Application of dynamic disorder approach to the temperature dependent non-exponential electron transfer kinetics in Rhodopseudomonas viridis

Abstract

The kinetics of electron transfer (ET) reaction from the proximal heme (c-559) of tetraheme cytochrome to the special pair of bacteriochlorophyll (P+), oxidized initially, was probed by absorption experiments in the reaction centre from Rhodopseudomonas viridis between temperatures of 295 K and 153 K. The decay of the kinetic curves is clearly non-exponential at the microsecond timescale. This points to the relevance of having possible influence of dynamic disorder on the reaction kinetics. In this work, based on the Sumi–Marcus model of electron transfer we present a theoretical study to rationalize the experimental results by a microscopic model in which the dynamics of protein is described in terms of the anomalous diffusion of a Brownian particle in a harmonic potential well under the action of fractional Gaussian noise. Starting from a non-Markovian diffusion equation supplemented with an exponential sink term that accounts for the electron transfer reaction between the donor and acceptor groups, we calculate the survival probability from the solution of the corresponding diffusion–reaction equation using the Wilemski–Fixman closure approximation. Our model provides excellent fits to the data, nonetheless being in microsecond timescale made it difficult to access through simulations. Importantly, a number of significant improvements have been made to the original work by our model, such as a single expression for the survival probability explains the kinetic profiles at all the temperatures, the initial decay at 153 K and 173 K are reproduced and the Arrhenius relationship for the relaxation times holds well down to the glass transition temperature. Employing the Arrhenius relation for the relaxation times we quantify the average activation energy for the conformational dynamics which is lower than the previous estimate. Our work suggests an alternative interpretation for the observed non-exponential ET kinetics associated with dynamic disorder, otherwise treated earlier with static heterogeneity.