Protonation structure of the closed-cubane conformation of the O2-evolving complex in photosystem II

Abstract In photosystem II (PSII), one-electron oxidation of the most stable state of the oxygen-evolving Mn4CaO5 cluster (S1) leads to the S2 state formation, Mn1(III)Mn2(IV)Mn3(IV)Mn4(IV) (open-cubane S2) or Mn1(IV)Mn2(IV)Mn3(IV)Mn4(III) (closed-cubane S2). In electron paramagnetic resonance (EPR) spectroscopy, the g = 4.1 signal is not observed in cyanobacterial PSII but in plant PSII, whereas the g = 4.8 signal is observed in cyanobacterial PSII and extrinsic-subunit-depleted plant PSII. Here, we investigated the closed-cubane S2 conformation, a candidate for a higher spin configuration that accounts for g > 4.1 EPR signal, considering all pairwise exchange couplings in the PSII protein environment (i.e. instead of considering only a single exchange coupling between the [Mn3(CaO4)] cubane region and the dangling Mn4 site). Only when a ligand water molecule that forms an H-bond with D1-Asp61 (W1) is deprotonated at dangling Mn4(IV), the g = 4.1 EPR spectra can be reproduced using the cyanobacterial PSII crystal structure. The closed-cubane S2 is less stable than the open-cubane S2 in cyanobacterial PSII, which may explain why the g = 4.1 EPR signal is absent in cyanobacterial PSII.

r + (3-6)]. Consequently, O 2 evolves during the S 3 to S 0 transition. The crystal structures obtained using the femtosecond X-ray free electron laser (XFEL) suggest that a water molecule is incorporated into the O5 moiety of the Mn 4 CaO 5 cluster during the S 2 to S 3 transition (7-9). The Mn 4 CaO 5 cluster is composed of the three Mn sites in the cubane region (Mn1, Mn2, and Mn3) and the dangling Mn site (Mn4) (Fig. 1). The Mn valence state of S 1 is Mn(III) 2 Mn(IV) 2 in the high oxidation state model and Mn(III) 4 in the low oxidation model (10). In the present study, if not otherwise specified, the S-states given refer to the high oxidation state model (11). As Mn2 and Mn3 are already oxidized to Mn(IV) in S 1 according to the redox potential (6), either Mn1(III) or Mn4(III) is the oxidation site in the S 1 to S 2 transition. Mn1(IV). . .O5 is short and Mn4(III). . .O5 is long upon oxidation of Mn1(III) to Mn1(IV) (closedcubane S 2 conformation), whereas Mn1(III). . .O5 is long and Mn4(IV). . .O5 is short upon oxidation of Mn4(III) to Mn4(IV) (opencubane S 2 conformation) (12,13). The open-cubane S 2 conformation was identified in the XFEL structures, but not the closedcubane S 2 conformation (7-9), which may be due to the opencubane S 2 conformation being energetically more stable than the closed-cubane S 2 conformation (14)(15)(16)(17).
In electron paramagnetic resonance (EPR) spectroscopy for the Mn 4 CaO 5 cluster, the g = 2 multiline and g > 4.1 signals are observed [e.g. (18)]. The g > 4.1 signals are classified into two cases: the g = 4.1 and g = 4.8 signals. The low-spin open-cubane and high-spin closed-cubane S 2 conformations (12,13) are likely to correspond to the g = 2 multiline and g = 4.1 signals, respectively. It should be noted that the g = 4.1 signal is distinct from the g = 4.8 signal. The g = 4.1 signal is observed in plant PSII, but not in cyanobacterial PSII under physiological conditions (19,20) O4-water chain the g = 4.8 signal is observed in cyanobacterial and extrinsicsubunit-depleted plant PSII. Taguchi et al. reported that the g = 4.1 signal was observed only in untreated spinach PSII, whereas the g = 4.7 to 4.9 signal was observed in cyanobacterial PSII [e.g. untreated and PsbO/V/U-depleted Thermosynechococcus vulcanus PSII and PsbO/V/U/Q'-depleted Cyanidioschyzon merolae PSII (21)], and PsbO/P/Q-depleted spinach PSII. This is consistent with the fact that in cyanobacterial PSII, the closed-cubane S 2 is unstable with respect to the open-cubane S 2 (14)(15)(16)(17), and only the open-cubane S 2 conformation was observed in the XFEL studies (7)(8)(9)22).
