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Zero, one and two-switch models of gene regulation

Intep, Somkid and Higham, D.J. (2010) Zero, one and two-switch models of gene regulation. Discrete and Continuous Dynamical Systems - Series B, 14 (2). pp. 495-513. ISSN 1531-3492

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    Abstract

    We compare a hierarchy of three stochastic models in gene regulation. In each case, genes produce mRNA molecules which in turn produce protein. The simplest model, as described by Thattai and Van Oudenaarden (Proc. Nat. Acad. Sci., 2001), assumes that a gene is always active, and uses a first-order chemical kinetics framework in the continuous-time, discrete-space Markov jump (Gillespie) setting. The second model, proposed by Raser and O'Shea (Science, 2004), generalizes the first by allowing the gene to switch randomly between active and inactive states. Our third model accounts for other effects, such as the binding/unbinding of a transcription factor, by using two independent on/off switches operating in AND mode. We focus first on the noise strength, which has been defined in the biological literature as the ratio of the variance to the mean at steady state. We show that the steady state variance in the mRNA and protein for the three models can either increase or decrease when switches are incorporated, depending on the rate constants and initial conditions. Despite this, we also find that the overall noise strength is always greater when switches are added, in the sense that one or two switches are always noisier than none. On the other hand, moving from one to two switches may either increase or decrease the noise strength.

    Item type: Article
    ID code: 13622
    Keywords: diffusion, Fano factor, Gillespie algorithm, intrinsic noise, markov jump process, multiscale, stochastic differential equation, transcription, translation, Mathematics, Discrete Mathematics and Combinatorics, Applied Mathematics
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
    Depositing user: Mrs Irene Spencer
    Date Deposited: 08 Jan 2010 11:07
    Last modified: 27 Mar 2014 11:27
    URI: http://strathprints.strath.ac.uk/id/eprint/13622

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