Experiments indicate that depolymerization of microtubules generates sufficient force to produce the minus-end-directed transport of chromosomes during mitosis (Koshland et al., 1988). In vitro, analogous transport of kinesin-coated microspheres exhibits a paradoxical effect. Minus-end-directed transport of the microspheres driven by depolymerization is enhanced by the presence of ATP, which fuels the motor action of kinesin driving the microspheres in the opposite direction, toward the plus end of the microtubule. Here we present a mathematical model to explain this behavior. We postulate that a microsphere at the plus end of the microtubule facilitates depolymerization and hence enhances minus-end-directed transport. The force-velocity curve of the model is derived; it has the peculiar feature that velocity is maximal at some positive load (opposing the motion) rather than at zero load. The model is used to simulate the stochastic process of microsphere-facilitated depolymerization-driven transport. Simulated trajectories at low load show distinctive runs and pauses, the statistics of which are calculated from the model. The statistics of the process provide sufficient information to determine all of the model's parameters.
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