The detailed character of the closed-cubane S 2 conformation, which corresponds to the observed high-spin S 2 (S = 5/2), is unclear. The EPR signals, including the g = 4.1 signal, are not fully reproduced in density functional theory (DFT) calculations (13,23), which ignores the influence of the PSII protein environment (13,23), as pointed out in ref. (24). Notably, the simulated EPR spectrum presented by Pantazis et al. (13) was obtained using a two-spin (Mn(IV) 3 , Mn4(III)) model ["effective coupling model" in ref. (13)], in which exchange couplings among the four Mn sites are simplified by a single exchange coupling between the Mn(IV) 3 cubane region and the dangling Mn4(III) site, eventually ignoring all pairwise exchange couplings of the four-spin (Mn1, Mn2, Mn3, Mn4) model. However, it remains unexamined whether the simplified model effectively represents the relevant exchange couplings. Indeed, the calculated g value was 2.9 for the closed-cubane S 2 conformation in the four spin (Mn1, Mn2, Mn3, Mn4) model as estimated from the simulated EPR spectrum shown in the Supplementary Material of ref. (13), which is not consistent with the experimentally measured g value of ∼4.1 (18). In DFT calculations by Pantazis et al., W2 was also assumed to be OH - (13). Although W2 was repeatedly assumed to be OHin some studies (12,13,(25)(26)(27), the reason is unclear. As far as we are aware, in 2011, Ames et al.
already reported that W2 = OHis the most consistent model based on a comparison of the ground-state spin multiplicity, spin expectation values, and metal-metal distances (12). They also observed that H 2 O at W2 released the proton to OHat W3, leading to the formation of OHat W2. However, it remains unclear why they originally placed OHat W3 to expect the W2 deprotonation. In addition, the model was comprised of only the minimum components, Mn 4 CaO 5 and the first sphere ligand groups. The model did not include any other protein components, e.g. the second sphere ligand residues (D1-Asp61 and CP43-Arg357) (12). Thus, the model cannot be considered to represent the Mn 4 CaO 5 cluster in the PSII protein environment. In 2020, it was reported that pK a (W2) is the lowest in the closed-cubane S 2 conformation in the absence of the PSII protein environment, whereas pK a (W1) is the lowest in the presence of the PSII protein environment, using a quantum chemical/molecular chemical (QM/MM) approach (28). The results also suggest that the low pK a (W2) value proposed by Ames et al. (12) is merely due to the absence of D1-Asp61, the H-bond acceptor of W1. W2 has no strong H-bond acceptor. Because W2 is H 2 O in the open-cubane S 2 conformation with oxidized Mn4(IV) (28)(29)(30)(31), it is more likely H 2 O in the closed-cubane S 2 conformation with reduced Mn4(III ).
Alternatively, Corry and O'Malley proposed that the opencubane S 2 conformation with O4 = OH -(and W2 = OH -) might correspond to a higher spin configuration on the basis of DFT calculations performed in the absence of the PSII protein environment (23). It remains unclear whether the proposal also holds true for PSII protein environment, since OHat O4 already releases the proton toward the O4-water chain during the S 0 to S 1 transition when W2 = H 2 O (36)(37)(38) ; Hat O4 may be energetically unstable even in S 2 with W2 = OH -. Neither the protonation structure nor the deprotonation site in the S 0 to S 1 transition was investigated in the presence of the PSII protein environment in ref. (23). Here, we investigated the origin of the g = 4.1 signal in EPR, using a QM/MM approach and considering the entire PSII protein environment.

