Critical computational analysis illuminates the reductive-elimination mechanism that activates for N2 reduction Simone Raugeia,1, Lance C. Seefeldtb,1, and Brian M. Hoffmanc,1

aPhysical and Computational Sciences Directorate, Pacific Northwestern National Laboratory, Richland, WA 99352; bDepartment of Chemistry and Biochemistry, Utah State University, Logan, UT 84322; and cDepartment of Chemistry, Northwestern University, Evanston, IL 60208

Contributed by Brian M. Hoffman, September 11, 2018 (sent for review June 18, 2018; reviewed by Victor S. Batista, Michael B. Hall, and Frank Neese)

Recent spectroscopic, kinetic, photophysical, and thermodynamic with an obligatory formation of 1 mol of H2 per mole of → − + measurements show activation of nitrogenase for N2 2NH3 N2 reduced, and a corresponding requirement of 8[e /H ], reduction involves the reductive elimination (re)ofH2 from two not 6, and as a result, the apparently “wasted” hydrolysis of [Fe–H–Fe] bridging hydrides bound to the catalytic [7Fe–9S–Mo–C– 4ATP(3–5). homocitrate] FeMo- (FeMo-co). These studies rationalize In recent years, we have demonstrated (6, 7) that this stoi- – ’ the Lowe Thorneley kinetic scheme s proposal of mechanistically chiometry arises because activation of nitrogenase for N2 re- obligatory formation of one H2 for each N2 reduced. They also duction involves the accumulation of four reducing equivalents provide an overall framework for understanding the mechanism at the active-site FeMo-co (4) to form a state with two [Fe–H– of by nitrogenase. However, they directly pose Fe] bridging hydrides and two sulfur-bound protons, denoted fundamental questions addressed computationally here. We here E4(4H), the Janus intermediate, and that breaking the N≡N report an extensive computational investigation of the structure triple bond requires the reductive elimination (re)ofH2 from and energetics of possible nitrogenase intermediates using struc- E4(4H) (6–9). This process corresponds to the forward direction tural models for the active site with a broad range in complexity, of the equilibrium in Fig. 2, which leads to the formation of a

while evaluating a diverse set of density functional theory CHEMISTRY diazene-level N2 reduction product [denoted as E4(2N2H)]; the flavors. (i) This shows that to prevent spurious disruption of reverse of this reaction is the oxidative addition (oa)ofH2 with FeMo-co having accumulated 4[e−/H+] it is necessary to include: release of N2 (6). EPR/electron nuclear double resonance all residues (and water molecules) interacting directly with FeMo-co (ENDOR) and photophysical measurements established re/oa via specific H-bond interactions; nonspecific local electrostatic in- as central to the mechanism of the wild-type enzyme and showed ii teractions; and steric confinement. ( ) These calculations indicate it to be a nearly isoergic (ΔG = −8 kJ/mol), kinetically ac- an important role of sulfide hemilability in the overall conversion cessible process (8, 9). Photophysical measurements further E iii of 0 to a diazene-level intermediate. ( )Perhapsmostim- re E iiia suggested that during activation of nitrogenase, 4(4H) and

portantly, they explain ( ) how the enzyme mechanistically BIOPHYSICS AND E4(2N2H) are likely connected via an H2-bound intermediate couples exothermic H2 formation to endothermic cleavage of E COMPUTATIONAL BIOLOGY ≡ re [ 4(H2)] (9). These studies provide an overall framework for un- the N N triple bond in a nearly thermoneutral /oxidative- derstanding the mechanism of nitrogen fixation by nitrogenase. addition equilibrium, (iiib) while preventing the “futile” gener- ation of two H without N reduction: hydride re generates 2 2 Significance an H2 complex, but H2 is only lost when displaced by N2,to form an end-on N2 complex that proceeds to a diazene-level intermediate. This report critically evaluates the mechanism by which ni- trogenase cleaves the N≡N triple bond. It assesses the ther- nitrogenase | mechanism | DFT | computation modynamic driving force provided by the accompanying, apparently “wasteful,” reductive elimination of an H2, and explains how the enzyme mechanistically couples exothermic iological nitrogen fixation is one of the most challenging H formation to endothermic triple-bond cleavage in a nearly chemical transformations in biology, the conversion of N to 2 B 2 thermoneutral equilibrium process, thereby preventing the . The catalyst for biological N2 fixation, the metal- “futile” generation of two H2 without N2 reduction. This eval- loenzyme nitrogenase, is known in three different forms (1) with uation rests on a critical assessment of the density functional the most abundant being the Mo-dependent enzyme, which is theory flavors needed to properly treat nitrogenase, and a composed of the electron-donating Fe and the catalytic demonstration that to prevent spurious disruption of FeMo-co − + MoFe protein. The Fe protein, a homodimer, delivers one upon 4[e /H ] accumulation, one must employ a nitrogenase electron at a time during transient association with the MoFe structural model that includes all residues interacting directly protein heterotetramer with dissociation of the two with FeMo-co, either via specific H-bond interactions, non- specific electrostatic interactions, or steric confinement. driven by the hydrolysis of two ATP to two ADP/Pi per electron transfer (ET) event (2). The reduction of N2 takes place on the – – – – Author contributions: S.R., L.C.S., and B.M.H. designed research; S.R. performed research; [7Fe 9S Mo C homocitrate] FeMo-cofactor (FeMo-co) in the S.R., L.C.S., and B.M.H. analyzed data; and S.R., L.C.S., and B.M.H. wrote the paper. – active site of the MoFe protein (Fig. 1), with the [8Fe 7S] P- Reviewers: V.S.B., Yale University; M.B.H., Texas A&M University; and F.N., Max Planck cluster in the MoFe protein acting as an ET intermediary. Institute for . Lowe and Thorneley put forward a kinetic model for catalysis Conflict of interest statement: B.M.H. and F.N. are coauthors on a 2017 research article. by the MoFe protein, including rate constants for formation of Published under the PNAS license. each intermediate state, designated as En, where n indicates the 1To whom correspondence may be addressed. Email: [email protected], lance. number of electrons and protons accumulated. This scheme in- [email protected], or [email protected]. corporates a controversial limiting stoichiometry: This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1810211115/-/DCSupplemental. − + N2 + 8e + 16ATP + 8H → 2NH3 + H2 + 16ADP + 16Pi, [1]

www.pnas.org/cgi/doi/10.1073/pnas.1810211115 PNAS Latest Articles | 1of10 Downloaded by guest on September 27, 2021 To evaluate these proposals and in so doing answer funda- mental questions of nitrogenase catalysis, we have carried out an in-depth evaluation of a variety of DFT flavors, structural models, and oxidation states of the resting state, and show that the proper incorporation of all interactions with the protein environment that envelops FeMo-co at the enzyme active site is critical to stabilize FeMo-co and prevent its disruption upon protonation. The resulting structural model is then used to characterize the alternative E4 “protonation isomers,” including, but not limited to, characterization of the ground-state structure of E4(4H). In doing this, we are led to consider the hemilability of Fe–S bonds during catalysis (28–30). With this foundation, we are able to answer two of the key unresolved mechanistic questions: (i) what is the overall ther- modynamic driving force for the process by which ATP-coupled electron delivery (Eq. 1) leads to N2 reduction with loss of H2 at the E4 mechanistic stage; (ii) how does the enzyme mechanisti- cally prevent the even more favorable production of a second H2 without reduction of N2, namely, how is re of H2 mechanistically coupled to cleavage of the N≡N triple bond. Computational Methods Structural Models. The FeMo-co strongly interacts with the sur- rounding protein environment mostly via hydrogen bonding and electrostatic interactions. Therefore, any quantitative computa- Fig. 1. Structure of the FeMo-co binding pocket as obtained from MD tional investigation of its activity must include a realistic repre- simulations (22) (A) and schematic representation of FeMo-co (standard sentation of the enzymatic pocket. In particular, as shown in Fig. atom numbering) (B). For simplicity, only the polar H atoms are shown. The 1, in addition to the coordination bonds with ligands, Fe - color coding of atoms is as follows: rust, Fe; yellow, S; cyan, C; purple, Mo; 1 α-275Cys, Mo-α-442His ( numbering) (2), red, O; blue, N; light gray, H. Hydrogen bonds are shown as thin red sticks. R The cartoon representation of the protein in cyan color is reported with the and Mo- -homocitrate, FeMo-co engages several hydrogen

