Effective statistics of molecular motors with linear and nonlinear springs

In eukaryotic cells, molecular motors are used for the active transport of cargo along microtubules. In this talk, we will model two-motor ensembles through a system of stochastic differential equations with switching. Effective statistics for velocity and diffusivity of these systems can be obtained through homogenization and renewal theory arguments, permitted through a separation of time scales between motor and cargo dynamics.  We will show that the behavior of ensembles can differ greatly depending on the choice of spring for modeling the motor tether. In particular, a nonlinear spring allows for temporarily unengaged motors.  This requires an augmented state space when using a Markov chain analysis to account for both taut and relaxed motor configurations.