Generalized determinant solution of the discrete-time totally asymmetric exclusion process and zero-range process

Brankov, J.G.; Priezzhev, V. B.; Shelest, R. V.

doi:10.1103/physreve.69.066136

Cited by 28 publications

(39 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Some other updates that we will not discuss further here have been proposed, such as sequential update ordered backward or forward in space [45,55,54,291,116] or sublattice update [158,121,287,290]. They can be seen as particular realisations of the frozen shuffle update.…”

Section: Update Schemementioning

confidence: 99%

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

2015

View full text Add to dashboard Cite

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.

show abstract

Section: Update Schemementioning

confidence: 99%

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

2015

View full text Add to dashboard Cite

show abstract

“…Of course, it is independent of t 0 because of the time shift invariance. It is essential that determinant form (4) of G t (x | x 0 ) generalizes to the GGF (also see [24]). N -point configurations (x, t) and (x 0 , t 0 ) be given such that t i > t 0 i for i = 1, .…”

Section: Proposition 31 the Gf Has The Determinant Formmentioning

confidence: 99%

“…For this, we introduce a generalized GF (GGF) [24], which can be explained using the language of nonintersecting lattice paths. We consider the two-dimensional integer lattice L = Z 2 .…”

Section: Proposition 31 the Gf Has The Determinant Formmentioning

confidence: 99%

Multiparticle space-time transitions in the totally asymmetric simple exclusion process

Povolotsky

Priezzhev

2011

Theor Math Phys

Self Cite

View full text Add to dashboard Cite

We study correlation functions of the totally asymmetric simple exclusion process (TASEP) in discrete time with backward sequential update. We prove a determinant formula for the generalized Green's function describing transitions between particle positions at given instants. As an example, we calculate the current correlation function, i.e., the joint probability distribution of times required by each particle to travel a given distance. An asymptotic analysis shows that current fluctuations converge to the Airy2 process.

show abstract

“…It follows easily from (2) that F GUE(n) (η) = det(D j−i+1 φ 1/2 (η)) 1≤i,j≤n . (4) This formula, given in [18], can also be obtained directly from the GUE eigenvalue measure, see Proposition 2.3 below.…”

Section: Introductionmentioning

confidence: 96%

A multi-dimensional Markov chain and the Meixner ensemble

Johansson

2010

Ark. Mat.

View full text Add to dashboard Cite

We show that the transition probability of the Markoc chain $(G(j,1),...,G(j,n))_{j\ge 1}$, where the $G(i,j)'s$ are certain directed last-passage times, is given by a determinant of a special form. An analogous formula has recently been obtained by Warren in a Brownian motion model. Furthermore we demonstrate that this formula leads to the Meixner ensemble when we compute the distribution function for $G(m,n)$. We also obtain the Fredholm determinant representation of this distribution, where the kernel has a double contour integral representation.Comment: 14 page

show abstract

Generalized determinant solution of the discrete-time totally asymmetric exclusion process and zero-range process

Cited by 28 publications

References 37 publications

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

Multiparticle space-time transitions in the totally asymmetric simple exclusion process

A multi-dimensional Markov chain and the Meixner ensemble

Contact Info

Product

Resources

About