Heat flow in proteins: Computation of thermal transport coefficients

The rate of vibrational energy transfer and thermal transport coefficients are computed for two structurally distinct proteins, green fluorescent protein (GFP) and myoglobin. The computation of thermal transport coefficients exploits the scaling of the energy diffusion coefficient with the vibrational mode frequency of a protein. Near 300 K we find that vibrational energy transfer due to anharmonicity contributes substantially to thermal transport because of the localization of many thermally accessible normal modes. The thermal diffusivity for the beta-barrel GFP is larger than that for myoglobin, particularly at low temperature due to a mean free path for vibrational energy propagation that is twice as large at low frequency. Vibrational energy transfer is also faster in GFP than in myoglobin for most vibrational modes.