TASEP on parallel tracks: Effects of mobile bottlenecks in fixed segments

• The first hybrid model of site-associated and particle-associated disorder.
• The model exhibits two-phase coexistence.
• A novel parameter to control the width of two-phase coexistence region.
• A new adaptation of the single-bottleneck approximation scheme.
• Potential application to the traffic of polymerase motors in living cells.

We study the flux of totally asymmetric simple exclusion processes (TASEPs) on a twin co-axial square tracks. In this biologically motivated model the particles in each track act as mobile bottlenecks against the movement of the particles in the other although the particles are not allowed to move out of their respective tracks. So far as the outer track is concerned, the particles on the inner track act as bottlenecks only over a set of fixed segments of the outer track, in contrast to site-associated and particle-associated quenched randomness in the earlier models of disordered TASEP. In a special limiting situation the movement of particles in the outer track mimic a TASEP with a “point-like” immobile (i.e., quenched) defect where phase segregation of the particles is known to take place. The length of the inner track as well as the strength and number density of the mobile bottlenecks moving on it are the control parameters that determine the nature of spatio-temporal organization of particles on the outer track. Variation of these control parameters allows variation of the width of the phase-coexistence region on the flux–density plane of the outer track. Some of these phenomena are likely to survive even in the future extensions intended for studying traffic-like collective phenomena of polymerase motors on double-stranded DNA.