A perturbed two-level model for exciton trapping in small photosynthetic systems

The study of exciton trapping in photosynthetic systems provides significant information about migration kinetics within the light harvesting antenna (LHA) and the reaction center (RC). We discuss two random walk models for systems with weakly coupled pigments, with a focus on the application to small systems (10-40 pigments/RC). Details of the exciton transfer to and from the RC are taken into consideration, as well as migration within the LHA and quenching in the RC. The first model is obtained by adapting earlier local trap models for application to small systems. The exciton lifetime is approximated by the sum of three contributions related to migration in the LHA, trapping by the RC, and quenching within the RC. The second model is more suitable for small systems and regards the finite rate of migration within the LHA as a perturbation of the simplified model, where the LHA and the RC are each represented by a single pigment level. In this approximation, the exciton lifetime is the sum of a migration component and a single nonlinear expression for the trapping and quenching of the excitons. Numerical simulations demonstrate that both models provide accurate estimates of the exciton lifetime in the intermediate range of 20-50 sites/RC. In combination, they cover the entire range of very small to very large photosynthetic systems. Although initially intended for regular LHA lattices, the models can also be applied to less regular systems. This becomes essential as more details of the structure of these systems become available. Analysis with these models indicates that the excited state decay in LH1 is limited by the average rate at which excitons transfer to the RC from neighboring sites in the LHA. By comparing this to the average rate of transfer within the LHA, various structural models that have been proposed for the LH1 core antenna are discussed.