Coordinates and atomic partial charges
The atomic coordinates were obtained from the X-ray diffraction (XRD) crystal structure of PSII monomer unit "A" of the PSII complexes from Thermosynechococcus vulcanus at a resolution of 1.9Å (PDB code, 3ARC) (1). The closed-cubane S 2 conformation was not observed in the 1F-XFEL structures (9,22). In the present study, the initial coordinates of the closed-cubane S 2 conformation was obtained, using the energetically more stable open-cubane S 2 conformation (14-17) as an initial structure and analyzing the potential-energy profile for the O5 position between Mn1 and Mn4 in QM/MM calculations, as done previously (15). The resulting initial coordinates were again fully optimized in the absence of the O5 constraint in QM/MM calculations. Note that the structural difference in the Mn 4 CaO 5 region between the XRD and 1F-XFEL is negligibly small, in particular, when the QM/MM optimized geometry is considered, since the calculated E m values, which is sensitive to the difference in the electronic structure of the Mn 4 CaO 5 cluster and the adjacent protein environment, are substantially the same (39). The heavy-atom positions were fixed while the H-atom positions were optimized with CHARMM (40). Water molecules in the crystal structures were represented explicitly as the flexible simple point-charge water model in the MM region. No other water molecules were added, as most of all water molecules adjacent to the Mn 4 CaO 5 cluster are likely to have been identified due to the particularly low disorder in the region of the XRD structure (1). All titratable groups were ionized. D1-His337 was considered to be protonated (29). Atomic partial charges were obtained from the CHARMM22 (41) parameter set for amino acids and previous studies for cofactors (36), respectively.  atoms and 6-31G * for other atoms] (42) using the QSite (43) program. Counter ions were added to neutralize the system. In the QM region, all atomic coordinates were relaxed using the default geometry optimization algorism of QSite with the convergence criteria listed in Table S1. The results obtained using QSite were also evaluated by comparing with those obtained using ORCA (44) (e.g. Tables 2 and 3, see below). For the QM and MM regions, the van-der-Waals parameters of the OPLS2015 force field were used (45). In the MM region, the H-atom positions were energetically optimized, and the heavy-atom positions were fixed using the OPLS2005 force field, because the MM region is used mainly to reproduce (long-distance) electrostatic interactions with the QM region and the heavy-atom positions in the MM region should remain unchanged with respect to those in the original crystal structure. Thus, atoms on the QM surface at the QM/MM interface can be affected predominantly by H-bond or van-der-Waals- contact partners on the MM surface, without causing the unrealistic heavy-atom displacement of the MM region (artifact). The initial-guess wavefunctions were obtained using the ligand field theory (46) implemented in the QSite program. For the closedcubane S 2 conformation and the open-cubane S 2 conformation in the protein environment, the QM region was defined as the Mn 4 CaO 5 cluster (Mn 4 CaO 5 , the side-chains of D1-Asp170, D1-Glu189, D1-His332, D1-Glu333, D1-Asp342, and CP43-Glu354; the carboxy-terminal group of D1-Ala344; and water molecules, W1-W4), O4-water chain (W539, W538, and W393) (36,37), Cl-1 binding site (Cl-1, W442, W446, and the side-chains of D1-Asn181 and D2-Lys317), second-sphere ligands (side-chains of D1-Asp61 and CP43-Arg357), and H-bond network of TyrZ (side-chains of D1-Tyr161, D1-His190, and D1-Asn298, W5, W6, and W7) (47,48).

QM/MM calculations
The QM/MM-optimized geometry was used as the initial geometry to analyze the potential energy profiles of the H-bond (e.g. O···H + ··· O). The focusing H atom was moved along the O. . .O Hbond by 0.05Å, after which the geometry was optimized by constraining the O-H + and H + -O distances, and the energy was calculated.

