Flash-induced oxygen evolution in photosynthesis: simple solution for the extended S-state model that includes misses, double-hits, inactivation, and backward-transitions

Flash-induced oxygen evolution in higher plants, algae, and cyanobacteria exhibits damped period-four oscillations. To explain such oscillations, Kok suggested a simple phenomenological S-state model, in which damping is due to empirical misses and double-hits. Here we developed an analytical solution for the extended Kok model that includes misses, double-hits, inactivation, and backward-transitions. The solution of the classic Kok model (with misses and double-hits only) can be obtained as a particular case of this solution. Simple equations describing the flash-number dependence of individual S-states and oxygen evolution in both cases are almost identical and, therefore, the classic Kok model does not have a significant advantage in its simplicity over the extended version considered in this article. Developed equations significantly simplify the fitting of experimental data via standard nonlinear regression analysis and make unnecessary the use of many previously developed methods for finding parameters of the model. The extended Kok model considered here can provide additional insight into the effect of dark relaxation between flashes and inactivation.