Dynamics and thermodynamics of a nonlinear model for DNA denaturation

Abstract

We present a model for the dynamical structure of DNA that can be considered as an extension of the usual Ising-like statistical approach to the melting curves. The model uses the stretching of the hydrogen bonds in a base pair as its main variable. Numerical simulations at constrained temperature show that it provides a good qualitative description of the collective motions of the base pairs, including their large-amplitude fluctuational openings and the emergence of the denaturation bubbles from the thermal fluctuations. The results are in good agreement with a statistical-mechanics analysis of the denaturation and specific-heat curves, performed with the transfer-integral method, provided that discreteness effects are treated exactly by a numerical solution of the transfer-integral operator. Second-order self-consistent phonon theory agrees with the exact transfer-integral results in the low- and intermediate-temperature ranges and explains the phonon softening observed in the molecular-dynamics simulations. When the temperature approaches the denaturation temperature, the second-order self-consistent phonon results deviate significantly from the exact ones, pointing to the fundamental role of nonlinear processes in DNA denaturation.