Modeling of the actin-cytoskeleton in symmetric lamellipodial fragments

The pushing structures of cells include laminar sheets, termed lamellipodia, made up of a meshwork of actin filaments that grow at the front and depolymerise at the rear, in a treadmilling mode. We here develop a mathematical model to describe the turnover and the mechanical properties of this network. Our basic modeling assumptions are that the lamellipodium is idealized as a two-dimensional structure, and that the actin network consists of two families of possibly bent, but locally parallel filaments. Instead of dealing with individual polymers, the filaments are assumed to be continuously distributed. The model has the potential to include the effects of (de)polymerization, of the mechanical effects of cross-linking, bundling, and motor proteins, of cell-substrate adhesion, as well as of the leading edge of the membrane. In the first version presented here, the total amount of F-actin is prescribed by assuming a constant polymerisation speed at the leading edge and a fixed total number and length distribution of filaments. We assume that cross-links at filament crossing points as well as integrin linkages with the matrix break and reform in response to incremental changes in network organisation. In this first treatment, the model successfully simulates the persistence of the treadmilling network in radially spread cells.