Theory of fluorescence induction in photosystem II: derivation of analytical expressions in a model including exciton-radical-pair equilibrium and restricted energy transfer between photosynthetic units

The theoretical relationships between the fluorescence and photochemical yields of PS II and the fraction of open reaction centers are examined in a general model endowed with the following features: i) a homogeneous, infinite PS II domain; ii) exciton-radical-pair equilibrium; and iii) different rates of exciton transfer between core and peripheral antenna beds. Simple analytical relations are derived for the yields and their time courses in induction experiments. The introduction of the exciton-radical-pair equilibrium, for both the open and closed states of the trap, is shown to be equivalent to an irreversible trapping scheme with modified parameters. Variation of the interunit transfer rate allows continuous modulation from the case of separated units to the pure lake model. Broadly used relations for estimating the relative amount of reaction centers from the complementary area of the fluorescence kinetics or the photochemical yield from fluorescence levels are examined in this framework. Their dependence on parameters controlling exciton decay is discussed, allowing assessment of their range of applicability. An experimental induction curve is analyzed, with a discussion of its decomposition into alpha and beta contributions. The sigmoidicity of the induction kinetics is characterized by a single parameter J related to Joliot's p, which is shown to depend on both the connectivity of the photosynthetic units and reaction center parameters. On the other hand, the relation between J and the extreme fluorescence levels (or the deviation from the linear Stern-Volmer dependence of 1/phi f on the fraction of open traps) is controlled only by antenna connectivity. Experimental data are consistent with a model of connected units for PS II alpha, intermediate between the pure lake model of unrestricted exciton transfer and the isolated units model