Elastically coupled two-dimensional Brownian motors

Many workers have theoretically and numerically studied Brownian motors (ratchet models) as models for molecular motors for many years. Their studies have been mainly concerned about one-dimensional motion of a particle or coupled particles experiencing spatially asymmetric interaction force. In this paper, we introduce a coupled flashing ratchet model, that is, elastically coupled Brownian particles with their own easily advancing directions under the on-and-off (or occasional) influence of two- dimensional interaction force asymmetric in the easily advancing direction of each particle. The dynamics of the model is investigated by computer simulation and characteristic motion of the particles in the two- dimensional space is observed. Our model is also studied as that for molecular motors in muscle contraction and the simulation results are compared with those of in vitro biological experiments in motility assays of the molecular motors. We succeed in reproducing the experimental results qualitatively with our model.