Nonergodic complex medium dynamics affecting protein electron transfer

The standard description of long-range protein electron transfer anticipates an exponential decay of the reaction rate with the donor-acceptor distance due to decaying tunneling probability. In contrast, dynamical models of electron transfer predict a rate turnover to a plateau specified by the protein-water dynamics at shorter distances. The turnover distance is affected by the medium dynamics which is often complex, involving a number of relaxation times. The reaction time also specifies the time scale on which the medium dynamics can affect the reaction dynamics, thus imposing a nonergodic cutoff of the medium relaxation spectrum. The model presented here considers the effects of both the complex medium dynamics and the nonergodic dynamical constraints on the distance dependence of the reaction rate. Considering specific parameters of electron transfer in azurin, it shows that that the dynamical turnover disappears for fast reactions in the picosecond time domain due to nonergodic restrictions on the medium relaxation spectrum.