Kinetic Understanding of N₂ Reduction versus H₂ Evolution at the E₄(4H) Janus State in the Three Nitrogenases

Abstract

The enzyme nitrogenase catalyzes the reduction of N₂ to ammonia but also that of protons to H₂. These reactions compete at the mechanistically central ‘Janus’ intermediate, denoted E₄(4H), which has accumulated 4e⁻/4H⁺ as two bridging Fe-H—Fe hydrides on the active-site cofactor. This state can lose e⁻/H⁺ by hydride protonolysis (HP) or become activated by reductive elimination (re) of the two hydrides and bind N₂ with H₂ loss, yielding an E₄(2N2H) state that goes on to generate two NH₃ molecules. Thus, E₄(4H) represents the key branch point for these competing reactions. Here, we present a steady-state kinetic analysis that precisely describes this competition. The analysis demonstrates that steady-state, high-electron flux turnover overwhelmingly populates the E₄ states at the expense of less reduced states, quenching HP at those states. The ratio of rate constants for E₄(4H) hydride protonolysis (k_HP) versus reductive elimination (k_re) provides a sensitive measure of competition between these two processes and thus is a central parameter of nitrogenase catalysis. Analysis of measurements with the three nitrogenase variants (Mo-nitrogenase, V-nitrogenase, and Fe-nitrogenase) reveals that at a fixed N₂ pressure their tendency to productively react with N₂ to produce two NH₃ molecules and an accompanying H₂, rather than diverting electrons to the side reaction, HP production of H₂, decreases with their ratio of rate constants, k_re/k_HP: Mo-nitrogenase, 5.1 atm⁻¹; V-nitrogenase, 2 atm⁻¹; and Fe-nitrogenase, 0.77 atm⁻¹ (namely, in a 1:0.39:0.15 ratio). Moreover, the lower catalytic effectiveness of the alternative nitrogenases, with more H₂ production side reaction, is not caused by a higher k_HP but by a significantly lower k_re.

Graphical Abstract

Nitrogenase is the bacterial enzyme responsible for biological nitrogen fixation, the reduction of N₂ to two NH₃ molecules.^1–3 There are three known forms of nitrogenase, designated as the molybdenum-dependent Mo-nitrogenase, the vanadium-dependent V-nitrogenase, and the iron-only Fe-nitrogenase, each encoded by a unique gene cluster.^4–8 Each nitrogenase comprises an electron-delivery Fe protein and a catalytic protein, the latter being denoted MoFe protein (MoFe), VFe protein (VFe), and FeFe protein (FeFe), respectively. Each catalytic protein contains a complex metal cluster called the FeMo-cofactor (FeMo-co), FeV-cofactor (FeV-co), and FeFe-cofactor (FeFe-co), as the active site for substrate reduction.^4,5,9–12 A structural representation of the FeMo-co in the resting state is shown in Figure 1. A recent structure of the VFe protein shows that the FeV-co has a structure similar to that of the FeMo-co but has V replacing Mo and one bridging S replaced by a carbonate.¹³ No structure is available for the FeFe-co, but available spectroscopic signatures indicate that the overall structure is similar to those of the FeMo-co and FeV-co.¹¹

Figure 1.

Structure of the core of the FeMo-cofactor, looking down on the Fe2,3,6,7 face.

Mo-nitrogenase is the best characterized of the three nitrogenase forms. During catalysis, the Fe protein transiently associates with the MoFe protein, donating a single electron to the FeMo-co during association, mediated by an [8Fe-7S] cluster (P-cluster).^9,14–16 Each electron delivery is coupled to the hydrolysis of two molecules of ATP by the Fe protein, the P_i release of which is known to be the overall rate-limiting step of catalysis.¹⁷ Studies of the enzyme trapped during catalysis have shown how electrons and protons accumulate on the FeMo-co and how the enzyme is activated for N₂ binding and reduction.^9,18–20 In short, before N₂ can be reduced, four electrons and protons must accumulate on the FeMo-co to create a state denoted E₄(4H), which stores these reducing equivalents as two Fe–H–Fe bridging hydrides. Recent structural and theoretical studies reveal that accumulation of electrons and protons on the FeMo-co can break one or both of the Fe–S–Fe bonds for a “belt” sulfide, thus opening coordination sites for binding of the hydrides to Fe atoms.^13,21–24 These hydrides can produce H₂ through two different reactions (Figure 2). Protonolysis of one hydride (HP) results in the formation of H₂ and the “relaxation” of the E₄(4H) state back to the E₂(2H) state; HP of the second hydride then generates E₀. In competition with HP at E₄(4H) is the reductive elimination (re) of both hydrides to make H₂, which is released upon N₂ binding, in a process that leads to a diazene-level complex [E₄(2N2H)]. Two molecules of NH₃ are then generated through addition of four additional electrons/protons. As shown in Figure 2, the activation for catalysis by re of H₂ is reversible, with the oxidative addition (oa) of H₂ by E₄(2N2H) leading to N₂ release.^9,18–21,25 As a result of the mechanistically required release of H₂ for enzyme activation, the re/oa equilibrium incorporates an “eight-electron” limiting stoichiometry (eq 1) for N₂ reduction¹⁹

$$\begin{gathered} {\text{N}}_2+8{\text{H}}^{+}+16\text{MgATP}+8{\text{e}}^{-} \\ \to 2{\text{NH}}_3+{\text{H}}_2+16\text{MgADP}+16{\text{P}}_{\text{i}} \end{gathered}$$ (1)

as proposed by Lowe and Thorneley.^26,27 This limiting stoichiometry is, in fact, approached under high N₂ pressures.²⁸

Figure 2.

