Insights into the protonation state and spin structure for the g = 2 multiline electron paramagnetic resonance signal of the oxygen-evolving complex

Abstract In photosystem II (PSII), one-electron oxidation of the most stable oxidation state of the Mn4CaO5 cluster (S1) leads to formation of two distinct states, the open-cubane S2 conformation [Mn1(III)Mn2(IV)Mn3(IV)Mn4(IV)] with low spin and the closed-cubane S2 conformation [Mn1(IV)Mn2(IV)Mn3(IV)Mn4(III)] with high spin. In electron paramagnetic resonance (EPR) spectroscopy, the open-cubane S2 conformation exhibits a g = 2 multiline signal. However, its protonation state remains unclear. Here, we investigated the protonation state of the open-cubane S2 conformation by calculating exchange couplings in the presence of the PSII protein environment and simulating the pulsed electron–electron double resonance (PELDOR). When a ligand water molecule, which forms an H-bond with D1-Asp61 (W1), is deprotonated at dangling Mn4(IV), the first-exited energy (34 cm−1) in manifold spin excited states aligns with the observed value in temperature-dependent pulsed EPR analyses, and the PELDOR signal is best reproduced. Consequently, the g = 2 multiline signal observed in EPR corresponds to the open-cubane S2 conformation with the deprotonated W1 (OH−).


