Energy relaxation of the amide-I mode in hydrogen-bonded peptide units: a route to conformational change

A one-site Davydov model involving a C[Double Bond]O group engaged in a hydrogen bond is used to study the amide-I relaxation due to Fermi resonances with a bath of intramolecular normal modes. In the amide-I ground state, the hydrogen bond behaves as a harmonic oscillator whose eigenstates are phonon number states. By contrast, in the amide-I first excited state, the hydrogen bond experiences a linear distortion so that the eigenstates are superimpositions of number states. By assuming the hydrogen bond in thermal equilibrium at biological temperature, it is shown that the amide-I excitation favors the population of these excited states and the occurrence of coherences. Due to the interaction with the bath, the vibron decays according to an exponential or a biexponential law depending on whether the Fermi resonance is wide or narrow. Therefore, each excited state relaxes over a set of number states according to specific pathways. The consequence is twofold. First, the relaxation leads to a redistribution of the number state population which differs from the initial Boltzmann distribution. Then, it allows for coherence transfers so that, although the vibron has disappeared, the hydrogen keeps the memory of its initial distortion and it develops free oscillations.