Theory of photosynthetic membrane influence on B800-B850 energy transfer in the LH2 complex

Photosynthetic organisms rely on a network of light-harvesting protein-pigment complexes to efficiently absorb sunlight and transfer excitation energy to reaction center proteins where charge separation occurs. In photosynthetic purple bacteria, these complexes are embedded within the cell membrane, with lipid composition affecting complex clustering, thereby impacting inter-complex energy transfer. However, the impact of the lipid bilayer on intra-complex excitation dynamics is less understood. Recent experiments have addressed this question by comparing photo-excitation dynamics in detergent-isolated light-harvesting complex 2 (LH2) to LH2 complexes embedded in membrane discs mimicking the biological environment, revealing differences in spectra and energy-transfer rates. In this paper, we use available quantum chemical and spectroscopy data to develop a complementary theoretical study on the excitonic structure and intra-complex energy-transfer kinetics of the LH2 of photosynthetic purple bacteria Rhodoblastus (Rbl.) acidophilus (formerly Rhodopseudomonas acidophila) in two different conditions: the LH2 in a membrane environment and detergent-isolated LH2. We find that dark excitonic states, crucial for B800-B850 energy transfer within LH2, are more delocalized in the membrane model. Using nonperturbative and generalized Förster calculations, we show that such increased quantum delocalization results in a 30% faster B800 to B850 transfer rate in the membrane model, in agreement with experimental results. We identify the dominant energy-transfer pathways in each environment and demonstrate how differences in the B800 to B850 transfer rate arise from changes in LH2's electronic properties when embedded in the membrane. Furthermore, by accounting for the quasi-static variations of electronic excitation energies in the LH2, we show that the broadening of the distribution of the B800-B850 transfer rates is affected by the lipid composition. We argue that such variation in broadening could be a signature of a speed-accuracy trade-off, commonly seen in biological process.