Reactions of the E₄ state. The E₄(4H) state (center) is shown relaxing to the left by hydride protonolysis (HP) to generate E₂(2H) with rate constant k_HP or reacting with N₂ to the right through the reductive elimination/oxidative addition (re/oa) equilibrium that activates nitrogenase to break the N≡N bond. Although this process is an equilibrium, the oa of H₂ is not significant in our experiments (see the Supporting Information), so only the “forward”, re rate constant, k_re, is shown. Note that the positioning of hydrides and protons is a matter of current interest, with plausible alternative possibilities; for the sake of concreteness, our own current best guess is shown, also noting the possible lability of an Fe–S bond with a dotted line. “2N2H” denotes a diazene-level intermediate.⁹

Recent studies indicate that all three nitrogenases follow a similar re/oa mechanism of nitrogen fixation.²⁹ However, compared to the Mo-nitrogenase, the V- and Fe-nitrogenases exhibit significant differences in the relative rates of the two reaction pathways, H₂ formation and N₂ reduction. For example, under a 1 atm partial pressure of N₂ [P(N₂)], the observed ratio of H₂ formed per N₂ reduced for Fe-nitrogenase is ~7, whereas it is ~3 for V-nitrogenase and ~2 for Mo-nitrogenase.^4,21,29–31

The stoichiometry of eq 1 was incorporated into a detailed kinetic scheme for the Mo-nitrogenase from the bacterium Klebsiella pneumoniae painstakingly developed by Lowe, Thorneley, and others (here termed the LT scheme).²⁷ Although this scheme provides a framework for mechanistic studies of nitrogenase, the inclusion of all the steps in the complete catalytic cycle of nitrogen fixation came at the cost of significant uncertainties in key rate constants, in particular those associated with reactions of the critical E₄(4H) inter- mediate.³² As a consequence, it is not feasible to obtain the large number of variables associated with this model with sufficient precision to use the model to compare the alternative nitrogenases.

To gain a precise description of the reactions at the E₄(4H) state of the three nitrogenases, we have developed a kinetic description of steady-state turnover that optimally provides an analysis of the competing reactions of this ‘Janus’ intermediate.⁹ It focuses on the competition between progress toward NH₃ formation through N₂ binding/H₂ re to generate E₄(2N2H) and the relaxation toward the resting state by H₂ formation through HP (Figure 2). Application of this kinetic model to measurements of turnover of catalysis by the three nitrogenases provides quantitative comparisons of the catalytic behavior of their Janus intermediates and critical insights into the differences in their reactivity.

MATERIALS AND METHODS

Reagents and General Procedures.

All reagents were obtained from Sigma-Aldrich (St. Louis, MO), Fisher Scientific (Fair Lawn, NJ), or Bio-Rad (Hercules, CA) unless specified otherwise and used without further purification. Argon and dinitrogen gases were purchased from Air Liquide America Specialty Gases LLC (Plumsteadville, PA). Proteins and buffers were manipulated anaerobically in septum-sealed serum vials and flasks using a vacuum Schlenk line, an argon or dinitrogen atmosphere, and gastight syringes. Gas transfers were made using gastight syringes.

Bacterial Growth and Protein Purification.

Fe-nitro- genase proteins (FeFe and Fe protein) were expressed and purified from Azotobacter vinelandii strain DJ1255 as previously described.²⁹ Mo-nitrogenase proteins (MoFe and Fe proteins) were expressed and purified from A. vinelandii strains DJ995 (His-MoFe protein) and DJ884 (Fe protein) as previously described.^33–35 Protein concentrations were determined using the Bio-Rad DC Protein Assay Kit.

Proton and Dinitrogen Reduction Assays.

Substrate reduction assays were performed in 9.4 mL serum vials containing a MgATP regeneration buffer (6.7 mM MgCl₂, 30 mM phosphocreatine, 5 mM ATP, 0.2 mg/mL creatine phosphokinase, and 1.2 mg/mL BSA) and 10 mM sodium dithionite in 100 mM MOPS buffer at pH 7.0. Reaction vials were made anaerobic, and their headspaces adjusted to the partial pressure of N₂ desired with the remaining headspace consisting of argon. The FeFe or MoFe protein was then added to the vials; the vials were vented to atmospheric pressure, and the reactions were initiated by the addition of the appropriate Fe protein. FeFe and MoFe concentrations in reactions were 0.1 mg/mL, corresponding to ~0.42 and ~0.4 nmol, respectively, per reaction vial. All data reported here were collected at a 1:30 FeFe:Fe protein molar ratio and a 1:20 MoFe:Fe protein molar ratio, except in a series of measurements designed to test the specific activity as a function of the electron flux, which is controlled by this ratio. Reactions were conducted at 30 °C for 8 min and then stopped by the addition of 300 μL of 400 mM EDTA (pH 8.0). To minimize the effects of slow re-reduction of Fe protein by sodium dithionite under low-flux conditions (high ratio of MoFe protein to Fe protein), The flux dependence of N₂ reduction by Mo-nitrogenase employed a buffer containing a MgATP regeneration system (5 mM MgCl₂, 22 mM phosphocreatine, 3.8 mM ATP, 0.15 mg/mL creatine phosphokinase, and 0.8 mg/mL BSA) with 0.125 mM 1,4-dithiothreitol, 0.6 mM flavodoxin in the hydroquinone state (Fld^HQ), and 12 mM sodium dithionite in 100 mM MOPS at pH 7.3. The Fe protein concentration was fixed at 0.1 mg/mL, and the MoFe protein concentration was varied from 0.2 to 6.4 mg/mL to give a [MoFe]:[Fe] ratio from 0.5 to 16. The reaction mixtures were incubated at 30 °C for 30 s under 1 atm of N₂, and then the reactions were stopped by the addition of 500 μL of 400 mM EDTA at pH 8.0. H₂ and NH₃ were quantitated according to published methods.^36,37

Kinetic Analysis.

