Simulating energy flow in biomolecules: Application to tuna cytochrome c

By constructing a continuity equation of energy flow, one can utilize results from a molecular dynamics simulation to calculate the energy flux or flow in different parts of a biomolecule. Such calculations can yield useful insights into the pathways of energy flow in biomolecules. The method was first tested on a small system of a cluster of 13 argon atoms and then applied to the study of the pathways of energy flow after a tuna ferrocytochrome c molecule was oxidized. Initially, energy propagated faster along the direction perpendicular to the heme plane. This was due to an efficient through-bond mechanism, because the heme iron in cytochrome c was covalently bonded to a cysteine and a histidine. For the oxidation of cytochrome c, electrostatic interactions also facilitated a long-range through-space mechanism of energy flow. As a result, polar or charged groups that were further away from the oxidation site could receive energy earlier than nonpolar groups closer to the site. Another bridging mechanism facilitating efficient long-range responses to cytochrome c oxidation involved the coupling of far-off atoms with atoms that were nearer to, and interacted directly with, the oxidation site. The different characteristics of these energy transfer mechanisms defied a simple correlation between the time that the excess energy of the oxidation site first dissipated to an atom and the distance of the atom from the oxidation site. For tuna cytochrome c, all of the atoms of the protein had sensed the effects of the oxidation within ~40 fs. For the length scale of energy transfer considered in this study, the speed of the energy propagation in the protein was on the order of 10⁵ m/s.