Totally asymmetric exclusion process on chains with a double-chain section in the middle: Computer simulations and a simple theory

Abstract

Computer simulations of the totally asymmetric simple-exclusion process on chains with a double-chain section in the middle are performed in the case of random-sequential update. The outer ends of the chain segments connected to the middle double-chain section are open, so that particles are injected at the left end with rate alpha and removed at the right end with rate beta. At the branching point of the graph (the left end of the middle section) the particles choose with equal probability 1/2 which branch to take and then simultaneous motion of the particles along the two branches is simulated. With the aid of a simple theory, neglecting correlations at the junctions of the chain segments, the possible phase structures of the model are clarified. Density profiles and nearest-neighbor correlations in the steady states of the model at representative points of the phase diagram are obtained and discussed. Cross correlations are found to exist between equivalent sites of the branches of the middle section whenever they are in a coexistence phase.

The zone strong coupling two-channel totally asymmetric simple exclusion processes

“…Therefore, β eff always satisfies the conditions (19). However, this equation yields physically rational values of the effective existence rate only when the term in the square root is positive, i.e.…”

“…However, many real phenomena are described using parallel-chain asymmetric exclusion processes. Recently, parallel-chain ASEPs [14][15][16] and parallel-chain ASEPs with junctions [17][18][19][20] have been considered. In these investigations, the coupling between different chains was indirect, for instance hopping between the chains was forbidden.…”

Position-Induced Phase Change in a TASEP with a Double-Chain Section (a Model of Biological Transport)

“…The idea of studying networks, composed of chain segments, which exhibit the bulk behavior of an open TASEP under boundary conditions given in terms of effective input and output rates, was first advanced in our work [25]. The network considered there is shown schematically in Fig.…”

“…This year, the cases of multiple competing TASEPs with a shared reservoir of particles [32,33], and TASEP with Langmuir kinetics and memory reservoirs [34] were studied too. The next section is devoted to the single chain TASEP, then a short overview is given on the TASEP with a double-chain section in-between [25]. The last section is devoted to our new Monte Carlo simulation results displaying a novel property of the model with the double-chain section in the maximum-current phase.…”

“…Another challenging problem, from both biological and mathematical point of view, is the consideration of biochemical transport phenomena on networks with non-trivial topology. Our goal here is to present a study of the effects, arising in TASEP, defined on a simple example of such a network: a linear chain of attachment sites with a double-chain defect inserted in it [25]. For other studies of TASEP on topologies more complex than a single segment see [26,27,28,29].…”