purpose to highlight the surrounding protein environment. The N2 access bonds with the protein backbone, side chains, and water mole- channel is indicated with the thick blue arrow. cules present in the enzymatic pocket, which are known to be abundant near the FeMo-co (31). Some of these interactions are not evident from a simple investigation of the available crys- However, they directly pose a number of fundamental questions tallographic structures, as they are a representation of the that are addressed computationally in this report. First, we ad- most populated configuration at the temperature at which “ ” E dress the protonation isomers at the 4 level of electron ac- they were solved (typically 100 K). At room temperature, a cumulation, in particular the disposition of the two [Fe–H–Fe] multitude of local minima very close in free energy are ac- moieties of the mechanistically central E4(4H) intermediate. This cessible, and this conformational complexity finely tunes contentious question has not been resolved experimentally, and chemical reactivity. its computational examination has required us to carry out a In the present work, we use a structural model of nitrogenase critical evaluation of the computational methodology required to based on submicrosecond force-field–based molecular dynamics study the nitrogenase catalytic mechanism. Computational stud- (MD) simulations (32). The model includes all of the residues ies of nitrogenase (10–22), mostly based on broken-symmetry interacting directly with FeMo-co both via specific H-bond in- (BS) density functional theory (DFT), have provided a wealth teractions and nonspecific electrostatic interactions (Fig. 1), of information about the electronic structure of the FeMo-co while the rest of the protein is described with a polarizable (resting) state E (14, 15). However, early work was con- continuum (33). Five different structural models of decreasing 0 SI Appendix strained by the uncertainty as to the existence/identity of the complexity were examined ( , Fig. S1). Model (a). The full model (a) includes the FeMo-co with truncated cofactor central atom, and the limited size of the structural Cys His – modifications of the α-275 , α-442 ligands (Azotobacter models adopted (10 13, 16, 18). Recently, computational inves- vinelandii R tigations have begun to use larger structural models of the cat- numbering), -homocitrate, and all of the MoFe alytic pocket (20, 21, 23–27). However, these included studies protein residues and water molecules that engage hydrogen- bonding interactions with the FeMo-co, or are known to be addressing the structure of E (4H) that advanced novel mecha- 4 important of the catalytic activity (α-70Val and α-96Arg). , nistic proposals that are difficult to reconcile with the chemical , arginine, valine, and R-homocitrate residues were expectations and experimental evidence. Notably, work by Siegbahn (20, 23), Rao et al. (21), and McKee (22) suggested the pro- tonation of the FeMo-co central atom during catalysis, while Siegbahn (20, 23) even proposed a Fe-bound methyl in- N2 H2 termediate as the central E4 catalytic species. Very recently, re Einsle and coworkers (28) were able to solve the structure of the 2N2H as-isolated VFe protein and observed replacement of the S2B oa N2 H2 sulfide that bridges Fe2–Fe6. This led them to propose the two E – hydrides of 4(4H) state bridge the Fe2 Fe6 center, and that this E (4H) E (2N2H) is the state that reductively eliminates H2, leaving a vacant binding site for N2. This proposal likewise needs computational Fig. 2. Schematic of the reductive-elimination (re)/oxidative-addition (oa)

assessment. mechanism. 2N2H indicates a diazene-level N2 reduction product.

2of10 | www.pnas.org/cgi/doi/10.1073/pnas.1810211115 Raugei et al. Downloaded by guest on September 27, 2021 modeled as methylthiolate, imidazole (or 4-methyl-imidazole), that both pure generalized gradient approximation (GGA) and methylguanidinium, and tert-butyl and dimethyl glycolate, re- hybrid functionals consistently reproduce Noodleman’s results. spectively. Recent reports highlighted that the protonation state Recent large-scale calculations carried out by Bjornsson and of the homocitrate may influence the electronic properties of coworkers (26, 27) corroborated these early studies. We note FeMo-co (24, 25). In the present study, homocitrate was con- that, although BS-DFT is effective in resolving the questions of sidered fully deprotonated. Arginines were considered pro- nitrogenase function addressed here, the approximate nature of tonated, whereas the effect of both neutral (δ- and e-form) and the adopted functionals, coupled with the single determinant protonated forms of α-442His was explored. The backbone of framework of the theory, is unable to capture finer quantitative α-356Gly, α-357Gly, 358Leu, and α-359Arg, which interacts with details associated with the complex transformations at the FeMo-co, FeMo-co via N–H hydrogen bonds, was modeled as a methyl- as noted below. Ser ammine terminated triglycine. α-278 forms hydrogen bonds For each En, there are various possible patterns that maximize with FeMo-co with both the side chain and the backbone N–H, the antiferromagnetic coupling, which are in the absence of the and it was included in full as C-methylated serine. The steric potential due to the protein environment equienergetic. The Val confinement exerted by the protein matrix on α-70 and asymmetry of the protein environment breaks the degeneracy of Arg α-96 was included by adding one ethane molecule next to these spin patterns. As shown in SI Appendix,Fig.S2,theenergy Val Gly α-70 at the location of the backbone C atoms of α-66 , the difference between patterns can be as high as 23 kJ/mol for E . Similar α Asn α Val α gly 0 side chain of -98 , the backbone of -70 and -69 , and a differences are found for the other En states investigated. In the fol- SI Appendix A bridging water molecule ( , Fig. S1 ). It is important lowing, for each En, the lowest energy spin pattern was adopted. to point out that it is crucial to include the residues around The present DFT calculations explored seven exchange and Val Arg α-70 and α-96 to avoid unrealistic, large conformational correlation functionals: BP86, BLYP, PBE, B3LYP, PBE0, M06, reorganization of residues as observed in other reports (20, 23). and M06-2X, primarily focusing on the GGA BP86 (34–36) The C atoms of the ethane molecule were kept fixed at their functional and the hybrid B3LYP functional (37–39). However, a equilibrium distance. The atoms at the locations where the resi- result discussed without explicit mention of functional is derived dues were truncated were also fixed during the geometry opti- with BP86 for reasons discussed in SI Appendix, section S3. The SI Appendix mizations. The list of the frozen atoms is provided in , Ahlrichs VTZ basis set was used for all Fe atoms (40), the Los section S7. Alamos National Laboratory basis set LANL2TZ with an ef- Starting from the full model (a), we generated four additional fective core potential was employed for the Mo atom (41), and CHEMISTRY models by progressively deleting residues, as follows. the 6-311++G** basis set was employed for all atoms coordinated Model (b). Model (b) deletes all water molecules interacting with SI Appendix B to metal atoms, including protic and hydridic hydrogen atoms FeMo-co ( , Fig. S1 ). and all of the atoms with which they interact via a covalent c α Gly Model (c). Model ( ) further deletes the backbone of -356 , bond or a hydrogen bond, and finally the 6-31G* basis set (42) α-357Gly, 358Leu, and α-359Arg (SI Appendix, Fig. S1C). d was adopted for all other atoms. All calculations were per- Model (d). Model ( ) additionally omits the side chain and the formed with the NWChem quantum chemistry package (43). backbone N–Hofα-278Ser (SI Appendix, Fig. S1D). Val Arg Oxidation state. Various different oxidation states for Fe centers of Model (e). Model (e) further removes the residues α-70 , α-96 , E S = α Arg the FeMo-co in the 0 ( 3/2) have been proposed over the BIOPHYSICS AND and -359 , yielding a minimal model that includes only FeMo-co years. There is now general consensus (27, 44) that the proper α Cys α His R SI COMPUTATIONAL BIOLOGY and its ligands -275 , -442 ,andMo- -homocitrate ( E 3+ 2+ 3+ Appendix E oxidation state of 0 is [Mo 3Fe 4Fe ]. The majority of the ,Fig.S1 ). calculations presented in this work were performed on E in this The initial position of atoms was obtained from previous MD 0 oxidation state. However, for a better assessment of the general simulation studies (32). Specifically, we performed a clustering validity of our results, selected E and E species were also in- analysis of the MD trajectory to find groups of similar frames, 0 4 vestigated for an electron counting corresponding to the more and then adopted the frame closest to the center of the largest + + + oxidized E (S = 3/2) state, [Mo3 1Fe2 6Fe3 ]. The current group (representing about the 80% of the configurational space 0 consensus is that FeMo-co in E has a low-spin Mo(III) (27, 44), of the residues included in the quantum-mechanical model). The 0 consistent with ENDOR measurements that show small hyper- representative MD configuration we adopted for the present fine couplings to 95Mo (27). In all of our calculations on E ,Mo study contains the same number of water molecules present in 0 has a very low spin density, regardless of the exchange and the starting Protein Data Bank (PDB) structure (2). The validity correlation functional that is adopted (as described directly be- of the adopted structural model is discussed in detail below. We SI Appendix E will show that it is imperative to include all of the residues low) ( , Tables S2 and S3). In 4, we again find a Mo interacting with FeMo-co, that is, model (a), to obtain mean- (III) oxidation state, but the metal ion can assume low- or high- ingful mechanistic predictions. In particular, the protein cage spin configurations depending on the location of the hydrogen helps stabilize the FeMo-co and avoid artifacts such as those atoms and the functional employed, with GGA functionals (e.g., reported in recent investigations, where the protonation of the BP86) preferentially yielding low spin configurations (low spin densities) and hybrid functionals (e.g., B3LYP) favoring high central carbide up to CH3 (20, 23), with consequent disruption of SI Appendix – the cofactor, was found very favorable and erroneously proposed spin states (higher spin densities; ,TablesS4 S11). 95 E 95 to be a key catalytic step. Mo ENDOR experiments on 4(4H) have shown small Mo couplings in E4, little changed from the Mo hyperfine coupling Electronic Structure Calculations. in E0, which not only implies the persistence of the Mo(III) BS-DFT. It is commonly accepted that BS-DFT calculations rep- oxidation state, but also suggests that the low spin state persists resent a good compromise between computational efficiency and as well (45, 46). In that sense, the ENDOR measurements support accuracy, and DFT has been widely applied to the study of the choice of the GGA functionals as being most appropriate FeMo-co. Noodleman and coworkers (14) reported an exhaus- for the present investigation. tive search for the lowest-energy electronic wavefunction of Spin states. Spectroscopic investigations have provided the spin – FeMo-co in the S = 3/2 E0 state for a minimal active-site model, state of various intermediates in the Lowe Thorneley kinetic which corresponds to model (e) described above, including only model, notably for this report, E0, E2, and both E4(4H) and E E FeMo-co and its ligands. It was shown that, as expected, the E0 4(2N2H). As recently established (47), not only 0 but also the (S = 3/2) state maximizes the antiferromagnetic coupling E2 intermediates have a total spin S = 3/2, while the two E4 between the Fe centers. Later, Harris and Szilagyi (16) showed intermediates have S = 1/2 (6). Therefore, calculations were

Raugei et al. PNAS Latest Articles | 3of10 Downloaded by guest on September 27, 2021 performed for the observed S = 3/2 spin state (E0 and E2)and equilibria between the lowest-energy E4 isomers, E4(4H), (b) (c) the two S = 1/2 (E4) states within the BS approach (16). Be- E4(4H) , E4(4H) ,andE4(2H;H2), using a simple line cause of the single-determinant nature of BS-DFT, what is searchbasedonconstrainedgeometry optimizations, whereby calculated are not the pure S = 3/2 or S = 1/2 spin states, but a given Fe/H distance is gradually varied between the limiting rather a mixed determinant with MS = 3/2 or MS = 1/2 compo- values assumed in two targeted E4 species. In a similar man- nents (27, 44). This is an important point that should be kept in ner, we studied the release of H2 from E4(2H,H2)andE4(2H, mind, as the energies of the proper pure spin states can be quite H2;N2) by a stepwise increase of the distance between Fe2 and different from the BS-DFT energies. Clearly, all of the many the center of mass of the H2 molecule. In all of the cases, for DFT studies reported in the literature suffer from the same each targeted distance, the position of all atoms was relaxed, problem. The energy of the pure spin states can be estimated except for the atoms at the truncation points, as discussed in using the Heisenberg spin ladder framework (14, 15, 48–50), Structural Models above. which might be problematic for the FeMo-co because of the large exchange coupling constants (14, 15). A few recent pio- Results neering studies point the way beyond DFT in addressing the We investigated five structural models of the nitrogenase active nitrogenase problem (51–53). Conclusions drawn below are site [models (a)to(e)], with the extent of incorporating inter- tempered by this recognition. For a more straightforward actions with the protein environment pictured in Fig. 1 in- comparison between computation and experiment, we will still creasing in the order, model (e) → model (a), using a variety of refer to the S = 3/2 and S = 1/2 state for E0 and E4, rather than DFT flavors, various protonation states of FeMo-co, as well as M = M = S 3/2 and S 1/2, respectively. different oxidation states for E0. The majority of the calculations Initial guesses were constructed according to the spin config- were performed starting from the electron count associated with SI Appendix 3+ 2+ 3+ urations of , Table S1 from atomic guesses corre- the “oxidized” Mo 3Fe 4Fe E0 (S = 3/2) oxidation state with 2+ S = 3+ S = 3+ S = His sponding to Fe ( 2), Fe ( 5/2), and Mo ( 3/2; α-195 doubly protonated. The latter choice was based on pKa different choices yielded similar results). Three BS solutions values estimates for the doubly protonated α-195His higher than His were shown to maximize the antiferromagnetic coupling be- 10. The pKa of α-195 was estimated from the free energy for His tween spins in the E0 (S = 3/2) state [see SI Appendix, Fig. S2, transferring either the e-orδ-proton for the protonated α-195 corresponding to the state BS7 proposed by Noodleman and to histidine in water, for which an accurate value of the pKa is coworkers (14)]; initial geometries were optimized for the anti- available. This calculation was performed using our largest ferromagnetic coupling with the lowest energy (16, 27). Then, for model. For completeness, selected structures were also analyzed E 3+ 2+ 3+ each n state and its isomers that are considered (see below), all for the more oxidized [Mo 1Fe 6Fe ] E0 (S = 3/2) state and of the 35 possible BS solutions were explored at both BP86 and for neutral α-195His. B3LYP level (SI Appendix, Table S1). There are eight magnetic The structure and the corresponding energetics of various 3+ 2+ 3+ centers in FeMo-co (1Mo , 3Fe , and 4Fe ). In the absence critical E4 protonation states were calculated at both BP86 and of an external magnetic field, we can set the spin of one of the B3LYP level of theory. We found that the two functionals pro- centers (for instance, Mo) arbitrarily either up or down, which vide a similar picture of the energy landscape of the E4 isomers; leaves a total of 7!/(4!·3!) = 35 possible spin up and spin down differences will also be discussed. Because BP86 predicts a low- combinations for both S = 1/2 and 3/2 total spin states, if we do spin Mo(III) state for both E and E , consistent with the + + 0 4 not distinguish the specific location of Fe2 and Fe3 centers. available ENDOR data and X-ray/computational studies (27, For a more detailed discussion, see ref. 27. Finally, the geometry 44), as well as for other reasons to be given below, the energies of the BS solutions within 20 kJ/mol from the lowest-energy discussed here refer to this functional unless noted; B3LYP solution was further optimized for E0, the first four lowest- energies are nonetheless given as appropriate. A detailed dis- energy E4 protomers, the protonated CH E4 isomer (see below), cussion on the performance of these and other functionals is and all of the diazene-level N2 reduction E4 states. presented in SI Appendix, section S3. Medium effects. The COSMO polarizable dielectric continuum Because of the large number of possible isomers, the energetic (33) was used to describe the protein environment not explicitly comparisons mostly included only the total electronic energy and considered in our structural models along with atomic radii continuum corrections for the protein environment, that is, according to ref. 54. A dielectric continuum should be always without including zero-point energy and vibrational corrections used with care, as the dielectric properties of a protein are ill to free energy, as their inclusion would have required compu- defined. Ideally, one could assume that the larger the adopted tationally very expensive vibrational frequency calculations for a structural model is, the smaller the dependence on the dielectric large number of structures. Rather, frequency calculations were constant of the continuum. In the present work, two dielectric performed only on the low-lying intermediates of mechanistic constants were examined, e = 4 and 10. As shown in SI Appendix, significance. the energy differences between E4 isomers calculated with our largest structural model show little dependence (smaller than Protonation States of E4. Previous computational studies on a 10 kJ/mol) on the choice of e, in contrast to what observed for simplified model of nitrogenase (19), which included only FeMo- the smaller models, where far larger variations are observed. This co and its ligands, revealed that μ2-S atoms are preferentially − + result suggests that the residues included in our largest model protonated over μ3-S atoms and that accumulation of [e /H ] indeed well describe the local environment of FeMo-co. All of the pairs starting from E0 proceeds by the alternate protonation of energies discussed in this paper are calculated for e = 4, as we μ2-S atoms and Fe atoms. Examination of a number of possible think this is more appropriate to describe the hydrophobic pro- protonation states for the extended model (a) confirmed these tein scaffold beyond the outer coordination sphere of FeMo-co. initial observations. The relative energetics and the structure of Free-energy corrections. Free-energy corrections were estimated all of the E4 states we analyzed is reported in SI Appendix, Fig. using harmonic vibrational frequencies after projecting out the S3, while the states relevant to the present discussion are listed in spurious imaginary frequencies associated with the frozen atomic Fig. 3. The computations here performed on model (a) indicate positions. that, among the three μ2-S atoms, protonation of S5A and S2B Exploration of possible pathways for interconversion of E4 isomers and H2 (located on the reactive face; Fig. 1) is more favorable than the release. The size of the working structural model [model (a)] protonation of S3A, which is located in a protein matrix cleft and precluded a full transition state search based on vibrational receives hydrogen bonds from the protein backbone (Fig. 1). frequencies. We estimated the energetic barrier associated with There are three low-lying E4 states that differ by the location of

4of10 | www.pnas.org/cgi/doi/10.1073/pnas.1810211115 Raugei et al. Downloaded by guest on September 27, 2021 one hydride (Fig. 3). Consistent with low-temperature ENDOR decreases considerably but still remains far above E4(4H) (ΔE = results (6, 7), and in keeping with previous exploratory calcula- +81.6 kJ/mol). Also for this isomer, addition of dispersion cor- tions (9), the lowest-energy state has two hydrides asymmetrically rections (55–57) has only a small effect. For example, the BP86- – – bridging Fe2 Fe6 and Fe3 Fe7, and two protonated sulfur atoms D3 energy relative to E4(4H) is +106.6 kJ/mol. This finding is in (S5A and S2B). We will refer to this state as E4(4H). contrast to recent reports by Siegbahn (20, 23), Rao et al. (21), E (b) ΔE = The next state, indicated as 4(4H) ,liesonly 4.8 kJ/mol and McKee (22) that E4(3H;CH) is lower in energy than E4(4H) higher then E4(4H), and differs from it in that the Fe2–H–Fe6 (20–23). Frequency calculations on the first four low-energy E (b) (b) (c) bridging hydride has migrated to Fe2 in 4(4H) , with Fe6 thus states E4(4H), E4(4H) , E4(4H) ,andE4(2H;H2) allowed esti- binding a terminal hydride and acting as one terminus of the hy- mation of free energies, and confirmed the relative ordering dis- ΔE = (b) (c) dride bridge. Next higher in energy ( 10.5 kJ/mol) is a cussed above, and locate E4(4H) , E4(4H) ,andE4(2H;H2)at E (c) – dihydride species 4(4H) with both hydrides bridging the Fe2 ΔG = 4.1, 13.6, and 8.8 kJ/mol above the E4(4H) baseline, re- Fe6 centers, similar to the E4 intermediate recently proposed by spectively, as shown in Fig. 3. Einsle for the FeV-cofactor in the vanadium nitrogenase (28). Geometry optimizations of these states with neutral, rather Slightly higher in energy still (ΔE = 16.3 kJ/mol) we found a than protonated, α-195His provide similar qualitative ordering, E (b) dihydrogen intermediate 4(2H;H2) with a strongly activated but with E4(4H) , and E4(2H;H2) located only at ΔE = 4.1 and d – = (b) dihydrogen moiety [ (H H) 1.00 Å, vs. 0.7 Å for the isolated 8.3 kJ/mol from E4(4H). Finally, analysis of E4(4H), E4(4H) , molecule] located on Fe2. E4(2H;H2), and E4(3H,CH) based on the assumption that the E As schematically depicted in Fig. 3, the 4 isomers containing resting-state E0 (S = 3/2) exhibits an electron count corre- 3+ 2+ 3+ two hydrides bound in some way to the Fe2 have the Fe2–S2B sponding to the oxidation state [Mo 1Fe 6Fe ] provided a E (c) – (b) bond broken or partially broken. In addition, 4(4H) Fe2 Fe6 similar energy ordering with E4(4H) , E4(2H;H2) at only ΔE = – dibridged dihydride has a very elongated Fe6 S2B bond [2.72 Å 5.7 and 7.1 kJ/mol above E4(4H), while E4(3H,CH) is more than E E (b) vs. 2.32 and 2.48 Å in 4(4H) and 4(4H) , respectively]. In the ΔE = 140 kJ/mol above E4(4H). next section, we will comment on the possible role of the hemilabile Taken altogether, our computations show that likely there are at – Fe S bond(s) in the activity of nitrogenase. Addition of disper- least four low-lying E4 isomers in equilibrium with each other. sion corrections (55–57) has only a minimal effect on this ladder Although the energy difference between them is small and well of states. For instance, the relative BP86-D3 (56, 57) energies of the within typical DFT errors, the finding that the state with the lowest

E CHEMISTRY four low-energy 4 states are 0, 12.2, 14.3, and 20.7 kJ/mol. At energy has two [Fe–H–Fe] bridging hydrides, E4(4H), is consistent (c) B3LYP level of theory, only E4(4H), E4(4H) ,andE4(2H;H2) were with the conclusion from low-temperature ENDOR measurements E (b) identified as lowest-energy isomers. Instead, 4(4H) was found (6), while the characterization of a low-lying H2 complex, E4(2H; to be unstable. Indeed, geometry optimizations started from the H2), possibly involved during reductive elimination of the hy- E (b) E 4(4H) BP86 structure yielded either the 4(2H;H2)state,which drides of E4(4H), is consistent with recent photophysical studies + E E (c) is located at 27.5 kJ/mol above 4(4H), or the 4(4H) ,whichis showing that re of H2 involves such a complex (8, 9). nearly degenerate with the E4(4H) being located at only 2.8 kJ/mol above it. A simple line search for a possible pathway connecting Role of the FeMo-Co Environment. The major improvement in the

these states carried out at the BP86 level of DFT indicates that the present computations compared with other recent mechanistic BIOPHYSICS AND studies (20–23) is that we incorporated the entire protein envelope migration of the hydride between Fe3 and Fe7 in the lowest-lying COMPUTATIONAL BIOLOGY (b) ‡ E4(4H) to Fe2 of E4(4H) (ΔE ∼ 29 kJ/mol), and of one of the around FeMo-co, including the full set of hydrogen-bonding inter- (b) (b) two hydrogens between Fe2 and Fe6 in E4(4H) to Fe2 in E4(4H) actions from both protein residues and water molecules (Fig. 1). ‡ [ΔE ∼ 14 kJ/mol relative to E4(4H)] is facile. To obtain a detailed understanding of the importance of the different In computations with the large model (a) of Fig. 1, we found interactions, we examined structural models (b) through (e)of that protonation of the central carbide, with the concomitant progressively decreasing complexity (Fig. 4). These unambiguously formation of a deformed E4(3H,CH) FeMo-co state (Fig. 4 and shows that the local environment around FeMo-co plays a cru- SI Appendix,Fig.S3), is extremely unfavorable (ΔE =+121.4 kJ/mol). cial role in stabilizing the cofactor and controlling the reaction Using hybrid functionals, such as B3LYP, the energy of E4(3H;CH) pathway.

Fig. 3. Relative free energy (black) and energy (red) of various E4 species potentially involved in FeMo-co reductive activation and the breaking of the N2 triple bond. Protic and hydridic hydrogens are indicated in green and red, respectively.

Raugei et al. PNAS Latest Articles | 5of10 Downloaded by guest on September 27, 2021 Fig. 4. Effect of the enzymatic environment around FeMo-co on the relative stability of the bridging hydride state E4(4H) and C-protonated state E4(3H,CH). (A) Models used in the present study, with the labels of the residues sequentially removed from the full model (a): highlighted in blue [model (b)], green [model (c)], red [model (d)], and black [model (e)], respectively (SI Appendix, Fig. S1). (B) Corresponding relative electronic energy (no polarizable continuum corrections applied) as obtained from DFT/BP86 and DFT/B3LYP level of theory (values in parentheses).

SI Appendix, Fig. S1 depicts the five levels of incorporating the portant stabilizing role on E4(4H). Although the progression of protein environment of FeMo-co adopted in the present work: Fig. 4 presents a clear trend in the energetics, which shows the (i) represents the full (largest) model employed in our study, open core to be irrelevant to function, quantitatively, even these which includes all residues enclosing FeMo-co (see Methods for results might not yet be at convergence. In all likelihood, more listing), and, in particular all of the residues interacting via H- extended models should be used to properly describe the highly bonding and electrostatic interactions (Fig. 1); (ii) eliminates the anisotropic protein environment beyond the second coordination water molecules interacting with FeMo-co; (iii) additionally sphere of the FeMo-co, as included in the present study. Indeed, eliminates the backbone of the residues H-bonded to the bottom of it has been shown for other systems, such as the photosystem II FeMo-co; (iv) also removes the side chain and the backbone N–H (58–60), that the field arising from the highly heterogeneous of α-278Ser, thus eliminating most of the H bonds to FeMo-co; protein scaffold finely tunes activity. and (v) shows a minimal model, which includes only the cofactor We note that Siegbahn’s original model (20) corresponded and its ligands. The models adopted by Siegbahn (20, 23) and roughly to our model (d), but in a recent communication (23), he Rao et al. (21) are similar to our models (c) and (d), in that they extended his initial structural model to match the size of our lack the majority of the H-bond cage around FeMo-co, while largest model, in response to some experimental data from our McKee’s model (22) is identical to our minimal model (e). In team suggesting an equilibrium involving a dihydrogen species particular, although Rao et al. (21) performed a multiscale [the E4(2H;H2) species discussed below] (9). The results with the quantum-chemical study that included the full protein scaffold, larger model repeated Siegbahn’s former observation of a fa- they still missed the majority of the active-site interactions, as vorable protonation of the central carbon. However, although they simply adopted one of the available X-ray structures and the size (number of atoms) of his expanded model (23) is com- neglected the presence of water, which is known to be present parable with ours, this new model is fundamentally identical to near the FeMo-co (31). Any realistic model must include hy- the original one (20) in that it does not incorporate crucial in- drogen bonding from water as well as the protein residues, and teractions with the protein residues and water molecules around most of the H-bonding network becomes apparent only after the FeMo-co core; the additional residues are only around the computationally relaxing the protein in its aqueous environ- homocitrate tail. Thus, our study demonstrates that it is only the ment at room temperature. The representative MD configu- failure to incorporate the protein envelope encapsulating FeMo- − + ration (32) we adopted in the present study contains the same co that results in an open FeMo-co core upon [e /H ] delivery, number of water molecules present in the starting PDB struc- and that inappropriately appears to make protonation of the ture (2). However, in our model, FeMo-co has been evolved central carbon atom thermodynamically favorable. according to MD simulations during which hydrogen bonds However, what is the actual role of the protein environment? form the water molecules and protein residues; the most rep- To what degree are the H-bonding interactions energetically resentative configuration has been chosen for the calculation as stabilizing the core of the reduced FeMo-co, and to what degree described in Computational Methods. does the protein confining cage stabilize its geometry? To better As shown in Fig. 4, with the resulting full model (a), the characterize which effect dominates, for each of the models (a) native-like FeMo-co core of E4(4H) is about 98 kJ/mol (BP86) or to (d), we removed all of the protein residues and water mole- 62 kJ/mol (B3LYP) more stable than the (deformed) C-protonated cules and recalculated the energies without relaxing the geom- − + E4(3H,CH) core at this level of [e /H ] accumulation. The pro- etries of FeMo-co (SI Appendix, Fig. S4). Indeed, using the gressive elimination of protein cage around the cofactor reverses geometry of FeMo-co from models (a) and (b), we obtain that (el) the order; elimination of the five water molecules present on one of E4(4H) is still more stable than E4(3H;CH) by ΔE = 105.8 and the FeMo-co sides lowers the gaps between E4(4H) and E4(3H,CH) 89.8 kJ/mol (BP86), respectively (difference in the total energy to 75 kJ/mol (BP86) or 53 kJ/mol (B3LYP) in favor of E4(4H). without PCM corrections); in contrast, using the geometry of Removal of the backbone chain on the bottom of the cofactor in FeMo-co from model (c), which lacks the protein residues on model (c) (i.e., opposite to the FeMo-co Fe2,3,6,7 catalytic face) the bottom of the FeMo-co, we obtain the reverse result with (el) makes E4(3H,CH)morestablethanE4(4H) by 35 kJ/mol (BP86). E4(3H;CH), now more stable than E4(4H) by ΔE = 63.3 kJ/mol. Ser Elimination of α-278 (which engages H bonds with FeMo-co In model (d), the stability of FeMo-co from model E4(3H;CH) trough the side-chain OH and the backbone NH) in model (d) relative to that of E4(4H) increases to 151.9 kJ/mol, a value that is brings the energy gap to 119 kJ/mol (BP86) or 89 kJ/mol (B3LYP) close to the value obtained directly with model (e), with FeMo-co (el) in favor of the E4(3H,CH); the situation is even more extreme of E4(3H;CH) more stable than that of E4(4H) by ΔE = with the minimal model (e), where the open core is over 120 kJ 132.4 kJ/mol. Regarding the FeMo-co geometry itself, going more stable at both BP86 and B3LYP levels of theory. From from model (a) to model (e), a contraction of the majority of thetrendoftherelativestabilityofE4(4H) to E4(3H;CH), it is the Fe–S distances is observed for E4(4H) (up to 4% for the evident that all of the residues at the active site play an im- Fe1–S1A and Fe7–S4B),whileanexpansionofmostoftheFe–S

6of10 | www.pnas.org/cgi/doi/10.1073/pnas.1810211115 Raugei et al. Downloaded by guest on September 27, 2021 distances is observed for E4(3H;CH)(upto3%forFe3–S5A What differentiates the behavior of S5B and S2B in E4(4H) is and Fe6–S1B). likely to be in some part the presence of the H bond to S2B from His Remarkably, the change in the difference in energies between 195 ; in the low-lying states with broken Fe–S2B bond, rear- E E FeMo-co in the 4(4H) and 4(3H;CH) states with the model rangement of the bridging hydrides makes S2B unique. We hy- occurs almost exclusively through changes in the energy of pothesize that, as proposed for some H2-producing catalytic systems E E 4(3H;CH); the energy of 4(4H) is rather insensitive to the size (29, 30), the hemilability of the Fe–S2B bond is important to creating of the model, varying by less than 20 kJ/mol passing from model an efficient H2 re pathway with the concomitant binding of N2 a e ( ) to model ( ). This can be clearly appreciated from the data in which Fe2 first binds both hydrides, and then forms H2.We reported in SI Appendix, Fig. S4, where the energy of FeMo-co in conclude, anticipating the results presented in the next sec- E E the 4(4H) and 4(3H,CH) states as obtained from the five tion, that upon release of H2 and binding of N2,theFe2–S2B models studied here are compared with that of FeMo-co in the bond is restored. The reversible breaking of this Fe–S bond E0. These results indicate that the protein envelope is (as might further demonstrates its hemilabile nature. To the best of our have been expected) complementary to the geometry of the knowledge, this behavior of the Fe–S bond in nitrogenase has closed-core FeMo-co observed in the resting state, and that the been proposed previously only by Einsle and coworkers (28). protein scaffold enforces this geometry upon FeMo-co all along the catalytic cycle, quite likely with the benefit that it prevents Thermodynamics of N2 Activation. It is possible to achieve a pro- the enzyme from destroying its active-site cluster through carbide found understanding of the thermodynamic necessity of coupling re ≡ protonation to form CH4. Our analysis indicates that all of the H2 formation via to cleavage of the N N triple bond by looking protein envelope around of FeMo-co is responsible for the sta- at the overall process for the formation of any of the diazene-level E E E E bilization of E4(4H) over E4(3H;CH), but with a more prominent intermediates [ 4(2H;N2), 4(H;N2H), or 4(NHNH)] from 0. role of the residues on the bottom, which appear to structurally Focusing just on the formation of E4(NHNH), as displayed in Fig. 5, confine the cofactor, preventing the decomposition upon re- the overall process is exergonic by ΔGE4 = −103 kJ/mol at pH 7 (a duction seen in the computations that do not include them (20, detailed discussion on how this value was calculated is presented in 23). Further details of the role of the protein environment in SI Appendix,sectionS5). What makes this process so favorable can stabilizing the cofactor and determining the actual mechanism of be understood by decomposing it into the two parts shown in Fig. 5: + N reduction are presented in SI Appendix. (i) the endergonic formation of E4(NHNH) from E0,N2,2H ,and 2 −

2e , the latter provided by the Fe protein and the hydrolysis of four CHEMISTRY – Fe S Bond Hemilability. We analyzed the structures of all four ATPs, with ΔGDZ =+67 kJ/mol; and (ii) the exergonic formation E E E (b) + − lowest-energy 4 electron-accumulation isomers, 4(4H), 4(4H) , of H2 from 2H ,and2e , again provided by the Fe protein with E (c) E 4(4H) ,and 4(2H;H2), which are very close in energy, and in ATP hydrolysis, with ΔGH2 = −170 kJ/mol. Thus, although direct SI Ap- addition the structure of E4(3H;CH). As can be seen from formation of E4(NHNH) without generation of H2 is thermo- pendix E ,TableS13, all of the bond distances for FeMo-co in the 4 dynamically unfavorable, nitrogenase couples this unfavorable E states are similar to those in 0, with two notable exceptions. The reaction of N2 with a highly favorable one, generation of H2, – – first one is the expected marked elongation in Fe3 CandFe7 C resulting in an overall exergonic process to drive N2 fixation. E distances in the extremely high-energy 4(3H;CH) species (1.6 and Following Bucket and Thauer (61), this process may therefore BIOPHYSICS AND 1.3 Å relative to E0, respectively) as a consequence of the disruption “ ”

be viewed as cluster-based electron bifurcation, in which two COMPUTATIONAL BIOLOGY of FeMo-co upon protonation of the central carbon. In contrast, for hydride electron pairs split, with an exergonic reaction involving all of the species that are potentially energetically accessible and one pair (H2 formation) driving an endergonic reaction involving – mechanistically important, the Fe C bond lengths change by less the other (N2 triple-bond cleavage). than 0.1 Å relative to E0. In short, in energetically accessible states, the Fe–C bonds are maintained. N2 Activation by Reductive Elimination. MD simulations (32) showed The second exception is the Fe2–S2B bond for some isomers that access of small substrates to the active site is very facile and with protonated S2BH. Generally, we observe that protonation of suggested that N2 and H2 are always present in the catalytic Val His an S atom bound to two metal ions causes a maximum increase pocket near the Fe2–Fe6 edge confined by α-70 and α-195 . – – of the Fe S bonds of 0.1 0.2 Å, while protonation of an S atom Guided by these simulations, possible N2 binding sites were ex- (b) (c) bound to three metal ions causes a maximum lengthening of the plored for the four low-lying E4(4H), E4(4H) , E4(4H) , and – E Fe S bond up to 0.4 Å. In keeping with this behavior, in 4(4H) E4(2H;H2) isomers, using the BP86 functional. First, geometry where Fe3/Fe7 is bridged both one of the two bridging hydrides and by the protonated S5B, the Fe3–S5B bond elongates by 0.2 Å and the bond to Fe7 by less than 0.1 Å. The second hydride of E4(4H) bridges Fe2/Fe6, as does the protonated S2B. However, in contrast, the Fe2–S2B bond in E4(4H) elongates by almost 0.4 Å. (b) This bond is actually broken in the low-energy isomers E4(4H) , (c) E4(4H) , and E4(2H;H2), with the Fe2–S2B distance increased by about 1.6 Å in these cases. Higher-energy isomers again are characterized by an increase of the Fe2–S2BH bond distance, in line with the other Fe–S bonds of S bound to two metal ions. In (c) the double-bridged Fe2/Fe6 dihydride E4(4H) , also the Fe6–S2B distance considerably elongates, being about 0.40 Å longer than (c) in E4(4H). The behavior of the Fe6–S2B in E4(4H) is even more dramatic at the B3LYP level of theory, whereby the Fe6–S2BH bond further elongates and, when 195His doubly protonated, the S2BH deprotonates and H2S is formed upon proton transfer from His Fig. 5. The energetics of formation of E4(NHNH) from the enzymatic reac- 195 , which remains coordinated to Fe6. Release of S2B (as − tants and its decomposition into two individual two-electron, two-proton HS ) via the formation of a doubly bridged Fe2/Fe6 dihydride, processes, each involving the hydrolysis of 2ATP: N binding and formation E (c) 2 similar to 4(4H) , has been recently proposed to be central for of E4(NHNH); release of H2 formed by re from E4(4H). These are coupled N2 activation in vanadium nitrogenase (28). through displacement by N2 of the H2 formed by re.

Raugei et al. PNAS Latest Articles | 7of10 Downloaded by guest on September 27, 2021 optimizations were performed constraining the N2 molecule to available for binding and activating N2, explaining why only E stay at a Fe–N2 distance typical of metal–N2 molecular com- 4(2H; H2)isabletobindN2. plexes. Then the structures were relaxed without the constraint. The NBO analysis indicates that in this double adduct, the All attempts to find a stable N2-bound state to either E4(4H), two remaining reducing equivalents are distributed within the (b) (c) E4(4H) ,orE4(4H) failed. In contrast, E4(2H;H2), resulting FeMo-co core, primarily on the Fe; the Mo valency does not from the reductive formation of H2, with retention of the H2 change. The N2 moiety receives a fraction of the reducing equiva- π bound to the doubly reduced FeMo-co core, reacts with N to lents via -acceptor (FeMo-co-to-N2) interactions: N2 assumes an 2 − e form a asymmetrically bridged, end-on Fe2–(N2)–Fe6 adduct, overall net negative charge of 0.29 , nearly equally distributed E (2H;H ;μ-N ), reminiscent of the side-on, end-on N bridging between the two N atoms. Extension of the NBO analysis to the 4 2 2 2 – E mode reported for a few classes of complexes (62, 63). The end-on Fe2 (N2)moiety(62)of 4(2H;N2) reveals that the bond – σ E (2H;H ;μ-N ) state is ΔG = 29.2 kJ/mol above E (4H) (Fe – between Fe2 (N2) is characterized by negligible -donor interac- 4 2 2 4 2 π NandFe–N distances of 1.87 and 2.07 Å, respectively) (Fig. tions (N2-to-FeMo-co) and large -acceptor (FeMo-coto-N2)in- 6 σ 3). Upon formation of E (2H;H ;μ-N ), the H becomes less teractions. Thus, according to the NBO formulation, the -charge 4 2 2 2 e activated, with the H–H distance shortening from 1.00 Å in transferred from N2 to FeMo-co is about 0.01 , while the charge π e E (2H;H ) to 0.84 Å and a concomitant reduction of the Fe – backtransferred to N2 because of -acceptor effects is 0.29 ,which 4 2 2 − e S bond of 0.2 Å. Release of H from E (2H;H ;μ-N ), yielding results in a large net fractional negative charge on N2 ( 0.41 2B 2 4 2 2 – the E (2H;N ) state with N bound end-on to Fe and resto- according to NBO atomic charge partitioning). The N N bond 4 2 2 2 E d – = ration of the Fe –S bond, is thermodynamically favorable distance in 4(2H;N2)is (N N) 1.14 Å, only 0.04 Å longer than 2 2B SI Appendix (ΔG = −33.7 kJ/mol; Fig. 3). in the free molecule ( ,Fig.S6). This contrasts with the The energy barrier for H release from both E (2H;H ) and bond elongation observed in typical metal dinitrogen complexes, 2 4 2 where N–N is considered “strongly” activated at d(N–N) > E4(2H;H2;μ-N2) was estimated using the line search approach discussed in Methods. A monotonic increase of energy was 1.20 Å (66). However, in contrast to the majority of the model E dinitrogen complexes, protonation of the distal N atom in obtained when exploring elimination of H2 from 4(2H;H2) with E the search carried out until the energy had increased by over 4(2H;N2) is thermodynamically accessible, being endergonic 50 kJ/mol, increasing the Fe –H distance from its equilibrium by 24.2 kJ/mol, while no protonation of the proximal N atom 2 was found. We do not discuss the protonation mechanism of value of about 1.5 to 3.5 Å. This is a consequence of the high E N2, which is the subject of an ongoing investigation. However, energy of the 4(2H)* FeMo-co state, with its doubly reduced Fe our analysis suggests that the first proton most likely is delivered core produced by H2 loss. In short, the H2-bound state, E4(2H; re E by the protonated S2B, which in turn is promptly reprotonated by H2), is readily formed by of the two hydrides of 4(4H), but α-195His, the first of two instances in this investigation where this it does not release that H2. In contrast, a barrier of only about residue acts as a proton “buffer” (see below). We remark that E μ 28 kJ/mol was estimated for H2 release from 4(2H;H2; -N2) histidine is often used to rapidly shuttle protons in enzymes, a when using the same constrained optimization approach, with an prototypical example being carbonic anhydrase (67). estimated Fe –H distance at the transition state of 2.1 Å (SI 2 2 Upon N2 protonation, the N–N distance increases to 1.27 Å Appendix,Fig.S5). Although at this point the computations do not and the N2H moves from Fe2 to a bridging position between Fe2 definitively discriminate between a concerted and stepwise pro- and Fe (SI Appendix, Fig. S6). The second protonation of N is E μ 6 2 cess, the striking difference observed between 4(2H;H2; -N2) exergonic by ΔG = −12.4 kJ/mol, with the resulting transdiazene- E 2 and 4(2H;H2) offers an explanation for the experimental report bound intermediate E (η -NHNH) + H located at ΔG = re 4 2 of an H2 complex as an intermediate in ,withH2 lost only upon +1.4 kJ/mol from E4(4H) + N2. The diazene moiety asymmet- N2 binding. The computations also explain the implication drawn rically binds side-on between Fe2 and Fe6 with Fe2–N1,Fe2–N2, from HD formation during turnover under N2 and D2,thatH2 is and Fe6–N2 distances of about 1.92, 1.88, and 1.96 Å. Re- released only concomitant with binding of N2 (4,8,9). markably, the N–N distance (1.39 Å) is considerably longer than The pictorial representation of all of the states discussed the distance in the isolated transdiazene molecule (1.25 Å) cal- here is shown in SI Appendix,Fig.S6, and an animation pro- culated at the same level of theory. vided as Movie S1 illustrates the proposed overall process of re On the basis of these purely thermodynamics considerations, of the hydrides to form H2, followed by the described reaction the present calculations suggest that formation of the dihydrogen with N2 leading to release of the H2. Although, as noted, the adduct E4(2H;H2), followed by N2 binding and loss of H2, leads data reported in Fig. 3 are obtained at BP86 level, the B3LYP to a diazene-level intermediate E4(2N2H) with an overall equilibrium functional provides a consistent picture (SI Appendix,Fig.S7). free energy consistent with the experimental free-energy change ΔG To understand the role of re, we further analyzed the bonding of approximately −8 kJ/mol (8). Thus, depending on which of the two E and the electron distribution in the various 4 species. Previous E4(2N2H) isomers is the equilibrium product of the re of H2 and analysis of the electronic properties of the E2(2H) state (19), binding of N2, the computations yield the following (Fig. 3): carried out within the natural bond orbital (NBO) framework (64, 65), indicated that the Fe–H can be described as polarized E4ð4HÞ + N2 ⇄ E4ð2N2HÞ + H2; − e covalent bonds, with charge buildup on the H atom of about 0.2 , ΔG = −4.5 kJ=mol or 1.4 kJ=mol. [2] as expected from the difference in electronegativity of the atoms E E (b) involved. The same is true for the 4(4H) and 4(4H) in- The former ΔG value refers to the formation of E (N ), the latter SI Appendix 4 2 termediates. Nonetheless, as shown in , Fig. S4, the to the formation of E (NHNH) (ΔG = −17.7 or 19.9 kJ/mol at – E E (b) 4 two Fe H bonds in 4(4H) and 4(4H) , whether involving B3LYP level; SI Appendix,Fig.S7); the relative free energy of these bridging or terminal hydrides, each can be viewed as two- two states is within the computational error. Regardless of this electron covalent bonds that together store the four re- minor uncertainty, the present result is very important, as it ducing equivalents. As also discussed in SI Appendix,Fig.S4, clearly supports and illuminates the experimentally proposed re upon formation and release of H2, two electrons are first mechanism by indicating that the formation of the diazene- stored in and then depart with the H2 molecule. This process level E4(2N2H) intermediates, in particular the diazene-bound in- leaves two reducing equivalents (i.e., electrons) on the FeMo- termediate E4(NHNH), is indeed essentially thermoneutral as co core, which is at the heart of the re mechanism (6, 7, 9): as reported (8) and becomes thermodynamically accessible through the H2 molecule forms, two reducing equivalents become the re/oa equilibrium process. This is a truly remarkable enzymatic

