Redox potentials along the redox-active low-barrier H-bonds in electron transfer pathways †

Low-barrier H-bonds form when the p K a values of the H-bond donor and acceptor moieties are nearly equal. Here, we report redox potential ( E m ) values along two redox-active low-barrier H-bonds in the water-oxidizing enzyme photosystem II (PSII), using a quantum mechanical/molecular mechanical approach. The low-barrier H-bond between D1-Tyr161 (TyrZ) and D1-His190 is located in the middle of the electron transfer pathway. When the proton is at D1-His190, E m (TyrZ) is the lowest and can serve as an electron donor to the oxidized chlorophyll P D1 (cid:2) + . E m (TyrZ) and E m (D1-His190) are equal, and the TyrZ (cid:3)(cid:3)(cid:3) D1-His190 pair serves as an electron acceptor to Mn 4 CaO 5 when the proton is at TyrZ. In the low-barrier H-bond between D1-His215 and plastoquinone Q B , located at the terminus of the electron transfer pathway, the driving force of electron transfer and electronic coupling between Q A and Q B are maximized when the proton arrives at Q B . It seems likely that local proton transfer along redox-active low-barrier H-bonds can alter the driving force or electronic coupling for electron transfer. The driving force of water oxidation in photosystem II (PSII) is provided by light-induced charge separation in the reaction center. In PSII, the reaction center has a pair of chlorophylls (P D1 /P D2 accessory chlorophylls (Chl D1 /Chl D2 ), pheophytins

The driving force of water oxidation in photosystem II (PSII) is provided by light-induced charge separation in the reaction center. In PSII, the reaction center has a pair of chlorophylls (P D1 /P D2 ), accessory chlorophylls (Chl D1 /Chl D2 ), pheophytins (Pheo D1 /Pheo D2 ), and plastoquinones (Q A /Q B ) in the heterodimeric D1/D2 protein subunit pairs (Fig. 1a). 1 Electronic excitation of Chl D1 leads to the formation of a charge-separated state [P D1 P D2 ] + Pheo D1 À ; 2 electron transfer subsequently occurs via Q A to Q B . Q B reduction is linked to Q B protonation. After the second electron transfer, doubly protonated Q B H 2 is released from the binding site toward the bulk water region: the quinone pool. In [P D1 P D2 ] + , the cationic state is more populated on P D1 than P D2 (P D1 + : P D2 + = 80 : 20 [3][4][5][6]. P D1 + has a significantly high redox potential (E m ) for one-electron oxidation (41100 mV [6][7][8][9] ), which makes P D1 + abstract electrons from the substrate water molecules at the Mn 4 CaO 5 cluster (700-800 mV 10 ) via redoxactive D1-Tyr161 (TyrZ; Fig. 1b). TyrZ must form a hydrogen bond (H-bond) with D1-His190 to serve as a redox-active cofactor. Notably, TyrZ and D1-His190 form a significantly short (2.46 Å 11 ) low-barrier H-bond. 12,13 Low-barrier H-bonds can form only when the pK a values of the H-bond donor and acceptor moieties are nearly equal. 14,15 The shape of the potential energy curve of a low-barrier H-bond is symmetric, while the curve of a standard H-bond is asymmetric because pK a (donor) 4 pK a (acceptor) 16 (Fig. 1c and d).
The pK a value of tyrosine (B10) is higher than that of histidine (B7) in water. In the PSII protein environment, a cluster of water molecules (whose positions are fixed by the components of the Mn 4 CaO 5 cluster) donates a stable H-bond to the phenolic O site of TyrZ and decreases pK a (TyrZ) to the level of pK a (D1-His190), forming a low-barrier H-bond. 12,13 In PSII, low-barrier H-bond formation is also observed at the terminus of the electron transfer pathway (Q B and the H-bond partner D1-His215) when the second electron transfer from Q A À to Q B H occurs. 17  Initially, the redox-active group was identified as D1-His190 based on observations of radical formation in the Ca 2+ -depleted PSII. 20,21 Later, it was proposed that TyrZ, not D1-His190, was the origin of the radical state. 22 Since then, TyrZ has been regarded as a redox-active group in the electron transfer pathway. Indeed, E m (TyrZ) is lower than E m (D1-His190), however the E m difference is not significantly large when the proton is at the TyrZ moiety. 10 E m values of the H-bond donor and acceptor moieties along low-barrier H-bonds have not been reported. Here, we report E m of the two redox-active low-barrier H-bonds, considering the entire electron and proton transfer pathways quantumchemically in the presence of the PSII protein environment.

