Understanding non-reducible N₂ in the mechanism of Mo–nitrogenase

Abstract

In my proposed mechanism of Mo–nitrogenase there are two roles for separate N₂ molecules. One N₂ diffuses into the reaction zone between Fe2 and Fe6 where a strategic gallery of H atoms can capture N₂ to form the Fe-bound HNNH intermediate which is then progressively hydrogenated through intermediates containing HNNH₂, NH and NH₂ entities and then two NH₃ in sequence. The second N₂ can be parked in an N₂-pocket about 3.2 Å from Fe2 or bind end-on at the exo coordination site of Fe2. This second N₂ is outside the reaction zone, not exposed to H atom donors, and so is ‘non-reducible’. Here density functional calculations using a 485+ atom model describe the thermodynamics for non-reducible N₂ moving between the N₂-pocket and the exo-Fe2 position, for the resting state and 19 intermediates in the mechanism. The entropy component is estimated and included. The result is that for all intermediates with ligation by H or NH_x at the endo-Fe2 position the free energy for association of non-reducible N₂ at exo-Fe2 is negative. There remains some uncertainty about the status of exo-Fe2–N₂ during the step in which H₂ exchanges with the incoming reducible N₂, where at least two unbound molecules are present. At Fe2 it is evident that attainment of octahedral coordination stereochemistry dominates the binding thermodynamics for non-reducible N₂. Possibilities for experimental support of these computational conclusions are discussed.

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1. Introduction

Nitrogenase, the enzyme that has evolved as the natural source of nitrogen for the earth's biosphere,¹ catalyses the conversion of inert N₂ to NH₃ under ambient conditions which contrast strongly with the extreme conditions required for the Haber–Bosch industrial manufacture of ammonia.² How does the enzyme achieve a catalysis that chemists have failed to replicate?^3,4 Extensive experimental investigation involving reaction kinetics,^5,6 mutations of amino acids surrounding the active site,^7–21 vibrational and spin resonance spectroscopy,^22–30 crystal structures,^31,32 cryo-electron microscopy^4,33 and density functional simulations.^34–43 still leave many aspects of the chemical mechanism unresolved.

This is partly due to experimental difficulties in isolating and investigating intermediates under physiological turnover conditions, because unavoidable protons are a substrate of the enzyme and mixtures of transient intermediates occur.^32,44 Furthermore, the overall chemical reaction eqn (1) implies a mechanistic cycle with at least 27 steps: eight introductions of a proton, eight additions of an electron, N₂ binding, breaking the N–N bond, formation of six N–H bonds, two dissociations of NH₃ and formation of one H–H bond.

N₂ + 8e⁻ + 8H⁺ → 2NH₃ + H₂ (1)

The protein domain in which this chemistry occurs is shown in Fig. 1. The catalytically active site is the iron–molybdenum cofactor, FeMo-co, a CFe₇MoS₉ cluster with homocitrate and His442 coordination to Mo and Cys275 coordination at Fe1: throughout this paper amino acids are numbered according to crystal structure PDB 3U7Q of Mo–nitrogenase species Azotobacter vinelandii (Av). Mutagen-reactivity experiments show that the active domain of FeMo-co is the front face, Fe2–S2B–Fe6–S3B–Fe7 enclosed by Val70 and Arg96.^{8,10–12,17,19,45–49} There is a significant hydrogen bond between Nε of His195 and S2B. The four penultimate water molecules of the proton supply chain are shown, with hydrogen bonds to O3, O6 and O5 of homocitrate, and the final proton directed towards S3B. Protons are translocated along the complete chain (not shown) by a Grotthuss mechanism.⁵⁰

Fig. 1 Structure of the active site of Mo–nitrogenase, with FeMo-co at the centre. Significant surrounding amino acids (all in the α-domain) and water molecules are included, with labels for Av1 protein, crystal PDB 3U7Q. Homocitrate C atoms are dark green and hydrogen bonds are striped. The reaction zone is the Fe2–Fe6–Fe7 face, under the side chain of Val70 and bounded by the side chain of Arg96. The proposed N₂ entry pocket is between His195 and Ser278, approaching Fe2. The four penultimate water molecules of the proton supply chain are shown, with hydrogen bonds to O3, O6 and O5 of homocitrate, and with the final proton directed towards S3B.

Fig. 1 also marks the vicinity of the N₂-pocket. This is a position where N₂ can be parked ready to bind at exo-Fe2. As shown in Fig. 2 this pocket lies on a hydrophobic N₂ ingress channel intruding from the protein surface towards Fe2. Smith et al. explored this pathway with molecular dynamics simulations,⁵¹ and showed how it is gated at the protein surface by significant movements of residues His383, Tyr281 and Arg277, shaded blue on Fig. 2. The free energy change for passage of exogenous N₂ through this ingress channel was calculated as ca. +3 kcal mol⁻¹.⁵¹ Gee et al. studied the pathway taken by CO photolabilised from exo-Fe2–CO, including a ‘docking site’ about 5 Å from Fe2. This docking site for CO is close to the N₂-pocket.

Fig. 2 The putative N₂ ingress channel and N₂-pocket (blue enclosure) in structure PDB 3U7Q. The blue shaded residues, His383, Arg281 and Tyr277 are at the surface opening of the channel.⁵¹ Exogenous N₂ can enter this hydrophobic channel and park in the N₂-pocket located between the His196–His195 chain on one side and Ser278 on the other, and then move from the N₂-pocket to the exo coordination position of Fe2, indicated by the red enclosure.

1.1. Overall mechanism

Using density functional simulations with a 485+ atom model of the active domain, I have developed a chemical mechanism for the complete cycle that effects eqn (1). The sequence of intermediates and reaction steps is outlined in Scheme 1. In Panel A the green enclosure describes the preparative phase, accumulating H atoms on FeMo-co, and the yellow enclosure shows the formation of bound H₂, the H₂/N₂ exchange, and the capture of N₂ to form the intermediate with bound HNNH. This crucial step in which N₂ is activated has been described in detail.⁵² Panel B of Scheme 1 describes the subsequent steps in which the N–N bond is broken with concerted formation of NH₃ bound at Fe6, and subsequent dissociation of this first NH₃. Details of the reactions and intermediates in the Panel B part of the mechanism have also been published.⁵³ Panel C of Scheme 1 outlines the steps and intermediates involved in formation and dissociation of the second NH₃, and finally recovery of the resting state.

Scheme 1 The full cycle for my proposed chemical mechanism of nitrogenase, showing all major intermediates and reaction steps in minimal skeleton representation. At each stage the numbers of added electrons and protons are indicated by the red status boxes. The arrow clusters indicate the sequence of steps in which a proton is introduced from the proton supply chain^37,50 onto S3B, probably triggered by entry of an electron,⁶⁵ followed by reconfiguration of S3B–H and migration as H atoms across the cluster to sites on Fe atoms or to S2B.

Other authors have proposed different mechanisms for all or parts of the Mo–nitrogenase reaction.^{35,40,42,43,54–64} I have reviewed mechanisms proposed prior to 2020.³⁷ The reason for presenting my new full mechanism here will become evident in the following section, where the dual roles of N₂ in the mechanism are described, and the question investigated in the present paper is explained.

1.2. Dual roles of N₂

The N₂ entry pocket located between His195 and Ser278 is near the exo coordination position of Fe2, where end-on (η¹) coordination of N₂ is feasible.⁶⁶ The position of this exo-Fe2–N₂ entity is emphasised in red on Fig. 2. It is possible for a second N₂ molecule to enter along this ingress channel, then diffuse past exo-Fe2–N₂ and enter the reaction zone,^66,67 where, after exchanging with H₂ it is captured in the N₂ activation step⁵² (yellow enclosure of Scheme 1 Panel A). It is also possible that N₂ can approach FeMo-co along a different path described by Morrison et al. following investigations of the protein structure with the CAVER software. This alternate path passes near the sidechains of Tyr229, Val70, Met279, Ser278 and Cys275 and is discussed further in section 4.2.

At this point it is important to recognise that there is no experimental evidence for N₂ at the exo-Fe2 position in any of the multiple crystal structures of the resting protein. This raises a basic question, which is the subject of this paper. If exo-Fe2–N₂ is absent in the resting state, what is its participation in the many other intermediates and reaction steps? Reference to Scheme 1 shows exo-Fe2–N₂ marked as present in the central stages of the overall reaction. In this paper I report computational results on the thermodynamics of N₂ binding at exo-Fe2 and rationalise the occurrence of exo-Fe2–N₂ in the various intermediates of the cycle.

N₂ at exo-Fe2 is not entirely passive, because it can have a mechanistic role. The HD reaction of nitrogenase, D₂ + 2e⁻ + 2H⁺ → 2HD, occurs only in the presence of N₂.^68–70 There are many experimental data relating to the HD reaction: they are mechanistically informative and are summarised in ref. 71. A key datum is that the K_m(N₂) for HD formation and the K_m(N₂) for NH₃ production are different.⁷⁰ I have reported a computationally simulated detailed mechanism for the HD reaction, which accounts for all experimental data, and in which exo-Fe2–N₂ is the promoting N₂. To differentiate the two roles, N₂ that is reduced by nitrogenase to NH₃ was dubbed ‘reducible’ N₂, and N₂ that is not reduced but is required for the HD reaction was dubbed ‘promotional’ N₂.⁶⁷

Promotional N₂ coordinated at the exo-Fe2 position is located away from potential hydrogen atom donors, and hydrogenation of this N₂ is not feasible. There is a clear differentiation of ‘reducible’ N₂ that enters a strategically propitious gallery of H atoms in the reaction zone between Fe2 and Fe6,⁵² and exo-Fe2–N₂ which is awkwardly positioned for the formation of H–N bonds,⁶⁷ and is labeled ‘non-reducible’ N₂ in this paper.

