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In many examples in intracellular transport, cargoes transported by molecular motors display a motion that is bidirectional rather than unidirectional. This type of motion, also observed in acto-myosin systems, typically appears in the presence of two groups of motors with opposite polarity, and enables an object to move efficiently in two directions. Bidirectional motion can be seen as a consequence of the collective behavior of molecular motors. We propose an analytic theory for the calculation of the reversal time. We consider the bidirectional motion as a first exit problem in a non-equilibrium system. We identify the noise strength by doing an expansion of a master equation and apply the Wentzell-Freidlin theory to define an effective nonequilibrium potential and provide analytical estimates of the reversal time. Our results match very well with the results of stochastic simulations. With high probability, a reversal event takes place along an "optimal trajectory" in the space of configurations.
We also discuss another collective effect (an oscillatory instability) appearing in the same model and compare our results to a recent experiment indicating that the acto-myosin system can become self-oscillatory when subjected to an elastic load. Instabilities due to molecular motors might be relevant for describing mechanical oscillations in a variety of biological systems, including muscles, sensory hair-cell bundles of the inner ear, and flagella. |
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