Toward understanding the S2-S3 transition in the Kok Cycle of Photosystem II: Lessons from Sr-Substituted Structure

Understanding the water oxidation mechanism in Photosystem II (PSII) stimulates the design of biomimetic artificial systems that can convert solar energy into hydrogen fuel efficiently. The Sr2+ substituted PSII is active but slower than with the native Ca2+ as an oxygen evolving catalyst. Here, we use Density Functional Theory (DFT) to compare the energetics of the S2 to S3 transition in the Mn4O5Ca2+ and Mn4O5Sr2+ clusters. The calculations show that deprotonation of the water bound to Ca2+ (W3), required for the S2 to S3 transition, is energetically more favorable in Mn4O5Ca2+ than Mn4O5Sr2+. In addition, we have calculated the pKa of the water that bridges Mn4 and the Ca2+/Sr2+ in the S2 using continuum electrostatics. The calculations show that the pKa is higher by 4 pH units in the Mn4O5Sr2+.

The oxygen evolving complex (OEC) is a unique natural bioinorganic cluster that catalyzes the water oxidation reaction in the 5-steps (S0, S1, S2, S3, S4) Kok cycle. 1,2, The core of the OEC contains a metal cluster of four Mn and one Ca 2+ connected through bridging oxygens. [2][3][4] Ca 2+ depletion 5,6 blocks the S2-S3 transition, while replacing Ca 2+ with Sr 2+ reduces the catalytic activity. [7][8][9][10] Calcium and strontium belong to group 2 alkaline earth metals in the periodic table. Thus, they are chemically similar and have a stable oxidation state of +2. However, Ca 2+ is a stronger Lewis acid, which indicates that aqua-Ca 2+ compounds have a lower pKa than aqua-Sr 2+ (measured pKa is 2 pH unit lower). This difference in proton affinity of the bound waters may be the reason for the difference in the catalytic activity in the Sr-substituted PSII. [10][11][12] Here, we use Density Functional Theory (DFT) to compare the energetics of the S2-S3 transition in the native and Sr-substituted PSII.
Experimental 13 and theoretical studies [14][15][16] have proposed that the S2-S3 transition passes through an intermediate step in which the S2 EPR signal changes from the multiline g=2 signal to the g=4.1. In the g=4.1 EPR state Mn1, Mn2, Mn3 are in the IV oxidation state, while Mn4 is in the III state (Fig 1). 17 In the g=2 redox isomer M1 is Mn 3+ while M4 is Mn 4+ . In addition, timeresolved photothermal beam deflection measurements suggest that a proton is released from the OEC or surroundings when the nearby Tyr, Yz, is oxidized before Mn oxidation in the S2-S3 transition. 18,19 Based on classical electrostatic calculations and DFT study 14 , we previously proposed that the S2-S3 transition starts by the transition from g=2 to g=4.1 structure followed by deprotonation of the W3 Ca 2+ ligand. 20 This is coupled to the protonation of HIS190 upon the oxidation of the secondary donor Yz * . The deprotonated W3 moves toward Mn4 adding the sixth ligand to its coordination shell to facilitate its oxidation to IV state. Similar mechanisms have been proposed by previous theoretical [21][22][23][24] and experimental 10 studies.
Here, we compare the energies of two structures of the S2 g=4.1 state, A in which HIS190 and W3 are neutral ( Figure 1A) and B with protonated HIS190 + and W3 is a OHbridge between Mn4 and Ca 2+ ( Figure 1B) in both Mn4O5Ca 2+ and Mn4O5Sr 2+ clusters. The structures were optimized at the DFT level using the B3LYP functional and 6-31G(d) basis sets for N, O, C and H atoms, while SDD are used for Mn, Ca and Sr. All the Mn ions are in the high spin state. Furthermore, the energies are compared using different levels of theory; B3LYP/6-31G+(d) and B97D/6-31G+(d). 25,26 The energy differences between the A and B states (∆G(B-A)) at different level of theory are shown in (Table 1). In general, the B state (protonated HIS190 and hydroxyl on W3) is always more favorable for the Mn4O5Ca 2+ than the Mn4O5Sr 2+ cluster. The large energy difference obtained for the Mn4O5Sr 2+ cluster using B3LYP/6-31G(d) level of theory indicates the importance of including diffuse functions in the basis sets when modeling large ions. These diffuse functions provide flexible representation to the tail part of the atomic orbitals further from the nucleus. 25,26 Sr 2+ is larger than Ca 2+ by 0.1Å, which elongates the interatomic distances between the Sr 2+ and the rest of atoms in the Mn cluster. This is seen in the optimized structures of the A and B states with Ca 2+ and Sr 2+ clusters ( Table 2). In addition, the dispersion interaction between the metal and the water ligand is expected to push the water away in case of Sr 2+ , which will result in smaller electrostatic interactions and a higher pKa. This is found for aqua-Ca 2+ and aqua-Sr 2+ compounds, where the water bound to Sr 2+ have a higher pKa than those bound to Ca 2+ . Thus, the Sr 2+ structure is more stable with neutral W3 ( Figure 1A). However, with Ca 2+ , W3 deprotonates forming a hydroxide that moves to bridge Mn4 and Ca 2+ ( Figure 1B). The optimized DFT structures show that Mn-Sr 2+ distances are in general longer than Mn-Ca 2+ . In the A state the Sr 2+ -W3(HOH) distance is longer by 0.1Å than Ca 2+ -W3(HOH), while in the B state the Sr 2+ -W3(OH)distance is 0.2Å longer. The Mn1 to Ca 2+ , is longer because Ca 2+ moves significantly toward Mn4 after the deprotonation of W3. 13.0 -8.0 -6.4 Energy differences are expressed in Kcal/mol. The transition from A to B state is more favorable in the Mn4O5Ca 2+ cluster than the Mn4O5Sr 2+ To further compare the Mn4O5Ca 2+ the Mn4O5Sr 2+ , we calculated the pKa of W3 in the A state for both clusters using continuum electrostatics. 27,28 W3 has a pKa of 6.5 for the Mn4O5Ca 2+ and 10.3 in the Mn4O5Sr 2+ . The lower pK of W3 in Ca 2+ structure is expected as W3 is significantly closer to the positively charged ions (Ca 2+ , Mn4(III) and Mn1(IV) ( Table 2). This conclusion is supported by the DFT calculations, which show that B is lower energy than A indicating the easier deprotonation in case of the Mn4O5Ca 2+ .
An open question is what the source of the proton which is released after Yz is oxidized but before the OEC advances to the S3 state. 3,29 As there are no protons bound to the bridging oxygens in the S2 state, the donors are likely to be terminal water ligands bound to Mn4 water 30,31 or to Ca. 32 Previous studies have shown the Mn4-bound water W1 to be upon the formation of tyrosyl radical, however the proton is trapped by the neaby acceptor D61. 16,33,34 The present study utilizes the S2 g=4.1 models for Ca 2+ and Sr 2+ to understand the nature of deprotonation event. Our DFT calculations support the deprotonation of W3 in the S2 to S3 transition, which is also supported by the XFEL structures comparing S1, S2 and S3 states. 28 All distances are reported in Å. In general, the interatomic distances are longer for Sr 2+ .

Supporting Information
The Supporting Information includes details of the continuum electrostatic calculations and the optimized atomic coordinates of the optimize A and B structures.