A model for actin-filament length distribution in a lamellipod

A mathematical model is derived to describe the distributions of lengths of cytoskeletal actin filaments, along a 1 D transect of the lamellipod (or along the axis of a filopod) in an animal cell. We use the facts that actin filament barbed ends are aligned towards the cell membrane and that these ends grow rapidly in the presence of actin monomer as long as they are uncapped. Once a barbed end is capped, its filament tends to be degraded by fragmentation or depolymerization. Both the growth (by polymerization) and the fragmentation by actin-cutting agents are depicted in the model, which takes into account the dependence of cutting probability on the position along a filament. It is assumed that barbed ends are capped rapidly away from the cell membrane. The model consists of a system of discrete-integro-PDE's that describe the densities of barbed filament ends as a function of spatial position and length of their actin filament "tails". The population of capped barbed ends and their trailing filaments is similarly represented. This formulation allows us to investigate hypotheses about the fragmentation and polymerization of filaments in a caricature of the lamellipod and compare theoretical and observed actin density profiles.