Modeling Molecular Traffic: Theory, Simulations, and Potential Applications (thesis)

Abstract

I present a traffic model inspired by the motion of molecular motors along microtubules, represented by particles moving along a one-dimensional track of variable length. As the particles move unidirectionally along the track, several processes can occur: additional particles can attach at an unoccupied site, particles already on the track can move to the next open site, or particles on the track can detach. I study the model using mean-field theory and Monte Carlo simulations, with a focus on the steady-state properties and the time evolution of the particle density and particle currents. I then expand the model to include two-dimensional side-stepping along a cylindrical microtubule, as well as bidirectional movement of two different species of motors along tracks of fixed and variable length. Though each model expansion adds complexity, I keep the model general to allow for versatile applications throughout non-equilibrium statistical physics and biology.