Kinetic equations were modeled in Mathcad 15 or Sigmaplot version 12.5 and fit to experimental data using the latter.

RESULTS AND DISCUSSION

Developing a Kinetic Scheme for Reactions at E₄(4H).

A simplified version of the LT kinetic scheme for N₂ fixation that focuses on electron accumulation and centrally important re/oa equilibrium is shown in scheme A of Figure 3. It includes delivery of four e⁻/H+ to form E₄(4H), with the hydrogenase-like side reaction, formation of H₂ through HP, in states E_n (n = 2–4), and the catalytic re of H₂ with N₂ binding by E₄(4H) to generate the diazene-level intermediate, E₄(2N2H) (Figure 2). The subsequent formation of two NH₃ molecules through accumulation of an additional 4 equiv by E₄(2N2H) is represented as a single overall process with a composite rate constant (k_cat). Following the strategy we developed in studying electrochemical H₂ production,³⁸ depicted in scheme B of Figure 3, we capture the essence of kinetic scheme A, the competition between nitrogenase on one hand acting “simply” as a hydrogenase through electron accumulation starting at E₀ with H₂ production by HP at E₂(2H) and E₄(4H) and on the other performing its function of N₂ fixation through “capture” of E₄(4H) by N₂ binding/H₂ re and release, to generate E₄(2N2H), which irreversibly proceeds to generate two NH₃ molecules. Scheme B omits the reaction in which E₄(4H) is regenerated through oa of H₂ by E₄(2N2H) with N₂ liberation (Figure 2), as being negligible in our measurements, because the partial pressures of H₂ generated are so small. This approach is confirmed by a detailed analysis presented in the Supporting Information.

Figure 3.

As described in the text, scheme A is a simplified LT kinetic scheme for N₂ fixation; its essence is captured by scheme B. This scheme in turn is further simplified under high-flux, steady-state turnover conditions to scheme C, which evolves into truncated kinetic scheme D.

Scheme B in turn can be mapped onto scheme C under steady-state turnover conditions. When E₀ is formed either by HP at E₂(2H) or by NH₃ formation, it is promptly rereduced to E₂(2H), so the E₀-forming processes are instead treated as “directly” generating E₂(2H). In this mapping, the rate constant for electron accumulation (k_ac) is a composite representative of the processes of electron delivery by Fe protein to MoFe protein, while the NH₃-producing catalytic rate constant (k_cat) in the final step of the cycle is to be understood as a composite corresponding to addition of six e⁻/H⁺ per N₂ reduced, four involved in NH₃ formation by reduction of diazene-level intermediate E₄(2N2H) and two more associated with the prompt reduction to E₂(2H) of resting state E₀ formed upon release of the second of two NH₃ molecules (compare scheme C with schemes A and B). Finally, liberation of H₂ by E₂(2H) without a change in state reflects HP at E₂(2H) and rapid return of E₀ thus formed to E₂(2H).

Considering the behavior of E₂(2H) more closely, every time it is generated, it is reduced to E₄(4H) with rate constant k_ac, with a probability f_ac = k_ac/(k_ac + k_HP), or liberates H₂ with a rate constant k_HP, with a probability f_HP = k_HP/(k_ac + k_Hp). High-flux conditions may then be defined as occurring when the rate of electron delivery during electron accumulation (rate constant k_ac) is much greater than that for the competing H₂ production by HP (rate constant k_HP) at states E_n (n = 2 or 3) in scheme A, namely f_HP → 0 in schemes B and C, leading to catalytic behavior according to scheme D, in which all reaction occurs at E₄(4H).

Such a high-flux condition is achievable, despite the fact that the overall electron-delivery process is well-known to be slow,¹⁷ because of a peculiarity in nitrogenase function. As reported by Lowe and Thorneley, after delivery of an electron from the Fe protein, H₂ can only be released from free MoFe protein, namely after the oxidized Fe protein dissociates and before another reduced Fe protein binds.²⁷ As a result, the competition between the release of H₂ from free MoFe protein and conversion to the next higher E_n state is governed by the rate of binding of a reduced Fe protein to the MoFe protein. With high concentrations of reduced Fe protein relative to MoFe protein (high flux), this rate is increased to the point that reduced Fe protein binds to MoFe protein rapidly compared to the rate of release of H₂ by MoFe protein. As a consequence, states E_n (n = 2 and 3) do not release H₂ by the HP process, and instead, the states “before” E₄(4H) E_n (n < 4) progressively accept (e⁻/H⁺) until they are converted to E₄(4H). This state then reacts, either by HP or by the re process. As a result, the enzyme under high flux, as described by scheme D, behaves in a fashion not, to the best of our knowledge, noted previously: H₂ production at electron-accumulation stages, E_n (n ≤ 3) is suppressed during turnover as these states become depopulated in favor of an E₄-level state, either E₄(4H) or E₄(2N2H) depending on the partial pressure of N₂; although E₀ is regenerated by N₂ fixation, under high flux it is promptly returned to E₂(2H). In short, during catalysis, the enzyme effectively cycles between the two E₄ states and the little-populated E₂(2H), and thus, kinetic scheme C evolves into truncated scheme D. In this report, we validate scheme C and confirm that high-flux conditions convert it into scheme D.