Introduction
The Mn 4 CaO 5 cluster in photosystem II (PSII) plays a vital role as the catalytic center for oxidizing substrate water molecules (1, 2). The oxidation state of the Mn 4 CaO 5 cluster, denoted as S n (n = 0, 1, 2, or 3), increases with electron transfer (Fig. 1), leading to O 2 evolution during the S 3 to S 0 transition. As the reaction progresses, protons are released in the S 0 → S 1 → S 2 → S 3 → S 0 transitions with a stoichiometry of 1:0:1:2. The Mn 4 CaO 5 cluster consists of three Mn and one Ca sites in the cubane region (Mn1, Mn2, Mn3, and Ca) and a dangling Mn site (Mn4) (Fig. 1). Two ligand water molecules, W1 and W2, are present at the Mn4 site, while two additional water molecules, W3 and W4, are located at the Ca site. In the high oxidation state model for S 1 (3), the Mn valence state is Mn(III) 2 Mn(IV) 2 and Mn2 and Mn3 are already oxidized to Mn(IV) based on the redox potential (4). Thus, either Mn1(III) or Mn4(III) serves as the oxidation site in the S 1 to S 2 transition.
In the S 2 to S 3 transition, a water molecule is incorporated into the Mn 4 CaO 5 cluster according to the XFEL structures (7)(8)(9)(10). This transition also involves a two-step proton transfer process: the release of the proton from the Mn 4 CaO 5 cluster and the transient protonation of D1-Asp61 (15)(16)(17)(18), followed by subsequent proton transfer via D1-Glu65/D2-Glu312 toward the lumenal bulk surface (19). The experimentally observed small (∼1) and large (∼2) kinetic isotope effects (20) likely correspond to the first and second processes, respectively.
Electron paramagnetic resonance (EPR) spectroscopy is a method to determine the spin structure and the protonation state of the Mn 4 CaO 5 cluster and W1-W4. In EPR spectroscopy, two signals are observed as follows: the g = 2 multiline signal and the g ≥ 4.1 signals (e.g. (21)(22)(23)(24)(25)). The g ≥ 4.1 signals can be categorized into two groups as follows: the g = 4.1 signal and the g ∼ 5 signal (26,27). The g = 4.1 signal corresponds to the high-spin closed-cubane S 2 conformation (5,6,28), while the g ∼ 5 signal geometry has not been identified yet. To determine the protonation state of the Mn 4 CaO 5 cluster and the ligand water molecules (W1-W4), results were usually interpreted using quantum chemical calculations of the high-spin S 2 conformation conducted mostly in the absence of the PSII protein environment for simplicity (5,6,29,30). These theoretical models with the isolated Mn 4 CaO 5 cluster proposed that W1 = H 2 O and W2 = OH − (5,6,30). In contrast, recent theoretical studies conducted in the presence of the PSII protein environment indicated that W1 = OH − and W2 = H 2 O for the g = 4.1 signal, as the g = 4.1 EPR signal was reproduced only when the high-spin closed-cubane S 2 conformation (total spin S = 5/2) had W1 = OH − and W2 = H 2 O, not W1 = H 2 O and W2 = OH − (Fig. 1B) (28). The g = 4.1 signal was observed in plant PSII, but not in cyanobacterial PSII under physiological conditions (31,32). This observation aligns with the energetically unstable nature of the closed-cubane S 2 conformation in cyanobacterial PSII (28). Thus, it is a prerequisite to consider the protein environment in theoretical calculations when interpreting EPR spectroscopy (28).
On the other hand, the g = 2 multiline signal corresponds to the open-cubane S 2 conformation with low spin (S = 1/2) (5,6). T 1 (electron spin-lattice relaxation time) measurements indicated that an excited spin state manifold exists 22-37 cm −1 above the ground state manifold corresponding to the g = 2 multiline signal (33,34). The 55 Mn electron nuclear double resonance (ENDOR) analysis was used to probe the hyperfine interaction (HFI) constants (e.g. the isotropic part of the effective HFI constant A iso ) of Mn sites in the S 2 low-spin state (35,36 where A i,iso is the isotopic part of the HFI constant for the i-th Mn site (Mn(i), where i = 1, 2, 3, and 4), a i,iso is the intrinsic HFI constant, and ρ i is the spin projection (36). Importantly, the equation is guaranteed only in the absence of the zero-field splitting (ZFS), i.e. the anisotropy of the spin projection matrices ρ i can be neglected and ρ i are proportional to the identity matrix (36). Although Eq. 1 is applicable to the model compounds of a two-spin system (38), it remains unclear whether the Mn 4 CaO 5 cluster is the case. Using Eq. 1, the A iso values in the low-spin S 2 state were calculated in the absence of the PSII protein environment with density functional theory (DFT) methods, e.g. ( (37). Therefore, the inconsistency in the HFI constants suggests that the proposed methodology based on the comparison between calculated and experimentally measured HFI constants is not conclusive enough to determine the protonation state of the Mn 4 CaO 5 cluster.
The spin structure of the low-spin S 2 state has also been studied using pulsed electron-electron double resonance (PELDOR)/ double electron-electron resonance (DEER) (39,40). PELDOR can provide direct measurement of spin densities, by detecting a dipole interaction between tyrosine D radical (TyrD • ) and the spin densities on each Mn site of the Mn 4 CaO 5 cluster. Thus, PELDOR can directly obtain the spin densities, enabling a straightforward comparison with the spin densities calculated using the PSII structure. PELDOR studies indicated a spin configuration of (↑↓↑↓) for (Mn1, Mn2, Mn3, and Mn4), with Mn1 having a large positive spin projection (ρ 1 = 1.97), Mn3 having a small positive spin projection (ρ 3 = 1. 19), and Mn2 and Mn4 having negative spin projections (ρ 2 = −1.2 and ρ 4 = −0.96) (39). Consistently, Stich et al. (41) also reported a large spin projection for Mn1 with the D1-His332 ligand (ρ 1 = 1.77) using the electron spin-echo envelope modulation (ESEEM). The large spin on Mn1 suggested in PELDOR (39) and ESEEM (41) studies was consistent with the ENDOR (37) results, but not with the previous calculations of HFI constants in the absence of the PSII protein environment (34,36). As calculations of the HFI constants suffer from the uncertainty (29,35,37), the comparison between the spin projection distribution suggested in PELDOR and ESEEM studies and that calculated in theoretical models is more likely to provide further insights into the relevant spin structure of the Mn 4 CaO 5 cluster in the PSII protein environment. Thus, the protonation state of the Mn 4 CaO 5 cluster in the open-cubane S 2 conformation corresponding to the g = 2 multiline signal has not been identified unambiguously, despite the extensive EPR studies including ENDOR, PELDOR, and ESEEM. Moreover, most theoretical calculations used to interpret spectroscopic results were conducted in the absence of the PSII protein environment (5,29,34,37), which may be a reason for the uncertainty in the protonation state of the Mn 4 CaO 5 cluster.
Here, we investigate the origin of the g = 2 multiline signal, using a quantum mechanical/molecular mechanical (QM/MM) approach and considering interactions between the open-cubane S 2 conformation and the PSII protein environment.