The objective of the investigation reported below is to determine when non-reducible N₂ is present in the intermediates of Scheme 1. What are the thermodynamics and kinetics for movement of the N₂ molecule between a parked position in the N₂-pocket, or coordinated at exo-Fe2? This information is needed to justify correct models, with exo-Fe2–N₂ included or excluded, in calculations of the thermodynamics of each of the steps in the complete mechanism, Scheme 1.

2. Methodology

2.1. Model

The computed protein model is a 485+ atom extract from crystal PDB 3U7Q, including all relevant amino acids. This is my standard model for simulations of nitrogenase reactions and reactivity.^{37,39,52,53,66,71} This model includes nine of the ten active-site residues that are conserved across all analyzed extant nitrogenases:⁷² the exception Gly424 is outside the reaction zone. Details, and the rationale for inclusion of amino acids and truncation of uninvolved side chains, are provided in the ESI.† The coordinated alcoholate O7 atom of homocitrate is protonated and hydrogen bonded to O1. The standard constraining strategy with 28 distance constraints is described in the ESI.† At some stages in the mechanism the protein structure is expanded slightly in the reaction zone, as previously described and rationalised, and this is controlled via the distance constraints Cα(Val70)–C^c and Cα(Val70)–CZ(Arg96), here set to the values used in prior calculations of the intermediates and reaction steps.^52,53 At the H₂/N₂ exchange stage there are two unbound molecules, H₂ and reducible N₂, and therefore calculation of the exo-Fe2–N₂ binding trajectories required additional constraints for stability of the computational model: the coordinates of unbound H₂ and unbound reducible N₂ were fixed.

2.2. Electronic states

The electronic states of FeMo-co and its ligated forms are characterised by the spin densities on the Fe atoms, and the total spin S. There are multiple combinations of positive and negative spin densities on the Fe atoms, and I have previously presented a qualitative theory of relative stability, based on maximisation of antiferromagnetic interactions (opposite spin signs, weakly bonding) along the axial edges of the central Fe₆ prism of FeMo-co.⁶⁷ Intermediates with ligation at Fe2 and/or Fe6 usually have diminished Fe spin densities relative to Fe3, Fe4, Fe5, Fe7 and so the antiferromagnetic interactions involving Fe2 and Fe6 are less stabilising than the two other possibilities with oppositely signed spin pairs Fe3–Fe7 or Fe4–Fe5. These two favourable electronic states have negative spin densities on Fe3 and Fe5 (labelled ‘35’), or on Fe4 and Fe7 (‘47’). Diagrams explaining this argument are provided in ref. 67. The superior stability of the ‘35’ and ‘47’ electronic states is consistent with the findings and procedures of other authors,^{34,35,40–43,73–76} and these states were used in the present calculations, consistent with the spin and electronic states used for calculation of the reaction steps in the mechanism.

The DMol procedure for control of electronic states involves input of signs and starting magnitudes of atom spin densities, which are then able to adjust without constraint during scf convergence. This permits electronic states to change during an energy minimisation calculation, and all reaction trajectories were checked for such changes. Control of electronic states in the calculations reported here was via input spin populations for Fe1, Fe3, Fe4, Fe5 and Fe7.

2.3. DMol protocol

Density functional (DF) calculations use the DMol methodology of Delley,^77–82 using numerical DF solutions of free atoms for the basis sets. The basis set is DNP (double numerical plus polarisation). Details of this methodology and its advantages are contained in refs. 77 and 80. Highly accurate DFT solutions for the separated atoms limit are obtained. This methodology intrinsically provides reliable energies at long interatomic distances, and is capable of accurate descriptions of weak bonding and dispersion energies. The ability of the DMol methodology to incorporate long-range dispersion has been well demonstrated. Zhang et al. reported very good agreement between the experimental interatomic potential energy curves and the DMol/PBE calculated potential energy curves for the inert-gas pairs He₂ Ne₂ and HeNe, and excellent agreement for the HeAr and NeAr pairs relevant to the dispersion interactions in the nitrogenase intermediates.⁸³ Todorova and Delley used this DMol/DNP/PBE methodology to optimize the crystal structures of a comprehensive set over 40 molecular crystals in which dispersion and intermolecular interactions determine the crystal packing and crystal lattice parameters.⁸² This set of molecular crystals ranged over amino acids, aliphatic and aromatic hydrocarbons, ice, H₂S, S₈, C₆₀, and the inert gases Ne, Ar, Kr and Xe. The PBE functional overestimates lattice parameters by about 4%, while the PBE_sol functional yields lattice parameters with an average systematic error of less than 1%. The dispersion interactions in this variety of molecular crystals are very similar to those in proteins.