Low-barrier H-bond switching from an electron donor to an acceptor
The potential-energy profile of the H-bond shows that TyrZ and D1-His190 form a low-barrier H-bond. The difference between pK a (TyrZ) and pK a (D1-His190) is nearly zero along the low-barrier H-bond. However, the difference between E m (TyrZ) (i.e., Tyr-O À / Tyr-O ) and E m (D1-His190), (i.e., N-His-N À /N-His-N or HN-His-N/HN-His-N + ) depends on the H + position (Fig. 2, right panel). E m (TyrZ) decreases and E m (D1-His190) increases as the proton moves from TyrZ to D1-His190. When H + arrives at the lower E m moiety (D1-His190), E m (TyrZ) is the lowest and the driving force for electron transfer from TyrZ to oxidized chlorophyll P D1 + is the largest. The highest occupied molecular orbital (HOMO) is predominantly localized at the TyrZ moiety. Thus, the TyrZ moiety can serve as an electron donor to P D1 + most effectively when the proton is at the D1-His190 moiety. Note that the H + atom position does not affect the E m values of other cofactors in the electron transfer pathway. In contrast, when H + is at the TyrZ moiety, E m (TyrZ) and E m (D1-His190) are equal, and the highest occupied molecular orbital (HOMO) is delocalized over the two moieties (Fig. 2b, left panel). In this case, the driving force for election transfer from the oxygen-evolving complex (i.e., Mn4 III/IV ) to the TyrZÁ Á ÁD1-His190 pair is largest (Fig. 2b, right panel). Thus, the entire TyrZÁ Á ÁD1-His190 moiety cooperatively serves as an electron acceptor when electron transfer occurs from the oxygen-evolving complex.

Low-barrier H-bond maximizing electronic coupling and driving force
As an electron transfers to Q B H , a low-barrier H-bond forms between D1-His215 and Q B H /Q B H À , 17 facilitating Q B H 2 release (ii) Electronic coupling. The HOMO is predominantly localized at the Q B H /Q B H À moiety when H + is at the D1-His215 moiety (Fig. 3a, left panel). E m (D1-His215) decreases to the same level as E m (Q B H /Q B H À ) and the HOMO is delocalized over the D1-His215 and Q B pair when H + arrives at Q B H /Q B H À (Fig. 3b, (Fig. 3b, left panel).

