Theoretical study of collective modes in DNA at ambient temperature

The instantaneous normal modes corresponding to radial hydrogen bonds vibrations, torsion, and axial compression fluctuations of a DNA molecule model at ambient temperature are theoretically investigated. Due to thermal disorder, normal modes are not plane waves with a single wave number q but have a finite and frequency dependent damping width. The density of modes ρ(ν), the average dispersion relation ν(q), as well as the coherence length ξ(ν) are analytically calculated. The Gibbs averaged resolvent is computed using a replicated transfer matrix formalism and variational wave functions for the ground and first excited state. Our results for the density of modes are compared to Raman spectroscopy measurements of the collective modes for DNA in solution and show a good agreement with experimental data in the low frequency regime ν<150 cm−1. Radial optical modes extend over frequencies ranging from 50 to 100 cm−1. Torsional and compressional acoustic modes are limited to ν<25 cm−1. Normal modes are highly disordered and coherent over a few base pairs only (ξ<15 Å) in good agreement with neutron scattering experiments.