It is centrally important that, although in steady-state experiments described by schemes C and D, k_ac and k_cat are composite rate constants, rate constants k_HP and k_re correspond precisely to the rate constants for reaction of E₄(4H) in scheme A and, indeed, in the full LT scheme. Moreover, the beauty of high-flux, steady-state experiments (scheme D) is that they emphasize the role of E₄(4H) as the ‘Janus’ intermediate, which acts as a catalytic “branch point” that reacts through one of two channels. It can “fall back” in a “hydrogenase- like” catalytic cycle, releasing H₂ by the first-order HP process (rate constant k_HP) without further electron accumulation, regenerating E₂(2H), or it can be “captured” by second-order reaction with N₂ (rate constant k_re) with accompanying release of H₂ formed by re, to produce E₄(2N2H), which irreversibly proceeds to generate two NH₃ molecules with composite rate constant k_cat. High-flux experiments thus provide precision measurements of the centrally important mechanistic rate constants that define the E₄(4H) branch point: k_HP and k_re.

Kinetic Analysis.

As shown in the Supporting Information, according to schemes C and D, during steady-state turnover the differential equations for the rates of formation of H₂ and NH₃ and loss of N₂ are zero-order in time, and the rates of NH₃ formation/N₂ loss and of H₂ formation can be written as shown in eq 2

$$\frac{{\text{dNH}}_3}{\text{d}t}=-2\frac{{\text{dN}}_2}{\text{d}t}\stackrel{\text{SS}}{\to }{k}_{{\text{NH}}_3}\cdot E_0^0\frac{{\text{dH}}_2}{\text{d}t}\stackrel{\text{SS}}{\to }{k}_{{\text{H}}_2}{E}_0^0$$ (2)

where $E_0^0$ is the total enzyme concentration. As a result, the total formation of NH₃/loss of N₂ and the formation of H₂ during a turnover experiment are simply proportional to their respective rate constants. The rate constants for the production of the NH₃ product and loss of N₂ for schemes C and D are given by eq 3 where the numerical factor ($\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$) converts eq 2 to the rate of NH₃ formation per electron, according to the stoichiometry of eq 1. The maximum velocity for NH₃ production is set by the equation $\overline{k}=k_{\text{cat}}{k}_{\text{ac}}/\left(k_{\text{cat}}+k_{\text{ac}}\right)$, whose form causes it to equal the smaller of the two rate constants, k_ac and k_cat. The bracketed term in eq 3 has the form

$$\begin{array}{ll}{k}_{NH3}=2k_{N2}\stackrel{SS}{\to }\left(\frac{1}{4}\right)\frac{\left(k_{re}{P}_{N2}\right)}{\left(1+\left(\frac{k_{HP}}{k_{ac}}\right)\right)+\frac{\left(k_{\mathit{re}}{P}_{N2}\right)}{\overline{k}}}& \boxed{\overline{\mathrm{k}}=\frac{k_{ac}{k}_{cat}}{k_{ac}+k_{cat}}}\\ =\left(\frac{1}{4}\right){\frac{\left(k_{re}^z{P}_{N2}\right)}{1+\frac{\left(k_{re}^z{P}_{N2}\right)}{\overline{k}}}}_{\searrow \left(\frac{1}{4}\right)\overline{k};P_{N2}\to \infty }^{\nearrow \left(\frac{1}{4}\right)\left(k_{re}^z{P}_{N2}\right);P_{N2}\to 0}& \boxed{\begin{array}{l}{k}_{re}^z=\frac{k_{re}}{\left(1+\left(\frac{k_{HP}}{k_{ac}}\right)\right)}\\ \stackrel{\frac{k_{HP}}{k_{ac}}\to 0}{\to }{k}_{re}\end{array}}\\ =\left(\frac{1}{4}\right)\overline{k}\left[\frac{\frac{\left(k_{re}^z{P}_{N2}\right)}{\overline{k}}}{1+\frac{\left(k_{re}^z{P}_{N2}\right)}{\overline{k}}}\right]=\left(\frac{1}{4}\right)\overline{k}\left[\frac{K_a^z{P}_{N2}}{1+K_a^z{P}_{N2}}\right]& \boxed{K_a^z=\frac{k_{re}^z}{\overline{k}}}\end{array}$$ (3)

of a binding isotherm, with the apparent binding constant equaling the ratio ${K_{\text{a}}}^z={k_{re}}^z/\overline{k}$. We allow for variations in flux, namely the rate constant ratio, z = k_HP/k_ac > 0 and thus variations in HP at the E₂(2H) state, but have simplified the appearance of the equation by defining the apparent rate constant, k_re^z, in terms of the true k_re and z, as indicated. For the sake of completeness, we note this equation can be rewritten in the form of a hyperbola or Michaelis-Menten equation (eq 4). The corresponding rate constant for H₂ production for scheme C is presented in eq 5.

