Nonequilibrium steady states of matrix-product form: a solver's guide

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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“…Depending on the entrance and exit rates α and β, three different phases can be reached [43] in the stationary state:…”

Section: Phase Diagrammentioning

confidence: 99%

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

2015

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“…We do not describe here the very well known asymmetric exclusion process (see [24] for a review). We consider directly the stationary states.…”

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confidence: 99%

Shared information in stationary states at criticality

Alcaraz¹,

Rittenberg²

2010

J. Stat. Mech.

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We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behavior of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

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“…In this case one can show analytically (Blythe and Evans, 2007) that the maximal flux of particles (≈ translation rate) is 0.25. If one allows each of the transition rates to deviate from 1 (while keeping the mean transition rate at 1) then the average maximal flux (i.e.…”

Section: Dependence On Codon Ordermentioning

confidence: 93%

“…"traffic jams"). Various aspects of those have been widely studied using various simplified model systems (most notably TASEP (Blythe and Evans, 2007;Greulich et al, 2012)) and simulations (Ciandrini et al, 2010;Tuller et al, 2011).…”

Section: Dependence On Codon Ordermentioning

confidence: 99%

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Charting the dynamics of translation

2014

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a b s t r a c tCodon usage bias (CUB) is the well-known phenomenon that the frequency of synonymous codons is unequal. This is presumably the result of adaptive pressures favouring some codons over others. The underlying reason for this pressure is unknown, although a large number of possible driver mechanisms have been proposed. According to one hypothesis, the decoding time could be such a driver. A tacit assumption of this hypothesis is that faster codons lead to a higher translation rate which in turn is more resource efficient. While it is generally assumed that there is such a link, there are no rigorous studies to establish under which conditions the link between translation speed and rate actually exists. Using a computational simulation model and explicitly calculated codon decoding times, this contribution maps the entire range of dynamical regimes of translation. These simulations make it possible to understand precisely under which conditions translation speed and rate are linked.

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Nonequilibrium steady states of matrix-product form: a solver's guide

Cited by 626 publications

References 211 publications

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

Shared information in stationary states at criticality

Charting the dynamics of translation

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