Traffic jam on a cellular scale: molecular motors walking on microtubules
Methode: Mean field modelling, Monte Carlo simulations
Inside a cell there are polymers called Microtubules which can be likened to microscopic versions of highways. These highways are utilised by molecular motors, like nanoscopic cars, transporting cargo from outside of the cell to inside as far as to the nucleus. Some motors move in an asymmetric fashion: they don't go reverse but only forward. The motors do not always remain attached to the microtubules; they detach into the background and can reattach from the background onto the microtubule. Also the motors are exclusive; no two motors can occupy the same place on the microtubule. Such a biological system is referred to as a driven active system and has been studied extensively theoretically under the name of TASEP (Totally asymmetric exclusion principle). Such systems exhibit very interesting phase behavior: high- low coexistence phase separated by stable or unstable discontinuities in the density profile . When there are two species of motors (A and B) present on the microtubule, which move in opposite directions, traffic jams are unavoidable. However, when A and B run into each other, they can switch lanes and continue their motion and hence 'ease' the traffic jam. The goal of the project is to model such behavior. We will use a double lane system, with two families of oppositely moving motors. The project will be divided into theory and simulations. The theoretical part would require (a) mean-field modelling of the density distribution of the motors on the double lane and (b) calculating the residence time of a motor, i.e., how much time a motor spends on a given site . The simulations part of the project would require Monte Carlo particle-based simulations on a one dimensional lattice.