Asymptotic analysis of microtubule-based transport by multiple identical molecular motors
We describe a system of stochastic differential equations (SDEs) which model the interaction between processive molecular motors, such as kinesin and dynein, and the biomolecular cargo they tow as part of microtubule-based intracellular transport. We show that the classical experimental environment fits within a parameter regime which is qualitatively distinct from conditions one expects to find in living cells. Through an asymptotic analysis of our system of SDEs, we develop a means for applying in vitro observations of the nonlinear response by motors to forces induced on the attached cargo to make analytical predictions for two parameter regimes that have thus far eluded direct experimental observation: (1) highly viscous in vivo transport and (2) dynamics when multiple identical motors are attached to the cargo and microtubule. âº We study the interaction of multiple molecular motors and their intracellular cargo. âº Experiments tend to report single motors working in low viscosity medium. âº Our SDE framework reveals important separations in length and time scales. âº Stochastic averaging permits rigorous analysis. âº In vitro, one motor is better than two, but in vivo, two is better than one.