Spatio-temporal dynamics of optical molecular motors

Molecular motors are multicomponent molecular structures that consume energy to induce motion and to generate forces. Their dynamics covers various time and length scales and critically depends on chemical-mechanical coupling, external forces and molecular properties such as diffusion, particle distribution and density. The complex behavior of these systems consequently offers a formidable challenge for theoretical descriptions and numerical approaches that aim to provide a computational laboratory for a fundamental analysis of the underlying interaction mechanisms as well as interpretations or to study control of the system's behavior. Coupling a linear molecular motor system to an energy supply can induce movement of the motor molecules along a filamentous structure. The complex dynamics of bound (i.e. attached to a filament) and free (i.e. diffusing in the surrounding medium) molecular motors thereby may depend on the diffusive properties of the molecules and on the excitation process driving the motor system. Our theory is therefore based on spatially dependent Fokker-Planck equations for the dynamics of bound and free motors. The model considers spatially inhomogeneous transition rates coupling the energetic sublebels of the molecules as well as spacial fluctuations and diffusion. Computational modelling of the spatio-temporal dynamics of molecular motors shows that both. molecular diffusion and bandwidth of the transition rate set an upper limit to the efficiency of the motor progression. A sufficiently small molecular diffusion as well as a thorough adjustment of transition rates lead to a regular forward propagation while for high diffusion and improperly chosen rates spatio-temporally diverging particle distributions may evolve. Suitable excitation conditions for efficient movement-control are discussed.