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Cite This: Inorg. Chem. 2019, 58, 9672−9690

Geometry and Electronic Structure of the P‑Cluster in Nitrogenase Studied by Combined Quantum Mechanical and Molecular Mechanical Calculations and Quantum Refinement Lili Cao,† Melanie C. Börner,†,‡ Justin Bergmann,† Octav Caldararu,† and Ulf Ryde*,† †

Department of Theoretical Chemistry, Lund University, Chemical Centre, P.O. Box 124, SE-221 00 Lund, Sweden Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany

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‡

S Supporting Information *

ABSTRACT: We have studied the geometry and electronic structure of the P-cluster in nitrogenase in four oxidation states: PN, P1+, P2+, and P3+. We have employed combined quantum mechanical and molecular mechanical (QM/MM) calculations, using two different densityfunctional theory methods, TPSS and B3LYP. The calculations confirm that the side chain of Ser-188 is most likely deprotonated in the partly oxidized P1+ state, thereby forming a bond to Fe6. Likewise, the backbone amide group of Cys-88 is deprotonated in the doubly oxidized P2+ state, forming a bond to Fe5. The calculations also confirm the two conformations of the P-cluster in the atomic-resolution crystal structure of the enzyme, representing the PN and P2+ states, but show that the finer differences between the two structures are not fully reflected in the crystal structure, because the coordinates of only two atoms differ between the two conformations. However, the recent crystal structure of the P1+ state seems to be of lower quality with many dubious Fe−Fe and Fe−S distances. Quantum refinement of this structure indicates that it is a mixture of the P1+ and P2+ states but confirms that the side chain of Ser-188 is most likely deprotonated in both states. TPSS gives structures that are appreciably closer to the crystal structures than does B3LYP. In addition, we have studied all 16−48 possible broken-symmetry states of the four oxidation states of the P-cluster with DFT in the one or two observed spin states. For the reduced PN state, we can settle the most likely state from the calculated energies and geometries. However, for the more oxidized states there are large differences in the predictions obtained with the two DFT methods.

■

(FeII8 ) resting state is termed PN. Oxidation of this state yields the one-electron oxidized (partially oxidized) state, P1+, the two-electron oxidized state, P2+, and the three-electron oxidized state, P3+.10−12 Higher oxidation states have also been observed, but they are irreversible and are not believed to be catalytically relevant.11 The structure of the P-cluster is redox-dependent.13−15 It undergoes remarkable conformational changes upon 2-electron oxidation: In the PN state, each Fe ion is coordinated by three bridging sulfide ions and one terminal or bridging Cys ligand as is shown in Figure 2a. The structure can be described as two [Fe4S4] cubanes, sharing a central hexa-coordinate sulfide ion13−15 (labeled S1; naming of atoms and protein residues is taken from the high-resolution crystal structure of nitrogenase from A. vinelandii, PDB file 3U7Q).6 Upon oxidation by two electrons, the positions of two Fe ions in the P-cluster change. Fe5 and Fe6 dissociate from S1 and form new bonds to the backbone amide N atom of residue Cys-88 and to the side-

INTRODUCTION Nitrogenase (EC 1.18/19.6.1) is the only enzyme that can cleave the triple bond in N2, forming ammonia and making nitrogen available to biological organisms.1−3 Therefore, it plays a fundamental role in life on earth. The nitrogenase reaction is very demanding, requiring 16 molecules of ATP for each N2 molecule processed: N2 + 8e− + 8 H+ + 16 ATP → 2 NH3 + H2 + 16 ADP + 16 Pi. It forms one molecule of H2 as a compulsory byproduct. Crystallographic studies have shown that the catalytic reaction takes place at a complicated FeMo cluster with the composition MoFe7S9C(homocitrate), which is bound to the protein by a cysteine (Cys) and a histidine (His) residue.4−8 In some nitrogenases, the Mo ion is replaced by vanadium or iron.9 The FeMo cluster has been thoroughly studied by both experimental and computational methods. Electrons are delivered to the MoFe protein from another protein, called the Fe protein, which also binds and hydrolyses the ATP molecules (Figure 1). The electrons are delivered to the FeMo cluster via another cluster, the P-cluster, which is a Fe8S7Cys6 assembly. Several oxidation states have been observed for the P-cluster: The fully reduced, all-ferrous © 2019 American Chemical Society

Received: February 11, 2019 Published: July 8, 2019 9672

DOI: 10.1021/acs.inorgchem.9b00400 Inorg. Chem. 2019, 58, 9672−9690

Article

Inorganic Chemistry

Figure 1. Nitrogenase MoFe protein from Azotobacter vinelandii (Protein Databank (PDB) file 3U7Q).6 The structure is a dimer of heterodimers and four subunits are shown in different colors. The metal clusters are highlighted in a space-filling model and marked in yellow (P-cluster) and cyan (FeMo cluster).

chain O atom of serine residue Ser-188, respectively (cf. Figure 2b). Thereby, they move toward their new ligands, causing the right-hand-side cubane in Figure 2b to open.13,14 Very recently, the structure of the P1+ state was also reported, showing an intermediate structure: It retains coordination of Ser-188 to Fe6, but Fe5 does not coordinate to the backbone N of Cys-88 to Fe5 (Figure 2c).16 Interestingly, there is no consensus about the relevance of the P-cluster oxidation states for the physiological function of nitrogenase. The P2+ state is stable and has been captured in crystal structures,6 but there is no conclusive evidence for its involvement in nitrogenase activity.14,17 According to the deficit−spending model,18 the PN-cluster transfers an electron to the FeMo-cofactor in a rate-determining step, which is assumed to be conformationally gated. This is followed by a rapid reduction of the P1+-cluster by the Fe protein. This sequence of events is assumed to be repeated for all eight electron-transfer events in the catalytic cycle.18 Consequently, it suggests that only the PN/P1+ redox couple is relevant during nitrogenase catalysis.19 However, Owens et al. showed that the coordination of the P-cluster by a backbone amide N atom and a hard O-based amino acid ligand is highly conserved among nitrogenases from different organisms.14 Those nitrogenases that do not have a Ser residue at position 188 possess a Tyr residue at position 99, which coordinates to Fe8 in the P2+ state. This indicates that the P2+ state may have a functional importance for some steps in the reaction mechanism of nitrogenase. Likewise, a study by Rupink et al.12 suggests that the P-cluster may act as two coupled [Fe4S4] clusters, each capable of donating one electron to the FeMo cofactor. They concluded that neither a one- nor a two-electron process can be ruled out. Since most studies focused on the first four electron-transfer events in the catalytic cycle, they conjectured that two-electron transfer events could occur in later FeMo cofactor reduction steps. The protonation state of the Ser-188 and Cys-88 residues, which can function as ligands to the P-cluster, is also controversial. Both amino acids are assumed to be protonated in the PN state.13 However, in order to coordinate to the Fe ions they are likely to be in their deprotonated, anionic forms (i.e., an alkoxide group for Ser-188 and a deprotonated amide

Figure 2. Redox-dependent conformational changes of the P-cluster. The panels show the (a) PN resting state, (b) the P2+ oxidized state, and (c) the P1+ partly oxidized state. In panel (b) the residues and the name of the metal ions are indicated. Panels (a and b) are derived from the 1.0 Å resolution crystal structure of the nitrogenase from A. vinelandii (PDB file 3U7Q),6 whereas panel (c) comes from the 2.1 Å structure from the same organism (PDB file 6CDK). Color key: Fe ions, orange; sulfur, yellow; oxygen, red; nitrogen, blue; and carbon, green.

group for Cys-88D).14,20 This suggests that the oxidation of the P-cluster by two electrons is accompanied by the release of two protons. However, redox titrations indicated that only the P2+/ P1+ redox-couple is pH-dependent, whereas no evidence could be found for a coupled electron- and proton-transfer for the more reduced couple P1+/PN.21,22 Another possibility is that the serine ligand is deprotonated in all oxidation states and acts as a reversible redox switch.14 The crystal structure of the P1+ state was accompanied by computational studies indicating that Ser-188 and Cys-88 are protonated in the PN state and deprotonated when binding to their respective Fe ion.16 9673

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distorted, open cubane close to the new ligands has five or seven unpaired electrons (S2 = 5/2 or S2 = 7/2), whereas a spin of S1 = 1/2 is assigned to the other cubane. Parallel coupling of the partial spins leads to Stot = 3 or 4, respectively.23,25 The P3+ state is a physical mixture of the Stot = 1/2 and 7/2 spin states. In computational studies with density functional theory (DFT), antiferromagnetically coupled systems are commonly treated with the broken symmetry (BS) approach,26,27 employing different orbitals for the spin-up and spin-down electrons. For the catalytic FeMo cluster, several computational studies have described the electronic structure, providing firm evidence which of the 35 possible BS states is most stable in the resting state of the protein and also in other relevant catalytic states.27−34 However, for the P-cluster, such information is currently missing, prohibiting a detailed study of electron-transfer processes between the P-cluster and the FeMo cluster. However, an unpublished manuscript available on arXiv describes density matrix renormalization group (DMRG) complete active space calculations on the P-cluster in the PN, P1+, and P2+ states with active spaces of 73−77 orbitals.35 This multiconfigurational approach provides a correct and more accurate description of the electronic structure and the spin states than BS-DFT calculations, but owing to the lack of a thorough treatment of dynamic correlation, energies of the various electronic states are probably not more accurate than those obtained with DFT. Moreover, information about the size of the basis set is lacking, so it cannot be judged how converged the calculations are. A previous similar study on [2Fe2S] and [4Fe4S] clusters have shown that DMRG typically gives at least 1 order of magnitude more electronic states than BS-DFT.36 In this work, we provide a thorough DFT study of possible BS states for the four oxidation states of the P-cluster. As in our previous studies, we employ the combined quantum mechanics and molecular mechanics (QM/MM) approach, using two different DFT functionals. Moreover, we provide a further discussion of the geometry of the P-cluster in the various oxidation states and the deprotonation of the Ser-188 and Cys88 residues, supported by quantum-refinement calculations of the recent crystal structure of the putative P1+ state.16

