On the guiding principles for understanding of geometrical structures of the CaMn₄O₅ cluster in oxygen-evolving complex of photosystem II. Proposal of estimation formula of structural deformations via the Jahn–Teller effects

Atmospheric oxygenation and evolution of aerobic life on our earth are a result of water oxidation by oxygenic photosynthesis in photosystem II (PSII) of plants, algae and cyanobacteria. The water oxidation in the oxygen-evolving complex (OEC) in PSII is expected to proceed through five oxidation states, known as the S_i (i = 0, 1, 2, 3 and 4) states in the Kok cycle, with the S₁ being the most stable state in the dark. The OEC in PSII involves the active catalytic site made of four Mn ions and one Ca ion, namely the CaMn₄O₅ cluster. Past decades, molecular structures of the CaMn₄O₅ cluster in OEC in PSII have been investigated by the extended X-ray absorption fine structure (EXAFS). The magneto-structural correlations were extensively investigated by electron paramagnetic resonance (EPR) spectroscopy. Recently, Kamiya and Shen groups made great breakthrough for determination of the S₁ structure of OEC of PSII by the X-ray diffraction (XRD) and X-ray free-electron laser (XFEL) experiments, providing structural foundations that are crucial for theoretical investigations of the CaMn₄O₅ cluster. Large-scale quantum mechanics/molecular mechanics calculations starting from the XRD structures elucidated geometrical, electronic and spin structures of the CaMn₄O₅ cluster, indicating an important role of the Jahn–Teller (JT) effect of Mn(III) ions. This paper presents theoretical formulas for estimation of the JT deformations of the CaMn₄O₅ cluster in OEC of PSII. Scope and applicability of the formulas are examined in relation to several different structures of the CaMn₄O₅ cluster proposed by XRD, XFEL, EXAFS and other experiments. Implications of the computational results are discussed for further refinements of geometrical parameters of the CaMn₄O₅ cluster.