EPR spectrum calculations
The exchange coupling value, J ij , between Mn(i) and Mn(j) (i, j = 1, 2, 3, 4) were calculated using the broken symmetry approach (13,49,50). Under the classical spin approximation, the total energies of individual spin configurations in the closed-cubane S 2 conformation, where (Mn1, Mn2, Mn3, Mn4) = (IV, IV, IV, III), are expressed in terms of the following equation (50): where S E sc is the total energy of the system for the total spin S and, sc is the spin configuration of (Mn1, Mn2, Mn3, Mn4) [e.g. (↑↓↓↑)], and J ij is the exchange interaction between the i-th and j-th ions. S E sc was obtained from QM/MM calculations (Table S2). The pairwise J values were obtained as the best solution in the least-squares sense, solving the linear equations (eqs. 1 to 8) with the singular value decomposition (49). To calculate the total energy, the adiabatic approximation (i.e. using the optimized structures of all possible spin configurations) was performed (50). Note that the results were essentially the same when the vertical approximation (i.e. using the QM/MM-optimized geometry of the ground-state spin configurations) (50) was performed (Tables S3  and S4).
Spectral simulations were performed using the MATLAB R2019a software (The Mathworks, Inc) as done in previous studies (51). The effective Hamiltonian of the spin state of the Mn 4 CaO 5 cluster can be expressed bŷ
whereŜ i , andÎ i are the operators of electron spin and nuclear spin of the i-th Mn ion, respectively, g i is the g-tensor of the i-th Mn ion, A i is the effective hyperfine tensor of the i-th Mn ion, and β is the Bohr magneton. Here, g i is approximated to be isotropic and independent of Mni (g i = 2).Ĥ ZFS andĤ ex are Hamiltonians of the zero-field splitting (ZFS) and the exchange, respectively, and are espressed asĤ where D is the ZFS tensor of the cluster, J ij is the exchange interaction between the i-th and j-th Mn ions. Using the principle axes x, y, and z of D,Ĥ ZFS is expressed aŝ where D and E are ZFS parameters, which are obtained from the principle value of D total , andŜ 2 total,p is the operator of the p (x, y, or z) component ofŜ total .
The model Hamiltonian (eqs. 9, 11, and 13) is used in the simulations. Here, Mn1, Mn2, and Mn3 are Mn(IV) (S 1 = S 2 = S 3 = 3/2), and Mn4 is Mn(III) (S 4 = 2) with D = -0.445 and E/D = 0.25 (52). Di-agonalizingĤ, we obtain the eigen energy E n (B 0 ) of the n-th state |n(B 0 )> as a function of B 0 , where the hyperfine splitting term is not included (51). The transition probability P k n from the initial state |n(B 0 )> to the final state |k(B 0 )> is given by the following equation based on the Fermi's golden rule, whereŜ total is the operator of the total spin of the system and B 1 is the magnetic field of the external microwave with the angular frequency ω and ω is set to be 9.50 GHz. Assuming that the hyperfine interactions are approximated by using an isotropic Gaussian, the δ function in eq. 14 is replaced with the spectral lineshape of where is the width and is set to be 0.033 cm −1 (corresponding to 350 G). Then, the following equation was obtained : Taking the integral over all directions of B 0 and B 1 (B 0 ⊥ B 1 ), the absorption spectrum I(B 0 ) as a function of B 0 can be calculated by

EPR spectra for the W1 and W2 protonation states
The values of exchange coupling J were calculated based on these five QM/MM-optimized geometries ( Fig. 2A). The calculated J values depend on the protonation states of W1 and W2 (Table 1). In particular, the magnitude of exchange J coupling between Mn3 and Mn4 (|J 34 |) is significantly large (>∼30 cm -1 ) when W1 = OH -(discussed later). Using all six pairwise J values, the energy levels that correspond to the EPR spectrum were calculated (Fig. 3). The g ∼ 4 EPR spectrum originates from the isolated |S| = 5/2 system, which is comprised of S z = ±1/2, ±3/2, and ± 5/2 states (13) (Fig. 4A). When W2 = OH - (Figs. 3C and D), which was assumed in ref. (13), the energy level of the first excited spin state (S = 13/2; i.e. 13/2 E in eq. 1) is too low (27 to 40 cm -1 ; Table S2) in comparison with that of the ground spin state (S = 5/2; i.e. 5/2 E in eq. 5) to reproduce the g ∼ 4 EPR spectrum (e.g. see the fourth-lowest energy at the magnetic field B 0 = 0 in Figs. 3 and 4B). For the same reason, the EPR spectrum was also not reproduced when W1 = H 2 O and W2 = H 2 O (Fig. 3E).
