Kinetic-dynamic model for conformational control of an electron transfer photocycle: mixed-metal hemoglobin hybrids

It is becoming increasingly clear that the transfer of an electron across a protein-protein interface is coupled to the dynamics of conformational conversion between and within ensembles of interface conformations. Electron transfer (ET) reactions in conformationally mobile systems provide a "clock" against which the rapidity of a dynamic process may be measured, and we here report a simple kinetic (master equation) model that self-consistently incorporates conformational dynamics into an ET photocycle comprised of a photoinitiated "forward" step and thermal return to ground. This kinetic/dynamic (KD) model assumes an ET complex exists as multiple interconverting conformations which partition into an ET-optimized (reactive; R) population and a less-reactive population ( S). We take the members of each population to be equivalent by constraining them to have the same conformational energy, the same average rate constant for conversion to members of the other population, and the same rate constants for forward and back ET. The result is a mapping of a complicated energy surface onto the simple "gating", two-well surface, but with rate constants that are defined microscopically. This model successfully describes the changes in the ET photocycle within the "predocked" mixed-metal hemoglobin (Hb) hybrid, [alpha(Zn), beta(Fe3+N 3 (-))], as conformational kinetics are modulated by variations in viscosity (eta = 1-15 cP; 20 degrees C). The description reveals how the conformational "routes" by which a hybrid progresses through a photocycle differ in different dynamic regimes. Even at eta = 1 cP, the populations are not in fast exchange, and ET involves a complex interplay between conformational and ET processes; at intermediate viscosities the hybrid exhibits "differential dynamics" in which the forward and back ET processes involve different initial ensembles of configurational substates; by eta = 15 cP, the slow-exchange limit is approached. Even at low viscosity, the ET-coupled motions are fairly slow, with rate constants of <10 (3) s (-1). Current ideas about Hb function lead to the testable hypothesis that ET in the hybrid may be coupled to allosteric fluctuations of the two [alpha 1, beta 2] dimers of Hb.