were incorporated, including discretized actin monomer diffusion, Monte-Carlo filament kinetics, and flexible filament and plasma membrane mechanics. Model parameters were estimated from the literature and simulation, providing values for the extent of the leading edge-branching/capping-protective zone (5.4 nm) and the autocatalytic branch rate (0.43/sec). For a given set of parameters, the system evolved to a steady-state filament count and velocity, at which total branching and capping rates were equal only for specific orientations; net capping eliminated others. The standard parameter set evoked a sharp preference for the +/- 35 degree filaments seen in lamellipodial electron micrographs, requiring approximate to 12 generations of successive branching to adapt to a 15 degree change in protrusion direction. This pattern was robust with respect to membrane surface and bending energies and to actin concentrations but required protection from capping at the leading edge and branching angles >60 degrees. A +70/0/-70 degree pattern was formed with flexible filaments approximate to 100 nm or longer and with velocities approximate to 20% of free polymerization rates.