Lattice model for self-assembly with application to the formation of cytoskeletal-like structures.

We introduce a stochastic approach for self-assembly in systems far from equilibrium. The building blocks are represented by a lattice of discrete variables (Potts-like spins), and physically meaningful mechanisms are obtained by restricting transitions through spatially local rules based on experimental data. We use the method to study nucleation of filopodia-like bundles in a system consisting of purified actin, fascin, actin-related protein 2/3 , and beads coated with Wiskott-Aldrich syndrome protein. Consistent with previous speculation based on static experimental images, we find that bundles derive from Lambda-precursor-like patterns of spins on the lattice. The ratcheting of the actin network relative to the surface that represents beads plays an important role in determining the number and orientation of bundles due to the fact that branching is the primary means for generating barbed ends pointed in directions that allow rapid filament growth. By enabling the de novo formation of coexisting morphologies without the computational cost of explicit representation of proteins, the approach introduced complements earlier models of cytoskeletal behavior in vitro and in vivo.