The calculations were all-electron, spin-unrestricted, with no imposed symmetry. The conductor-like screening model (COSMO)^84–86 was used with a dielectric constant of 5. Constraints on interatomic distances used the Lagrange Multiplier Algorithm. Output spin populations were calculated by the Mulliken method.⁸⁷

2.4. Validation

Assessment of the accuracy of the computational procedures is made through reference to experimental geometrical and thermochemical data. Thorhallsson et al. consider that agreement with the dimensions of the crystal structure is essential for gauging the quality of the computational protocols.³⁵Table 1 shows that the agreement between calculated and experimental lengths for C^c–Fe bonds and for Fe–S bonds in resting FeMo-co is 0.01 Å or better. Specific distances, tabulated in the ESI,† have an average deviation of 0.02 Å between calculated and experimental.

Table 1 Calculated distances (Å) for the resting state of FeMo-co, for unprotonated and protonated forms of His195, in comparison with the crystallographic distances (PDB 3U7Q). Basis set DNP, functional PBE, S = 3/2, electronic state 235

Distance	xtl 3U7Q	Calculated with His195 unprotonated	Calc–xtl	Calculated with Hs195 protonated	Calc–xtl
Mean Fe–Fe	2.627	2.636	0.009	2.636	0.009
Mean Fe–S	2.231	2.233	0.002	2.240	0.010
Mean Fe–Mo	2.694	2.710	0.016	2.716	0.022
Mean C^c–Fe	1.999	1.993	−0.006	1.995	−0.004

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The DMol/PBE method reproduces experimental enthalpy data on the binding of N₂. Relevant ΔH_exp/ΔH_calc comparisons from ref. 88 (kcal mol⁻¹) are: (a) exp 17.6, calc 20.0, 18.8; (b) exp ∼10, calc 10.2; (c) exp 22.8, calc 25.9. Other relevant assessments of DMol accuracy vs. experiment have examined the electron affinities of atoms and molecules,⁸⁹ the enthalpies of formation for small (<100 electrons) molecular and atomic species,⁹⁰ the structures of metal–sulfide clusters,⁹¹ photo-induced conversion of [Os(NH₃)₅(η¹-N₂)]²⁺ to [Os(NH₃)₅(η²-N₂)]²⁺ (i.e. end-on to side-on bonding of N₂),⁹² the geometry and vibrational frequencies of [(NH₃)₅Ru(pyrazine)Ru(NH₃)₅]^4+,5+,6+,⁹³ and protonation reactions involving hydrogen bonding.⁹⁴

2.5. Mapping the potential energy surface

My calculations of the reactivity and reactions of nitrogenase, and the development of mechanism, are based on the mapping of potential energy surfaces. The revealed energy minima, as possible intermediates, are assessed by mapping the potential energy ridge(s) between them, and locating transition states. This deploys a general procedure,^37,50,95,96 that works well for multidimensional potential energy surfaces as are common in the reactions of nitrogenase at the FeMo-co catalytic site. The procedure (detailed in the ESI†) automatically moves down a ridge between minima to obtain the transition state.

3. Results

The thermodynamics of N₂ binding end-on at the exo-Fe2 position were calculated for the resting state and 19 intermediates along the mechanism pathway. The computational procedure first determines the transition state (TS) for N₂ binding, and then follows the trajectories from the TS to the associated and dissociated structures. Geometry and energy can be determined precisely for the associated structure and the transition state, but the limit of the dissociation trajectory has some uncertainty. The dissociation trajectory towards the N₂-pocket is tracked by monitoring the Fe2–N distance as well as structural changes in the FeMo-co cluster. These include the Fe2–C^c distance which responds to the trans Fe2–N interaction, together with the coupled Fe6–C^c distance. An important parameter is the endo angle at Fe2 (angle S2B–Fe2–S2A, specifically identified on Fig. 1) which varies according to the contents (i.e. H, N₂H_x, NH_y) of the intermediate, and also can change substantially as N₂ moves into the N₂-pocket. When it reaches the pocket, N₂ starts to tumble at an Fe2–N distance ranging 3.1 to 3.3 Å. As a consequence of these variabilities, the energy of the dissociated state is less certain, and because it affects the calculated association energy and the calculated association barrier these two potential energies are quoted at 1 kcal mol⁻¹ precision. At the H₂/N₂ exchange stage of the mechanism there are two unbound molecules, H₂ and reducible N₂, in addition to non-reducible N₂, and therefore the calculation of trajectories required additional constraints in the computational model: the positions of H₂ and reducible N₂ were fixed.

