Traffic of cytoskeletal motors with disordered attachment rates

Motivated by experimental results on the interplay between molecular motors and tau proteins, we extend lattice-based models of intracellular transport to include a second species of particle which locally influences the motor-filament attachment rate. We consider various exactly solvable limits of a stochastic multi-particle model before focusing on the low-motor-density regime. Here, an approximate treatment based on the random walk behaviour of single motors gives good quantitative agreement with simulation results for the tau-dependence of the motor current. Finally, we discuss the possible physiological implications of our results.