Spontaneous symmetry breaking in a microtubule-like system

This paper studies asymmetric exclusion processes on a microtubule-like system with two species of particles. The model is motivated by the structure of microtubules and kinesins and dyneins moving along microtubules in opposite directions. The proposed model is similar to that in J. Phys. A 40, 2275 (2007) in which two-channel TASEPs with narrow entrances and parallel update are studied. This paper extended the above-mentioned work to a multiple-channel hollow cylinder case. Thus, each channel has two nearest neighbors in our model. The corresponding rule for narrow entrances is that particles cannot enter the system if either of two nearest-neighbor sites on neighboring channels is occupied by the other species of particles. The phase diagram of the model is obtained from a mean-field approximation and verified by computer simulations. It is shown that the spontaneous symmetry breaking exists with two asymmetric phases: high/low density and low/low density. The flipping process of particles is observed. Bulk density and particle currents are computed. Monte Carlo simulation results deviate from the mean-field prediction when entrance rate α is high, which is due to neglecting correlations among particles in mean-field calculations. The results are also compared with that obtained from two-channel system with one neighbor narrow entrance in parallel update.