Strathprints logo
Strathprints Home | Open Access | Browse | Search | User area | Copyright | Help | Library Home | SUPrimo

Switching and diffusion models for gene regulation networks

Intep, Somkid and Higham, Desmond J. and Mao, X. (2009) Switching and diffusion models for gene regulation networks. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 8 (1). pp. 30-45. ISSN 1540-3459

[img]
Preview
PDF (mmsgene.pdf) - Submitted Version
Download (227Kb) | Preview

    Abstract

    We analyze a hierarchy of three regimes for modeling gene regulation. The most complete model is a continuous time, discrete state space, Markov jump process. An intermediate 'switch plus diffusion' model takes the form of a stochastic differential equation driven by an independent continuous time Markov switch. In the third 'switch plus ODE' model the switch remains but the diffusion is removed. The latter two models allow for multi-scale simulation where, for the sake of computational efficiency, system components are treated differently according to their abundance. The 'switch plus ODE' regime was proposed by Paszek (Modeling stochasticity in gene regulation: characterization in the terms of the underlying distribution function, Bulletin of Mathematical Biology, 2007), who analyzed the steady state behavior, showing that the mean was preserved but the variance only approximated that of the full model. Here, we show that the tools of stochastic calculus can be used to analyze first and second moments for all time. A technical issue to be addressed is that the state space for the discrete-valued switch is infinite. We show that the new 'switch plus diffusion' regime preserves the biologically relevant measures of mean and variance, whereas the 'switch plus ODE' model uniformly underestimates the variance in the protein level. We also show that, for biologically relevant parameters, the transient behaviour can differ significantly from the steady state, justifying our time-dependent analysis. Extra computational results are also given for a protein dimerization model that is beyond the scope of the current analysis.

    Item type: Article
    ID code: 13621
    Keywords: diffusion, hybrid model, Gillespie’s algorithm, Ito lemma, Markov chain, slow scale simulation, stochastic simulation algorithm, transcription, tran-sition rate, translation, Mathematics, Physics and Astronomy(all), Modelling and Simulation, Chemistry(all), Ecological Modelling, Computer Science Applications
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
      Depositing user: Mrs Irene Spencer
      Date Deposited: 17 Dec 2009 13:15
      Last modified: 05 Sep 2014 13:47
      URI: http://strathprints.strath.ac.uk/id/eprint/13621

      Actions (login required)

      View Item

      Fulltext Downloads: