Effect of heterogeneity in the distribution of ligands and proteins among disconnected particles: the binding of ubiquinone to the bacterial reaction center

The decay from the photo-induced charge separated state of a photosynthetic reaction center (RC) depends strongly on the occupancy of the binding site of the secondary quinone, Q(B). In the case of RCs from the purple bacterium Rhodobacter sphaeroides, the kinetics of charge recombination following a single turnover ash of light were found to be markedly different in detergent micelles and phospholipid vesicles at the same quinone to RC ratio. We ascribed this behavior to a statistical heterogeneity in the number of RC and quinone molecules distributed among the micelle and vesicle population. A general description of this heterogeneity in terms of the distribution functions of RC and quinone among the host particle ensemble was developed and the kinetics of charge recombination were calculated accordingly. The results obtained by assuming that the distribution functions of RC and quinone are gamma-distributions agree with the measured kinetics and show deviations from the behaviour of a homogeneous system. The deviations are particularly strong at a low mean number of proteins and ligands per host particle. The model developed has a general relevance to the study of quinone membrane protein interactions in both artificial and native vesicular systems.