An overview of theories related to vibrational energy relaxation (VER) in proteins is presented. VER of a selected mode in cytochrome c is studied by using two theoretical approaches. One approach is the equilibrium simulation approach with quantum correction factors, and the other is the reduced model approach, which describes the protein as an ensemble of normal modes interacting through nonlinear coupling elements. Both methods result in similar estimates of the VER time (subpicoseconds) for a CD stretching mode in the protein at room temperature. The theoretical predictions are in accord with previous experimental data. A perspective on directions for the detailed study of time scales and mechanisms of VER in proteins is presented.W hen a protein is excited by ligand binding, ATP attachment, or laser pulses, vibrational energy relaxation (VER) occurs. Energy initially ''injected'' into a localized region flows to the rest of the protein and surrounding solvent. VER in large molecules (including proteins) is an important problem for chemical physics (1,2). Even more significant is the challenge to relate VER to fundamental reaction processes, such as a conformational change or electron transfer of a protein, associated with protein functions. The development of an accurate understanding of VER in proteins is an essential step toward the goal of controlling protein dynamics (3).Because of the advance of laser technology, there have been many experimental studies of VER in proteins (4-17). These experimental works are impressive, but it is difficult to derive detailed information from the experimental data alone. Theoretical approaches, including atomic-scale simulations, can provide more detailed information. In turn, experimental data can be used to refine simulation methods and empirical force fields. This combination of experimental and theoretical studies of protein structures and dynamics has begun to blossom. As experimental methods develop further and theoretical approaches grow in accuracy, the relationship will become fruitful.There have been many theoretical tools (see Theories) developed to analyze VER in proteins. Some aspects of VER in proteins can be explained by perturbative formulas based on the equilibrium condition of the bath (see Cyt c), but the use of the perturbative formulas may be too restrictive to describe protein dynamics generally at room temperature. In this article, we not only discuss the success of such established methods but also present a perspective on the study of VER in proteins.
TheoriesIn this section, we present a selective overview of theories appropriate for the study of VER in proteins. For the most part, these theories have been developed to deal with VER in liquids, solids, or glasses. For recent reviews, see refs. 18-20. We refer to two distinct categories; one is based on equilibrium dynamics and Fermi's golden rule, whereas the other is based on nonequilibrium dynamical models.Fermi's Golden Rule. If (i) there is a clear separation between the system and bath, (...