More indisputable information is available about the spin states of the P-cluster. Detailed studies have been performed, in which electron paramagnetic resonance data and Mössbauer parameters have been assigned to the various P-cluster oxidation states.23,24 The P-cluster is a spin-coupled system featuring relatively strong magnetic interactions between the metal sites, mediated by bridging sulfide ligands.23 In accordance with smaller FeS clusters, all Fe ions of the Pcluster are in their high-spin state and couple antiferromagnetically to a lower net spin state. In the resting state, all iron ions are in the high-spin ferrous oxidation state (Fe2+, d6, S = 2). PN is diamagnetic (Stot = 0), while the oxidized states are paramagnetic, with one, two, or three ferric (Fe3+, d5, S = 5/2) Fe ions, respectively.22,23 There are two possible views to describe the spin distribution of the P-cluster. The spin density may either be delocalized over the entire [Fe8S7] cluster or reside largely on one of the two merged [Fe4S4] cubanes, with the net spins of the two moieties ferromagnetically coupled to the global spin state. Mouesca and co-workers23 suggest that the first option is less likely, because the coupling between the cubanes is expected to be weak compared to the coupling within each cubane. This proposal is based on the fact that there are only two Fe−Fe distances shorter than 3 Å between the two cubanes. In addition, bridging Cys residues and the sixcoordinate sulfide are believed to be less effective in mediating exchange coupling than sulfides within a cubane. Mouesca et al. have collected the experimental data for the four P-cluster oxidation states as summarized in Table 1.23 In Table 1. Experimentally Observed Spin States of the PCluster in the Various Oxidation States (Stot),23,24 Together with Individual Spin and Charge of the Two Cubane Subclustersa cubane 1

cubane 2

ox state

[Fe8S7] charge

Stot

charge

S1

charge

S2

PN

+2

P1+

+3

P2+

+4

P3+

+5

0 1/2 5/2 3 4 1/2 7/2

0 +1 0 +1 +1 +1 +2

0, 4 1/2, 4 0 1/2 1/2 1/2 0

0 0 +1 +1 +1 +2 +1

0, −4 0, −7/2 5/2 5/2 7/2 0 7/2

■

a

Suggested by Mouesca et al.23 or by Li et al.35 (in bold face). Cubane 1 consists of Fe1−Fe4 and cubane 2 of Fe5−Fe8, of which Fe5 and Fe6 coordinate to Cys-C88 and Ser-D188 in the oxidised states. The charges refer to [Fe4S4] clusters, excluding charges on the coordinating amino acids and including the bridging S12− ion in both clusters.

METHODS

Protein. The QM/MM calculations were based on the 1.0 Å crystal structure of nitrogenase from A. vinelandii (PDB file 3U7Q).6 The setup of the protein is identical to that of our previous study of the protein.37 The entire heterotetramer was included in the calculations, because the various subunits are entangled without any natural way to separate them. All crystal-water molecules were kept in the calculations, except 26 that overlapped with each other or with protein atoms.37 The QM calculations were concentrated on the Pcluster binding at the interface between the C and D subunits. The FeMo cofactors and the P-cluster binding at the A−B interface were modeled by MM in the fully reduced and resting states, respectively.37 The protonation states of all residues were the same as before:29,32,37,38 All Arg, Lys, Asp, and Glu residues were assumed to be charged, except Glu-C153, C440, and D231 (the letters “C” and “D” before the residue number indicate what subunit they belong to; subunits A and B are identical to the C and D residues, respectively). Cys residues coordinating to Fe ions were assumed to be deprotonated. His-C274, C451, D297, D359, and D519 were assumed to be protonated on the ND1 atom; His-C31, C196, C285, C383, D90, D185, D363 and D457 were presumed to be protonated on both the ND1 and NE2 atoms (and therefore

the resting PN state, both cubanes can be described as neutral [Fe4S4] moieties. They are both diamagnetic (S1 = S2 = 0), resulting in a diamagnetic global spin state (Stot = 0). The oneelectron oxidized state P1+ is a physical mixture of Stot = 1/2 and Stot = 5/2 states. The wave function of the unpaired electron is suggested to be localized on one of the cubanes.12,23 In P2+, the two cubanes are expected to be both in the [Fe4S4]+ state (i.e., formally with three ferrous and one ferric iron site in each half). However, due to the additional Ser and Cys ligands in one of the cubanes, the spin properties of the two cubanes differ from each other so that the spin density resides largely on one P-cluster moiety. It was suggested that the more 9674

DOI: 10.1021/acs.inorgchem.9b00400 Inorg. Chem. 2019, 58, 9672−9690

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Inorganic Chemistry

Table 2. Definition of the 36, 32, or 48 BS States, Indicating Which Four or Three Fe Ions Have Minority Spin (β)a BSa1 BSa2 BSa3 BSa4 BSa5 BSa6 BSa7 BSa8 BSa9 BSb1 BSb2 BSb3 BSb4 BSb5 BSb6 BSb7 BSb8 BSc1 BSc2 BSc3 BSc4 BSc5 BSc6 BSc7 BSc8 BSc9 BSc10 BSc11 BSc12

Type A: 36 BS States with Two β Spins in Each Subcluster BSa10 (1, 4, 6, 8) BSa19 (3, 4, 5, 8) BSa28 BSa11 (1, 3, 6, 8) BSa20 (2, 4, 5, 8) BSa29 BSa12 (1, 2, 6, 8) BSa21 (2, 3, 5, 8) BSa30 BSa13 (3, 4, 6, 7) BSa22 (1, 4, 5, 8) BSa31 BSa14 (2, 4, 6, 7) BSa23 (1, 3, 5, 8) BSa32 BSa15 (2, 3, 6, 7) BSa24 (1, 2, 5, 8) BSa33 BSa16 (1, 4, 6, 7) BSa25 (3, 4, 5, 7) BSa34 BSa17 (1, 3, 6, 7) BSa26 (2, 4, 5, 7) BSa35 BSa18 (1, 2, 6, 7) BSa27 (2, 3, 5, 7) BSa36 Type B: 32 BS States with 3 + 1 Spins in Each Subcluster (2, 3, 4, 5) BSb9 (1, 2, 4, 5) BSb17 (1, 6, 7, 8) BSb25 (2, 3, 4, 6) BSb10 (1, 2, 4, 6) BSb18 (1, 5, 7, 8) BSb26 (2, 3, 4, 7) BSb11 (1, 2, 4, 7) BSb19 (1, 5, 6, 8) BSb27 (2, 3, 4, 8) BSb12 (1, 2, 4, 8) BSb20 (1, 5, 6, 7) BSb28 (1, 3, 4, 5) BSb13 (1, 2, 3, 5) BSb21 (2, 6, 7, 8) BSb29 (1, 3, 4, 6) BSb14 (1, 2, 3, 6) BSb22 (2, 5, 7, 8) BSb30 (1, 3, 4, 7) BSb15 (1, 2, 3, 7) BSb23 (2, 5, 6, 8) BSb31 (1, 3, 4, 8) BSb16 (1, 2, 3, 8) BSb24 (2, 5, 6, 7) BSb32 Type C: 48 BS States with 2 β Spins in One Subcluster and 1 β Spin in the Other Subcluster (1, 2, 5) BSc13 (2, 3, 5) BSc25 (1, 5, 6) BSc37 (1, 2, 6) BSc14 (2, 3, 6) BSc26 (2, 5, 6) BSc38 (1, 2, 7) BSc15 (2, 3, 7) BSc27 (3, 5, 6) BSc39 (1, 2, 8) BSc16 (2, 3, 8) BSc28 (4, 5, 6) BSc40 (1, 3, 5) BSc17 (2, 4, 5) BSc29 (1, 5, 7) BSc41 (1, 3, 6) BSc18 (2, 4, 6) BSc30 (2, 5, 7) BSc42 (1, 3, 7) BSc19 (2, 4, 7) BSc31 (3, 5, 7) BSc43 (1, 3, 8) BSc20 (2, 4, 8) BSc32 (4, 5, 7) BSc44 (1, 4, 5) BSc21 (3, 4, 5) BSc33 (1, 5, 8) BSc45 (1, 4, 6) BSc22 (3, 4, 6) BSc34 (2, 5, 8) BSc46 (1, 4, 7) BSc23 (3, 4, 7) BSc35 (3, 5, 8) BSc47 (1, 4, 8) BSc24 (3, 4, 8) BSc36 (4, 5, 8) BSc48 (3, (2, (2, (1, (1, (1, (3, (2, (2,

4, 4, 3, 4, 3, 2, 4, 4, 3,

7, 7, 7, 7, 7, 7, 6, 6, 6,

8) 8) 8) 8) 8) 8) 8) 8) 8)

(1, (1, (1, (3, (2, (2, (1, (1, (1,

4, 3, 2, 4, 4, 3, 4, 3, 2,

5, 5, 5, 5, 5, 5, 5, 5, 5,

7) 7) 7) 6) 6) 6) 6) 6) 6)

(3, (3, (3, (3, (4, (4, (4, (4,

6, 5, 5, 5, 6, 5, 5, 5,

7, 7, 6, 6, 7, 7, 6, 6,

8) 8) 8) 7) 8) 8) 8) 7)

(1, (2, (3, (4, (1, (2, (3, (4, (1, (2, (3, (4,

6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7,

7) 7) 7) 7) 8) 8) 8) 8) 8) 8) 8) 8)

a

Numbering according to Figure 2. dispersion corrections were included with the DFT-D3 approach54 and Becke−Johnson damping,55 as implemented in Turbomole. The QM system consisted of the full P-cluster with all coordinating Cys residues, modeled by CH3S−. In addition, a CH3OH model of Ser-D188 was included, and Cys-C88 was modeled by CH3CONHCH2CH2S− (i.e., including the backbone between Gly87C and Cys-C88). This model was then studied in four different protonation states: (1) The backbone N group of Cys-C88 and the side chain of Ser-D188 were both protonated. Thus, the model was Fe8S7(CH3S)5(CH3CONHCH2CH2S)(CH3OH) with a net charge of −4 in the PN state. (2) Ser-D188 was deprotonated, but Cys-C88 was still protonated. (3) The backbone N of Cys-C88 was deprotonated, and Ser-D188 was protonated. (4) Both Cys-C88 and Ser-D188 were deprotonated (i.e., the model was Fe 8 S 7 (CH 3 S) 5 (CH 3 CONCH2CH2S)(CH3O) with a net charge of −4 in the P2+ state). In the employed crystal structure (3U7Q),6 the P-cluster was reported to be a mixture of the PN and P2+ oxidation states, although in practice coordinates of only two atoms differ, Fe5 and Fe6. If not otherwise stated, then the calculations were started for PN from the crystal structure of PN and those of the three other oxidation states were started from the crystal structure of P2+. All QM calculations of the P-cluster were based on the brokensymmetry approach.26,27 Thus, each Fe ion is in the high-spin (S = 2 or 5/2) state, but the spins couple antiferromagnetically to a lower net spin. For each oxidation state, we studied the one or two experimentally observed spin states, shown in Table 1.23,24 A starting wave function with the correct spin state was obtained by the fragment approach by Szilagyi and Winslow.56 This gave one of the possible BS states. The other BS states were obtained by simply swapping the coordinates of the Fe ions in an automatic manner.57

positively charged). The remaining 14 His residues were modeled with a proton on the NE2 atom. The protonation states were thoroughly studied in our previous article.37 MM Calculations. All MM calculations were performed with the Amber software.39 For the protein, we used the Amber ff14SB force field,40 and water molecules were described by the TIP3P model.41 For the metal sites, the MM parameters were the same as in our previous investigation:37 We employed restrained electrostatic potential charges,42 obtained from electrostatic potentials calculated at the TPSS/def2-SV(P) level of theory43,44 and sampled with the Mertz−Kollman scheme.45 The metal sites were treated by a nonbonded model with QM charges for the metal and the ligands.37 Metal sites outside the QM system were kept at the crystal-structure geometry. The protein was solvated in a sphere with a radius of 70 Å of water molecules around the geometrical center of the protein. A total of 160 Cl− and 182 Na+ ions were added at random positions (but not inside the protein)37 to neutralize the protein and give an ionic strength of 0.2 M.46 The final system contained 133 915 atoms. The added protons, counterions and water molecules were optimized by a simulated annealing calculation (up to 370 K), followed by a minimization, keeping the other atoms fixed at the crystal-structure positions.37 QM Calculations. All QM calculations were performed with the Turbomole software (versions 7.1 and 7.2).47 We employed two DFT methods, TPSS43 and B3LYP,48−50 and two different basis sets of increasing size, def2-SV(P)44 and def2-TZVPD.51 The calculations were sped up by expanding the Coulomb interactions in an auxiliary basis set, the resolution-of-identity (RI) approximation.52,53 Empirical 9675

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Inorganic Chemistry The various BS states are defined by which Fe ions have the minority (β) spin. They are defined in Table 2. It should be noted that the BS approach is only an approximation and does not give pure spin states. A proper description of these complicated coupled spin systems require multiconfigurational treatments, such as those done in the DMRG study,35 although the lacking treatment of dynamic correlation makes the energetic results less reliable. QM/MM Calculations. The QM/MM calculations were performed with the ComQum software.58,59 In this approach, the protein and solvent are split into two subsystems: System 1 (the QM region) was relaxed by QM methods, whereas system 2 contained the remaining part of the protein and the solvent. It was kept fixed at the original coordinates (equilibrated crystal structure). In the QM calculations, system 1 was represented by a wave function, whereas all the other atoms were represented by an array of partial point charges, one for each atom, taken from the MM setup. Thereby, the polarization of the QM system by the surroundings is included in a self-consistent manner. When there is a bond between systems 1 and 2 (a junction), the hydrogen link-atom approach was employed: The QM system was capped with hydrogen atoms (hydrogen link atoms, HL), the positions of which are linearly related to the corresponding carbon atoms (carbon link atoms, CL) in the full system.58,60 All atoms were included in the point-charge model, except the CL atoms.61 The total QM/MM energy in ComQum was calculated as58,59 HL CL HL EQM/MM = EQM1 + ptch2 + E MM12, q = 0 − E MM1, q = 0 1

1

quantum mechanics (QM) calculation (in analogy to the QM/MM calculations), yielding a QM energy for system 1, EQM1. To avoid double counting, we must then subtract the MM energy of system 1, EMM1: Ecqx = wAE X‐ray + EMM12 + wQMEQM1 − EMM1

Thereby, we introduce an accurate energy function for the system of interest. Such an energy function is implemented in the software ComQum-X,63 which is a combination of the software Turbomole47 and the crystallography and NMR system (CNS),69,70 version 1.3. The factor wQM in eq 3 is another weight, which is needed because the CNS MM force field is based on a statistical analysis of crystal structures.71 Therefore, the force constants are not energy-derived, as is the QM term, but they are given in arbitrary statistical units. Experience has shown that the CNS force constants are typically 3 times larger than energy-based force constants,71 and wQM = 3 has therefore been used throughout this work.63 Crystallographic refinement is traditionally performed without any electrostatic interactions, because hydrogen atoms are not discerned in the structure. We followed this custom and excluded electrostatics and hydrogen atoms from all crystallography and MM calculations (but they are of course included in the QM calculations). In analogy with the QM/MM calculations, the QM system was truncated by H atoms. The quantum-refinement calculations were based on the recent crystal structure of the putative P1+ state of the P-cluster.16 Coordinates, occupancies, B factors, and structure factors were obtained from PDB file 6CDK. From these files, we also obtained the space group, unit-cell parameters, resolution limits, R factors, and the test set used for the evaluation of the Rfree factor. The full protein was used in all calculations, including all crystal water molecules. In each cycle of the geometry optimization, the surrounding protein was allowed to relax by one cycle of crystallographic minimization and one cycle of individual B-factor refinement. However, the new coordinates and B factors were accepted only if the R factor was reduced. For the protein, we used the standard CNS force field (protein_rep.param, water_rep.param, and ion.param). The metal sites were treated as individual isolated ions, whereas the MM force field for other nonstandard residues were downloaded from the heterocompound information center Uppsala.72 The wA factor was determined by CNS to 3.68. Electron density maps were generated using phenix.maps. The QM calculations were performed at the TPSS/def2-SV(P) level of theory. The quality of the models was compared using the real-space difference density Z-score73 (RSZD), calculated by EDSTATS (part of the CCP4 package), which measures the local accuracy of the model. The maximum of the absolute values of the positive and negative RSZD (combined RSZD) for the whole P-cluster, together with the six Cys ligands, the neighboring Gly-C87 and Ser-D188, was taken as the quality metric. RSZD should typically be less than 3.0 for a good model.

(1)

where EHL QM1+ptch2 is the QM energy of the QM system truncated by HL atoms and embedded in the set of point charges modeling system 2 (but excluding the self-energy of the point charges). EHL MM1,q1=0 is the MM energy of the QM system, still truncated by HL atoms, but without any electrostatic interactions. Finally, ECL MM12,q1=0 is the classical energy of all atoms in the system with CL atoms and with the charges of the QM region set to zero (to avoid double counting of the electrostatic interactions). Thus, ComQum employs a subtractive scheme with electrostatic embedding and van der Waals link-atom corrections.62 The geometry optimizations were continued until the energy change between two iterations was less than 2.6 J/mol (10−6 a.u.) and the maximum norm of the Cartesian gradients was below 10−3 a.u. The QM/MM geometry optimizations were performed using the TPSS-D3 or B3LYP-D3 methods and the def2-SV(P)44 basis set. Single-point QM/MM energy calculations were then performed with the larger def2-TZVPD basis set.51 Quantum Refinement. Quantum refinement is standard crystallographic refinement supplemented by QM calculations for a small but interesting part of the protein.63−65 Crystallographic refinement programs change the protein model (coordinates, occupancies, B factors, etc.) to improve the fit of the observed and calculated structure-factor amplitudes (usually estimated as the residual disagreement, the R factor). Owing to the limited resolution normally obtained for biomolecules, the experimental data are supplemented by some chemical information, usually in the form of a MM force field.66 Then, the refinement takes the form of a minimization or simulated annealing calculation by molecular dynamics using an energy function of the form Ecryst = wAE X‐ray + EMM12

(3)

■

RESULT AND DISCUSSION In this paper, we have studied the geometric and electronic structure of the P-cluster in nitrogenase with QM/MM methods and quantum refinement. We have considered four different oxidation states, PN, P1+, P2+, and P3+. We first discuss the best BS state for each oxidation state in separate sections. Then, we discuss the geometries of the various states and compare them to the available crystal structures. Finally, we perform a quantum refinement of the crystal structure of the putative P1+ state. BS States of the P-cluster in the PN State. We started by investigating the relative energies of the various BS states for the PN state of the P-cluster, using QM/MM calculations with model 1 as the QM system (i.e., including models of Ser-D188 and Cys-C88 in their protonated states). As mentioned in the Introduction, the PN state involves eight Fe ions in the reduced

(2)

where EX‑ray is a penalty function that describes how well the model agrees with the experimental data (we have used a maximumlikelihood refinement target using amplitudes, MLF67,68). EMM12 is an MM energy function with bond, angle, dihedral, and nonbonded terms (for the entire protein), and wA is a weight factor, which is necessary because EMM12 is in energy units whereas EX‑ray is unit-less. It determines the relative importance of the crystallographic raw data and the MM force field for the final structure. Quantum chemistry can be introduced in this function by replacing the MM potential for a small region of the protein (system 1) by a 9676

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Figure 3. Relative energies (compared to BSb11) of the various type A and B BS states of PN, calculated with the TPSS-D3/def2-SV(P) and B3LYP-D3/def2-SV(P) methods. The inset illustrates the spins of the best state, BSb11.

(2.8−2.9 Å distance and each sharing a bridging Cys ligand; the other intercubane Fe−Fe pairs have appreciably longer distances, 3.5−7.5 Å). However, there are five additional states with this property and they are up to 105 kJ/mol less stable. Still, it is the only state with minority spin on the two Fe ions that are not connected to the central S1 atom (Fe3 and Fe7). If the basis set is increased to def2-TZVPD, then the relative energies (also shown in Figure 3) change by less than 11 kJ/ mol. This agrees with our previous results for the FeMo cluster, showing that the energies are quite insensitive to the basis set.29,32 The correlation between the results obtained with the two basis sets is R = 0.85. Therefore, BSb11 remains most stable by at least 57 kJ/mol. However, most type-A states are somewhat stabilized relative to the type-B states, and BSa7 becomes most stable among the latter states, 91 kJ/mol less stable than the BSb11 state. If the energies are instead evaluated by B3LYP-D3/def2SV(P) calculations (on structures optimized with this method; single-point calculations on TPSS structures are highly unreliable), then energies change much more (by up to 114 kJ/mol), with no correlation between the two sets of results (cf. Figure 2). All states are improved relative to the BSb11 state, and the variation becomes smaller, up to 60 kJ/mol. The best state is still BSb11. Thus, it has antiferromagnetic coupling between both the close intercubane pairs. However, it is only 6 kJ/mol more stable than the BSa1 state which has β spin on Fe3, Fe4, Fe7, and Fe8. In fact, there are 13 type-A states and 3 type-B states within 20 kJ/mol. Thus, the BS states are closelying for the PN state of the P-cluster with B3LYP. Mulliken spin populations on the Fe ions for the various states are listed in Tables S1a,b (TPSS and B3LYP, respectively). As expected, they are quite similar. With TPSS, they vary between 2.6 and 3.6 (with a positive or negative sign). The largest spin is always found on Fe7 or Fe3, except for the most stable BSb11 state, for which it is found on Fe6 (3.4). With B3LYP, the spin populations are larger and more similar, 3.5−3.6 for the type-A states and 3.6−3.7 for the type B states, as was also observed for the MoFe cluster.38 However, the largest spin is still found on either Fe7 or Fe3 (except for BSb5). The DMRG study35 suggests that the most stable state is BSb12 (with β spin on Fe1, Fe2, Fe4, and Fe8). This state is

Fe(II) state. Each of these is in the high-spin state, but they couple antiferromagnetically to give a vanishing total spin, Stot = 0. Mouesca et al. suggested that already within each cubane subcluster, the spins are coupled to a singlet state (S1 = S2 = 0), and such a state was also suggested by Keable et al.16 Thus, each cubane contains two Fe ions with a surplus of α electrons and two with a surplus of β electrons. For each cubane, this can be obtained in 6 different ways (two Fe ions can be picked out 4! of four in 2!·2! = 6 ways). In total, we therefore get 6 × 6 = 36 possible BS states, but only 18 of these are distinct, because the selection of α and β spin is arbitrary when there is an equal number of Fe ions with α and β spin in both clusters. These are called type-A states. They are shown in the first part of Table 2 and they all start with an “a” (e.g., BSa1). In contrast, it has been experimentally observed that the fully reduced cubane Fe4S4 cluster is in the S = 4 state.74,75 This state can be obtained by coupling three Fe with α spin and one Fe with β spin (4 + 4 + 4 − 4 = 8 unpaired spins). Therefore, a Stot = 0 state of the P-cluster can be found by antiferromagnetically coupling two such subclusters, each with S = 4. This is actually the ground state found in the DMRG study.35 This can be obtained in 4 × 4 = 16 different ways (one atom out of four should be selected to be minority spin for each subcluster). These are called type-B states. They are also shown in Table 2 (middle part) and they all start with a “b” (e.g. BSb1; for the P1+ state, for which it matters which cluster has the majority α spin, there are 16 additional states). In analogy with our previous study of the FeMo cluster,29 we have investigated these 18 + 16 BS states with two different QM methods. First, we optimized all states with QM/MM, using the TPSS-D3/def2-SV(P) method. The results in Figure 3 show that the 18 type-A BS states lie quite close in energy, within 34 kJ/mol, whereas the 16 type-B states have energies that vary by up to 114 kJ/mol. There is only a minor variation in the MM energies of the various states, up to 11 kJ/mol. The most stable state is BSb11, which is 101 kJ/mol more stable than the best type-A state, BSa11, and 54 kJ/mol more stable than the second-best state, BSb9. BSa11 has a minority spin on Fe3 and Fe7 in the two clusters. This is partly expected, because it involves antiferromagnetic coupling between both pairs of close intercubane Fe ions, Fe4−Fe5 and Fe2−Fe8 9677

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Figure 4. Relative energies of the various BS states of P1+ calculated with TPSS-D3 and B3LYP-D3/def2-SV(P), Stot = 1/2 (a) type A, (b) type B, or (c) Stot = 5/2 type C. The three figures have the same energy scale (i.e., with BSb11 for TPSS and BSa19 for B3LYP as the reference). The insets show BSa19 in (a) and BSb11 and BSb26 in (b). 9678

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For the BSb11 state, the highest spin population at the TPSS level is found on Fe6, 3.7, indicating that this is the oxidized atom (the Mulliken spin populations on the eight Fe ions are listed for all BS states in Table S2a). This reflects that the negatively charged and hard Ser ligand localizes the most oxidized state to Fe6. The total spin is also higher on this subcluster, 7.5, compared to −6.9 for the other subcluster. In fact, for all type-B states, the largest (absolute) spin population is always found on the Fe6 or Fe7 atoms (3.5−3.8). However, for BSb17−BSb32, S1 is always (positive and) larger than |S2|, indicating that the first subcluster is oxidized. The spin populations from the B3LYP calculations are similar, but larger and more similar, as for the PN state. For the best type-A BS states at the B3LYP level, the largest spin populations are found on the Fe6 and Fe7 ions (3.9 and 3.7, respectively). The two Fe ions with β spin in this subcluster are lower, giving a net spin for the Fe ions in this subcluster of 0.4 and −0.1 for the other subcluster. This indicates a ferromagnetically coupled pair of two Fe(2.5) ions, antiferromagnetically coupled to another pair of two Fe(II) ions, as often observed for the [Fe4S4]+ state.25 We have also considered the Stot = 5/2 state. It is somewhat harder to imagine how it may arise, but following Mouesca et al., we have assumed that one of the two subclusters remains in the reduced [Fe4S4]0 state. However, it is then required that one of the Fe(II) ions is in the intermediate-spin Fe(II) state (S = 1) and that the three Fe (II) ions have an α spin and the Fe(III) ion has a β spin (4 + 4 + 2 − 5 = 5 unpaired spins). The single Fe ion with β spin can be selected in four different ways, which should be combined with the six possibilities for the [Fe4S4]0 cluster. Moreover, we tested having only one β spin in either of the subclusters, giving a total of 48 different BS states. We call this type C of the BS states. Interestingly, the optimized wave functions turned out to be different from this description: No Fe ion had significantly more spin than the others. As for the Stot = 1/2 states, Fe6 normally had the largest spin population, although in 11 of the BS states, it was instead Fe7, and Fe2 or Fe3 in three of the BS states. However, the largest absolute spin, 3.5−3.8, was only 0.02−0.4 larger than the second largest spin. Likewise, for only six BS states, the lowest (absolute) spin was less than 2 and in only five states, the difference between the two lowest spins was more than 1. All these cases were also high in energy. The state with the lowest energy at the TPSS-D3/def2SV(P) level is BSc39 (Figure 4c), which has β spin on Fe3, Fe6, and Fe7 (cf. the lower part of Table 2). It has the highest spin on Fe6 (−3.7) and a relatively low spin on the three α Fe ions in the first subcluster, Fe1, Fe2, and Fe4 (3.2−3.3) as well as on Fe5 (3.2). Thus, it is best interpreted as an oxidized subcluster 2 in the S2 = 1 state (the sum of the four Fe ions is −0.7), whereas the first subcluster is in the reduced state with only one β spin and reduced spin on each Fe ion, giving S1 = 6.2 (i.e., quite close to what was found for the type-B states). However, this structure is 45 kJ/mol less stable than the best Stot = 1/2 state (BSb11). There are two more structures of this type with energies within 11 kJ/mol of BSc39 (BSc27 and BSc35). In these, Fe3 still has β spin as well as Fe5 and either Fe6 or Fe8, but otherwise they have a quite similar electronic structure. With the def2-TZVPD basis set, they are both slightly lower in energy (5−6 kJ/mol) than BSc39, but they are still 43−45 kJ/mol worse than the best Stot = 1/2 state. With B3LYP, all the Stot = 5/2 states are strongly destabilized compared to the Stot = 1/2 states. The best state

64 kJ/mol less stable than BSb11 in our calculations with TPSS-D3 and 19 kJ/mol with B3LYP-D3. In addition to this state, they present six states within 30 kJ/mol of the ground state, including one BS state (BSb9, which is 54 and 12 kJ/mol less stable than the BSb11 state in our calculations, but 26 kJ/ mol higher than BSb12 in their calculations), four Fe orbital excitations (i.e., involving different sets of Fe 3d orbitals), and one triplet state. BS States of the P-cluster in the P1+ State. Next, we studied the partly oxidized P1+ state. As mentioned above, it is oxidized by one electron, giving the Fe 7II Fe 1III state. Experimentally, it is observed to be a physical mixture of Stot = 1/2 and 5/2 states. The former state can be obtained by combining a reduced cubane subcluster ([Fe4S4]0, S1 = 0) and an oxidized subcluster ([Fe4S4]+, S2 = 1/2) with a surplus of a single spin (i.e., a type-A state). The latter is normally suggested to consist of a pair of reduced Fe(II) and another pair of partly oxidized Fe(2.5) ions.25 Mouesca et al. suggested that it is the Fe1−Fe4 subcluster that is oxidized, although it would seem more likely that the other subcluster, with the deprotonated Ser ligand, is oxidized (we have tested both possibilities). As before, there are six possible BS states of a reduced cubane and also six possibilities to select a pair of Fe ions from the other cubane to be partly oxidized with opposite spins (or equivalently one as Fe(III) and α spin, and another Fe ion also with α spin). However, in this case, all 36 combinations are distinct, because one spin is dominant (α; cf. Table 2). Alternatively, the Stot = 1/2 state can be obtained by removing one electron from the type-B states of PN (i.e., with one subcluster with S = 4 and the other with S = −7/2). This is a low-lying state in the DMRG study.35 Here, 32 different BS states are possible, as is shown in Table 2, because the oxidized Fe ion can be in both subclusters. Following the recent crystal structure of this state,16 we have employed in all calculations a model with Ser-D188 deprotonated and coordinating to Fe6, whereas the backbone of Cys-C88 is included in the calculations but is protonated and does not bind to Fe5. The relative energies of the 36 type-A BS states of the P1+ cluster in the S = 1/2 state are shown in Figure 4a, and the 32 B-type BS states are shown in Figure 4b. It can be seen that at the TPSS-D3 level the most stable state is still BSb11 (i.e., with β spin on Fe1, Fe2, Fe4, and Fe7 and with minority spin on the terminal Fe3 and Fe7 atoms in each subcluster). However, BSb26 is only 4 kJ/mol less stable (2 kJ/mol with the def2TZVPD basis set). It has β spin on Fe3, Fe5, Fe7, and Fe8, and therefore minority spin on Fe3 and Fe6. The third-best state is BSb9, 19 kJ/mol above BSb11 (also with the def2-TZVPD basis set). The type-A states are at least 41 kJ/mol less stable than BSb11 (26 kJ/mol with the def2-TZVPD basis set). The lowest type-A state is BSa19, which has β spin on Fe3, Fe4, Fe5, and Fe8 (cf. Table 2). However, with the B3LYP-D3 method, the results are different. Then, the type-A states are most stable. The best state is BSa19, but the BSa23 state (with β spin on Fe1, Fe3, Fe5, and Fe8) is only 2 kJ/mol less stable and is actually the most stable state with the def2-TZVPD basis set, by 1 kJ/mol. There are four additional type-A states within 12 kJ/mol. The best type-B state is BSb9 (with β spin on Fe1, Fe2, Fe4, and Fe5), and it is 11 kJ/mol less stable than the BSa19 state. The BSb11 state that was best with TPSS is 38 kJ/mol less stable than BSa19, and there are seven type-B states that are more stable than it. 9679