$$\begin{gathered} k_{{\text{N}}_2}=\left(\frac{1}{2}\right)k_{{\text{NH}}_3}\underset{\text{high}\text{flux}}{\overset{\text{SS}}{\to }}\left(\frac{1}{8}\right)\frac{v_{\text{max}}{P}_{{\text{N}}_2}}{{K_{\text{m}}}^z+P_{{\text{N}}_2}} \\ {K_{\text{m}}}^z=\frac{1}{{K_{\text{a}}}^z};v_{\text{max}}=\overline{k} \end{gathered}$$ (4)

$$\begin{gathered} k_{H2}\stackrel{SS}{\to }\frac{1}{2}\left[\frac{k_{HP}\left(1+\left(\frac{k_{HP}}{k_{ac}}\right)\right)+\left(\frac{1}{4}\right)\left(1+4\left(\frac{k_{HP}}{k_{ac}}\right)\right)\left(k_{re}{P}_{N2}\right)}{\left(1+\left(\frac{k_{HP}}{k_{ac}}\right)\right)+\frac{\left(k_{re}{P}_{N2}\right)}{\overline{k}}}\right] \\ =\frac{1}{2}{\left[\frac{k_{HP}+\left(\frac{1}{4}\right)\left(1+4\left(\frac{k_{HP}}{k_{ac}}\right)\right)\left(k_{re}^z{P}_{N2}\right)}{1+\frac{\left(k_{re}^z{P}_{N2}\right)}{\overline{k}}}\right]}_{\searrow (\frac{1}{8})•\overline{k};P_{N2}\to \infty }^{\nearrow (\frac{1}{2})k_{HP};P_{N2}\to 0} \end{gathered}$$ (5)

When $P_{{\text{N}}_2}\to 0$, H₂ is produced solely by HP with a rate constant $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ k_HP (per electron). At a high $P_{{\text{N}}_2}$, H₂ is produced solely by the re process, at a rate equaling the rate of consumption of N₂; HP at E₂(2H) is associated with the terms involving the k_HP/k_ac ratio in the numerator of the first form of eq 5.

Schemes B and C and the resultant steady-state turnover rate constants provide a clear mathematical formulation of the competition at the E₄(4H) branch point between the first- order process of H₂ formation by HP without N₂ binding and the second-order re process in which the binding and reduction of one N₂ accompanies the re of one H₂. This ability of a second-order process to outcompete a first-order one is most clearly captured by taking the ratio of the rate constants for production of H₂ (eq 3) and N₂ consumption (eq 4), denoted r, which can be written as shown in eq 6. According to eq 6, at

$$\begin{gathered} r=\frac{k_{H2}}{k_{N2}}=2\frac{k_{H2}}{k_{NH3}}\stackrel{SS}{\to }{\left[\frac{k_{HP}+\left(\frac{1}{4}\right)\left(1+4\left(\frac{k_{HP}}{k_{ac}}\right)\right)\left(k_{re}^z{P}_{N2}\right)}{\left(\frac{1}{4}\right)\left(k_{re}^z{P}_{N2}\right)}\right]}_{\searrow \left(1+4\left(\frac{k_{HP}}{k_{ac}}\right)\right);P_{N2}\to \infty }^{\nearrow \frac{4}{\left(k_{re}^z{P}_{N2}\right)}\to \infty ;P_{N2}\to 0} \\ \begin{array}{c}=\left[\frac{1+\left(\frac{1}{4}\right)\left(1+4\left(\frac{k_{HP}}{k_{ac}}\right)\right)\left(\frac{k_{\mathit{re}}^z}{k_{HP}}\right)P_{N2}}{\left(\frac{1}{4}\right)\left(\frac{k_{re}^z}{k_{HP}}\right)P_{N2}}\right]\\ =\left[\frac{1+\left(\frac{1}{4}\right)\left(1+4\left(\frac{k_{HP}}{k_{ac}}\right)\right)•\rho P_{N2}}{\left(\frac{1}{4}\right)•\rho P_{N2}}\right]\end{array}\boxed{\rho =\left(\frac{k_{re}}{k_{HP}}\right)} \end{gathered}$$ (6)

low values of $P_{{\text{N}}_2}$, the rate of H₂ production by HP from E₄(4H) becomes independent of $P_{{\text{N}}_2}$ as $P_{{\text{N}}_2}\to 0$, while the rate of N₂ consumption, through reductive elimination and production of H₂ and two NH₃ molecules, falls in proportion to $P_{{\text{N}}_2}$. Hence, as $P_{{\text{N}}_2}\to 0$, the ratio r approaches infinity. At the other extreme, as $P_{{\text{N}}_2}$ increases so that re of H₂ with N₂ consumption becomes much faster than HP at E₄(4H), $k_{re}{P}_{{\text{N}}_2}\gg k_{\text{HP}}$, the ratio r tends toward a limiting value that depends on the extent of H₂ formation at the E₂(2H) stage of scheme C, which increases with the value of k_HP/k_ac (eqs 5 and 6). If turnover is in the high-flux limit, k_HP/k_ac → 0, there is no HP at the E₂(2H) state, scheme C evolves into scheme D, and these equations predict that the limiting value at high $P_{{\text{N}}_2}$ is r = 1. HP at E₂(2H) is abolished, and HP at E₄(4H) is totally outcompeted by N₂ binding with re and release of H₂. One H₂ is liberated as one N₂ binds and is reduced to two NH₃ molecules.

Turnover of Nitrogenases.

Figure 4 presents a plot of the specific activities for NH₃ production at equal concentrations of Mo-nitrogenase and Fe-nitrogenase as a function of the partial pressure of N₂ $\left(P_{{\text{N}}_2}\right)$ overlaid by the fits of these two data sets to eq 3. It is noteworthy that the apparent binding affinity constant, $K_{\text{a}}=k_{re}/\overline{k}$, and the maximum velocity $\overline{k}$ obtained in the fits to the specific activities for Fe-nitrogenase (Table 1) are 4- and 10-fold smaller, respectively, than for Mo-nitrogenase. Figure 5 overlays the measurements of r as a function of $P_{{\text{N}}_2}$ for all three nitrogenases with the fits to eq 6. Table 1 lists the parameters derived from the fits for both Mo- and Fe-nitrogenases, including k_re, k_HP, $\overline{k}$, and the value for the central parameter of catalysis, the ratio of reaction rate constants at the E₄ level, ρ = k_re/k_HP.

