Simulating the role of microtubules in depolymerization-driven transport: a Monte Carlo approach

In this paper we present a model that simulates the role of microtubules in depolymerization-driven transport. The model simulates a system that consists of a 13-protofilament microtubule with "five-start" helical structure and a motor protein-coated bead that moves along one of the protofilaments of the microtubule, as in in vitro experiments. The microtubule is simulated using the lateral cap model, with substantial generalizations. For the new terminal configurations in the presence of the bead, rate constants for association and dissociation events of tubulin molecules are calculated by exploring the geometric similarities between different patterns of terminal configurations and by decomposing complex patterns into simpler patterns whose corresponding rate constants are known. In comparison with a previous model, in which simplifications are made about the structure of the microtubule and in which the microtubule can only depolymerize, the detailed structure of the microtubule is taken into account in the present model. Furthermore, the microtubule can be either polymerizing or depolymerizing. Force-velocity curves are obtained for both zero and non-zero tubulin guanosine 5'-triphosphate (GTP) concentrations. By analyzing the trajectory of the bead under different parameters, the condition for "run and pause" is analyzed, and the time scale of "run" and "pause" is found to be different for different motor proteins. We also suggest experiments that can be used to examine the results predicted by the model.