Cellular automaton model of the actin cytoskeleton

We describe a cellular automaton model of the actin cytoskeleton. The model incorporates spatial and temporal behavior at the macromolecular level and is relevant to the viscous nonequilibrium conditions suspected to occur in vivo. The model includes cation and nucleotide binding to actin monomers, actin nucleation and polymerization into filaments, cross-linking with alpha-actinin, monomer sequestration with profilin, filament severing, capping and nucleation with gelsolin, binding of profilin and gelsolin to membrane-bound phosphatidylinositide biphosphate (PIP2), and regulation of cross-linking and severing by changing calcium levels. We derive 1) equations for the molecular translation and rotation probabilities required for the cellular automaton simulation in terms of molecular size, shape, cytoplasmic viscosity, and temperature; and 2) equations for the binding probabilities of adjacent molecules in terms of experimentally determined reaction rate constants. The model accurately captures the known characteristics of actin polymerization and subsequent ATP hydrolysis under different cation and nucleotide conditions. An examination of gelation and sol-gel transitions resulting from calcium regulation of alpha-actinin and gelsolin predicts an inhomogeneous distribution of bound alpha-actinin and F-actin. The double-bound alpha-actinin (both ends bound to F-actin) is tightly bunched, while single-bound alpha-actinin is moderately bunched and unbound alpha-actinin is homogeneously distributed. The spatial organization of the alpha-actinin is quantified using estimates of fractal dimension. The simulation results also suggest that actin/alpha-actinin gels may shift from an isotropic to an amorphous phase after shortening of filaments. The gel-sol transition of the model shows excellent agreement with the present theory of polymer gels. The close correspondence of the model's predictions with previous experimental and theoretical results suggests that the model may be pertinent to better understanding the spatial and temporal properties of complex cytoskeletal processes.