A Master Equation Theory of Fluorescence Induction, Photochemical Yield, and Singlet-triplet Exciton Quenching in Photosynthetic Systems

A master equation theory is formulated to describe the dependence of the fluorescence yield (phi) in photosynthetic systems on the number of photons (Y) absorbed per photosynthetic unit (or domain). This theory is applied to the calculation of the dependence of the fluorescence yield on Y in (a) fluorescence induction, and (b) singlet exciton-triplet excited-state quenching experiments. In both cases, the fluorescence yield depends on the number of previously absorbed photons per domain, and thus evolves in a nonlinear manner with increasing Y. In case a, excitons transform the photosynthetic reaction centers from a quenching state to a nonquenching state, or a lower efficiency of quenching state; subsequently, absorbed photons have a higher probability of decaying by radiative pathways and phi increases as Y increases. In case b, ground-state carotenoid molecules are converted to long-lived triplet excited-state quenchers, and phi decreases as Y increases. It is shown that both types of processes are formally described by the same theoretical equations that relate phi to Y. The calculated phi (Y) curves depend on two parameters m and R, where m is the number of reaction centers (or ground-state carotenoid molecules that can be converted to triplets), and R is the ratio phi (Y leads to infinity)/(Y leads to 0). The finiteness of the photosynthetic units is thus taken into account. The m = 1 case corresponds to the "puddle" model, and m leads to infinity to the "lake," or matrix, model. It is shown that the experimental phi (Y) curves for both fluorescence induction and singlet-triplet exciton quenching experiments are better described by the m leads to infinity cases than the m = 1 case.