Random intermittent search and the tug-of-war model of motor-driven transport

We formulate the 'tug-of-war' model of microtubule cargo transport by multiple molecular motors as an intermittent random search for a hidden target. A motor complex consisting of multiple molecular motors with opposing directional preference is modeled using a discrete Markov process. The motors randomly pull each other off of the microtubule so that the state of the motor complex is determined by the number of bound motors. The tug-of-war model prescribes the state transition rates and corresponding cargo velocities in terms of experimentally measured physical parameters. We add space to the resulting Chapman–Kolmogorov (CK) equation so that we can consider delivery of the cargo to a hidden target at an unknown location along the microtubule track. The target represents some subcellular compartment such as a synapse in a neuron's dendrites, and target delivery is modeled as a simple absorption process. Using a quasi-steady-state (QSS) reduction technique we calculate analytical approximations of the mean first passage time (MFPT) to find the target. We show that there exists an optimal adenosine triphosphate (ATP) concentration that minimizes the MFPT for two different cases: (i) the motor complex is composed of equal numbers of kinesin motors bound to two different microtubules (symmetric tug-of-war model) and (ii) the motor complex is composed of different numbers of kinesin and dynein motors bound to a single microtubule (asymmetric tug-of-war model)