Article

# Multiple phase transitions in a system of exclusion processes with limited reservoirs of particles and fuel carriers

Journal of Statistical Mechanics Theory and Experiment (Impact Factor: 2.4). 01/2012; 2012(03). DOI: 10.1088/1742-5468/2012/03/P03002

Source: arXiv

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**ABSTRACT:**We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths and entry and exit rates, competing for a finite reservoir of particles. We present relations for the partitioning of particles between the reservoir and the lattices: These relations allow us to show that competition for particles can have nontrivial effects on the phase behavior of individual lattices. For a system with nonidentical lattices, we find that when a subset of lattices undergoes a phase transition from low to high density, the entire set of lattice currents becomes independent of total particle number. We generalize our approach to systems with a continuous distribution of lattice parameters, for which we demonstrate that measurements of the current carried by a single lattice type can be used to extract the entire distribution of lattice parameters. Our approach applies to populations of TASEPs with any distribution of lattice parameters and could easily be extended beyond the mean-field case.Physical Review E 01/2012; 85(1 Pt 1):011142. DOI:10.1103/PhysRevE.85.011142 · 2.29 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We report here results on the study of the totally asymmetric simple exclusion process, defined on an open network, consisting of head and tail simple-chain segments with a double-chain section inserted in between. Results of numerical simulations for relatively short chains reveal an interesting feature of the network. When the current through the system takes its maximum value, a simple translation of the double-chain section forward or backward along the network leads to a sharp change in the shape of the density profiles in the parallel chains, thus affecting the total number of particles in that part of the network. In the symmetric case of equal injection and ejection rates α=β>1/2 and equal lengths of the head and tail sections, the density profiles in the two parallel chains are almost linear, characteristic of the coexistence line (shock phase). Upon moving the section forward (backward), their shape changes to the one typical for the high- (low-) density phases of a simple chain. The total bulk density of particles in a section with a large number of parallel chains is evaluated too. The observed effect might have interesting implications for the traffic flow control as well as for biological transport processes in living cells. An explanation of this phenomenon is offered in terms of a finite-size dependence of the effective injection and ejection rates at the ends of the double-chain section.Physical Review E 06/2013; 87(6-1):062116. DOI:10.1103/PhysRevE.87.062116 · 2.29 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The traffic of molecular motors is often represented by means of Poissonian particles moving on a unidimensional track. However, biological ‘particles’ generally advance with complicated stepping cycles, passing through different biochemical and conformational states. In this contribution we review an extension of the typical exclusion process, the archetypical model of unidimensional transport; we explore it first from a theoretical point of view, and then we show how it has been possible to provide quantitative comparisons to experiments in the context of mRNA translation.Traffic and Granular Flow '13, Edited by Mohcine Chraibi, Maik Boltes, Andreas Schadschneider, Armin Seyfried, 01/2015: chapter Molecular Motors with a Stepping Cycle: From Theory to Experiments: pages 619-627; Springer International Publishing., ISBN: 978-3-319-10629-8