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Figure 5. Relative energies of the various BS states of P2+ calculated with TPSS-D3 and B3LYP-D3/def2-SV(P), (a) Stot = 4 or (b) Stot = 3. The two figures have the same energy scale, which is relative to BSc35 (Stot = 4) for TPSS and relative to BSc24 (Stot = 4) for B3LYP. The insets in (a) show the spins of BSc24 and BSc35.

higher energy that has five Fe ions with an α spin and three with a β spin (two in one subcluster and one in the other). This is the same spin pattern as in our type-C calculations and it corresponds to our BSc35 state (with a β spin on Fe3, Fe5, and Fe8). It is our second-lowest type-C state with TPSS (with both basis sets) and the seventh lowest state at the B3LYP level. In addition, there are three Fe excitations within 35 kJ/ mol of the ground state. BS States of the P-cluster in the P2+ State. Next, we turn to the doubly oxidized P2+ state. Experimentally, it has been reported to be in either the Stot = 3 or 4 state, although Mouesca et al. argued quite strongly that Stot = 4 is the proper spin state.23 As can be seen in Table 1, both subclusters are expected to be in the oxidized [Fe4S4]+ state, but one with S = 1/2 and the other with S = 5/2 or 7/2. As discussed in the previous section, S = 5/2 can only be obtained if one of the Fe

is BSc40, but it is 99 kJ/mol less stable than the best Stot = 1/2 state (BSa19). It has a−3.8 spin on Fe4 and a 3.4−3.5 spin on Fe1−Fe3, giving a 6.4 spin on the first subcluster and a −0.4 spin on the second. Calculations with the larger def2-TZVPD basis set gives similar results (within 11 kJ/mol), although they further destabilize the Stot = 5/2 states. In the DMRG study, the lowest Stot = 1/2 state has five Fe ions with an α spin in cluster 2 and three Fe ions with a β spin (all in the same subcluster). Such a state cannot be obtained with BS-DFT. However, the second lowest state (only 3 kJ/ mol less stable) is of BSc11 (i.e., identical to the lowest state found by TPSS). Besides these two states, only four states involving Fe excitations are presented within 25 kJ/mol of the ground state. For the Stot = 5/2 states, again, the lowest state cannot be represented by BS-DFT, but there is a state at 17 kJ/mol 9680

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Figure 6. Relative energies of the various BS states of P3+ calculated with TPSS-D3 and B3LYP-D3/def2-SV(P), (a) Stot = 1/2 or (b) Stot = 7/2. The two figures have the same energy scale, which is relative to BSc35 for TPSS and relative to BSa30 for B3LYP. The insets show BSa14 and BSa30 in (a) and BSc35 in (b).

structures have three α spins in the first subcluster (the best state with three α spins in the second subcluster is 52 kJ/mol less stable than BS35). Moreover, also the second largest (and often also the third largest) spin are also from the second subcluster. Thus, the best states seem to consist of a reduced [Fe4S4]0 cluster in the S1 = 4 state (3 × 4 = 12 α and 4 β spins) coupled to a doubly oxidized [Fe4S4]2+ cluster in the S2 = 0 state. The corresponding Stot = 3 states are at least 35 kJ/mol higher in energy at the TPSS level (39 kJ/mol with the def2TZVPD basis set), in agreement with the suggestions by Mouesca et al.23 Again, the best states have three α spins in the first subcluster and the largest spins in the second subcluster, but now Fe6 has a β spin so that the net spin of the Fe ions in the second subcluster are slightly negative (−0.3 to −0.8), partly compensating for the spins of the first subcluster, which also are somewhat lower. As for the P1+ states, there is no

ions is (formally) in the intermediate-spin state, whereas S = 7/2 can be obtained with all ions in the high-spin state, if the oxidized Fe ion has the minority spin (4 + 4 + 4 − 5 = 7 unpaired spins). In both cases, three of the ions should have the majority spin (α). We have tested all 48 BS possibilities with one subcluster having two β spins and the other having one β spin (i.e., type-C states). The calculations were performed on a model with both Ser-D188 and the backbone of Cys-C88 deprotonated and coordinating to Fe6 and Fe5, respectively. The results are shown in Figure 5a,b. From Figure 5a, it can be seen that the best Stot = 4 state at the TPSS level is BSc35. It is 18 kJ/mol better than the second-best state (17 kJ/mol with the def2-TZVPD basis set), BSc47, and 35 kJ/mol better than the third-best state (BSc27; 43 kJ/mol with the larger basis set). As for the P1+ state, most states, including the best ones, have the largest spin on Fe6, which in most cases is an α spin. However, all the low-energy 9681

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subcluster and the best state with three α-spin Fe in the second subcluster is 46 kJ/mol less stable than BSc35. As usual, the largest absolute spins (3.6−3.8) are always found for Fe6 or Fe5. Only three BS states have the second largest spin in the first subcluster, whereas for most BS states this applies to the third largest spin. However, for BSc35, all four of the largest absolute spin populations are found for the second subcluster. At the TPSS level, the Stot = 7/2 states are appreciably more stable than the Stot = 1/2 states, by 33 kJ/mol for the most stable states of each type (24 kJ/mol with the def2-TZVPD basis set). Unfortunately, the results at the B3LYP level of theory are different. In particularly, the Stot = 1/2 states are strongly stabilized and become more stable than the best Stot = 7/2 states, by 19 kJ/mol (21 kJ/mol with the def2-TZVPD basis set). The best Stot = 1/2 state is BSa30 with β spin on Fe1, Fe2, Fe5, and Fe7. However, there are eight other states within 10 kJ/mol and with the def2-TZVPD basis set; instead, BSa14 is lowest in energy. The Mulliken spin populations are quite similar to those obtained with TPSS, but 0.2−0.4 larger in magnitude and with a smaller variation, 0.5−0.7. Still, with only one exception, the sum of the four spins in the first subcluster is larger than that of the second subcluster, confirming that the former is oxidized by only one step. Among the Stot = 7/2 states, BSc22 has the lowest energy, 4 kJ/mol lower than BSc35 (but with the def2-TZVPD basis set, BSc35 is 2 kJ/mol lower). The spin populations are quite similar to those obtained with TPSS, although they are slightly larger in magnitude and the variation is slightly smaller, 0.4− 0.6. Geometries of the QM/MM Structures. Next, we consider the geometries of the various oxidation states of the P-cluster. We concentrate on the TPSS results, because this functional gave more accurate structures than B3LYP for the FeMo cluster,31,38 and we will show below that the same applies for the P-cluster. The most striking difference between the four oxidation states is of course the Fe6−O distance to the side chain of Ser-D188 and the Fe5−N distance to the backbone of Cys-C88, reflecting the deprotonation of these residues in the higher oxidation states, as can be seen in Figure 7. The Fe6−O distance is 3.25−3.40 Å in the various BS states of PN, whereas it decreases to 1.86−1.92 Å in P1+. It remains essentially the same in P2+, 1.87−1.91 Å, but decreases to 1.85−1.87 Å in P3+. Likewise, the Fe5−N distance is 3.40− 3.57 Å in PN and 3.33−3.67 Å in P1+ but decreases to 1.99− 2.05 Å in P2+ and further to 1.97−2.01 Å in P3+. For the P1+ state, we have also done some calculations with alternative protonation states (Figure 7e−f). If both Ser-D188 and the backbone of Cys-C88 are protonated (Figure 7f), then the Fe5−N distance is always long in the various BS states, 3.30−3.64 Å (Table S5). However, the Fe6−O distance shows a much larger variation, 2.26−3.33 Å, reflecting that a protonated alcohol can also coordinate to the metal. If CysC88 is deprotonated but Ser-D188 is protonated, then the Fe5−N distance becomes short, 1.99−2.05 Å (Table S6). However, the Fe6−O distance is either rather short and coordinating, 2.31−2.60 Å, or long and noncoordinating, 3.00−3.50 Å, with approximately a 2:1 proportion. Apparently, the two states represent two different local minima, and the results depend on the starting structure. If the optimization is instead started from the crystal conformation of the reduced state (in which Ser-D188 and the backbone of Cys-C88 do not coordinate), then only the nonbonded state of Ser-D188 is

