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We study the active dynamics of single and interacting cytoskeletal filaments in motility assays, in which immobilized motor proteins bind the filaments to a surface and actively pull them along this surface. We present a model which couples the overdamped dynamics of filaments, the active dynamics of motor heads, and the elasticity of motor stalks and which can be used for Langevin dynamics simulations. Single filaments perform a persistent random walk, which we characterize by several simulation results. For interacting filaments with a repulsive interaction of filaments, the motor-driven dynamics of filaments leads to a non-equilibrium phase transition which generalizes the isotropic-nematic phase transition of the corresponding equilibrium system, the hard-rod fluid. Langevin dynamics simulations and analytical theory show that the motor activity enhances the tendency for nematic ordering.
Kierfeld et al. (2008) studied this question.