Effective transport statistics for cooperative molecular motor ensembles with tether slack

We improve upon our previous work using asymptotic analysis to characterize analytically the effective transport properties of a stochastic model for an ensemble of a cargo being pulled by two molecular motors walking on a microtubule. The governing equations are a system of stochastic differential equations with stochastic switching due to attachment and detachment kinetics of the molecular motors from the microtubule. Our model adopts a nonlinear tether which exerts no force when end-to-end distances are sufficiently small. This challenges some of the scale separation arguments from our previous work, and we modify the asymptotic analysis accordingly. In particular, spatial dynamics of the molecular motors may not always reach their quasi-stationary distribution within a particular attachment state. Rather, molecular motors tend to have a slack connection to the cargo for a while after they reattach, and we incorporate some first passage time analysis to determine if the tether becomes taut again. Through these and other modifications to the asymptotic analysis argument, the theoretical statistics for the run length, run time, and velocity of the motor-cargo ensemble can be brought into reasonable agreement with direct model simulations of two-motor ensembles consisting of kinesin-1 and kinesin-2. Additionally, we propose a new data fitting approach to obtain a double-exponential parameterization for the detachment rate of a motor as a function of the momentary force on its tether to the cargo, which is continuous at low load. Such a modified parameterization is needed to avoid artifacts in theoretical modeling of intracellular transport.