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 f or the primary photophysical and photochemical processes of photosyste m II that includes reversible exciton trapping by open (PHQ(A)) and cl osed (PHQ(A)-) reaction centers (RCs), charge stabilization as well as quenching by oxidized (P+HQ(A)(-)) RCs. For the limiting case of perf ectly connected photosynthetic units (''lake model'') and thermal equi librium between the primary radical pair (P+H-) and the excited single t state, the primary reactions can be mathematically formulated by a s et of coupled ordinary differential equations (ODE). These were numeri cally solved for weak flashes in a recursive way to simulate experimen ts with continuous illumination. Using recently published values for t he molecular rate constants, this procedure yielded the time dependenc e of closed RCs as well as of the fluorescence yield (= fluorescence i nduction curves). The theoretical curves displayed the same sigmoidal shapes as experimental fluorescence induction curves. From the time de velopment of closed RCs and the fluorescence yield, it was possible to check currently assumed proportionalities between the fraction of clo sed RCs and either (a) the variable fluorescence, (b) the complementar y area above the fluorescence induction curve, or (c) the complementar y area normalized to the variable fluorescence. By changing selected m olecular rate constants, it is shown that, in contrast to current beli efs, none of these correlations obeys simple laws. The time dependence of these quantities is strongly nonexponential. In the presence of su bstances that quench the excited state, the model predicts straight li nes in Stern-Volmer plots. We further conclude that it is impossible t o estimate the degree of physical interunit energy transfer from the s igmoidicity of the fluorescence induction curve or from the curvature of the variable fluorescence plotted versus the fraction of closed RCs .