Bridging the gap between Kok-type and kinetic models of photosynthetic electron transport within Photosystem II

Historically, two modeling approaches have been developed independently to describe photosynthetic electron transport (PET) from water to plastoquinone within Photosystem II (PSII): Markov models account for losses from finite redox transition probabilities but predict no reaction kinetics, and ordinary differential equation (ODE) models account for kinetics but not for redox inefficiencies. We have developed an ODE mathematical framework to calculate Markov inefficiencies of transition probabilities as defined in Joliot-Kok-type catalytic cycles. We adapted a previously published ODE model for PET within PSII that accounts for 238 individual steps to enable calculation of the four photochemical inefficiency parameters (miss, double hit, inactivation, backward transition) and the four redox accumulation states (S-states) that are predicted by the most advanced of the Joliot-Kok-type models (VZAD). Using only reaction kinetic parameters without other assumptions, the RODE-calculated time-averaged (e.g., equilibrium) inefficiency parameters and equilibrium S-state populations agree with those calculated by time-independent Joliot-Kok models. RODE also predicts their time-dependent values during transient photochemical steps for all 96 microstates involving PSII redox cofactors. We illustrate applications to two cyanobacteria, Arthrospira maxima and Synechococcus sp. 7002, where experimental data exists for the inefficiency parameters and the S-state populations, and historical data for plant chloroplasts as benchmarks. Significant findings: RODE predicts the microstates responsible for period-4 and period-2 oscillations of O₂ and fluorescence yields and the four inefficiency parameters; the latter parameters are not constant for each S state nor in time, in contrast to predictions from Joliot-Kok models; some of the recombination pathways that contribute to the backward transition parameter are identified and found to contribute when their rates exceed the oxidation rate of the terminal acceptor pool (PQH₂); prior reports based on the assumptions of Joliot-Kok parameters may require reinterpretation.