Steady state dynamics of molecular motors reveals load dependent cooperativity

Intracellular transport of cargoes inside eukaryotic cells is primarily carried out by bio-mechanical machines called molecular motors. These motors facilitate the directed transfer of intracellular cargo to desired locations inside the cell. In vivo modes of transport often involve multiple agents, possibly of different types, teaming up to carry a common cargo. We analyze the stochastic dynamics of such cargos and prove that the probability distribution of various motor-motor configurations in an ensemble reaches a unique steady state. Existence of such a unique steady state indicates a degree of robustness of the system of multiple motors sharing a cargo. Analysis of the steady state distribution for an ensemble of two kinesin motors for varying load forces reveals a degree of cooperativity between the motors, where configurations that have the two motors clustered together are favored for moderate loads. We further show that when subjected to high forces, such as those encountered due to obstacles along the path of travel, motors preferably adopt a configuration that facilitates high probability of regaining motion once the obstacle is removed. Simulation results of the steady state distribution of a two motor ensemble for low, moderate and high load forces are presented, which corroborate analytical studies.