In contrast, the g ∼ 4 EPR spectrum is reproduced only when W1 = OHand W2 = H 2 O (Fig. 3A and B), which is consistent with QM/MM-molecular dynamics studies by Narzi et al. that showed the OHformation at W1 in the closed-cubane S 2 conformation in response to the release of the proton toward D1-Asp61 (32). This is because the energy level of the first excited spin state (S = 7/2; i.e. 7/2 E in eqs. 2 to 4) is sufficiently higher (229 to 253 cm -1 ; Table  S2) than that of the ground spin state (S = 5/2; i.e. 5/2 E in eq. 5) and the energy levels in the |S| = 5/2 system (Fig. 4A) are sufficiently separated from those in the |S| = 7/2 system (Fig. 4A). The calculated g values of 4.0 reproduce the experimentally measured g value of 4.1 for the high-spin S 2 state more appropriately than the previously calculated g values of 2.9 (Fig. S2)  In cyanobacterial PSII, the Mn 4 CaO 5 cluster exists as the opencubane S 2 conformation [e.g. as observed in the XFEL structures (7-9)], because the closed-cubane structure is significantly unstable with respect to the open-cubene structure (14)(15)(16)(17). This is consistent with the fact that (i) the g = 4.1 EPR spectrum (not the g = 4.8 spectrum) was reproduced for the closed-cubene S 2 conformation (Fig. 3) and (ii) the g = 4.1 signal is not observed in cyanobacterial PSII (19)(20)(21).

ZFS scheme
In the present EPR spectrum simulation, the ZFS Hamiltonian H ZFS is described as (eq. 10) based on "the total-ZFS scheme", where the Mn 4 CaO 5 cluster is regarded as a single anisotropic spin systemŜ total (Fig. 5A). On the other hand, in "the onsite-ZFS scheme",Ĥ ZFS is expressed aŝ with the onsite-ZFS tensor D ij between the Mni and Mnj sites. Assuming that the ZFS effect induced by the spin dipoles is negligible of two distinct Mn sites (i.e. D i j = 0 for i = j),Ĥ ZFS can be recast asĤ where d 4 and e 4 are onsite ZFS parameters derived from the principle value of D 4 , andŜ 2 4,p is the operator of the p (x, y, or z) component ofŜ 4 . This approximation may be rationalized when the onsite-ZFS tensor D i for Mn(IV) is negligibly smaller than that for Mn(III) (53). Note that to the best of our knowledge, large D i is not reported for Mn(IV) in the Mn(III)Mn(IV) complexes, while D i for Mn(IV) is not necessarily small in mononuclear Mn complexes (54) (see below).
In the present study, the EPR spectra were also calculated using the original Mn4-site-ZFS parameter as used in ref. (13). The results obtained in the present study are similar to those in the total-ZFS scheme: only when W1 = OHand W2 = H 2 O, the calculated g values are 3.6 to 3.7 (Table 1 and Fig. S3) and reproduce the

Comparison between the total-and Mn4-site-ZFS schemes
It is unclear whether the Mn4-site-ZFS scheme is justified, as (i) the ZFS effect (D ij ) induced by spin dipoles of two distinct Mn sites may not be negligible and (ii) the onsite-ZFS tensor D i is not necessarily negligibly small even for Mn(IV) (54). In addition, (iii) EPR studies suggested that the z axis of the ZFS tensor (i.e. experimentally measured z axis) was oriented along the Mn4-O5 direction independently of the Mn4 valence (51). In the Mn4-site-ZFS scheme, the experimentally measured z axis should correspond to the z axis of the Mn4-site-ZFS tensor D 4 (D 4 -z axis). However, the direction of the experimentally measured z axis (51) may not be consistent with the direction of the D 4 -z axis, because the D 4 -z axis is directly associated with the Mn4-dz 2 axis (53), which is not always oriented along the Mn4-O5 direction (Table 1).
