Energy localization in the Peyrard-Bishop DNA model

Abstract

We study energy localization on the oscillator chain proposed by Peyrard and Bishop to model 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 on a long time scale. We use a localization criterion based on the information entropy and 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 ͑ Ͼ 2.25͒ (the only parameter of our normalized model), in agreement with the numerical calculations (an estimate for the biological value is = 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.

Stability Analysis of the Jacobian Elliptic Solutions for the Twisted Peyrard-Bishop-Dauxois Model with Solvent Interaction

“…iv) The Peyrard-Bishop model is a non-linear phonon 1D model where bubbles emerge as soliton-like solutions of undamped Newton's equations in a Morse potential (possibly with a noise term) [10][11][12]. This model describes, in a simplified way, the hydrogen bond and has been used successfully in numerous applications such as energy localization [13] or to calculate solitonic speed [14,15]. Experiments proved that the free energy of opening base pairs depends on the identity of the next base pairs; this is due to the stacking interaction between neighboring bases on the same strand [16].…”

High-order nonlinear excitations in the Joyeux-Buyukdagli model of DNA

“…In 1989, Peyrard and Bishop presented a model where DNA is viewed as a pair of harmonic chains coupled by a nonlinear potential (Morse potential) [14]. This model describes, by a simplified approach, the hydrogen bond and has been applied successfully to many applications such as energy localization [15] and calculation of solitonic speed [16]. In this model, the double strand corresponds to a Klein-Gordon chain, the variable parameters are the distances between nucleotides within each base pair, and only short-range interactions are considered because of the stacking coupling [17].…”

Analysis of Lattice Size, Energy Density and Denaturation for a One-Dimensional DNA Model

“…The PB model and some variations [5][6][7] have been used to study the dynamics [8][9][10] and the thermodynamics [11][12][13] of DNA. From the dynamical point of view, there are studies about localized energy modes [14] that were identified as precursors of the denaturation and transcription process.…”