Directed motion of periodically driven molecular motors: a graph-theoretical approach

We propose a numerical algorithm for calculation of quantized directed motion of a stochastic system of interacting particles induced by periodic changes of control parameters on the graph of microstates. As a main application, we consider models of catenane molecular motors, which demonstrated the possibility of a similar control of directed motion of molecular components. We show that our algorithm allows one to calculate the motion of a system in the space of its microstates even when the considered phase space is combinatorially large (~1 × 10(6) microscopic states). Several general observations are made about the structure of the phase diagram of the systems studied, which may be used for rational design and efficient control of new generations of molecular motors.