Figure 4.

Specific activities for NH₃ formation by Mo- and Fe-nitrogenases as a function of the partial pressure of N₂. Overlaid are fits to eq 3 obtained with SigmaPlot; values of k_re and K_a for MoFe (red trace) and FeFe (blue) are listed in Table 1. Assays were performed as described in Materials and Methods.

Table 1.

Kinetic Parameters Obtained from High-Flux Turnover

	ρ = kre/kHP (atm−1)a (r fit)	kre (s−1 atm−1)b (y)	$K_{\text{a}}=k_{re}/\overline{k}$ (atm−1)b (z)	kHP (s−1)c (calcd)	$\overline{k}\left(s^{-1}\right)$c (calcd)	ad
Mo	5.1 (1)	83 (5)	7.3 (5)	16.3	11.3	0.22
Fe	0.77 (5)	8.5 (5)	1.8 (2)	11	4.7	0.19
Mo/Fe	6.6	9.8	4.1	1.5	2.4

^aObtained from fits in Figure 5.

^bObtained from fits in Figure 4.

^cCalculated from other parameters.

^dObtained from fits in Figure 6.

Figure 5.

Ratio of H₂ formed to N₂ consumed as a function of the partial pressure of N₂ for Mo-nitrogenase (red) and Fe-nitrogenase (blue). Overlaid are fits to eq 6 using SigmaPlot. Values of ρ = k_re/k_HP are listed in Table 1. Assays were performed as described in Materials and Methods.

With a focus on the behavior of Mo-nitrogenase, consider the ratio r (Figure 5). The fit to eq 6 yields as the ratio of the rate constants for HP and for electron accumulation z = k_HP/k_ac = 0, which implies that the experiments are indeed performed under high-flux conditions, with HP fully suppressed at early stages of electron accumulation, E_n (n < 4), and that scheme D applies: both the reaction with N₂ with correlated H₂ production and the HP of H₂ are described by the intrinsic rate constants associated with reactions of E₄(4H), k_re and k_HP, respectively.

To test this analysis and conclusion, we performed a suite of experiments in which the electron flux is varied at a fixed $P_{{\text{N}}_2}$. As noted above, the competition between formation of H₂ through HP at E₂ or E₃ and conversion to the next higher E_n state is expressed in the ratio z = k_HP/k_ac and is governed by the rate of binding of a reduced Fe protein to the MoFe protein. This influence may be incorporated into the description of r through a decrease in z with increasing flux, z = a[MoFe]/[Fe], where the parameter, a, is a scale-factor that relates the two ratios. Equation 6, the ratio of product-formation rate constants, r, can then be rewritten in terms of this relationship (also see, SI), (eq 7).

$$r=\frac{k_{H2}}{k_{N2}}={\left[\frac{1+\left(\frac{1}{4}\right)\left(1+4\left(a•\frac{[\text{M}Fe]}{[Fe]}\right)\right)•\rho P_{N2}}{\left(\frac{1}{4}\right)•\rho P_{N2}}\right]}_{\boxed{z=\frac{k_{HP}}{k_{ac}}=a•\frac{[\text{M}Fe]}{[Fe]}}}$$ (7)

The plots of eq 7 in Figure 6 illustrate how, in the high-flux regime, where z ≪ 1, the ratio r is invariant with flux as expected, while as z increases and the system falls out of this regime, r increases. This measured ratio of H₂/N₂ as a function of the MoFe protein/Fe protein ratio shown in Figure 6 is consistent with an earlier study.³⁹

Figure 6.

Ratio of H₂ formed to N₂ consumed as a function of flux ([MFe:Fe], where M = Mo or Fe) for Mo-nitrogenase (red) and Fe-nitrogenase (blue). Traces were determined by fixing ρ to the value in Table 1 and fitting parameter a in eq 7 using SigmaPlot (Table 1). Assays were performed as described in Materials and Methods.

For Mo-nitrogenase, the measured dependence of r on [MoFe]/[Fe] at $P_{{\text{N}}_2}=1$ atm is captured with precision by eq 7 using the corresponding values of ρ and a (Table 1). The data show that Mo-nitrogenase reaches the high-flux regime when [MoFe]/[Fe] ≳ 1, while our experiments in Figures 4 and 5 were performed at [MoFe]/[Fe] = 1/20! This finding shows that scheme D indeed is appropriate for analysis of our experiments, with z → 0, that the apparent rate constant for re obtained by combining the parameters from the fits to the $P_{{\text{N}}_2}$ titration (Figure 4) with rate ratio r (Figure 5) (k_re^z, eq 3) is precisely the intrinsic value, k_re, that describes the re process of E₄(4H), and, finally, that rate constant k_HP is precisely the value for E₄(4H).

With this foundation, the plots in Figure 5, the “H₂/N₂” ratio, r, are shown to be a remarkable demonstration of the power of the present approach to reveal the kinetic basis for the different catalytic efficiencies of the alternative nitrogenases. The key difference is expressed in the ratio of reaction rate-constants at the E₄ level, ρ = k_re/k_HP, which captures the tendency for the E₄(4H) intermediate to undergo the re process with H₂ release upon N₂ binding and, ultimately, NH₃ formation (second-order rate constant, k_re), instead of producing H₂ by HP (first-order rate constant, k_HP). Equation 6 shows that ρ alone controls this branching at E₄(4H), and the plots of r as a function of $P_{{\text{N}}_2}$ for the two nitrogenases, which so beautifully overlay the data, are generated through the use of eq 6 merely by adjusting this single parameter (Table 1).

