Perturbed soliton-like molecular excitations in a deformed DNA chain

We study the nonlinear dynamics of a deformed Deoxyribonucleic acid (DNA) molecular chain which is governed by a perturbed sine-Gordon equation coupled with a linear wave equation representing the lattice deformation. The DNA chain considered here is assumed to be deformed periodically which is the energetically favourable configuration, and the periodic deformation is due to the repulsive force between base pairs, stress in the helical backbones and due to the elastic strain force in both the strands. A multiple scale soliton perturbation analysis is carried out to solve the perturbed sine-Gordon equation and the resultant perturbed kink and antikink solitons represent open state configuration with small fluctuation. The perturbation due to periodic deformation of the lattice changes the velocity of the soliton. However, the width of the soliton remains unchanged.

💡 Research Summary

The paper presents a comprehensive study of nonlinear excitations in a deformed DNA double helix, incorporating the elastic flexibility of the two strands. Starting from a plane‑base rotator model, the authors define rotational angles φₙ and φ′ₙ for the bases on each strand and longitudinal displacements yₙ and y′ₙ for the nucleotides. The total Hamiltonian consists of three parts: (i) the rotational kinetic energy and stacking interaction (parameter J), (ii) the hydrogen‑bonding term (parameter α), and (iii) the phonon energy of the longitudinal lattice together with linear coupling terms (β, γ) that link the phonon to stacking and hydrogen‑bonding interactions.

From this Hamiltonian, discrete equations of motion for φₙ, φ′ₙ, yₙ, and y′ₙ are derived (Eqs. 3a‑3d). By taking the continuum limit (small lattice spacing a) and expanding to third order, the authors obtain a coupled system: a perturbed sine‑Gordon equation for the combined rotational field Ψ = 2φ and a linear wave equation for the lattice displacement y. Assuming the complementary bases rotate in opposite directions (φ′ = −φ) and the two strands vibrate identically (y′ = y), the system reduces to

 Ψ_tt − Ψ_zz + sin Ψ = ε