In contrast, in the total-ZFS scheme, the orientation of the z axis of the total-ZFS tensor D (D-z axis) originates from not only the Mn4-dz 2 axis but also the entire electronic structure of the Mn 4 CaO 5 cluster and can be oriented along the different direction from the Mn4-dz 2 axis. Accordingly, the D-z axis is in line with the experimentally measured z axis (51). In the onsite-ZFS scheme (eq. 20), the D 4 -z axis is unlikely to represent the D-z axis in the total-ZFS scheme, probably because (i) the d 4 value is not sufficiently accurate and (ii) the ZFS effect (D ij ) induced by spin dipoles of two distinct Mn sites is not negligible.
Overall, the conclusion that the present EPR spectrum simulation with W1 = OHand W2 = H 2 O reproduces the g ∼ 4 signal (Fig. 3A, B and Fig. S3a, b) appropriately is valid regardless of the total-and Mn4-site-ZFS schemes. Because the experimentally measured z axis is not consistent with the EPR spectrum simulation based on the Mn4-site-ZFS scheme, the total-ZFS scheme seems to be more appropriate than the Mn4-site-ZFS scheme.

Comparison with previous studies: closed-cubane S 2 conformation with W2 = OH -
In previous studies by Pantazis et al. (13), the simulated EPR spectrum was eventually obtained using effective two-spin models. In ref. (13), the actual g value was calculated using six pairwise J values in the "four"-spin model is 2.9, not >4 (Table 1 and Fig. S2). In ref. (13), to approximate the four-spin model as the simplified two-spin model, a parameter "J eff " was introduced (Fig. 5B). g = 2.9, calculated using pairwise J values in the four-spin model (i.e. DFT calculation), corresponds to J eff = -2.3 cm -1 in the simplified twospin model [ Table 1 and Fig. S5 in ref. (13)]. If J eff = -10.6 cm -1 were obtained, g ∼ 4 might have been reproduced (Table 1). However, this is not the case with their DFT calculations (i.e. J eff = -2.3 cm -1 ) (13). Since it is impossible to reconstruct a four-spin model from the two-spin model (Fig. 5B), there is no corresponding Mn 4 CaO 5 cluster geometry with J eff = -10.6 cm -1 . (Note: their simulated EPR spectrum shown in Fig. 4 in ref. (13) was a typical spectrum obtained merely from one arbitrary atom with S = 5/2, not from the original/quantum-chemically optimized Mn 4 CaO 5 geometry in the crystal structure.) Thus, no EPR spectrum with g ∼ 4, which was calculated using "all six pairwise J values (13)" with W2 = OHin the relevant PSII structure (see below), was provided in ref. (13).
In ref. (13), the geometry was obtained in the absence of the PSII protein environment: the protein backbone and Cl-1 were also absent. The absence of the PSII protein environment leads to irrelevant structural changes as an artifact. In ref. (13), W446 at Cl-1 donates an H-bond to one of the carboxyl O sites of D1-Glu333 due to the absence of anionic Cl-1, which weakens the ligand interaction between D1-Glu333 and Mn4. Thus, the stabilization of oxidized Mn4(IV) by D1-Glu333 is underestimated (i.e. the stability of the open-cubane S 2 conformation is underestimated). The absence of Cl-1, which is closer to Mn4 (6.7Å) than Mn1 (7.9Å), also underestimates the stability of Mn(IV) (17). This explains why  the closed-cubane and open-cubane S 2 conformations are isoenergetic in ref. (13) in contrast to other studies (14)(15)(16)(17). The absence of the protein backbone in ref. (13) also induces alteration of the H-bond pattern in a cluster of water molecules near TyrZ (i.e. W3, W5, W6, and W7, Fig. 2) as an artifact. The absence of the protein backbone of D1-Phe182 makes W6 donate an H-bond to W5, which induces the H-bond donation of W5 to W2, stabilizing OHat W2 as an artifact (Fig. 2B). Thus, the conclusion of W2 = OHin the closed-cubane conformation (13) needs to be revisited.

