Conformational substates and barrier height distributions in ligand binding to heme proteins

Abstract

A model of the enthalpy barrier between the heme pocket and heme iron is proposed for the recombination of small ligands to heme proteins after flash photolysis. The model is based on the concept of conformational substates as developed by Frauenfelder and co-workers. The model assumes a temperature-independent energy surface which depends on a reaction coordinate (ligand–iron distance) and a protein coordinate x. The protein coordinate parameterizes the conformational substates of the protein. The conformational energy of the substates is given by an anharmonic power law Vν(x)∝x1/ν, x≥0 for the liganded (A) , unliganded (B), and transition states. The barrier height for the B→A transition depends on the protein coordinate because the conformational energy has different proportionality coefficients in state B and the transition state. The distribution of barrier heights at low temperature follows because the protein coordinate satisfies a Boltzmann distribution which depends on the appropriate conformational energy. The Boltzmann distribution at low temperature is determined by the temperature at which the conformational substates are frozen. The resulting temperature-independent barrier-height distribution is a gamma distribution which yields good fits to the low temperature rebinding kinetics. Above the freezing temperature, the gamma distribution is temperature-dependent owingto protein fluctuations among the conformational substates. If the conformational energies of states A and B are the same, the temperature-dependent distribution is determined by the low-temperature kinetics. The average rate coefficient for B→A transition at physiological temperature agrees with the same rate coefficient used by Frauenfelder and co-workers to within a factor of 3.