8of10 | www.pnas.org/cgi/doi/10.1073/pnas.1810211115 Raugei et al. Downloaded by guest on September 27, 2021 achievement, as the noncatalytic direct hydrogenation of N2 to revert to E4(4H) by oa of the H2; only after binding N2, form diazene is endergonic by more than 200 kJ/mol (68). forming E4(2H;H2;N2), does the enzyme release H2 and pro- An explanation for the stability of the FeMo-co diazene-bound ceed on to hydrogenated forms of N2. Indeed, any attempt to E intermediate 4(NHNH) is provided by the NBO analysis of this eliminate H2 directly from E4(2H;H2) failed. Instead, we SI Appendix state ( , Tables S14 and S15), which reveals that the found a low barrier for the release of H2 from E4(2H;N2;H2) ‡ diazene moiety interacts with FeMo-co via π(N=N) → d*(Fe2) (ΔE ∼ 28 kJ/mol). d* and (Fe6) charge donation, and that these strong bonding in- The thermodynamic analysis of N2 bond cleavage shows that, teractions considerably stabilize this highly energetic species. although direct formation of E4(NHNH) without generation of H2 Because of these strong interactions in the E4(NHNH) intermediate is thermodynamically unfavorable, nitrogenase couples this un- π – with the Fe2 and Fe6 centers, the character of the N N bond of favorable reaction of N2 with the highly favorable generation of – d the diazene is lost and replaced with Fe N bonds resulting from 3 H2, resulting in an overall exergonic process to drive cleavage of (Fe) [with a smaller extent of s(Fe)] and p(N) mixing. This enables the N≡N triple bond. However, thermodynamically, it is clearly far E the stepwise protonation of the N2 moiety to yield first 4(H; N2H) more favorable to simply generate two H by hydride protonation, E – – 2 and then 4(NHNH), during which the Fe2 NandFe3 Nin- returning the enzyme to E , than to generate only one H while – 0 2 teraction intensify and the Fe2 S2B bond breaks, with the sulfur carrying out the unfavorable N2 reduction. The key to catalytic α His picking up a proton from -195 . Upon removal of the N2Hor nitrogen fixation by nitrogenase thus is the mechanistic coupling E E NHNH fragments, the cluster returns to the 1(H) or 0 state, of the endergonic formation of E (2N2H) to the exergonic release – 4 respectively, the Fe2 S2B bond is restored, and the proton is of one H . That coupling of the two processes is captured in Fig. 5. α His 2 returned to -195 . We hypothesize that the hemilability of the The E4(4H) form(s) can undergo re of H2 to form E4(2H;H2), Fe–S bond is important for the overall catalytic efficiency: in ad- thereby capturing the free energy of H formation as reducing re – 2 dition to facilitating the of H2, it allows the formation of a Fe N power of this state’s doubly reduced FeMo-co. However, experi- bond and therefore helps stabilize the otherwise highly unstable ment shows this high-energy E4 state does not by itself release H2; N H and NHNH intermediates. The NBO analysis of all of the 2 if it did, D2 would react with the state produced, even in the ab- E (2N2H) states, quantifying the conclusions drawn above, is 4 sence of N2, contrary to observation (16). As the present com- summarized in SI Appendix, Tables S14 and S15. putations now show, it is the binding of N2 to the reductively activated H2 complex E4(2H;H2) state that mechanistically cou- Discussion and Conclusion re ples of H2 to N2 reduction: N2 binding induces the loss of H2 CHEMISTRY We have carried out an extensive BS DFT study of N activation 2 and leads to N2 reduction with formation of E4(NHNH) (Figs. 3 by nitrogenase. The analysis of structural models of the FeMo-co and 5). Although the exergonic production of H2 provides the environment with a wide range of complexity reveals that the thermodynamic driving force for the endergonic cleavage of the utilization of model (a), which incorporates the complete array N≡N triple bond, it is the mechanistic coupling of N2 binding with of direct interactions of FeMo-co with its surrounding protein the release H formed by re of the E (4H) bridging hydrides that is envelope, is required to give meaningful results, and to prevent 2 4 − + the true heart of the re mechanism of nitrogenase catalysis. disruption of FeMo-co that has accumulated 4[e /H ], through E the protonation of the central carbide. We find that this 4 state Supporting Information BIOPHYSICS AND exhibits a variety of low-lying isomers, with the lowest in energy Please see SI Appendix for a schematic representation of the structural

E – – COMPUTATIONAL BIOLOGY being 4(4H), which has two [Fe H Fe] bridging hydrides, as models adopted in the present study; relative energy of possible spin con-

observed in low-temperature ENDOR measurements (4) of the figuration for the E0 state; representation of relevant En states; relative single conformer captured when the enzyme is freeze-trapped energies of BS solutions and spin populations for E0 and selected E4 states as under turnover conditions. Because of the single determinant obtained at BP86 and B3LYP level of theory; statistical data on the devia- – – – nature of BS-DFT, these results provide only a qualitative idea tions from the crystal structure of Fe Fe, Fe C, and Fe S distances in the E0 state calculated using different exchange and correlation functionals; of the energy landscape of the possible E4 states. However, with this in mind, the results are suggestive that at ambient temper- structural data of the En states; benchmark of DFT exchange and correlation functionals; analysis of the protein environment and stability of FeMo-co; atures there may be a dynamic equilibrium among the four E4 isomers, E (4H), E (4H)(b), E (4H)(c), and E (2H;H ). We also natural bond orbitals analysis of selected E4 states; a discussion on the cal- 4 4 4 4 2 culation of the energetics reported in Fig. 5; and Cartesian coordinates of found that the re of H2 by E4(4H) to form the H2-bound complex ‡ the structures calculated in the present study. Please see Movie S1 for an E (2H;H ) has a low barrier (ΔE ∼ 22 kJ/mol). Although this 4 2 animation showing the mechanism for H2 re and N2 binding as inferred from value represents a coarse approximation to true activation en- the present study. ergy, it is consistent with the experimental evidence and suggests that, at room temperature, E4(4H) and E4(2H;H2) should be in ACKNOWLEDGMENTS. We are grateful to Dr. R. Morris Bullock and fast equilibrium (Fig. 3), illuminating the recent finding that an Dr. Michael T. Mock for stimulating discussions. We thank an anonymous reviewer for suggesting the analysis of the role of the protein environment H2 complex forms during re of the hydrides of E4(4H). Notably, re oa 2 on the structure of FeMo-co in the E4 state. This work was supported by the we found that the / equilibrium of Eq. , in which the loss of US Department of Energy (DOE), Office of Science, Basic Energy Sciences, H2 is coupled to N2 binding and the possible formation of a Division of Chemical Sciences, Geosciences, and Bio-Sciences Award diazene-level intermediate E4(2N2H), in particular to the dia- DE-AC05-76RL01830/FWP66476 (to S.R. and L.C.S.), by National Institutes of Health Award GM 111097 (to B.M.H.), and by National Science Foundation zene E4(NHNH) intermediate itself, is nearly equi-ergic, in close agreement with the recent direct measurement of this equi- Award MCB 1515981 (to B.M.H.). Computer resources were provided by the E re W. R. Wiley Environmental Molecular Sciences Laboratory, a DOE Office of librium (8). In this process, 4(4H) undergoes of H2 but Science User Facility located at Pacific Northwest National Laboratory and retains the H2 as the dihydrogen adduct E4(2H;H2), which can sponsored by DOE’s Office of Biological and Environmental Research.

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