Corry and O'Malley
proposed that the open-cubane S 2 conformation with O4 = OHmight correspond to a higher spin configuration on the basis of DFT calculations performed in the absence of the PSII protein environment (23). The corresponding g value calculated directly from the modeled J coupling is not reported in ref. (23). We calculated the g value on the basis of the J values. The calculated J values do not vary significantly with basis set and functional (Table 3). Furthermore, the EPR spectra obtained from the J values are similar with g = 4.0 (Fig. 6). Nevertheless, it should also be noted that not only S = 5/2 but also S = 1/2 is the energetically lowest state even in the atomic coordinates for the open-cubane S 2 geometry with O4 = OHused in ref. (23) (i.e. in the absence of the PSII protein environment) (Table S5), which is distinct from S = 5/2 being the only lowest state in the closed-cubane S 2 conformation (Table S2). These results suggest that the open-cubane S 2 conformation with O4 = OHcorresponds to a higher spin configuration in the absence of the PSII protein environment.
To evaluate whether the conclusion is also relevant to the PSII protein environment, we investigated the open-cubane S 2 conformation with O4 = OHin the PSII protein environment,  Fig. 7A], releasing the proton toward the O4-water chain (36). The present QM/MM calculation shows that even when W2 = OH -, the open-cubane S 2 conformation with O4 = OHis unstable, immediately releasing the proton toward the O4-water chain (Fig. 7C) and transforming into the energetically stable low spin configuration with S = 1/2 (Table S5).
The second water molecule H 2 O(2) is already absent in the model complex used by Corry and O'Malley, due to the absence of the entire PSII protein environment (23). If the second water molecule H 2 O(2) were absent and the H-bond network of the O4water chain were terminated at the first water molecule H 2 O(1), the energetically unstable OHat O4 could not release the proton toward H 2 O(1) due to significantly low pK a (H 2 O/H 3 O + ) (= -1.7) for a single water molecule. Thus, the open-cubane S 2 conformation with O4 = OHis an energetically unstable conformation in the PSII protein environment, having "an empty cavity" [i.e. low dielectric constant, 8.0 (23)] adjacent to "a highly deprotonatable OH -" at the O4 site.
The second water molecule H 2 O(2) is not explicitly assigned in recent XFEL structure in S 2 (1F-XFEL structure) reported by Ibrahim et al. (22). However, this is not due to the absence of the density of the water molecule but due to the high disorder of the water molecule (i.e. high dielectric constant), as suggested by Suga et al. (9). Indeed, the Fo-Fc map of the 1F-XFEL structure reported by Ibrahim et al. (22) shows that an unassigned density for water molecules exists in the corresponding region (Fig. 7B). As the region with a high dielectric constant resembles bulk water rather than vacuum and their DFT calculations, where the high dielectric region was replaced with a vacant cavity (23), did not consider water dynamics appropriately, the existence of the highly deprotonatable open-cubane S 2 conformation with O4 = OHis unlikely in the presence of the disordered water molecule in the actual protein environment. In addition, ESEEM and ENDOR data imply that the μ-oxo bridges of the Mn 4 CaO 5 cluster are already deprotonated in S 2 (and S 1 due to the absence of the proton release during the S 1 to S 2 transition) (25,(55)(56)(57)(58)(59)(60). They need to clarify (i) how the proton can remain bounded to O4 regardless of the H-bond formation between O4 and the proton-conducting O4-water chain (36,37) in the S 0 to S 1 and even S 1 to S 2 transitions and (ii) how the release of the proton occurs in the S 0 to S 1 transition.

Deprotonation of H 2 O at W1
Beal et al. proposed that the closed-cubane S 2 conformation with W1 = OHwas energetically unstable in the absence of the PSII protein environment (61). However, the present study shows that W1 = OHreproduces the g ∼ 4 EPR spectrum in the presence of the PSII protein environment (Fig. 3). It is unclear how they appropriately modeled the protein electrostatic environment, including the H-bond network of the ligand water molecules, irrespective of the absence of the PSII protein environment, since they did not provide the atomic coordinates of the closed-cubane S 2 conformation used in ref. (61). As far as we are aware from the atomic coordinates of the open-cubane S 2 conformations in refs. (23, 61) (Fig. 8), it seems most likely that their conclusion was deduced from Cl --depleted PSII, not from native PSII.
