Stochastic Spatial Modeling of Attachment and Detachment Processes in Molecular Motor-Cargo Systems

Intracellular transport is conducted largely by molecular motor proteins which process along cytoskeletal filaments, from which they can attach or detach. We describe an analytical framework to characterize motor attachment or reattachment times to microtubules in a parallel architecture as a function of the physical and geometric properties of the motor, the cargo to which it is attached, and possibly a second motor attached to the same cargo and a microtubule. The biophysical model is coarse-grained at the level of the macromolecular motors and formulated in terms of stochastic differential equations. Various asymptotic approximations based on ``small target'' first passage time calculations are possible depending on the relationship of the motor-cargo tether length, the distance between microtubules, whether the cargo has a rigid or lipid membrane surface, and the initial configuration of the motor and cargo relative to the parallel microtuble network. The same methodology also allows the computation of the probability distribution for which nearby microtubule a motor will attach next.