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Coupled oscillator models with no scale separation

Du Toit, Philip and Mezić, Igor and Marsden, Jerrold (2009) Coupled oscillator models with no scale separation. Physica D, 238 (5). pp. 490-501. ISSN 0167-2789. doi:10.1016/j.physd.2008.11.014.

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We consider a class of spatially discrete wave equations that describe the motion of a system of linearly coupled oscillators perturbed by a nonlinear potential. We show that the dynamical behavior of this system cannot be understood by considering the slowest modes only: there is an “inverse cascade” in which the effects of changes in small scales are felt by the largest scales and the mean-field closure does not work. Despite this, a one and a half degree of freedom model is derived that includes the influence of the small-scale dynamics and predicts global conformational changes accurately. Thus, we provide a reduced model for a system in which there is no separation of scales. We analyze a specific coupled-oscillator system that models global conformation change in biomolecules, introduced in [I. Mezić, On the dynamics of molecular conformation, Proc. Natl. Acad. Sci. 103 (20) (2006) 7542–7547]. In this model, the conformational states are stable to random perturbations, yet global conformation change can be quickly and robustly induced by the action of a targeted control. We study the efficiency of small-scale perturbations on conformational change and show that “zipper” traveling wave perturbations provide an efficient means for inducing such change. A visualization method for the transport barriers in the reduced model yields insight into the mechanism by which the conformation change occurs.

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Additional Information:© 2008 Elsevier B.V. Received 23 June 2008. Received in revised form 9 October 2008. Accepted 19 November 2008. Available online 10 December 2008. Communicated by V. Rom-Kedar. This research was partially supported by funding from AFOSR grant FA9550-06-1-0088 and from the DARPA RUM program through AFOSR contract FA9550-07-C-0024. Approved for public release; distribution is unlimited. PACS classification codes: 87.15.hp; 87.15.hj.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-06-1-0088
Defense Advanced Research Projects Agency (DARPA) RUM program through AFOSRFA9550-07-C-0024
Subject Keywords:coarse variables; reduced model; coupled oscillators; dynamics of biomolecules
Issue or Number:5
Record Number:CaltechAUTHORS:20090415-094125134
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13980
Deposited By: Tony Diaz
Deposited On:20 Apr 2009 19:32
Last Modified:08 Nov 2021 22:42

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