Formulas for intrinsic noise evaluation in oscillatory genetic networks

Yohei Ito, Kenko Uchida*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)


    The linear noise approximation is a useful method for stochastic noise evaluations in genetic regulatory networks, where the covariance equation described as a Lyapunov equation plays a central role. We discuss the linear noise approximation method for evaluations of an intrinsic noise in autonomously oscillatory genetic networks; in such oscillatory networks, the covariance equation becomes a periodic differential equation that provides generally an unbounded covariance matrix, so that the standard method of noise evaluation based on the covariance matrix cannot be adopted directly. In this paper, we develop a new method of noise evaluation in oscillatory genetic networks; first, we investigate structural properties, e.g., orbital stability and periodicity, of the solutions to the covariance equation given as a periodic Lyapunov differential equation by using the Floquet-Lyapunov theory, and propose a global measure for evaluating stochastic amplitude fluctuations on the periodic trajectory; we also derive an evaluation formula for the period fluctuation. Finally, we apply our method to a model of circadian oscillations based on negative auto-regulation of gene expression, and show validity of our method by comparing the evaluation results with stochastic simulations.

    Original languageEnglish
    Pages (from-to)223-234
    Number of pages12
    JournalJournal of Theoretical Biology
    Issue number2
    Publication statusPublished - 2010 Nov 21


    • Circadian oscillation
    • Floquet-Lyapunov theory
    • Linear noise approximation

    ASJC Scopus subject areas

    • Medicine(all)
    • Immunology and Microbiology(all)
    • Biochemistry, Genetics and Molecular Biology(all)
    • Agricultural and Biological Sciences(all)
    • Modelling and Simulation
    • Statistics and Probability
    • Applied Mathematics


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