Geminate recombination of the methionine ligand to the heme iron in ferrous cytochrome c protein following photodissociation displays rich kinetics. It is of particular interest to develop an understanding of fast and slow rebinding time scales, observed in experimental studies, in terms of features of the underlying complex energy landscape. The classical empirical force field in the heme pocket has been extended by incorporating ab initio potential energy surface calculations representing the ground singlet state and quintet state associated with methionine bond breaking and rebinding. An algorithm based on the Landau−Zener nonadiabatic transition theory has been employed to model the electronic surface hopping between two spin states during the process of ligand dissociation and recombination. Multiple conformational substates of the dissociated methionine ligand are found to participate in the reaction dynamics. Varying time scales for interconversion between substates lead to a mechanism elucidating the fast and slow rebinding time scales. The reaction system may be understood in terms of a two-dimensional reaction coordinate distinctly separated from the coupled bath of surrounding protein and solvent degrees of freedom. Insights into the reaction dynamics provided by this study lead to suggestions for future experiments to further probe the role of dynamic heterogeneity in the kinetics of ligand−protein binding.
■ INTRODUCTIONGeminate recombination of axial ligands to the iron atom in heme proteins, as one of the key steps of protein global structural dynamics and allostery, has been of great interest and widely studied both experimentally and theoretically in the past decades. Many of those studies have been dedicated to diatomic axial ligands, such as CO, NO, and O 2 in globins.1−27 From those studies, a deep and general understanding of protein dynamics, in terms of transitions between conformational substates, has developed and formed the foundation for modern "energy landscape" theories of protein dynamics and thermodynamics. In spite of this success, a rigorous understanding of molecular reaction dynamics for ligand rebinding in myoglobin has proven elusive. The Agmon−Hopfield 8 and Champion-Srajer 28,29 models of ligand rebinding define specific reaction coordinates for the rebinding process but also include an undefined protein coordinate as an essential component of the multidimensional reaction coordinate in addition to the surrounding bath. Although heme−ligand dissociation in heme proteins usually does not occur under normal conditions, heme−ligand bond breaking and rebinding take place during the process of internal and external ligand switching or competition in neuroglobin 30,31 as well as in a specific group of heme-based sensor proteins such as Ec DOS, DOSH, and CooA. 7,32,33 Understanding the kinetics and thermodynamics of internal ligand binding is essential to our knowledge of the composition and function of these heme proteins.Cytochrome c (cyt c) (Figure 1) is an essential ...