Control of a model of DNA division via parametric resonance

Wang Sang Koon, Houman Owhadi, Molei Tao, Tomohiro Yanao

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    We study the internal resonance, energy transfer, activation mechanism, and control of a model of DNA division via parametric resonance. While the system is robust to noise, this study shows that it is sensitive to specific fine scale modes and frequencies that could be targeted by low intensity electro-magnetic fields for triggering and controlling the division. The DNA model is a chain of pendula in a Morse potential. While the (possibly parametrically excited) system has a large number of degrees of freedom and a large number of intrinsic time scales, global and slow variables can be identified by (1) first reducing its dynamic to two modes exchanging energy between each other and (2) averaging the dynamic of the reduced system with respect to the phase of the fastest mode. Surprisingly, the global and slow dynamic of the system remains Hamiltonian (despite the parametric excitation) and the study of its associated effective potential shows how parametric excitation can turn the unstable open state into a stable one. Numerical experiments support the accuracy of the time-averaged reduced Hamiltonian in capturing the global and slow dynamic of the full system.

    Original languageEnglish
    Article number013117
    JournalChaos
    Volume23
    Issue number1
    DOIs
    Publication statusPublished - 2013 Mar 18

    Fingerprint

    Parametric Resonance
    division
    Division
    DNA
    deoxyribonucleic acid
    Parametric Excitation
    Hamiltonians
    Morse potential
    Morse Potential
    Internal Resonance
    exchanging
    Effective Potential
    Energy Transfer
    Model
    Energy transfer
    Electromagnetic fields
    Electromagnetic Fields
    Hamiltonian Systems
    excitation
    Averaging

    ASJC Scopus subject areas

    • Applied Mathematics
    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    Control of a model of DNA division via parametric resonance. / Sang Koon, Wang; Owhadi, Houman; Tao, Molei; Yanao, Tomohiro.

    In: Chaos, Vol. 23, No. 1, 013117, 18.03.2013.

    Research output: Contribution to journalArticle

    Sang Koon, Wang ; Owhadi, Houman ; Tao, Molei ; Yanao, Tomohiro. / Control of a model of DNA division via parametric resonance. In: Chaos. 2013 ; Vol. 23, No. 1.
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