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Reaction dynamics under confinement: an exact path integral treatment of a two-stage model of stochastic gene expression

Sharma, Rati and Cherayil, Binny J (2013) Reaction dynamics under confinement: an exact path integral treatment of a two-stage model of stochastic gene expression. In: Journal of Statistical Mechanics-Theory and Experiment . P10029_1-P10029_.

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Official URL: http://dx.doi.org/10.1088/1742-5468/2013/10/P10029

Abstract

Gene expression in living systems is inherently stochastic, and tends to produce varying numbers of proteins over repeated cycles of transcription and translation. In this paper, an expression is derived for the steady-state protein number distribution starting from a two-stage kinetic model of the gene expression process involving p proteins and r mRNAs. The derivation is based on an exact path integral evaluation of the joint distribution, P(p, r, t), of p and r at time t, which can be expressed in terms of the coupled Langevin equations for p and r that represent the two-stage model in continuum form. The steady-state distribution of p alone, P(p), is obtained from P(p, r, t) (a bivariate Gaussian) by integrating out the r degrees of freedom and taking the limit t -> infinity. P(p) is found to be proportional to the product of a Gaussian and a complementary error function. It provides a generally satisfactory fit to simulation data on the same two-stage process when the translational efficiency (a measure of intrinsic noise levels in the system) is relatively low; it is less successful as a model of the data when the translational efficiency (and noise levels) are high.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to IOP Publishing Ltd.
Keywords: Exact Results; Stochastic Particle Dynamics (Theory); Fluctuations (Theory); Gene Expression and Regulation (Theory)
Department/Centre: Division of Chemical Sciences > Inorganic & Physical Chemistry
Depositing User: Francis Jayakanth
Date Deposited: 26 Dec 2013 05:09
Last Modified: 26 Dec 2013 05:09
URI: http://eprints.iisc.ac.in/id/eprint/48073

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