indication of any intermediate-spin Fe ions−the lowest spin (which is always α) is 2.2−3.3 (3.1−3.3 for the best states). Unfortunately, the situation is quite different with the B3LYP functional. With this method, the BSc35 state for Stot = 4 is strongly destabilized, becoming 36 kJ/mol less stable than the BSc24 state (31 kJ/mol with the def2-TZVPD basis set) and 32 kJ/mol less stable than the BSc40 state, which were ∼60 kJ/mol less stable than the BSc35 state at the TPSS level. Interestingly, BS2c4 has three α spins in the second subcluster, including the two largest spins (i.e., giving [Fe4S4]+2 cluster in the S2 = 4), coupled to a reduced [Fe4S4]0 cluster in the S1 = 0 state. However, the BSc40 state is similar to the BSc35 one, but with a β spin on Fe4, Fe6, and Fe7, rather than on Fe3, Fe5, and Fe8. Moreover, BSc40 with Stot = 3 becomes similar in energy, only 8 kJ/mol higher than BSc24 with Stot = 4 (4 kJ/mol with the def2-TZVPD basis set). It has a similar electronic structure as BSc40 with Stot = 4, but with somewhat less α spin on many of the Fe ions and 0.5 more β spin on Fe4. In the DMRG study, there are more low-lying excited states for P2+ than for the other two oxidation states. Again, there are several low-lying states that cannot be represented by BS-DFT, but two of the lowest four states with both Stot = 3 and 4 correspond to the type-C BS states with the 2 + 1 β-spin pattern as in our calculations. For Stot = 4, the BSc39 state is lowest in energy, and the BSc37 state is 17 kJ/mol higher. For Stot = 3, the BSc35 and BSc13 states are within 8 kJ/mol of the ground state. However, none of these states are among the lowest in our calculations. BS States of the P-cluster in the P3+ State. Finally, we considered also the P3+ state. As mentioned above, it is experimentally observed to be a physical mixture of Stot = 1/2 and 7/2 states. Mouesca et al. suggested that the former is obtained by coupling of a singly oxidized [Fe4S4]+ cluster in the S1 = 1/2 state with a doubly oxidized [Fe4S4]+ cluster in the S2 = 0 state.23 Such states can be obtained with two α and two β Fe ions in each cluster, giving rise to 36 possible BS states, as before (type-A states). We have studied these states with the same model as for the P2+ state (i.e., with both SerD188 and the backbone of Cys-C88 deprotonated and coordinating to Fe6 and Fe5, respectively). The results in Figure 6a show that at the TPSS level there are four states with energies within 3 kJ/mol (but 13 kJ/mol with the def2-TZVPD basis set). The lowest is BSa21, which has β spins on Fe2, Fe3, Fe5, and Fe8. As for most of the other BS states, Fe6 has the largest (absolute) spin population (3.7− 3.8). The second largest is also from the second subcluster (Fe5, 3.6), which also applies to most BS states and indicates that this subcluster is more oxidized than the first subcluster. However, in variance to most of the other BS states, the third largest spin also comes from the second subcluster (Fe7 with 3.43 spin), but Fe3 has nearly the same spin (3.41). This indicates that the second subcluster is more oxidized than the first subcluster, but the sum of the Fe spins in the two subclusters are quite similar, 0.1 and 0.3. In fact, the variation in the Fe spins is quite restricted; the lowest absolute spin is 3.1 for BSa21 and 2.8−3.3 for all BS states. To obtain the Stot = 7/2 state, we used three α-spin Fe ions in one of the subclusters (type-C BS states) and tested 48 different BS states, as shown in Figure 6b. As with the P2+ state, BSc35 has the lowest energy, 9 and 23 kJ/mol lower than those for BSc47 and BSc43 (14 and 30 kJ/mol with the def2-TZVPD basis set). All these states have three α-spin Fe in the first 9682

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obtained, with Fe6−O distanced of 3.25−3.50 Å (and Fe5−N = 1.96−2.06 Å; Table S6c,d). For the most stable BS state at the TPSS level, Ser-D188 does not coordinate, and the best BS state with Ser-D188 coordinating is 25 kJ/mol less stable. However, at the B3LYP level, the situation is opposite. The best BS states have Ser-D188 coordinating and the best noncoordinating state is 19 kJ/mol higher in energy. The formation of the Fe5−N and Fe6−O bonds leads to an extensive reorganization of the structure of the second subcluster (Figure 7). In particular, the Fe5−S1 and Fe6−S1 bonds are cleaved (they increase by 1.2−1.4 Å between the PN and P2+ structures). Thereby, one of the corners of the cubane is removed, and the cluster opens up, leading to not only increased Fe5−Fe6, Fe5−Fe8, and Fe6−Fe8 distances within the cluster (by 1.3, 0.9, and 0.5 Å, respectively) but also an increased intercluster Fe4−Fe5 distance (by 1.1 Å). All the other short Fe−Fe and Fe−S distances (i.e., shorter than 3.0 and 2.5 Å, respectively, in the PN structure, 14 Fe−Fe distances and 32 Fe−S distances) change by less than 0.13 and 0.09 Å, respectively (besides a 0.20 Å shortening of the Fe8−S1 bond). For P1+ with a deprotonated Ser-D188 and protonated CysC88 (Figure 7e), the difference is smaller compared to PN: The Fe6−S1, Fe6−Fe8, Fe5−Fe6, and Fe2−Fe8 distances increase by 1.3, 0.7, 0.6, and 0.3 Å, respectively, whereas the other distances change by less than 0.16 Å. However, the structure of the P3+ state is similar to that of the P2+ state (Figure 7b,c): The Fe−Fe and Fe−S distances differ by 0.03 Å on average, with a maximum of 0.12 Å for the Fe2−Fe3 distance for the best BS states. The similarity is enhanced by the fact that both structures belong to the same BS state. In fact, the difference is similar to the difference in geometries of different BS states of the same oxidation state. For example, the Fe−Fe and Fe−S distances differ by an average of 0.03 Å between the two best BS states for P1+ (BSb11 and BSb26), with a maximum of 0.24 Å for Fe5−Fe6. Comparison to Crystal Structures for the PN and P2+ States. In the crystal structure used in our QM/MM calculations (3U7Q at 1.0 Å resolution),6 two conformations are reported for the P-cluster, interpreted as the PN (20% occupancy) and P2+ (80% occupancy) states. However, in practice the position of only two atoms differ, Fe5 and Fe6 (by 1.2 and 1.3 Å, respectively), whereas the coordinates of all the other atoms (including those of Cys-C88 and Ser-D188) are identical. Therefore, it cannot be expected that the structure of the P-cluster is as accurate as that of the FeMo cluster and other parts of the structure. The QM/MM structure of the best BS state (BSb11) of PN reproduces the crystal structure of the reduced P-cluster with a mean absolute deviation (MAD) of 0.05 and 0.06 Å for the short Fe−S and Fe−Fe distances, respectively, and with largest deviations of 0.22 and 0.17 Å for the Fe5−S1 and Fe6−Fe8 distances. This is significantly worse than for the FeMo cluster, for which the MAD for Fe−S and Fe−Fe distances are 0.02 and 0.05 Å and the maximum deviations are 0.06 and 0.09 Å,38 confirming that the structure of the P-cluster is worse than for other parts of the crystal structure (owing to the disorder). However, the deviation is larger for the second-best BS state (BSb15), with MADs of 0.07 and 0.07 Å and maximum deviations of 0.18 Å the Fe4− Fe5 distance and 0.18 Å for the Fe6−S2B bond. In fact, BS7 gives the lowest MAD deviations of all the 18 type-A and the 16 type-B BS states studied, confirming that this is most likely the best BS state for the PN state of the P-cluster (Figure 8a).

Figure 7. Optimized geometries of the four oxidation states, obtained at the TPSS-D3/def2-SV(P) level of theory: (a) PN (BSb11), (b) P2+ (BSc35, Stot = 4), (c) P3+ (BSc35, Stot = 7/2), as well as P1+ obtained with (d) deprotonated Ser-D188 and protonated Cys-C88, (e) protonated Ser-D188 and deprotonated Cys-C88, or (f) both SerD188 and Cys-C88 protonated (all three with BSb11, Stot = 1/2)). Only atoms in the QM system are shown. Color key: Fe ions, orange; sulfur, yellow; oxygen, red; nitrogen, blue; carbon, green; and hydrogen, white. 9683

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Inorganic Chemistry

Figure 8. Comparison between the 3U7Q crystal structure6 and the various BS states: (a) PN compared to the reduced crystal structure, (b) P2+ compared to the oxidized crystal structures (the Stot = 4 states). The figures show the MAD for the Fe−S, the Fe−Fe distances, and both distances together (all), as well as the maximum deviation for the Fe−S and Fe−Fe distances. All results are obtained at the TPSS-D3/def2-SV(P) level, except the last entry in panel (a) which shows the best BS (BSb11) state obtained with the B3LYP functional.

lower maximum deviations, 0.22 and 0.12 Å for the Fe6−Fe8 distance and the Fe6−S1 bond. If we instead consider the B3LYP structures, then the deviations are appreciably larger. For the best BS state of PN (BSb11), the MAD deviations in the Fe−S and Fe−Fe distances are 0.09 and 0.15 Å (last entry in Figure 8a). This is 2−3 times worse than for the best TPSS structure and actually worse than all the TPSS structures of the various BS states. Likewise, for the best B3LYP BS state of P2+, the MAD is 0.07 and 0.11 Å for the Fe−S and Fe−Fe distances, which is also appreciably more than for the TPSS structures. This is in agreement with results obtained for the FeMo cluster31,38 and the reason why we base the discussion of the geometries on the TPSS structures. The Fe5−N and Fe6−O distances in the crystal structure of the oxidized P-cluster are 2.12 and 1.92−1.93 Å, respectively. Both are somewhat longer than in the TPSS QM/MM

However, the maximum errors show more erratic variations, and they are not the lowest for BSb11. Likewise, the best BS state of P2+ (BSc35 with Stot = 4) reproduces the crystal structure of the oxidized P-cluster with MADs of 0.03 and 0.07 Å, for the Fe−S and Fe−Fe distances, with maximum deviations of 0.25 Å for the Fe6−Fe8 distance and 0.15 Å for the Fe6−S1 bond. This is the lowest MAD for the Fe−S bonds and for the Fe−S and Fe−Fe bonds together for all the tested BS states. However, BSc15 and BSc17 have the lowest MAD for the Fe−Fe bonds, 0.05 Å, and other states have lower maximum deviations. Still, our results show that the two structures of the P-cluster in the 3U7Q structure provide quite accurate coordinates for the PN and P2+ states of the Pcluster, and they will therefore in the following be used as reference structures of these two states. The best BS state of P3+ has similar MADs to the crystal structure of the oxidized P-cluster, 0.02 and 0.08 Å, but slightly 9684