Scheme 2 displays the calculated potential energies for the binding of N₂ from the N₂-pocket to exo-Fe2 coordination, colour coded as green when negative and blue when positive, together with the potential energy barrier for N₂ binding. The intermediates are sequenced according to the mechanism in Scheme 1, from the resting state, through 19 intermediates, and returning to the resting state. There are more than 19 intermediates in the complete mechanism, because each addition of an H atom involves several intermediates as H migrates from S3B to a target position on the active face, or to an N atom. However it became evident that it was not necessary to calculate the exo-Fe–N₂ association thermodynamics for all intermediates because there are patterns in the results which reveal the probable thermodynamics for all intermediates. This pattern is described in section 3.1.

Scheme 2 The principal intermediates of the complete mechanism, in sequence, with the calculated potential energies (kcal mol⁻¹) for N₂ binding end-on at exo-Fe2 from the N₂-pocket in the protein. Each box contains the association potential energy in red, the barrier energy in parentheses, the spin state and the electronic state. The electron–proton status of each intermediate is marked. Blue boxes signify positive N₂ binding energy: green boxes signify negative N₂ binding energy. Structural skeletons include exo-Fe2–N₂ where the binding is favourable. Structure rest-S2BH-6Hx-26H is bypassed in the mechanism but is included here to demonstrate the effect of the bridging ligand on the exo-Fe2–N₂ binding thermodynamics. The pathway from Fe2-brNH2-Fe6-3b2 to core could be viaFe2NH3 or Fe6NH3. Informative pictures of the structures are included in the ESI.†

The resting state and the first intermediates that follow, adding H atoms first at S2B, then at exo-Fe6 (rest-S2BH-6Hx), have positive binding energies for exo-Fe2–N₂, but after the third H is added at the endo-Fe6 position (rest-S2BH-6Hx-6Hn), this binding energy becomes negative. If the third H instead bridges Fe6 and Fe2 (rest-S2BH-6Hx-26H) the binding energy is −12 kcal mol⁻¹ with a small association barrier of 1 kcal mol⁻¹. Negative exo-Fe2–N₂ binding energies continue for the subsequent intermediates, first the formation of H₂ (Fe6-H2n), then pre-capture, then the H₂/N₂ exchange (H2/N2 exchange), capture of N₂ with formation of the HNNH intermediate (Fe2-brNH-NH-Fe6, then Fe2-brNH2-NH-Fe6), after breaking N–N (Fe2-brNH-Fe6NH3-S2BH), after dissociation of NH₃ from Fe6 and then on to formation of Fe2-brNH2-Fe6–3b2. The subsequent formation of the second NH₃ could occur at Fe2 or Fe6, and these two intermediates have distinctly different binding thermodynamics and kinetics for N₂ at exo-Fe2: −10[2] kcal mol⁻¹ for Fe2NH3 and −1[8] kcal mol⁻¹ for Fe6NH3. After dissociation of this NH₃, the intermediate core and the following intermediates that recover the resting state have positive N₂ binding energies. For all of the intermediates with negative binding energies the potential energy barriers to N₂ binding at exo-Fe2 are small, ≤8 kcal mol⁻¹ and the barriers for dissociation of this N₂ range 11 to 18 kcal mol⁻¹.

The main pattern evident in these results is that intermediates with ligation at the endo position of Fe2 have favourable thermodynamics for binding N₂ at exo-Fe2. Three intermediates, Fe6-H2n, pre-capture and N2/H2 exchange do not have an endo-Fe2 bond but have negative binding energies for exo-Fe2–N₂, and this is correlated with a modification of the geometric details of FeMo-co caused by abnormally long Fe6–C^c distances (2.2–2.3 Å) in these intermediates. Overall the pattern of results validates the assumption that in the central stages of the mechanism, from rest-S2BH-6Hx-6Hn to core, the exo-Fe2–N₂ binding energies will be negative, and also negative in the intermediates involving the reconfigurations of incoming H atoms around S3B and migrations to other sites, because these steps do not interfere with ligation at endo-Fe2.

