Parallel coupling of symmetric and asymmetric exclusion processes

Abstract

Abstract.A system consisting of two parallel coupled channels where particles in one of them follow the rules of totally asymmetric exclusion processes (TASEP) and in another one move as in symmetric simple exclusion processes (SSEP) is investigated theoretically. Particles interact with each other via hard-core exclusion potential, and in the asymmetric channel they can only hop in one direction, while on the symmetric lattice particles jump in both directions with equal probabilities. Inter-channel transitions are also allowed at every site of both lattices. Stationary state properties of the system are solved exactly in the limit of strong couplings between the channels. It is shown that strong symmetric couplings between totally asymmetric and symmetric channels lead to an effective partially asymmetric simple exclusion process (PASEP) and properties of both channels become almost identical. However, strong asymmetric couplings between symmetric and asymmetric channels yield an effective TASEP with nonzero particle flux in the asymmetric channel and zero flux on the symmetric lattice. For intermediate strength of couplings between the lattices a vertical cluster mean-field method is developed. This approximate approach treats exactly particle dynamics during the vertical transitions between the channels and it neglects the correlations along the channels. Our calculations show that in all cases there are three stationary phases defined by particle dynamics at entrances, at exits or in the bulk of the system, while phase boundaries depend on the strength and symmetry of couplings between the channels. Extensive Monte Carlo computer simulations strongly support our theoretical predictions. Theoretical calculations and computer simulations predict that inter-channel couplings have a strong effect on stationary properties. It is also argued that our results might be relevant for understanding multi-particle dynamics of motor proteins.

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

“…The characteristics of the stationary state, and in particular the phase diagram, were studied first in [155] in the case of very asymetric lane changes, and more recently obtained for more general rules from a stability analysis of the mean-field profiles [119]. The case of back-stepping was also considered [119,367].…”

Driven transport on parallel lanes with particle exclusion and obstruction

“…Further attention has been paid to transport along several coupled channels where particles move in parallel. This coupling can be either achieved by allowing lane-switching events [12,[29][30][31][32][33][34][35][36][37] or by a possible influence of a particle in one channel on the motion in the other channel [7,38]. Here we consider the latter case and investigate how mutual obstruction of motor proteins on neighboring lanes, for example, stemming from large cargos attached to them, affects the transport properties of the system.…”

Modelling interacting molecular motors with an internal degree of freedom

“…If we have a TASEP on two tracks, the track on which a particle is found can be considered as an internal state and the problem can therefore be mapped to particles moving on an effective single track. These kinds of models were considered in [34][35][36][37][38] where two particles with different internal states (different tracks) can be on the same effective site. Two-state generalization of a TASEP was also discussed in [39], where it is called the dual model.…”