Disordered totally asymmetric simple exclusion process: Exact results

Kolwankar, Kiran M.; Punnoose, Alexander

doi:10.1103/physreve.61.2453

Cited by 36 publications

(34 citation statements)

References 14 publications

(14 reference statements)

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“…Sequence inhomogeneity can lead to site-dependent rates of translocation of RNAP on its track. In the context of TASEP, which is a special limit of our model of RNAP traffic, effects of quenched random site-dependent hopping rates [59,60,61,62,63,64,65,66,67], have been investigated extensively over the last decade. Moreover, Brownian motors with quenched disorder [68,69,70,71] have also been studied.…”

Section: B Brief Review Of the Earlier Modelsmentioning

confidence: 99%

Interacting RNA polymerase motors on a DNA track: Effects of traffic congestion and intrinsic noise on RNA synthesis

Tripathi

Chowdhury

2008

Phys. Rev. E

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RNA polymerase (RNAP) is an enzyme that synthesizes a messenger RNA (mRNA) strand which is complementary to a single-stranded DNA template. From the perspective of physicists, an RNAP is a molecular motor that utilizes chemical energy input to move along the track formed by a DNA. In many circumstances, which are described in this paper, a large number of RNAPs move simultaneously along the same track; we refer to such collective movements of the RNAPs as RNAP traffic. Here we develop a theoretical model for RNAP traffic by incorporating the steric interactions between RNAPs as well as the mechano-chemical cycle of individual RNAPs during the elongation of the mRNA. By a combination of analytical and numerical techniques, we calculate the rates of mRNA synthesis and the average density profile of the RNAPs on the DNA track. We also introduce, and compute, two new measures of fluctuations in the synthesis of RNA. Analyzing these fluctuations, we show how the level of intrinsic noise in mRNA synthesis depends on the concentrations of the RNAPs as well as on those of some of the reactants and the products of the enzymatic reactions catalyzed by RNAP. We suggest appropriate experimental systems and techniques for testing our theoretical predictions.

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Section: B Brief Review Of the Earlier Modelsmentioning

confidence: 99%

Interacting RNA polymerase motors on a DNA track: Effects of traffic congestion and intrinsic noise on RNA synthesis

Tripathi

Chowdhury

2008

Phys. Rev. E

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“…Indeed, even if only a single site has a different hop rate to the rest, the steady state does not appear to have a manageable form [183,184]. On the other hand, some nontrivial symmetries in the disordered case have been identified [185,186].…”

Section: Particle-and Site-wise Disorder In the Asepmentioning

confidence: 99%

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

Blythe

Evans²

2007

J. Phys. A: Math. Theor.

634

1,014

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Abstract. We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of this class of driven diffusive systems-which includes exclusion processes-focusing on interesting physical properties, such as shocks and phase transitions. We then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form. In addition to a gentle introduction to this matrix product approach, how it works and how it relates to similar constructions that arise in other physical contexts, we present a unified, pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed. We also review a number of more advanced topics, including nonequilibrium free energy functionals, the classification of exclusion processes involving multiple particle species, existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled. We conclude with a brief discussion of open problems for future research.

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“…For this paradigmatic model of driven interacting particle systems many exact results are available [7]. As most of the real systems are not ideally translationally invariant, for instance the filaments on which molecular motors move are heterogeneous, a challenging problem is the study of spatially inhomogeneous versions of exclusion processes [8,9,10,11,12,13,14,15,16,17,18] for which the bulk of results is obtained by phenomenological methods based on the statistics of extremes, by mean field approximation and by Monte Carlo simulations. Most works concern the onedimensional totally asymmetric process where particles can hop only in one direction with site dependent quenched random rates.…”

Section: Introductionmentioning

confidence: 99%

Mean-field treatment of exclusion processes with random-force disorder

Juhász¹

2011

J. Stat. Mech.

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Abstract. The asymmetric simple exclusion process with random-force disorder is studied within the mean field approximation. The stationary current through a domain with reversed bias is analyzed and the results are found to be in accordance with earlier intuitive assumptions. On the grounds of these results, a phenomenological random barrier model is applied in order to describe quantitatively the coarsening phenomena. Predictions of the theory are compared with numerical results obtained by integrating the mean field evolution equations.

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Disordered totally asymmetric simple exclusion process: Exact results

Cited by 36 publications

References 14 publications

Interacting RNA polymerase motors on a DNA track: Effects of traffic congestion and intrinsic noise on RNA synthesis

Interacting RNA polymerase motors on a DNA track: Effects of traffic congestion and intrinsic noise on RNA synthesis

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

Mean-field treatment of exclusion processes with random-force disorder

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