3.1. Bonding interpretation

The results above show that the binding energy for N₂ at exo-Fe2 is negative when there is ligation at the endo-Fe2 position, and positive when this ligation is absent. The difference between Fe2NH3 (five-coordinate at Fe2, ΔE −10 kcal mol⁻¹) and Fe6NH3 (four-coordinate at Fe2, ΔE −1 kcal mol⁻¹) exemplifies this property. This preference for additional coordination (at exo-Fe2) in a site with larger coordination number (endo-Fe2 ligation) is contrary to the general expectation from coordination chemistry that additional coordination is favoured at a site with a smaller coordination number. The data in Fig. 3 provide some insight into the bonding interpretation of the apparently anomalous binding of N₂ at exo-Fe2. The key geometric property is the endo angle at Fe2 (S2B–Fe2–S2A), which varies considerably over the range of intermediates in the mechanism. Fig. 3 reveals separation of two groups of structures. Looking at the geometry of the dissociated structures (black circles), in one group (lavender colouration) the endo angle is ca. 120° and the stereochemistry at four-coordinate Fe2 is essentially trigonal pyramidal (as in the resting state). These structures have positive or small negative N₂ binding energies. Intermediates in the other group (yellow colouration) have distinctly larger endo angles as a consequence of a ligand (H or N) bound at the endo position, and so these dissociated forms have pseudo-square pyramidal coordination. For these the N₂ binding energy is favourably negative. The general property of almost all intermediates is that square-pyramidal five coordinate Fe2 binds N₂ to form pseudo-octahedral Fe2 more favourably than trigonal pyramidal four coordinate Fe2 binds N₂ to form pseudo-trigonal bipyramidal five coordinate Fe2. On Fig. 3 the labelled structures outside the lavender and yellow fields have ligands near the endo position of Fe2, but not bound to Fe2, allowing relatively small endo angles. These structures, which occur in the intermediates just prior to the N₂-capture phase of the mechanism, retain significantly negative N₂ binding energies. Fig. 3 also plots the endo angles in the corresponding structures with exo-Fe2–N₂ bound, and in all intermediates the endo angle increases (vertical red–black separations) with exo-Fe2–N₂ coordination. Note that in the favourably bound intermediates (yellow enclosure) the endo angles range upwards of 160° and the coordination stereochemistry of Fe2 is therefore close to octahedral.

Fig. 3 Relationships between the binding energy for N₂ at exo-Fe2 (kcal mol⁻¹) and the endo angle (°) at Fe2, S2B–Fe2–S2A, for the dissociated (black circles) and associated (red diamond) forms of each of the intermediates. Data pairs for each intermediate are linked vertically.

4. Discussion

4.1. Entropy

The binding of N₂ to FeMo-co involves a loss of entropy, and this penalty needs to be considered with the binding potential energies calculated here in assessing the viability of N₂ binding at exo-Fe2. Quantum calculation of this entropy change is not feasible for a large model containing sufficient protein. However, relevant experimental data are available and can be assessed in the framework of Scheme 3. The datum sought here is ΔS^assoc, for the binding of N₂ in the N₂ approach pocket of the protein to Fe of FeMo-co in the protein. Values for ΔS^model are available from measurements of N₂ binding to model complexes that have chemical similarities with the Fe sites of FeMo-co.^97,98 Data on the solubility of N₂ in various solvents yield values for ΔS^soln. With several assumptions ΔS^assoc can be approximated as the difference ΔS^model–ΔS^soln. The assumption that N₂–M bonding in the model complexes is similar to N₂–Fe2 bonding at FeMo-co is valid, as is the assumption that the influences of surrounds in the bound state, solution vs. protein, are very similar. The assumed similarity of N₂ in solution and N₂ in the protein pocket is less valid, given the difference in fluidity of the two condensed phases and the expected larger librational component of the entropy of N₂ in solution.

Scheme 3 Components of the analysis of entropy changes.

The data are in Table 2, and possess good consistency: ΔS^soln varies little for very different solvents. Average values −33 cal mol⁻¹ K⁻¹ for ΔS^model and −13 cal mol⁻¹ K⁻¹ for ΔS^soln, yield ΔS^assoc = −20 cal mol⁻¹ K⁻¹, so that −TΔS^assoc calculates as 6 kcal mol⁻¹. With the expectation that the entropy of N₂in proteo is more negative than that of N₂ in fluid solution, the conclusion is that −TΔS^assoc for N₂ in the protein is considerably less than 6 kcal mol⁻¹. Henchman and Irudayam report theoretical investigations of the entropic cost of small molecule binding in proteins, with a comprehensive discussion of other experimental and theoretical information.⁹⁹ None of the systems calculated there closely resemble N₂ in the nitrogenase protein, but it is worth noting that benzene within a small protein (T4-lysozyme) is calculated to have lost between −16 and −23 cal mol⁻¹ K⁻¹. If an entropy loss of this magnitude is applied instead of −13 cal mol⁻¹ K⁻¹ for ΔS^soln, −TΔS^assoc for N₂ in the protein is ca. 4 kcal mol⁻¹.

