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Control of a model of DNA division via parametric resonance

Koon, Wang Sang and Owhadi, Houman and Tao, Molei and Yanao, Tomohiro (2013) Control of a model of DNA division via parametric resonance. Chaos, 23 (1). Art. No. 013117. ISSN 1054-1500. doi:10.1063/1.4790835.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Owhadi, Houman0000-0002-5677-1600
Additional Information:© 2013 American Institute of Physics. Received 1 October 2012; accepted 15 January 2013; published online 14 February 2013. This work has been supported by the National Science Foundation under award number NSF-CMMI-092600. We would like to dedicate this paper to the memory of our close collaborator Jerrold E. Marsden. We thank Bryan Eisenhower for giving us the permission to use his figure. W.S.K. thanks Fields Institute for its invitation to the Marsden Conference (July 2012) where he had an opportunity to exchange ideas about this work with other participants.
Funding AgencyGrant Number
Subject Keywords:DNA, molecular biophysics, Morse potential, noise, numerical analysis
Issue or Number:1
Classification Code:PACS: 87.14.gk; 87.15.H-; 02.60.-x; 36.20.Ey
Record Number:CaltechAUTHORS:20130502-133827036
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Official Citation:Control of a model of DNA division via parametric resonance Wang Sang Koon, Houman Owhadi, Molei Tao, and Tomohiro Yanao, Chaos 23, 013117 (2013), DOI:10.1063/1.4790835
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38248
Deposited By: Tony Diaz
Deposited On:06 May 2013 19:19
Last Modified:09 Nov 2021 23:36

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