Scaling of Rates of Vibrational Energy Transfer in Proteins with Equilibrium Dynamics and Entropy.

Theoretical arguments and results of molecular dynamics (MD) simulations of myoglobin at 300 K are presented to relate rates of vibrational energy transfer across nonbonded contacts interacting via short-range potentials to dynamics of the contact. Both theory and the results of the simulations support a scaling relation between the energy transfer rate and the inverse of the variance in the distance between hydrogen-bonded contacts. The results of the MD simulations do not support such a relation for longer-range charged contacts. Instead, the energy transfer rate is found to scale as a power law in the distance between charged groups. The scaling between rates of vibrational energy transfer across nonbonded contacts interacting via short-range potentials and conformational dynamics suggests a relation between vibrational energy transfer rates and entropy associated with the dynamics of interacting residues. The use of time-resolved vibrational spectroscopy to determine change in conformational entropy with change in protein functional state is discussed, and an expression quantifying the connection is provided.