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


The TASEP is a paradigmatic model from non-equilibrium statistical physics,
which describes particles hopping along a lattice of discrete sites. The TASEP
is applicable to a broad range of different transport systems, but does not
consider the fact that in many such systems the availability of resources
required for the transport is limited. In this paper we extend the TASEP to
include the effect of a limited number of two different fundamental transport
resources: the hopping particles, and the "fuel carriers", which provide the
energy required to drive the system away from equilibrium. As as consequence,
the system's dynamics are substantially affected: a "limited resources" regime
emerges, where the current is limited by the rate of refuelling, and the usual
coexistence line between low and high particle density opens into a broad
region on the phase plane. Due to the combination of a limited amount of both
resources, multiple phase transitions are possible when increasing the exit
rate beta for a fixed entry rate alpha. This is a new feature that can only be
obtained by the inclusion of both kinds of limited resources. We also show that
the fluctuations in particle density in the LD and HD phases are unaffected by
fluctuations in the number of loaded fuel carriers, except by the fact that
when these fuel resources become limited, the particle hopping rate is severely

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Available from: Luca Ciandrini, Oct 03, 2015
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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
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    Physical Review E 06/2013; 87(6-1):062116. DOI:10.1103/PhysRevE.87.062116 · 2.29 Impact Factor
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    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.