  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.