Viewed from a different perspective, these measurements and their description by eq 6 clearly demonstrate that activation of E₄(4H) for N₂ binding indeed occurs through re and release of H₂. This coupling between N₂ binding and the release of H₂, which was first incorporated in the LT kinetic scheme, is highlighted in scheme D and, as visualized through the plot of r versus $P_{{\text{N}}_2}$ in Figure 5, both predicts and provides an explanation for the experimental finding that an extremely high $P_{{\text{N}}_2}$ does not entirely suppress H₂ formation by Mo-nitrogenase but instead leads asymptotically to the formation of one H₂ per formation of two NH₃ molecules per reduction of one N₂.²⁸ For $P_{{\text{N}}_2}=50$ atm, eq 6 yields an r value of 1.02 for Mo-nitrogenase, essentially reproducing the Burris value of r (1.13 ± 0.13).

With this analysis and the resulting parameters in hand, we can quantify the remark made above that under high flux all the electron accumulation stages, E_n (n ≤ 3), become depopulated in favor of an E₄-level state. According to this analysis, in these high-flux experiments, [MoFe]/[Fe] = 1/20, one calculates that ~99% of the cofactor is present in the E₄ state, as either E₄(4H) or E₄(2N2H), with the relative amounts depending on $P_{{\text{N}}_2}$. Moreover, direct calculation with the full scheme A gives an equivalent result.

Focusing next on Fe-nitrogenase, we find the measured flux dependence of the ratio r at $P_{{\text{N}}_2}=1$ plotted in Figure 6 shows that this enzyme also operates in the high-flux regime in our measurements. Fe-nitrogenase reaches the high-flux regime when [FeFe]/[Fe] ≳ 1, whereas our experiments in Figures 4 and 5 were performed at a far smaller ratio ([FeFe]/[Fe] = 1/30). Thus, here too, all catalytic reactions occur at the E₄(4H) state, and its catalytic properties captured in the reaction rate constants can be straightforwardly compared to those of Mo-nitrogenase through the kinetic analysis of the turnover experiments.

Comparison of the parameters derived from the N₂ consumption titration for Fe-nitrogenase (Figure 4) and the H₂/N₂ titration (Figure 5) with those of Mo-nitrogenase (Table 1) reveals that the major functional difference between the Mo- and Fe-nitrogenases is associated with rate constant k_re for H₂ re/N₂ binding by E₄(4H). The k_re for Mo-nitrogenase is 10-fold greater than that of Fe-nitrogenase, while the asymptotic maximum rate constant for N₂ reduction, proportional to $\overline{k}$, is twice as big. As a result, the apparent affinity constant for N₂, $K_{\text{a}}=k_{re}/\overline{k}$, is 4-fold greater for Mo-nitrogenase than for Fe-nitrogenase.

The higher H₂ production by the Fe-nitrogenase is best considered in terms of the N₂/H₂ ratio. The fits to the data in Figure 5 show that the k_re/k_HP ratio, which captures the tendency of E₄(4H) to undergo re rather than HP, is 7-fold larger for Mo-nitrogenase than for Fe-nitrogenase. Even though the value of k_HP determined for MoFe is indeed slightly higher than that for Fe-nitrogenase, because the Mo-nitrogenase value of k_re is 10-fold higher, there is a 7-fold greater preference for re instead of HP (rate ratio, ρ) for Mo-nitrogenase than for Fe-nitrogenase. Finally, even though Fe-nitrogenase is thus a considerably poorer N₂ fixation catalyst, because it follows the same mechanism as Mo-nitrogenase, in the high-flux limit that applies here, eq 6 nonetheless predicts that r → 1 at sufficiently high $P_{{\text{N}}_2}$; extrapolation of the Fe-nitrogenase curve in Figure 5 to 50 atm predicts an r value of 1.11.

Finally, the V-nitrogenase is widely understood to have catalytic efficacy midway between those of Mo- and Fe-nitrogenases, and the kinetic model developed here can quantify this point using only the single value of the H₂/N₂ ratio at $P_{{\text{N}}_2}=1$ available in the literature.^4,6,12,30,31 Given the intermediate behavior of V-nitrogenase and the finding that both more and less effective enzymes are in the high-flux regime during in vitro turnover, we may assume the same for V-nitrogenase, in which case the predicted curve of r versus $P_{{\text{N}}_2}$ for this enzyme is completely determined by the single parameter ρ, which is fixed by the single value of r at $P_{{\text{N}}_2}=1$; the resulting curve is plotted on Figure 5. The value of ρ and the curve it specifies indeed lie between those for Mo- and Fe-nitrogenase, which quantifies the relative tendency of E₄(4H) to follow its two alternative reaction channels. The ratio for V-nitrogenase relates to those of the other two nitrogenases as k_re/k_HP (Mo) = 5.1, k_re/k_HP (V) = 2, and k_re/k_HP (Fe) = 0.77. In other words, at a given pressure of N₂, V-nitrogenase is ~40% as likely to undergo reaction with N₂ as Mo-nitrogenase and Fe-nitrogenase is only 15% as likely to thus react.

