Theoretical fluorescence induction curves derived from coupled differential equations describing the primary photochemistry of photosystem II by an exciton-radical pair equilibrium

Fluorescence induction curves were calculated from a molecular model for the primary photophysical and photochemical processes of photosystem II that includes reversible exciton trapping by open (PHQ A ) and closed (PHQ - A ) reaction centers (RCs), charge stabilization as well as quenching by oxidized (P + HQ (-) A ) RCs. For the limiting case of perfectly connected photosynthetic units ("lake model") and thermal equilibrium between the primary radical pair (P + H - ) and the excited singlet state, the primary reactions can be mathematically formulated by a set of coupled ordinary differential equations (ODE). These were numerically solved for weak flashes in a recursive way to simulate experiments with continuous illumination. Using recently published values for the molecular rate constants, this procedure yielded the time dependence of closed RCs as well as of the fluorescence yield (= fluorescence induction curves). The theoretical curves displayed the same sigmoidal shapes as experimental fluorescence induction curves. From the time development of closed RCs and the fluorescence yield, it was possible to check currently assumed proportionalities between the fraction of closed RCs and either ( a ) the variable fluorescence, ( b ) the complementary area above the fluorescence induction curve, or ( c ) the complementary area normalized to the variable fluorescence. By changing selected molecular rate constants, it is shown that, in contrast to current beliefs, none of these correlations obeys simple laws. The time dependence of these quantities is strongly nonexponential. In the presence of substances that quench the excited state, the model predicts straight lines in Stern-Volmer plots. We further conclude that it is impossible to estimate the degree of physical interunit energy transfer from the sigmoidicity of the fluorescence induction curve or from the curvature of the variable fluorescence plotted versus the fraction of closed RCs.