Table 2 Entropy data in cal mol⁻¹ K⁻¹

System	ΔS^model	ΔS^soln	Ref.
[P(C6H11)3]2Cr(CO)3 in THF, 5.1 atm N2	−35.4 ± 2.3		97
[P(C6H11)3]2Mo(CO)3 in THF, 1 atm N2	−32.1 ± 3.2		97
(TPB)Co(N2) in toluene, 1 atm N2	−32(5)		98
Dissolved in cyclohexane, 1 atm N2		−11.1	100
Dissolved in n-decane, 1 atm N2		−13.6	101
Dissolved in 1-octanol, 1 atm N2		−12.7	101
Dissolved in octamethylcyclotetrasiloxane, 1 atm N2		−11.6	102
CCl4		−12.6	Quoted in ref. 103
Dissolved in ethanol plus 2-propanone (0.558 mol fraction ethanol)		−13.8	Ref. 104, quoted in ref. 103
Ethanol plus 2,2,4-trimethylpentane (0.739 mol fraction ethanol)		−13.9	Ref. 104, quoted in ref. 103

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Seefeldt, Peters et al. described the structure and dynamics of a modified MoFe protein (96Arg → Gln) containing an acetylene molecule in a pocket near the front face of FeMo-co but not bound to it.⁴⁷ They suggested that acetylene in the protein channel leading to its pocket has practically lost most of its gas phase entropy content.

After application of a −TΔS penalty of no more than 4 kcal mol⁻¹ to the intermediates in Scheme 2 that have a negative potential energy for binding of N₂ at exo-Fe2, all intermediates except two are calculated to have a negative free energy for this binding. The exceptions are N2/H2 exchange (ΔG ca. +1 kcal mol⁻¹) and Fe6NH3 (ΔG ca. +3 kcal mol⁻¹). As mentioned above the calculation of ΔE for N2/H2 exchange is less reliable than others, because three unbound molecules are involved, and therefore it is uncertain whether exo-Fe2–N₂ would dissociate at this stage in the mechanism. The next intermediate in the mechanism sequence, Fe2-brNH-NH-Fe6, certainly contains exo-Fe2–N₂ (ΔG ca. −6 kcal mol⁻¹).

It is assumed in this report and in my other accounts of aspects of the mechanism that any transfer of non-reducible N₂ between the N₂-pocket and the exo-Fe2 position is a process separate from the reaction steps from one intermediate to the next. It is conceivable that these processes could be concerted, but the conclusion that all intermediates from rest-S2BH-6Hx-6Hn to core have negative free energies for N₂ binding at exo-Fe2 suggests that this is unlikely.

4.2. Connecting with experiment

None of the experimental structures of the FeMo protein shows N₂ bound at the exo-Fe2 position, although the crystallisation systems used may not have contained N₂. The computational results here are consistent with this absence, because the binding potential energy in the resting state is calculated to be ca. +5 kcal mol⁻¹, and the entropy component makes the free energy change more positive. In the absence of definitive structures of intermediates in the central stages of the mechanism, obtained by crystallisation and diffraction, or by cryoEM,^4,105 how might experimental support for the proposed binding of N₂ at exo-Fe2 be sought?

One general approach in mechanistic studies is to mutate key residues in order to block the postulated function and diminish or prevent the outcome of the mechanism. In the present context this would involve modifying residues at some of the positions 278, 281, 277, 196, 383. However, because it has not yet been demonstrated computationally that any of the mechanistic steps in Scheme 1 is energetically too difficult when exo-Fe2–N₂ is absent, this strategy could be inconclusive. Calculations of the thermodynamics and viability of the mechanistic steps when exo-Fe2–N₂ is absent are still to be finalised. Uncertainty arises from the proposed dual roles of N₂. Simply put, if a blocking mutation inhibits NH₃ formation, is that due to a blockage of reducible N₂ reaching the reaction zone, or a blocked formation of exo-Fe2–N₂ required to promote one or more steps in the mechanism?

There is another factor. An alternative N₂ ingress channel has been proposed by Morrison et al. based on the locations of Xe atoms trapped in the MoFe protein (PDB 4WNA), together with the generation of potential substrate pathways using the program CAVER.¹⁰⁶ The results relevant here are shown in Fig. 4 (which is Fig. 3a in ref. 106) The Morrison pathway for substrates approaching the Fe2–Fe3–Fe6–Fe7 face of FeMo-co is the slate blue channel in Fig. 4. This channel extends from the Xe1 location which is 13 Å from Fe2. Fig. 5 shows the location of Xe1 and the direction of the Morrison channel drawn on the scenario of Fig. 2: the original ingress channel is labeled as Smith channel. It is obvious that these are two different pathways for the ingress of N₂. I have already shown that reducible N₂ can diffuse around bound non-reducible N₂,⁶⁶ but it is conceivable that the N₂ which is reduced in the reaction zone according to Scheme 1 enters along the Morrison pathway while the N₂ that binds at exo-Fe2 from the N2-pocket enters along the Smith pathway. Mutagenesis experimentation would need to target both of these pathways. Further speculation has limited value at this time. A definitive experimental structure of an intermediate in the Mo–nitrogenase physiological reaction is needed for direct confirmation of the presence of exo-Fe2–N₂.