As a final comment about kinetic approaches to nitrogenase function, note that the k_re/k_HP ratio = 5.1 atm⁻¹ derived in this fashion for A. vinelandii Mo-nitrogenase is of far higher precision but is satisfyingly similar to the ratio of rate constants measured by LT as refined by Wilson and Watt³² for a different Mo-nitrogenase, k_re/k_HP = 3.4 atm⁻¹ (conversion of their k_re in units of M⁻¹ s⁻¹ used a Henry’s law constant K of 6.1 × 10⁻⁴ M/atm).⁴⁰ However, the benefits of the approach presented here are highlighted by the remark by Wilson and Watt that the value they report for k_HP is “subject to error of a factor of approximately 2” whereas the key kinetic constants in Table 1 have errors of <10%. And, of course, the focused ability to compare the catalytically important rate constants associated with E₄(4H) among the three nitrogenases that is introduced by the current approach is entirely new.

CONCLUSIONS

The work reported here provides a kinetic analysis of nitrogenase reactivity that focuses on reaction at the catalytically central E₄ state and precisely describes observed H₂ production and N₂ consumption/NH₃ production under steady-state turnover conditions. The measurements as analyzed with the new kinetic model provide unprecedented insight into the catalytic behavior of the E₄(4H) ‘Janus’ intermediate, whose differing properties in the three nitrogenases give rise to their differing catalytic efficacy. Although electron transfer to the catalytic MFe proteins from the Fe protein is rate-limited by P_i release,¹⁷ analysis of the measurements shows that across a wide range of electron fluxes introduced by varying the protein concentration ratio, [MFe]/[Fe], the nitrogenase behaves in a fashion that had not been recognized previously: H₂ production is suppressed at the electron accumulation stages, E_n (n < 3), and during catalysis, the enzyme effectively cycles between the two states at the E₄ level and the little populated E₂(2H), as is captured by the truncated cycle of scheme D. We note that the ratio of MoFe protein to Fe protein measured inside the cell ([MoFe]/[Fe] = ¹/₂) corresponds to “high-flux” conditions (Figure 6), which means that the present measurements reproduce the enzyme’s behavior in vivo.⁴¹ It is significant that the ratio of nitrogenase component proteins inside the cell is small enough to minimize the wasteful H₂ formation by HP that would occur at concentration ratios greater than unity, yet at the same time, the ratio is not made even smaller, to no appreciable functional benefit, by the presence of excess Fe protein; the cell does not make more Fe protein than is necessary. This is of considerable physiological benefit, as protein production is a significant energy demand on the cell. It should be noted that Fe protein is also involved in the assembly of both of the metalloclusters contained with the MoFe protein, P-cluster, and FeMo-cofactor.⁴² However, the amount of Fe protein required to sustain these functions under steady-state growth conditions is likely to be minimal, indicating that the elevated level of Fe protein relative to MoFe protein within cells represents a physiologically relevant mechanism for maximizing catalytic efficiency.

The results further support the earlier findings that suggested that unlimited high pressures of N₂ could not completely suppress H₂ production and that the ratio of H₂ production to N₂ consumption in fact approaches unity at high pressures,^,28 behavior explained by the re/oa mechanism we have developed recently.^9,18–20 The kinetic analysis shows how this behavior arises: the second-order process of enzyme activation by H₂ re with liberation through N₂ binding outcompetes the first-order “decay” of E₄(4H) through the HP process.

Two striking differences in the function of Mo-, V-, and Fe-nitrogenases are revealed here. Most importantly, the observation that Fe-nitrogenase produces far more H₂ per N₂ reduced at $P_{{\text{N}}_2}\le 1$ atm than the Mo-enzyme arises not, as might have been expected, because Fe-nitrogenase exhibits a correspondingly greater rate constant for HP. Indeed, the rate constant for HP by E₄(4H) of Fe-nitrogenase is only 70% of that for Mo-nitrogenase! Instead, Mo-nitrogenase is a more efficient catalyst for N₂ reduction because of the roughly 10-fold greater second-order rate constant for the N₂-fixing pathway of E₄(4H) reactivity, resulting in a k_re/k_HP rate constant ratio of ~7 (Table 1): Mo-nitrogenase is simply a better N₂ reduction catalyst. Second, the maximum velocity for NH₃ formation, $\overline{k}$, for Mo-nitrogenase is 2 times that of Fe-nitrogenase, a finding reinforced by previous data demonstrating that electron flux through Mo-nitrogenase is roughly twice that of Fe-nitrogenase. These two differences account for the poorer catalytic efficiency of Fe-nitrogenase and can be extrapolated to the intermediate reactivity observed for V-nitrogenase.

An experimental and theoretical study of the differences among the nitrogenases will provide a fruitful avenue for improving our understanding of how the differences in the metal clusters and their surrounding protein environments tune the reactivity to favor N₂ reduction over H₂ evolution in the different forms of nitrogenase, as quantified by the kinetic analysis presented here.

ABBREVIATIONS

BSA

bovine serum albumin

FeFe-co

active-site cofactor of iron-only nitrogenase

FeMo-co

active-site cofactor of molybdenum-dependent nitrogenase

Fe-N₂ase

iron-only nitrogenase

FeV-co

active-site cofactor of vanadium-dependent nitrogenase

HP

hydride protonolysis

$\overline{k}$,

turnover number (kcat)

K

binding constant for N2 (kre/$\overline{k}$)

kac

rate constant for accumulation of electrons on a cofactor

kcat

turnover number

kHP

rate constant for hydride protonolysis

kre

rate constant for reductive elimination

LT

Lowe and Thorneley kinetic scheme

Mo-N2ase

molybdenum-dependent nitrogenase

oa

oxidative addition

$P_{{\text{N}}_2}$,

partial pressure of dinitrogen

r

$k_{{\text{H}}_2}/k_{{\text{N}}_2}$

re

reductive elimination

V-N2ase

vanadium-dependent nitrogenase

z

kHP/kac