Atomic coordinates
The X-ray diffraction structure of PSII monomer unit "A" (PDB code: 3ARC; 1.9-Å structure) (1) was used in the present study. It is worth noting that the 1.9-Å structure corresponds to S 1 (1). Although the X-ray diffraction structure might have experienced over-reduction during data collection, leading to elongated Mn-O bonds (42-48), Suga et al.
(2) reported that no significant structural difference exists between the XFEL structure for S 1 and the 1.9-Å structure. The S 2 -state structure, obtained from the single-flash-minus-dark isomorphous difference Fourier map (1F-XFEL structure) at a slightly lower resolution (e.g. PDB code, 6JLK (9)), shows no significant differences compared to the 1.9-Å structure. Notably, the 1.9-Å structure contains more water molecules (1,442 molecules) than the S 2 -state structure (1,289 molecules). Furthermore, the calculated redox potential values are also essentially the same for the 1F-XFEL and/or 1.9-Å structure (49). Additionally, the g = 4.1 signal for the closed-cubane S 2 conformation was also investigated using the 1.9-Å structures (28). To ensure consistency in the protein electrostatic environment for the QM/MM calculations and enable direct comparisons, the 1.9-Å structure was used for the open-cubane S 2 conformation in the present study. Water molecules, protonation state of titratable residues, and atomic partial charges were treated as done in previous studies (28).

QM/MM calculations
The unrestricted DFT method employing the B3LYP functional and LACVP* basis sets (Mn and Ca atoms: LANL2DZ [double ζ quality basis set with the Los Alamos effective core potential]; other atoms: and 6-31G*) (50) was used with the QSite (51) program as done in the previous study (28). The QM region was identical to that used for the closed-cubane S 2 conformation (28). See Supplementary Material for the atomic coordinates of the QM/ MM-optimized geometry.

Calculations of spin system
The exchange coupling values, J ij , between Mn(i) and Mn(j) (i, j = 1, 2, 3, 4, and i < j), were determined using the broken symmetry (BS) approach (6,52,53). Assuming the classical spin approximation, the total energies for distinct spin configurations can be described by the following equations (53): (6) 1/2 E (↑↑↓↓) = −6J 12 + 6J 13 + 6J 14 + (9/2)J 23 + (9/2)J 24 − (9/2)J 34 (7) 1/2 E (↑↓↑↓) = 6J 12 − 6J 13 + 6J 14 + (9/2)J 23 − (9/2)J 24 + (9/2)J 34 , 1/2 E (↑↓↓↑) = 6J 12 + 6J 13 − 6J 14 − (9/2)J 23 + (9/2)J 24 + (9/2)J 34 , (9) where S E sc is the total energy of the system for a given total spin S, obtained in QM/MM calculations (Table S1). The spin configuration sc refers to the configuration of spins for (Mn1, Mn2, Mn3, and Mn4), and J ij is the exchange coupling between Mn(i) and Mn(j). The pairwise J values were determined by solving the linear equations (Eqs. 1-8) using singular value decomposition to obtain the best solution in terms of the least-squares sense (52). Using the QM/MM-optimized geometries for all possible spin configurations, the total energy was calculated based on the adiabatic approximation (53). The effective Hamiltonian describing the spin state of the Mn 4 CaO 5 cluster can be expressed as follows: where Ŝ i is the operator for electron spin, Î i is the operator for nuclear spin, the g i value is the g-tensor, and A i is the effective hyperfine tensor in Mn(i). β is the Bohr magneton. In the present study, the g i value was approximated to be isotropic and independent of Mn(i), with a value of 2. Ĥ ZFS is the Hamiltonians of ZFS. Ĥ ex is the Hamiltonians of exchange interactions. The Ĥ ex term is expressed asĤ Because the ZFS parameters are unknown, Ĥ ZFS was neglected as done in the previous study (36). Here, Mn2, Mn3, and Mn4 are Mn(IV) (S 1 = S 2 = S 3 = 3/2) and Mn1 is Mn(III) (S 4 = 2). By diagonalizing Ĥ , the eigenenergy E n (B 0 ) of the n-th state |n(B 0 )> was determined as a function of B 0 , excluding the hyperfine splitting term (54). The n-th excited energy E n (n = 0 for the ground state) in the manifold spin states is obtained from E n (B 0 = 0). The spin projection ρ i for Mn(i) was calculated as is the total spin operator and 〈 A〉 in Eq. 12 represents the expectation value of A.

