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Energy Localization in the Peyrard-Bishop DNA model

Jayme De Luca·Elso Drigo Filho·Antonio Ponno·Jose Roberto Ruggiero
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Abstract

We study energy localization on the oscillator-chain proposed by Peyrard and Bishop to model the DNA. We search numerically for conditions with initial energy in a small subgroup of consecutive oscillators of a finite chain and such that the oscillation amplitude is small outside this subgroup for a long timescale. We use a localization criterion based on the information entropy and we verify numerically that such localized excitations exist when the nonlinear dynamics of the subgroup oscillates with a frequency inside the reactive band of the linear chain. We predict a mimium value for the Morse parameter $(μ>2.25)$ (the only parameter of our normalized model), in agreement with the numerical calculations (an estimate for the biological value is $μ=6.3$). For supercritical masses, we use canonical perturbation theory to expand the frequencies of the subgroup and we calculate an energy threshold in agreement with the numerical calculations.

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Jayme De Luca, Elso Drigo Filho, Antonio Ponno, Jose Roberto Ruggiero. 2004-07-30. Energy Localization in the Peyrard-Bishop DNA model. https://doi.org/10.1103/physreve.70.026213

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