Clis required in the S 2 to S 3 transition (62). When Clis depleted, the S-state transition is inhibited at the S 2 TyrZ r formation: that is, electron transfer occurs from TyrZ to P D1 r + , but subsequent electron transfer from S 2 to TyrZ r does not occur (62). A salt bridge forms between D1-Asp61 and D2-Lys317 upon the depletion of Cl - (63,64), which may inhibit the D1-Asp61 reorientation and the proton transfer from W1 via D1-Asp61 toward the bulk region in the S 2 to S 3 transition (35 (Fig. 9), which suggests that proton transfer can occur (28,35). The shape of the potential-energy curve for the H-bond between H 2 O at W1 and D1-Asp61 is less symmetric in the closed-cubane S 2 conformation than in the open-cubane S 2 conformation, which suggests that pK a (D1-Asp61) is slightly larger than pK a (W1) in the closed-cubane S 2 conformation due to reduced Mn4(III) (Fig. 9). However, the energy barrier for proton transfer from H 2 O at W1 toward deprotonated D1-Asp61 is low, as indicated by the presence of the local energy minimum at the D1-Asp61 moiety. It seems possible that the release of the proton from H 2 O at W1 toward deprotonated D1-Asp61 occurs in the closed-cubane S 2 conformation, which can be facilitated via proton-coupled electron transfer, as suggested in QM/MM-molecular dynamics studies (32). Because W1 is the ligand water molecule at Mn4(III) in the closedcubane conformation, the release of the proton from W1 can facilitate oxidation of Mn4(III) to Mn4(IV) via proton-coupled electron transfer. Fig. 3 shows that the EPR spectrum was not reproduced (due to the low energy level of the first excited spin state) when the proton of H 2 O at W1 is fully localized at the W1 moiety (W1 = H 2 O and W2 = H 2 O, Fig. 3E). It seems likely that either the migration of the proton toward the D1-Asp61 moiety (HO -. . .HOOC-Asp61) or the relocation of the D1-Asp61 proton toward the D1-Glu65/D1-Glu312 channel [HO -. . .O(OH)C-Asp61 (34, 35)] is a prerequisite for the g ∼ 4 signal formation.

Conclusions
Based on all six pairwise J values calculated in the presence of the PSII protein environment, g = 4.1 is obtained exclusively for the closed-cubane S 2 conformation with W1 = OH -. The result is consistent with QM/MM-molecular dynamics studies by Narzi et al. that showed the OHformation at W1 in the closed-cubane S 2 conformation in response to the release of the proton toward D1-Asp61 (32). The shape of the simulated EPR spectrum for W2 = OHdoes not resemble of that for typical g = 4.1 signal. The simulated EPR spectrum for the closed-cubane S 2 conformation presented in ref. (13) needs to be revisited. The D 4 -z axis in the Mn4-site-ZFS scheme is unlikely to represent the D-z axis in the total-ZFS scheme. The total-ZFS scheme seems to be more appropriate than the Mn4-site-ZFS scheme (Fig. 5).
The existence of the highly deprotonatable open-cubane S 2 conformation with O4 = OH -, which was proposed on the basis of DFT calculations performed by Corry and O'Malley in the absence of the PSII protein environment (23), is energetically unlikely in the presence of the disordered water molecule in the PSII protein environment (9,22) (Fig. 7), since their DFT models are unlikely to consider water dynamics sufficiently.
Although the g = 4.1 signal has not been reported for cyanobacterial PSII, the g = 4.1 signal (not the g = 4.8 signal) was reproduced if S 2 is in the closed-cubane conformation even in the cyanobacterial PSII crystal structure (Fig. 3). These suggest that the g = 4.1 conformation, i.e. the closed-cubane S 2 conformation, is unstable in cyanobacterial PSII, and the g = 4.8 conformation is unlikely to correspond to the closed-cubane S 2 conformation (Fig. 10) [e.g. (65)].

Supplementary Material
Supplementary material is available at PNAS Nexus online.