Discussion
The redox-active low-barrier H-bond between TyrZ and D1-His190 plays a dual role in electron transfer by serving as both an electron donor and an electron acceptor. The movement of the proton by only 0.35 Å from the D1-His190 moiety along the low-barrier H-bond alters E m by B120 mV and switches its role from an electron donor to acceptor (Fig. 2). As the proton moves back to the TyrZ moiety in the low-barrier H-bond, E m (TyrZ) and E m (D1-His190) become equal within the barrier-less potential (O TyrZ Á Á ÁH = 1.02 Å; Fig. 2b, right panel). Thus, TyrZÁ Á ÁD1-His190 can serve as both an electron donor and acceptor in the middle of the electron transfer pathway during the S-cycle without being destabilized by proton movement. Until now, it has been thought that D1-His190 is not redoxactive, but that TyrZ is 22 (however see ref. 20 and 21). However, this result suggests that both TyrZ and D1-His190 are redoxactive components in the electron transfer pathway, in particular when abstracting an electron from the oxygen-evolving complex (Fig. 2b).
On the other hand, movement of the proton by only 0.35 Å along the low-barrier H-bond between D1-His215 and Q B H / Q B H À increases E m (Q B H /Q B H À ) to the level of E m (D1-His215), leading to delocalization of the HOMO over the D1-His215 and Q B moiety. The involvement of D1-His215 in the electron acceptor decreases the donor-to-acceptor distance from [Q A ]to-[Q B ] to [Q A ]-to-[D1-His215] and increases the electronic coupling between the donor Q A and the acceptor Q B H /Q B H À , because the electronic coupling increases as the electron donor-to-acceptor distance decreases. 23,24 The role of the redox-active low-barrier H-bond in increasing electronic coupling is observed specifically for D1-His215Á Á ÁQ B H /Q B H À , since the axis of the low-barrier H-bond is consistent with the axis of the electron transfer pathway and delocalization of the HOMO over D1-His215 and Q B decreases the substantial donor-acceptor distance (Fig. 3, left panel).
In contrast to the TyrZÁ Á ÁD1-His190 H-bond, the difference between E m (D1-His215) and E m (Q B ) is small but not zero within the barrier-less potential as the proton moves to the Q B moiety (H D1-His215 Á Á ÁH = 1.43 Å; Fig. 3b, right panel). Indeed, the HOMO is still predominantly localized at Q B (Fig. S1, ESI †). Only after the proton exceeds the barrier-less potential by 0.1 Å is the HOMO evenly delocalized over D1-His215 and Q B and the difference between E m (D1-His215) and E m (Q B ) reaches zero (H D1-His215 Á Á ÁH = 1.53 Å, Fig. 3b, right panel). In reality, the low-barrier H-bond is unlikely to exist when H D1-His215 Á Á ÁH = 1.53 Å because the potential energy profile was obtained assuming the presence of the H-bond (see Methods). Consistently, the donor-acceptor NÁ Á ÁO distance (N D1-His215 Á Á ÁO QB ) is 2.47 Å when the proton is located at the D1-His215 moiety (N D1-His215 -HÁ Á ÁO QB ), and it is lengthened to 2.55 Å when the proton arrives at the Q B moiety (N D1-His215 Á Á ÁH-O QB ). Thus, Q B H 2 is released from the binding site (D1-His215) when H + leaves the barrier-less potential (after cleavage of the low-barrier H-bond). The irreversibility of the reaction is characteristic of, and required for, Q B serving as the terminal electron acceptor in the electron transfer pathway. Intriguingly, the corresponding change in the donor-acceptor distance in response to the H + movement is absent in the TyrZÁ Á ÁD1-His190 H-bond (O TyrZ -HÁ Á ÁN D1-His190 = 2.52 Å and O TyrZ Á Á ÁH-N D1-His190 = 2.50 Å). This is consistent with the role of the TyrZÁ Á ÁD1-His190 pair in the middle of the electron transfer pathway, which involves reversibly donating and accepting an electron during the entire S-cycle. As reported, environmental fluctuations may affect the potential energy profile, 25 particularly for standard H-bonds. Proton transfer is energetically uphill in the standard H-bond (Fig. 1c). To overcome this energy barrier, fluctuation/rearrangement of the protein environment is a prerequisite for unstable protonation of the acceptor moiety. In contrast, proton transfer is barrier-less in the low-barrier H-bond, which does not require the corresponding fluctuation/rearrangement of the protein environment (Fig. 1d). Consistently, the B-factors of TyrZ and D1-His190 are specifically low 11 because the H-bond network is fixed by the PSII protein electrostatic environment, namely the Mn 4 CaO 5 cluster and the ionized ligand residues. 12 For the redox-active low-barrier H-bonds to serve as a redoxactive cofactor in the electron transfer pathway, the presence of the protein electrostatic environment is a prerequisite. First, TyrZ and D1-His190 cannot form a low-barrier H-bond in the absence of the PSII protein environment 12 because of the difference in pK a (B3) between tyrosine and histidine. Second, the protein electrostatic environment is required for the formation of the downhill electron transfer pathway that proceeds from the Mn 4 CaO 5 cluster via TyrZ, as it increases E m (P D1 ) by B400 mV with respect to E m (Chla). 6,26 Thus, the environment, in which the pK a values of the proton donor and acceptor moieties are equal and the E m values of the electron donor and acceptor moieties are in the tunable range by proton transfer, is ultimately provided by the common protein electrostatic environment.
In summary, the pK a values of the two moieties are equal, but the E m values depend on the H + position in redox-active low-barrier H-bonds. The results also suggest that redox-active low-barrier H-bonds can differ in their characteristics, whether they serve as a redox-active cofactor in the middle of the electron transfer pathway (TyrZÁ Á ÁD1-His190) or in the terminus of the electron acceptor pathway (D1-His215Á Á ÁQ B ). These findings provide a key to understanding how nature optimizes electron and proton transfer in biological systems using abundantly available protons.

