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

Abstract

We formulate the ‘tug-of-war’ model of microtubule cargo transport by multiple molecularmotors as an intermittent random search for a hidden target. A motor complex consistingof multiple molecular motors with opposing directional preference is modeled using adiscrete Markov process. The motors randomly pull each other off of the microtubule sothat the state of the motor complex is determined by the number of bound motors. Thetug-of-war model prescribes the state transition rates and corresponding cargo velocitiesin terms of experimentally measured physical parameters. We add space to theresulting Chapman–Kolmogorov (CK) equation so that we can consider deliveryof the cargo to a hidden target at an unknown location along the microtubuletrack. The target represents some subcellular compartment such as a synapse in aneuron’s dendrites, and target delivery is modeled as a simple absorption process.Using a quasi-steady-state (QSS) reduction technique we calculate analyticalapproximations of the mean first passage time (MFPT) to find the target. We showthat there exists an optimal adenosine triphosphate (ATP) concentration thatminimizes the MFPT for two different cases: (i) the motor complex is composed ofequal numbers of kinesin motors bound to two different microtubules (symmetrictug-of-war model) and (ii) the motor complex is composed of different numbers ofkinesin and dynein motors bound to a single microtubule (asymmetric tug-of-warmodel).