PELDOR simulations
To simulate PELDOR measurements, the PELDOR result obtained from the previous experiments was used (39). PELDOR simulations were performed as done in the previous study (39). The signal amplitude X(τ′) depends on the time interval τ′ between the first and second pulses and can be expressed as follows: where p is the fraction of spin affected by the pumping pulse, and D is the dipole interaction between the two spins. The expression for D between the spin density distributions of TyrD • and the Mn 4 CaO 5 cluster is given by: where ρ i is the spin projection at the i-th (i = 1-7) carbon/oxygen atom of the TyrD • molecule and ρ j is the spin projection at Mn( j). R ij is the distance between the i-th (i = 1-7) carbon/oxygen atom of the TyrD • and Mn( j). h is the Planck constant, Θ ij is the angle formed between the external magnetic field H and the distance vector R ij . g 1 and g 2 are g-factors and were assumed to be 2.00, neglecting ρ anisotropy as a first-order approximation (37).The signal amplitude I(τ′) is calculated by integrating over all angles and can be expressed as:  (15)(16)(17)19), whereas W2 only interacts with water molecules. Thus, the release of W1 toward D1-Asp61 can occur easily with respect to deprotonation of W2. Once the protonated side-chain of D1-Asp61 is reoriented (19,55), the proton is further transferred toward the lumenal bulk surface. Based on these observations,  Table 1).

Exchange couplings
The exchange coupling values J ij were calculated using the five QM/MM-optimized geometries shown in Fig. 2 (Table 1).
Thus, the open-cubane S 2 conformation is most likely with W1 = OH − and W2 = H 2 O. Note that the protonation state with W1 = OH − and W2 = H 2 O was also reported for the closed-cubane S 2 conformation for the g = 4.1 signal (28).

PELDOR
The values of the spin projection ρ in the ground state of the spin Hamiltonian of Eq. (12) were calculated based on the five QM/ MM-optimized geometries (Fig. 2). Although the calculated ρ values depend on the protonation states of W1 and W2, ρ 1 is the largest among the four ρ i values for all protonation states ( Table 2). The PELDOR signal was simulated using the calculated ρ values (Fig. 3). The experimentally observed oscillation pattern (39) is best reproduced when W1 = OH − and W2 = H 2 O in the QM/MM calculation. In contrast, the observed pattern is not reproduced in the other protonation states as the frequencies in the calculated signals are shifted faster (i.e. the peak positions in the calculated signals are shifted). These results suggest that W1 = OH − and W2 = H 2 O are the protonation state for the low-spin state of the open-cubane S 2 conformation.
When W1 = OH − and W2 = H 2 O, the calculated ρ 1 value for Mn1(III) is 1.82 (Table 2), which is consistent with ρ 1 ≈ 2 suggested in previous PELDOR studies (39) and ρ 1 = 1.7 suggested in ENDOR and ESEEM studies (37,41). All of these studies show that ρ 1 has the largest magnitude among the four ρ i values (Table 2), including DFT calculations of the Mn 4 CaO 5 cluster performed by Ames et al. (5) in the absence of the PSII protein environment.

Uncertainty in the calculated A i,iso values
Ames et al. (5) performed DFT calculations without considering the PSII protein environment and found that the magnitude of the calculated ρ 1 value for Mn1(III) was the largest among those for the four Mn sites in the open-cubane S 2 conformation. This result is consistent with ESEEM (41), PELDOR (39), and the present calculation (Table 2).
While the ρ i value is already known and the a i,iso value can be calculated using the BS approach (52), if Eq. 1 was relevant to the Mn 4 CaO 5 cluster, all these studies would indicate that A i,iso was largest at Mn1(III) among the four Mn sites. However, in the same study, Ames et al. (5) controversially reported that the calculated A i,iso value was the largest at Mn4(IV). This inconsistency between experimentally measured A i,iso values (29, 37) and calculated A i,iso values (5) suggests that Eq. 1 is unlikely to be applicable to the Mn 4 CaO 5 cluster.
The source of the inconsistency may be due to insufficient consideration of anisotropy in Eq. 1. Eq. 1 is guaranteed only in the absence of ZFS (36) and may be applicable to the two-spin system in a model compound with the a i,iso values obtained using the BS calculation (38). However, it seems unlikely that Eq. 1 is directly applicable to the multi-coupled system due to its anisotropy. In particular, inter-dipole interactions cause the anisotropy in the Mn 4 CaO 5 cluster, because the total ZFS consists of ZFSs on the four Mn sites (56,57). Therefore, a direct comparison between A i,iso converted using Eq. 1 from calculated ρ i values and those measured experimentally has not been established in the Mn 4 CaO 5 cluster (e.g. (29,37)).