Methods
The atomic coordinates of PSII were obtained from the PSII crystal structure (PDB code, 3ARC). 11 The atomic charges of the other cofactors in the MM region were taken from a previous study. 27 E m calculations for the electron transfer pathway via TyrZÁ Á ÁD1-His190 The HOMO energy level is largely correlated with E m for oneelectron oxidation (e.g., ref. 28 and 29). For the Mn 4 CaO 5 cluster, the HOMO in S n corresponds to the molecular orbital, which predominantly contributes to the release of an electron in the S n to S n+1 transition. We included all redox-active cofactors (Mn 4 CaO 5 cluster, TyrZ, P D1 , and P D2 ) simultaneously in the QM region 30,31 (see below), identified HOMOs of Mn 4 CaO 5 , TyrZ, P D1 , and P D2 in S 1 on the basis of the Mulliken population analysis 32 (results provided in a previous study 10 where E HOMO is the HOMO energy level (meV). 10

QM/MM calculations
The unrestricted density functional theory method was employed with the B3LYP functional using the QSite program. 33 B3LYP is a widely used functional to calculate redox potentials and HOMO and LUMO energy levels (e.g., ref. 34 and 35). Using B3LYP can also make a comparison with our previous studies for Mn 4 CaO 5 , 10,36 TyrZ, 12,13 P D1 , 6,37 and Q B 17 in PSII. In the QM region, all the atomic coordinates were fully relaxed. In the MM region, the positions of the H atoms were optimized using the OPLS2005 force field, 38 while the positions of the heavy atoms were fixed.
To investigate the H-bond between D1-His215 and Q B , the LACVP**+ basis set was employed. The QM region was defined as [Q B , D1-His252, D1-Ser264, bicarbonate, Fe, D1-His215, D1-His272, D2-His214, and D2-His268]. We assumed a high-spin state (S = 2) of Fe 2+ and set the spin multiplicity of the system to S = 2 in the calculations for Q B H À and Q B H 2 . The MM region was defined as the D1 and D2 protein subunits, as in a previous study. 17 D1-His252 was considered to be protonated before Q B H 2 formation, 44 whereas all other titratable groups were in the standard protonation states. See ref. 17 for the QM/MMoptimized atomic coordinates.
To obtain the potential energy profiles of the OÁ Á ÁHÁ Á ÁN H-bond, the QM/MM optimized geometry was used as the initial geometry. The H atom under investigation was moved between O and N by 0.05 Å before the geometry was optimized by constraining the O-H and H-N distances, and the energy was calculated. This procedure was repeated until the H atom reached the O and N atoms. This approach, which is based on the single QM/MM-optimized geometry, provides the unique minimum-energy pathway, in particular for the H-bond between TyrZ and D1-His190, as demonstrated by analyzing protontransfer pathways in the different protein conformations. 12

Conflicts of interest
There are no conflicts to declare.