On Discovering Low Order Models in Biochemical Reaction Kinetics

Laura Giarre, Bamieh

    Risultato della ricerca: Paper

    4 Citazioni (Scopus)

    Abstract

    We develop a method by which a large number of differential equations representing biochemical reaction kinetics may be represented by a smaller number of differential equations. The basis of our technique is a conjecture that the high dimension equations of biochemical kinetics, which involve reaction terms of specific forms, are actually implementing a low dimension system whose behavior requires right hand sides that can not be biochemically implemented. For systems that satisfy this conjecture, we develop a simple approximation scheme based on multilinear algebra that extracts the low dimensional system from simulations of the high dimension system. We demonstrate this technique on a standard 10 dimensional model of circadian oscillations and obtain a 3 dimensional sub-model that has the same rhythmic, birhythmic and chaotic behavior of the original model.
    Lingua originaleEnglish
    Stato di pubblicazionePublished - 2007

    All Science Journal Classification (ASJC) codes

    • Electrical and Electronic Engineering

    Cita questo

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    title = "On Discovering Low Order Models in Biochemical Reaction Kinetics",
    abstract = "We develop a method by which a large number of differential equations representing biochemical reaction kinetics may be represented by a smaller number of differential equations. The basis of our technique is a conjecture that the high dimension equations of biochemical kinetics, which involve reaction terms of specific forms, are actually implementing a low dimension system whose behavior requires right hand sides that can not be biochemically implemented. For systems that satisfy this conjecture, we develop a simple approximation scheme based on multilinear algebra that extracts the low dimensional system from simulations of the high dimension system. We demonstrate this technique on a standard 10 dimensional model of circadian oscillations and obtain a 3 dimensional sub-model that has the same rhythmic, birhythmic and chaotic behavior of the original model.",
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    TY - CONF

    T1 - On Discovering Low Order Models in Biochemical Reaction Kinetics

    AU - Giarre, Laura

    AU - Bamieh, null

    PY - 2007

    Y1 - 2007

    N2 - We develop a method by which a large number of differential equations representing biochemical reaction kinetics may be represented by a smaller number of differential equations. The basis of our technique is a conjecture that the high dimension equations of biochemical kinetics, which involve reaction terms of specific forms, are actually implementing a low dimension system whose behavior requires right hand sides that can not be biochemically implemented. For systems that satisfy this conjecture, we develop a simple approximation scheme based on multilinear algebra that extracts the low dimensional system from simulations of the high dimension system. We demonstrate this technique on a standard 10 dimensional model of circadian oscillations and obtain a 3 dimensional sub-model that has the same rhythmic, birhythmic and chaotic behavior of the original model.

    AB - We develop a method by which a large number of differential equations representing biochemical reaction kinetics may be represented by a smaller number of differential equations. The basis of our technique is a conjecture that the high dimension equations of biochemical kinetics, which involve reaction terms of specific forms, are actually implementing a low dimension system whose behavior requires right hand sides that can not be biochemically implemented. For systems that satisfy this conjecture, we develop a simple approximation scheme based on multilinear algebra that extracts the low dimensional system from simulations of the high dimension system. We demonstrate this technique on a standard 10 dimensional model of circadian oscillations and obtain a 3 dimensional sub-model that has the same rhythmic, birhythmic and chaotic behavior of the original model.

    UR - http://hdl.handle.net/10447/12292

    M3 - Paper

    ER -