Fig. 4 Locations of Xe atoms in Av MoFe protein crystal PDB 4WNA and substrate channels calculated with the program CAVER: reproduced with permission from ref. 106. The light purple and cyan pathways connect the protein surface to the Xe1 site, from which substrate N₂ could continue towards the Fe2–Fe3–Fe6–Fe7 face of FeMo-co through the slate blue channel, and enter the reaction zone.

Fig. 5 The different positions and directions of the Smith channel⁵¹ and the Morrison channel.¹⁰⁶

4.3. The role of S2B

The mechanism in Scheme 1 involves a catalytic site, FeMo-co, that is structurally flexible but with intact intra-cluster bonding. In recent years the structural integrity of FeMo-co during catalysis has been questioned by the crystal structures and reactivities of Mo–nitrogenase isoforms in which S2B has been replaced by Se,¹⁰⁷ or CO,^108,109 or, controversially, by N₂.^110–113 The mechanistic relevance of these findings is unresolved, because the apparent displacement or replacement of S2B could reflect different dynamics between the time scales of substrate reduction and crystal growth.⁴

In my analyses of the mechanism, S2B is retained within intact FeMo-co, and in that position has crucial roles in which an H atom on S2B is used to form an H–N bond. One role is the N₂ capture step forming Fe2-brNH-NH-Fe6, and the second is the Fe2-brNH-Fe6-S2BH → Fe2-brNH2-Fe6 step. In both steps S2BH is needed to form an H–N bond on the His195 side of the reaction zone, and throughout the mechanism His195 functions as proton reservoir and proton buffer (evident in Scheme 1 Panel B and the recovery of the resting state in Panel C) via contact with S2B very similar in distance (ca. 3.2 Å) to the resting state crystal structure. Many components of the proposed mechanism would be invalidated if S2B were absent.

5. Conclusions

This investigation has clarified and quantified the occurrence of a non-reducible N₂ molecule in the proposed complete mechanism of Mo–nitrogenase. In the resting state this N₂ will occupy the N₂-pocket about 3.2 Å from Fe2. After introduction of three H atoms at positions surrounding the reaction zone this non-reducible N₂ will relocate to the exo position of Fe2 with end-on coordination. A separate (reducible) N₂ entering the reaction zone is progressively hydrogenated, through intermediates containing N₂H_x and NH_x entities coordinated at the endo position of Fe2, and this endo-Fe2 coordination favours retention of the exo-Fe2–N₂ moiety through this sequence of intermediates. In the last stages of the mechanism after dissociation of the second NH₃ and clearance of the endo-Fe position the thermodynamics favour return of non-reducible N₂ to the N₂-pocket. Some uncertainty remains about the status of exo-Fe2–N₂ during one step in which H₂ exchanges with the incoming reducible N₂.

Coordination at endo-Fe2 is confirmed as a structural feature that favours binding of N₂ at exo-Fe2, and attainment of pseudo-octahedral stereochemistry at Fe2 is evidently the dominant factor explaining the apparent paradox in which binding at the exo position of Fe2 is enabled by ligation at the endo position of the same Fe atom.

These results also justify the assumed presence of exo-Fe2–N₂ in the models used in previous calculations of the thermochemistry of mechanistic reaction steps.^52,53 The appropriate presence or absence of exo-Fe2–N₂ for each of the intermediates is included in the Scheme 1 presentation of the full mechanism. A central hypothesis is that exo-Fe2–N₂ is non-reducible because it is outside the reaction zone and not exposed to H atom donors.

For the resting state the binding free energy for exo-Fe2–N₂ is calculated to be ca. +9 kcal mol⁻¹, which is consistent with the absence of N₂ at Fe2 in all reported crystal structures of the MoFe protein.

Data availability

The data supporting this article have been included as part of the ESI.†

Electronic supplementary information (ESI) available: Description of the protein model and the structural constraints used, explanation of the electronic states, description of the density functional procedures and their validation, and description of procedures for determination of transition states and reaction trajectories. Atom coordinates, spin densities of Fe atoms, and pictorial representations of all structures and transition states are included in the ESI.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research was undertaken with the aid of resources from the National Computational Infrastructure Facility, enabled by the Australian Government. My research is funded by UNSW Sydney.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4dt03146f

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