Formation of OH − at W1 in EPR-detected S 2 in EPR experiments
H 2 O at W1 releases the proton during the S 2 to S 3 transition (19,55). In the actual S 2 state, the proton migrates along the low-barrier H-bond between W1 and D1-Asp61, as demonstrated in Fourier transform infrared spectroscopy (16) and theoretical (19,55) studies. However, at this stage, the proton is not yet released toward the lumenal bulk surface (e.g. (15,58)) (Fig. 4A). In contrast, the present results show that the open-cubane S 2 conformation with W1 = OH − and W2 = H 2 O is most consistent with the observed first excited energy ΔE 01 in T 1 measurements (33,34,59) (Table 1) and the observed PELDOR signal (39) (Fig. 3) for the low-spin S 2 state. That is, OH − already exists at W1 in the EPR-detected S 2 samples.
The difference in the protonation state between S 2 and EPR-detected S 2 could be due to the difference in the precursor. Although charge separation occurs in S 2 , S 2 does not proceed to S 3 at low temperature (∼200 K) in EPR measurements (60,61). However, the sample is under continuous-wave light conditions, which still allows P680 to be photoexcited, oxidizing [TyrZ-O − … H + …N-His190-NH] to [TyrZ-O • …HN-His190-NH] + and deprotonating the lowest-pK a site at the Mn 4 CaO 5 moiety in S 2 (e.g. (18,62)). As QM/MM calculations performed in the presence of the PSII protein environment have suggested that W1 is the lowest-pK a site among all titratable sites at the Mn 4 CaO 5 moiety in S 2 (63), it seems possible that W1 releases the proton, forming OH − under continuous-wave light conditions in EPR measurements (Fig. 4B). This may explain the discrepancy between S 2 and EPR-detected S 2 .

Conclusions
The exchange coupling J ij calculated in the presence of the PSII protein environment indicates that the spin configuration of the open-cubane S 2 conformation is (↑↓↑↓) or (↑↓↓↑) for Mn1(III) Mn2(IV)Mn3(IV)Mn4(IV) ( Table 1). Diagonalization of the spin Hamiltonian obtained using the J couplings shows that when W1 = OH − and W2 = H 2 O, the first excited energy (ΔE 01 = 34 cm −1 ) in the manifold spin states is consistent with the experimentally observed value (27-37 cm −1 ) ( Table 1). The magnitude of the calculated ρ 1 value for Mn1(III) is the largest among those for the four Mn sites in the open-cubane S 2 conformation (Table 2), which is consistent with ESEEM (41) and PELDOR (39) studies and previous DFT calculations conducted without considering the PSII protein environment (5). The PELDOR signal observed for the low-spin S 2 state (39) is reproduced only when W1 = OH − and W2 = H 2 O in the open-cubane S 2 conformation (Fig. 3). These results obtained from the present QM/MM calculations conducted in the presence of the PSII protein environment consistently suggest that the g = 2 multiline signal in EPR corresponds to the open-cubane S 2 conformation with W1 = OH − and W2 = H 2 O (Fig. 4B).

Supplementary Material
Supplementary material is available at PNAS Nexus online.

Data availability
All data are included in the manuscript and/or supporting information.  and (B) EPR-detected S 2 (W1 = OH − ) exposed to continuous-wave light for ∼5 minutes at low temperature (200 K). While the S 2 to S 3 transition is blocked, proton release from W1 can still occur, leading to the formation of OH − at W1 in the EPR-detected S 2 sample. Boxed states indicate resulting states.