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ensure that bond lengths and angles make chemical sense) is replaced by more accurate QM calculations for a small but interesting part of the protein.63−65 This is particularly important for metal sites, for which no accurate empirical potential is available. This approach has previously been successfully employed to determine the protonation state of the homocitrate ligand and for the entire FeMo cluster in nitrogenase.32,37 We performed five individual quantum-refinement calculations, modeling the P-cluster either in the PN state with both Ser-D188 and Cys-C88 protonated, in the P2+ state with both residues deprotonated or in the P1+ state with either both groups protonated, Ser-D188 deprotonated and Cys-C88 protonated, or Ser-D188 protonated and Cys-C88 deprotonated. In all cases, we used the best BS state obtained in this study (for TPSS). For P1+, we tested both the BSb11 and BSb26 states, which were essentially degenerate, but results are shown only for the former (the results are closely similar). The five structures are evaluated in Table 3 in terms of the sum of

structures, 1.99−2.05 and 1.87−1.91 Å, indicating that they are influenced by the distances in the reduced structure and therefore not accurately measured in the structure. Likewise, the corresponding distances in the structure of the reduced Pcluster, 3.21−3.28 Å, are also shorter than in calculations, 3.28−3.57 Å, probably for the same reason. However, it is quite clear that both residues are protonated in the reduced PN state and that they are deprotonated when they coordinate to their Fe ions. A protonated backbone amide never coordinates to Fe5 in any of our QM/MM structures, whereas a protonated Ser-D188 can coordinate to Fe6, but the Fe6−O distance is then 2.26−2.60 Å (i.e., much longer than in the crystal structure). Comparison to the Crystal Structure of the P1+ State. For the P1+ state, we can instead compare with the recent crystal structure of this state (PDB file 6CDK), although it is at a lower resolution, 2.1 Å, and the data is only 60% complete.16 It shows a Fe6−O bond of 1.93 Å, slightly longer than our estimates, 1.87−1.91 Å (P1+ with Ser-D188 deprotonated and Cys-C88 protonated in different BS states). However, the Fe5−N distance is 3.13 Å in subunit CD, showing that the backbone amide group is protonated and noncoordinating, slightly shorter than our estimates of 3.3−3.6 Å. However, in the other subunit of the crystal structure, the Fe5−N distance is only 2.24 Å, which is interpreted as the P2+ state. Our results indicate that it should rather be interpreted as a mixture of the P2+ and P1+ states, as a fully formed Fe5−N bond is appreciably shorter, 1.99−2.05 Å. Thus, the Fe6−O and Fe5−N bond lengths support the crystallographer’s suggestion that the 6CDK crystal structure in subunit CD contains the P1+ state with Ser-D188 deprotonated and Cys-C88 protonated.16 However, for the Fe−Fe and Fe−S bonds, the results are less clear. Compared to the PN state in the 3U7Q structure, the Fe5−Fe6, Fe6−Fe8, and Fe6−S1 distances have increased by 0.8−1.3 Å, as also observed for our optimized PN and P1+ structures. However, the Fe1−S3A and Fe2−S4A bonds have increased to nonbonding distances of 3.17 and 3.03 Å, and many other Fe−Fe and Fe−S distances have changed by 0.3−0.5 Å in a way that is not supported by neither the 3U7Q structure nor our optimized structures. The same applies when the P-cluster in the 6CDK structure is compared to the oxidized P2+ state in the 3U7Q structure: It shows that the Fe4−Fe5, Fe5−Fe8, and Fe5−S1 distances decrease by 0.8−1.2 Å, in agreement with the differences observed between the PN and P2+ states in the 3U7Q structure and between the P1+ and P2+ states in our calculations. However, there are also many changes in these distances of 0.3−0.9 Å that are observed in neither the 3U7Q structure nor our optimized structures, in particular the broken Fe1−S3A and Fe2−S4A bonds (3.17 and 3.03 Å). Consequently, there are rather large differences between our best P1+ state and the 6CDK crystal structure, giving a MAD of 0.24 Å and a maximum difference of 0.9 Å for Fe1−S3A. Therefore, we performed additional calculations to check whether we can find any better interpretation of the 6CDK crystal structure, using other protonation states of the P1+ state and quantum refinement. Quantum Refinement of the P-Cluster. To obtain further evidence about the protonation of the P-cluster in nitrogenase, we have performed quantum-refinement calculations of the crystal structure of the putative P1+ state (PDB file 6CDK).16 Quantum refinement is standard crystallographic refinement in which the empirical potential (employed to

Table 3. RSZD Scores of the P-Cluster, the Cys Ligands, As Well As the Neighboring Gly-C87 Residue and Ser-D188 in the Five Quantum-Refinement Calculationsa ox state

PN

P1+

P2+

Ser

prot

prot

deprot

prot

deprot

Cys

prot

prot

prot

deprot

deprot

Cys-C62 Gly-C87 Cys-C88 Cys-C154 Cys-D70 Cys-D95 Cys-D153 Ser-D188 Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Fe8 S1 S2A S3A S4A S2B S3B S4B sum

0.2 0.3 1.7 1.0 1.6 0.9 1.7 2.3 1.5 1.6 1.4 1.0 2.7 1.8 0.9 2.2 1.9 0.8 0.9 1.8 2.9 0.4 1.4 32.9

0.2 0.3 1.7 1.1 1.6 0.8 1.6 2.6 1.4 1.2 1.1 0.6 2.3 1.8 0.8 2.6 2.0 0.9 1.8 1.5 2.7 0.3 1.4 32.3

0.2 0.3 1.9 1.2 1.5 1.0 1.0 1.3 1.6 1.5 1.5 1.0 2.6 1.4 0.8 1.9 1.6 1.2 1.3 2.0 2.6 0.4 1.5 31.3

0.2 0.2 2.0 1.0 1.5 1.1 1.7 2.7 1.3 1.6 1.2 0.7 2.7 1.8 0.9 2.8 1.7 0.9 1.7 1.9 2.8 0.4 1.0 33.8

0.3 0.2 1.9 1.1 1.6 1.0 1.7 0.7 1.0 2.0 1.5 1.0 2.4 1.3 0.8 2.5 1.3 0.9 2.3 1.6 2.5 0.6 1.2 31.4

a With the P-cluster in different oxidation and protonation states. The last line shows the sum of the individual RSZD scores.

the maximum absolute RSZD score for the P-cluster, the six Cys ligands, the neighboring Gly-C87 residue, and Ser-D188. It can directly be seen that the two calculations with the side chain of Ser-D188 deprotonated give an appreciably better RSZD for this residue (0.7−1.3) than those for the other three calculations (2.3−2.7). This can be also seen in the electrondensity maps (Figure 9a,b). The same applies also to the Fe6 ion that is bound to Ser-D188 (1.3−1.4, compared to 1.8). This clearly shows that Ser-D188 is predominantly deproto9685

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and Cys-C88 protonated and for the doubly deprotonated P2+ state (31), but it is clearly worse around Fe5 and Cys-C88, as can be seen by comparing Figure 9b,c. The other three oxidation and protonation states give higher sums of the RSZD scores (32−34), mainly owing to worse description of the electron density around Ser-D188. Therefore, we can conclude that our quantum-refinement calculations confirm the suggestion of the crystallographers16 that the structure predominantly shows the P1+ state and that it involves a deprotonated Ser-D188 side chain and a protonated Cys-C88 backbone NH group. Next, we compare the 14 short Fe−Fe distances and the 32 Fe−S bonds in the quantum-refined structure of P-cluster (in the P1+ state with Ser-D188 deprotonated and Cys-C88 protonated) with the various crystal structures.6,16 From Table 4, it can be seen that the quantum-refined structure reproduces the 3U7Q crystal structure of the reduced P-cluster6 quite poorly, with MADs of the Fe−S and Fe−Fe bonds of 0.11 and 0.24 Å, and maximum deviations of 1.3 and 1.1 Å, respectively. However, the large deviations are restricted to a few bonds, Fe5−S1, Fe6−S1, Fe5−Fe6 and Fe6−Fe8 (i.e., all involving Fe5 and Fe6). This shows that the deviations are related to the oxidation and protonation state of the P-cluster and that it is unlikely that the cluster is reduced in this crystal structure. In contrast, the quantum-refined structure fits the crystal structure of the oxidized P-cluster6 appreciably better, with MADs of 0.06 and 0.16 Å and maximum deviations of 0.66 and 0.62 Å. Only four bonds have deviations of 0.4−0.7 Å, Fe5− S1, Fe4−Fe5, Fe5−Fe6 and Fe5−Fe8 (i.e., always involving Fe5), whereas all the other bonds differ by 0.17 Å or less. Compared to the 6CDK crystal structure of the P1+ state (used in the quantum refinement),16 the deviations of the quantum-refined structure are larger, with MADs of 0.26 and 0.21 Å and maximum deviations of 0.87 and 0.42 Å. Moreover, in contrast to the higher-resolution crystal structure, the largest deviation does not only involve the Fe5 and Fe6 ions, and there are many deviations of intermediate size (0.3−0.6 Å). These differences reflect the improvement of the crystal structure caused by the QM model of the P-cluster in the quantum-refinement calculations, and they reflect the lower resolution of the original crystal structure. Compared to our best QM/MM structure of P1+ (still with Ser-D188 deprotonated and Cys-C88 protonated; BSb19), the quantum-refined structure shows a similar fit as to the crystal structure of the oxidized P-cluster: the MADs are 0.08 and 0.14 Å, and the maximum deviations are 0.93 and 0.51 Å. In fact, there is one large deviation, viz. for the Fe5−S1 interaction. This distance (3.4 Å) is intermediate between that of the reduced (2.6 Å) and oxidized (3.8 Å) structures in the quantum-refined structure, indicating that the 6CDK crystal structure is a mixture of the P1+ and P2+ oxidation states. Consequently, it therefore also involves a mixture of the protonated and deprotonated state of the backbone of CysC88, as also indicated by the Fe5−N bond length, which is 2.78 Å, compared to 2.12 and 3.28 Å in the crystal structures of the oxidized and reduced P-cluster. There are also 0.3−0.5 Å deviations of the Fe5−Fe6 and Fe5−Fe8 interactions, which also show 1.0−1.4 Å differences between the crystal structures of the oxidized and reduced P-cluster. The energies of our calculations with a protonated Ser-D188 and a deprotonated backbone of Cys-C88 are directly comparable to those with the opposite protonation. The results show that the deprotonated Ser-D188 and protonated

Figure 9. Electron-density maps of the quantum-refined nitrogenase 6CDK structure16 with the P-cluster in (a) the P1+ state with both Ser-D188 and Cys-C88 protonated, (b) the P1+ state with Ser-D188 deprotonated and Cys-C88 protonated, or (c) the P2+ state with both Ser-D188 and Cys-C88 deprotonated. The 2mFo−DFc maps are contoured at 1.0 σ (blue) and the mFo−DFc maps are contoured at +3.0 σ (green; no difference density is seen at −3.0 σ level).

nated in the crystal structure, in agreement with the suggestion by the crystallographers.16 For the protonation of the Cys-C88 residue, the results are less clear. The RSZD scores of this residue and the neighboring Gly-87C residue, as well as for the Fe5 ion, which is bound to Cys-C88 in the P2+ state, are nearly the same for all five refinements (1.7−2.0, 0.2−0.3, and 2.3−2.7, respectively). Still, summing the RSZD scores of all residues, the lowest value is obtained for the P1+ state with Ser-D188 deprotonated 9686

