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

### Full-text

Luca Ciandrini, Oct 03, 2015 Available from: Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

- [Show abstract] [Hide abstract]

**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:**Cells are strongly out-of-equilibrium systems driven by continuous energy supply. They carry out many vital functions requiring active transport of various ingredients and organelles, some being small, others being large. The cytoskeleton, composed of three types of filaments, determines the shape of the cell and plays a role in cell motion. It also serves as a road network for the so-called cytoskeletal motors. These molecules can attach to a cytoskeletal filament, perform directed motion, possibly carrying along some cargo, and then detach. It is a central issue to understand how intracellular transport driven by molecular motors is regulated, in particular because its breakdown is one of the signatures of some neuronal diseases like the Alzheimer. We give a survey of the current knowledge on microtubule based intracellular transport. We first review some biological facts obtained from experiments, and present some modeling attempts based on cellular automata. We start with background knowledge on the original and variants of the TASEP (Totally Asymmetric Simple Exclusion Process), before turning to more application oriented models. After addressing microtubule based transport in general, with a focus on in vitro experiments, and on cooperative effects in the transportation of large cargos by multiple motors, we concentrate on axonal transport, because of its relevance for neuronal diseases. It is a challenge to understand how this transport is organized, given that it takes place in a confined environment and that several types of motors moving in opposite directions are involved. We review several features that could contribute to the efficiency of this transport, including the role of motor-motor interactions and of the dynamics of the underlying microtubule network. Finally, we discuss some still open questions.