Direct evidence for mode-specific vibrational energy relaxation from quantum time-dependent perturbation theory. III. The nu(4) and nu(7) modes of nonplanar nickel porphyrin models

Dependence of Vibrational Energy Transfer on Distance in a Four-Helix Bundle Protein: Equidistant Increments with the Periodicity of α Helices

Vibrational energy exchanges between various degrees of freedom are critical to barrier-crossing processes in proteins. Heme proteins are highly suitable for studies of the vibrational energy exchanges in proteins. The migration of excess energy released by heme in a protein moiety can be observed using time-resolved anti-Stokes ultraviolet resonance Raman spectroscopy. The anti-Stokes resonance Raman intensity of a tryptophan residue is an excellent probe for the excess energy and the spatial resolution of a single amino acid residue can be achieved. Here, we studied dependence of vibrational energy transfer on the distance in cytochrome b₅₆₂, which is a heme-containing, four-helix bundle protein. The vibrational energy transfer from the heme group to a single tryptophan residue introduced by site-directed mutagenesis was examined for different heme-tryptophan distances by a quasi-constant length with the periodicity of α helices. Taken together with structural data obtained by molecular dynamics simulations, the energy transfer could be well described by the model of classical thermal diffusion, which suggests that continuum media provide a good approximation of the protein interior, of which the atomic packing density is very high.