Control of a Model of DNA Division via Parametric Resonance

TL;DR

This paper models DNA division as a chain of pendula and demonstrates how parametric resonance can be used to control the process by targeting specific modes and frequencies, with potential electromagnetic applications.

Contribution

It introduces a reduced Hamiltonian model capturing the global dynamics of DNA division and shows how parametric excitation can stabilize the open state for control purposes.

Findings

Global and slow dynamics remain Hamiltonian despite parametric excitation

Parametric excitation can stabilize the open DNA state

Time-averaged reduced model accurately predicts full system behavior

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 (i) first reducing its dynamic to two modes exchanging energy between each other and (ii) 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.