Vibrational energy flow across heme–cytochrome c and cytochrome c–water interfaces

We examine vibrational energy transfer across the heme–protein and protein–solvent interfaces of cytochrome c, using, as appropriate, classical, semiclassical, and quantum approaches. To characterize energy flow across the interface between the heme and the rest of cytochrome c, we calculate communication maps for the protein in its native structure as well as two structures with Met80 dissociated from the heme at 300 K. The response to excess energy in the heme is mediated by covalent and hydrogen bonds to the heme, as well as several through-space interactions, including those involving the dissociated Met80. This observation suggests no energy flow bottleneck between the heme and Met80 that would impede rebinding kinetics at 300 K. We examine the possibility of additional bottlenecks to energy flow by calculating the temperature dependence of the ergodicity threshold in an imidazole-ligated Fe-porphyrin system that constitutes the core of the heme–histidine complex. The ergodic threshold, which we calculate quantum mechanically, corresponds to a temperature of about 140 K. We also address the flow of excess vibrational energy from the protein to the solvent. We calculate the thermal boundary conductance between cytochrome c and water semiclassically over a range of temperatures and find that the protein–water interface poses no greater resistance to thermal flow than the protein itself.