Getting work done by molecular motors
Methode: Mean field modelling, Monte Carlo simulations
Consider molecular motors walking on a microtubule. The motors are injected from one end and move to the opposite end of a microtubule They can undergo detachment on the way. Similarly, there can be attachment from the background to the microtubule. In the middle of the microtubule, there is a single alien particle which performs symmetric diffusion on the microtubule in a harmonic potential well and does not undergo detachment. Molecular motors are insensitive to the potential and run into a traffic jam scenario with this alien particle. The jamming is released only if the molecular motor detaches. The goal of the project is to characterise the fluctuations of the alien particle. In the absence of molecular motors, the mean position of the alien particle is right in the middle of the microtubule, i.e., at the bottom of the harmonic potential well. However, in presence of molecular motors, the mean position of the alien particle will be somewhat higher up the potential wall. The project will be divided into theory and simulations. The theory part will combine TASEP for molecular motors and equilibrium statistical mechanics for the alien particle. The simulations part of the project would require Monte Carlo particle-based simulations on a one dimensional lattice.