Exact matrix-product states for parallel dynamics: open boundaries and excess mass on the ring

Woelki, Marko; Schreckenberg, Michael

doi:10.1088/1742-5468/2009/05/p05014

Cited by 13 publications

(47 citation statements)

References 24 publications

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“…In the parallel update [116,324,392], all sites are updated at the same time. The state of a given site at time t + 1 depends on the state of this site and its neighbors at time t, through -when applied to the TASEP-the rules introduced in section 4.1.1.…”

Section: Update Schemementioning

confidence: 99%

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

2015

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Cells are the elementary units of living organisms, which are able to carry out many vital functions. These functions rely on active processes on a microscopic scale. Therefore, they are strongly out-of-equilibrium systems, which are driven by continuous energy supply. The tasks that have to be performed in order to maintain the cell alive require transportation of various ingredients, some being small, others being large. Intracellular transport processes are able to induce concentration gradients and to carry objects to specific targets. These processes cannot be carried out only by diffusion, as cells may be crowded, and quite elongated on molecular scales. Therefore active transport has to be organized.The cytoskeleton, which is composed of three types of filaments (microtubules, actin and intermediate filaments), determines the shape of the cell, and plays a role in cell motion. It also serves as a road network for a special kind of vehicles, namely the 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. The interest for this type of question was enhanced when it was discovered that intracellular transport 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. Our review includes on the one hand an overview of biological facts, obtained from experiments, and on the other hand a presentation of some modeling attempts based on cellular automata. We present some 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. Some important characteristics of axonal transport is that it takes place in a confined environment; Besides several types of motors are involved, that move in opposite directions. It is a challenge to understand how this bidirectional transport is organized. We review several features that could contribute to the efficiency of bidirectional transport in the axon, including in particular the role of motor-motor interactions and of the dynamics of the underlying microtubule network. Finally, we also discuss some open questions that may be relevant for future research in this field.

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Section: Update Schemementioning

confidence: 99%

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

2015

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“…Reference [18] gives a review of parallel TASEP on a ring with a focus on traffic applications. More recently, the steady-state of a parallel TASEP on a ring where particles can jump one or two sites ahead has been characterised as a scalar-pair factorised and a matrix-product state [22].…”

Section: Introductionmentioning

confidence: 99%

On the Blockage Problem and the Non-analyticity of the Current for Parallel TASEP on a Ring

2015

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The Totally Asymmetric Simple Exclusion Process (TASEP) is an important example of a particle system driven by an irreversible Markov chain. In this paper we give a simple yet rigorous derivation of the chain stationary measure in the case of parallel updating rule. In this parallel framework we then consider the blockage problem (aka slow bond problem). We find the exact expression of the current for an arbitrary blockage intensity ε in the case of the so-called rule-184 cellular automaton, i.e. a parallel tasep where at each step all particles free-to-move are actually moved. Finally, we investigate through numerical experiments the conjecture that for parallel updates other than rule-184 the current may be non-analytic in the blockage intensity around the value ε = 0.

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“…with q = 1 − p. In this paper we interpret W ({τ }) as the number of particle-hole domain walls in the configuration {τ }. This is one possible choice following [13]. Again the vectors W | and |V reflect the boundaries and the matrices D and E represent particles and holes respectively but are different from those for the random-sequential case.…”

Section: The Tasep and The Matrix Ansatzmentioning

confidence: 99%

The parallel TASEP, fixed particle number and weighted Motzkin paths

Woelki¹

2013

J. Phys. A: Math. Theor.

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In this paper the totally asymmetric exclusion process (TASEP) with parallel update on an open lattice of size L is considered in the maximum-current region. A formal expression for the generating function for the weight of configurations with N particles is given. Further an interpretation in terms of (u, l, d)-colored weighted Motzkin paths is presented. Using previous results (Woelki and Schreckenberg 2009 J. Stat. Mech P05014, Woelki 2010 Cellular Automata, pp 637-645) the generating function is compared with the one for a possible 2nd-class particle dynamics for the parallel TASEP. It is shown that both become physically equivalent in the thermodynamic limit.

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Exact matrix-product states for parallel dynamics: open boundaries and excess mass on the ring

Cited by 13 publications

References 24 publications

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

On the Blockage Problem and the Non-analyticity of the Current for Parallel TASEP on a Ring

The parallel TASEP, fixed particle number and weighted Motzkin paths

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