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Table 4. Comparison of the Quantum-Refined Structure of Nitrogenase with the P-Cluster in the P1+ State (with Ser-D188 Deprotonated and Cys-C88 Protonated; QM-ref), with the Crystal Structures of the P-cluster in the PN, P2+, and P1+ States,6,16 as Well as the QM/MM Structure of the Same P1+ Statea Fe6−O Fe5−N Fe1−SG Fe2−SG Fe3−SG Fe4−SG Fe5−SG Fe6−SG Fe7−SG Fe8−SG Fe1−S1 Fe1−S2A Fe1−S3A Fe2−S1 Fe2−S2A Fe2−S4A Fe3−S2A Fe3−S4A Fe3−S3A Fe4−S1 Fe4−S4A Fe4−S3A Fe5−S1 Fe5−S2B Fe5−S4B Fe6−S1 Fe6−S2B Fe6−S3B Fe7−S2B

QM-ref

PN

P2+

P1+

QM/MM

1.94 2.78 2.33 2.46 2.30 2.23 2.38 2.37 2.38 2.29 2.35 2.30 2.33 2.46 2.38 2.28 2.29 2.35 2.40 2.35 2.34 2.39 3.43 2.17 2.20 3.69 2.39 2.30 2.33

−1.27 −0.50 0.01 0.13 0.01 −0.09 0.11 0.11 0.02 −0.02 −0.03 −0.01 0.02 −0.02 0.08 0.00 0.01 0.09 0.07 −0.01 0.05 0.09 0.80 −0.28 0.00 1.13 −0.16 −0.02 0.01

0.01 0.66 0.01 0.13 0.01 −0.09 0.06 −0.01 0.02 −0.02 −0.03 −0.01 0.02 −0.02 0.08 0.00 0.01 0.09 0.07 −0.01 0.05 0.09 −0.38 −0.11 −0.11 −0.17 0.06 −0.02 0.01

0.00 −0.35 −0.09 0.00 0.02 −0.05 0.07 0.00 0.10 0.11 0.10 0.27 −0.85 0.38 0.47 −0.75 0.45 0.53 0.54 0.31 0.24 0.22 0.87 0.02 0.17 −0.14 0.37 0.16 0.20

0.05 −0.80 0.00 0.09 0.03 −0.12 −0.02 0.04 0.08 −0.08 −0.07 −0.05 −0.01 −0.02 0.03 −0.03 −0.07 0.04 0.03 −0.06 0.02 0.05 0.93 −0.17 −0.13 −0.02 0.04 −0.06 −0.01

Fe7−S3B Fe7−S4B Fe8−S1 Fe8−S3B Fe8−S4B Fe1−Fe2 Fe1−Fe3 Fe1−Fe4 Fe2−Fe3 Fe2−Fe4 Fe2−Fe8 Fe3−Fe4 Fe4−Fe5 Fe5−Fe6 Fe5−Fe7 Fe5−Fe8 Fe6−Fe7 Fe6−Fe8 Fe7−Fe8 MAD Fe−S MAD Fe−Fe max Fe−S max Fe−Fe

QM-ref

PN

P2+

P1+

QM/MM

2.33 2.33 2.32 2.37 2.33 2.39 2.74 2.67 2.74 2.45 2.83 2.82 3.28 3.63 2.76 2.81 2.77 3.15 2.78

0.01 0.03 −0.03 0.09 0.01 −0.13 −0.06 0.04 −0.02 −0.11 −0.11 0.10 0.33 1.09 −0.03 0.34 −0.06 0.85 0.03 0.11 0.24 1.27 1.09

0.01 0.03 −0.03 0.09 0.01 −0.13 −0.06 0.04 −0.02 −0.11 −0.11 0.10 −0.42 −0.35 −0.07 −0.62 −0.03 −0.14 0.03 0.06 0.16 0.66 0.62

0.17 0.24 −0.08 0.24 0.15 0.34 0.14 0.42 0.26 0.32 −0.22 0.15 0.33 0.27 0.01 0.18 −0.01 −0.24 0.05 0.26 0.21 0.87 0.42

−0.01 0.00 −0.22 0.06 0.01 −0.06 −0.04 0.13 −0.09 −0.03 −0.26 0.12 0.27 0.51 −0.09 0.34 0.01 0.04 0.00 0.08 0.14 0.93 0.51

a

The QM-ref column shows the actual Fe−S and Fe−Fe distances, whereas the other columns shows the difference between the QM-ref structure and the other structures (QM-ref−other), all in Å. The four last lines show the MAD and maximum deviations. Deviations larger than 0.3 Å are marked in bold face.

accurate. Instead, the QM/MM structure is probably the most accurate structure of this state.

Cys-C88 is appreciably more favorable, by 48 and 127 kJ/mol at the TPSS and B3LYP levels of theory, respectively, again supporting that the P1+ state involves deprotonated Ser-D188 and protonated Cys-C88. In the original publication, the crystal structure of P1+ was also supported by DFT calculations, primarily directed to estimate the relative stabilities of the four protonation states of the P-cluster (Ser-188 and Cys-88 protonated or not) in the PN, P1+, and P2+ states.16 This is a formidable task, as our previous studies on the protonation of homocitrate in the FeMo cluster showed.37 They also studied the BS states for the doubly protonated PN cluster and suggested that the best state is BSa14.16 This state is 44−87 kJ/mol less stable than BSb11 in our calculations (i.e., a strongly unfavorable state). They seem to have used this state for all the other protonation and oxidation states. This means that they studied an incorrect spin state of P2+ (Stot = 0, in contrast to the experimental observation of Stot = 3 or 4).23 For P1+, BSa14 is 50−119 kJ/mol less stable than BSa11. This illustrates the importance of determining the best BS state for each structure studied. In conclusion, our results show that the P-cluster in the 6CDK crystal structure is a mixture of the P1+ and P2+ oxidation states. The P1+ state most likely has a deprotonated side chain of Ser-D188 and a protonated backbone NH group of Cys-C88. The quantum-refined structure provides an appreciably better description of the P-cluster in the P1+ state than the original crystal structure. However, owing to the mixture of the two states, the detailed geometry cannot be

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CONCLUSIONS We have studied the geometry and electronic structure of the P-cluster in nitrogenase with QM/MM and quantum-refinement calculations. Our results support the suggestion16 that the side chain of Ser-188 is deprotonated in all the oxidized states (including P1+) and coordinates to Fe6. On the other hand, the backbone N atom of Cys-88 is deprotonated and coordinates to Fe5 in the doubly oxidized P2+ state and in the triply oxidized P3+ state, but not in the P1+ state. Our calculations show that the 3U7Q crystal structure6 is less accurate for the P-cluster than for other parts of the structure, because it is a mixture of the PN and P2+ states, which cannot be clearly discerned (the coordinates of only two atoms differ). The crystal structure of the putative P1+ state (6CDK)16 is less reliable, with several Fe−Fe and Fe−S distances deviating from our QM/MM structure and from the previous crystal structures by up to 0.9 Å. The quantumrefinement calculations indicate that it is a mixture of the P1+ and P2+ states. We strongly believe that the QM/MM calculations provide the most reliable structure of the P1+ state in nitrogenase. Structures obtained with the TPSS functional are appreciably closer to the crystal structures than those obtained with B3LYP. For all four oxidation states, we have studied all the 16−48 possible BS states for the one or two observed spin states 9687

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shown in Table 1. For the reduced PN state, both the energy and the geometry (compared to the crystal structure) indicates that BSb11 is the most likely state. In this state, both subclusters have only one Fe ion with minority spin (i.e., S2 = −S1 = 4) and these Fe ions are in the terminal positions (Fe3 and Fe7). For the other oxidation states, the results of the pure TPSS and the hybrid B3LYP functionals differ significantly, making it harder to reach any firm conclusion about the best BS states. However, nearly all calculations agree that Fe6 and Fe7 have the largest spin populations and therefore are the most oxidized, although their spins are only slightly higher than those of the other Fe ions in the P-cluster. For P1+, TPSS suggests that BSb11 is still the lowest state, although BSb26 comes very close in energy (2−4 kJ/mol). The type-A and Stot = 5/2 states are 26−43 kJ/mol higher in energy. In contrast, B3LYP prefers the BSa19−BSa24 states, which are all within 10 kJ/mol. The type-B states are at least 11 kJ/mol less stable, and the Stot = 5/2 states are strongly unfavorable. For the doubly oxidized P2+ state, our calculations confirm the suggestion by Mouesca et al.23 that the Stot = 4 state is more likely than the Stot = 3 state, although the two states are rather close in energy (within 8 kJ/mol) at the B3LYP level. BSc35 is most stable with TPSS but BSc24 with B3LYP. For the P3+ state, the TPSS calculations indicate that BSc35 of Stot = 7/2 is most stable, whereas B3LYP indicates that BSa14 or BSa30 of Stot = 1/2 is most stable. In both cases, states with the other Stot are quite high in energy (33 or 10−24 kJ/mol), in contrast to the experimental observation of both states. Our results, especially those with TPSS, agree partly with the DMRG results, in particular that the type-B BS states are favorable for PN and P1+ and that type-C BS states are favorable for the higher spin states of P1+ and P2+. However, undoubtedly more accurate quantum mechanical methods (treating both static and dynamic correlation) are needed to settle the relative energies of the various BS states of the Pcluster in nitrogenase. The present study provides a foundation for future QM studies of the interaction and electron transfer between the P and FeMo clusters in nitrogenase. Many studies assume that only the PN and P1+ states are involved in the catalytic reaction mechanism and that only two oxidation levels of the FeMo cluster (explaining why the P-cluster may deliver eight electrons at the same redox potential).3,76 For the time being, we recommend the use of the BSb11 state for both PN and P1+, as this state gave the best structure in the quantum refinement of P1+.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +46−46 2224502. Fax: +46−46 2228648. ORCID

Ulf Ryde: 0000-0001-7653-8489 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This investigation has been supported by grants from the Swedish research council (projects 2014-5540 and 201805003), from COST through Action CM1305 (ECOSTBio), from China Scholarship Council, from eSSENCE: the escience collaboration and from the Royal Physiographic Society in Lund. The computations were performed on computer resources provided by the Swedish National Infrastructure for Computing (SNIC) at Lunarc at Lund University and HPC2N at Umeå University.

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.9b00400. Mulliken spin populations of the various BS states, energies, Fe−O and Fe−N bond lengths of the various BS states for P1+ with models 1 and 3, as well as coordinates of the optimized structures of all the best BS states (PDF) 9688

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