On the dynamics of actomyosin systems and the origin of washboard potentials

The present note is devoted to a bird's eye view of an interdisciplinary research area in which the authors have been engaged during the past few years. Here the controversial question concerning the validity of the loose-coupling versus the lever-arm models in the actomyosin dynamics is addressed by re-interpreting the washboard model earlier proposed by some of us. Specifically, we consider the diffusive motion with jumps of a particle in the presence of an asymmetric periodic potential with a unique minimum subject to half-period wide shifts occurring at random Poisson distributed times. A number of relevant quantities are explicitly obtained via averages of functions of the random variable representing the particle position.