Computational Model Study of the Experimentally Suggested Mechanism for Nitrogenase

The mechanism for N2 activation in the E4 state of nitrogenase was investigated by model calculations. In the experimentally suggested mechanism, the E4 state is obtained after four reductions to the ground state. In a recent theoretical study, results for a different mechanism have been found in excellent agreement with available Electron Paramagnetic Resonance (EPR) experiments for E4. The two hydrides in E4 leave as H2 concertedly with the binding of N2. The mechanism suggested differs from the experimentally suggested one by a requirement for four activation steps prior to catalysis. In the present study, the experimentally suggested mechanism is studied using the same methods as those used in the previous study on the theoretical mechanism. The computed results make it very unlikely that a structure obtained after four reductions from the ground state has two hydrides, and the experimentally suggested mechanism does therefore not agree with the EPR experiments for E4. Another structure with only one hydride is here suggested to be the one that has been observed to bind N2 after only four reductions of the ground state.


INTRODUCTION
Nitrogenases are the only enzymes in nature that can convert nitrogen in air into useful products.To accomplish this task, the most common form uses a complicated cofactor consisting of seven irons and one molybdenum connected by sulfides. 1An unusual feature of the cofactor is a centrally bound carbide. 2 Another one is a homocitrate ligand bound to the molybdenum.An optimized structure obtained after four reductions (E 4 ) is shown in Figure 1.
A plausible mechanism for N 2 activation has been very difficult to obtain, but it has long been known that the first step in N 2 activation occurs after four reduction steps in the catalytic cycle in a state termed E 4 . 3A breakthrough in the understanding of activation occurred using EPR a decade ago.The main features obtained in the experimental EPR study of the N 2 activation in E 4 are the following 4−6 1. E 4 should have two hydrides.
2. These hydrides should form H 2 in a concerted process with N 2 binding.
3. The process is reversible by changing the pressures of H 2 and N 2 .
4. The barriers for formation of H 2 from a hydride and a proton must be higher than the one for the allowed formation of H 2 from the two hydrides.
5. A mutation of the second shell Val70 significantly disturbs the nitrogenase activity. 7he EPR experiment explained the surprising fact that for each N 2 , there is a release of one H 2 .The overall reaction is Figure 1.Model used for the present study shows which amino acids were included.The model is built on the X-ray structure 3U7QS 2 and is shown here after four reductions from the ground state with two hydrides and two protonated sulfides.
In the experimentally suggested mechanism, E 4 is obtained after four reductions of the ground state E 0 . 4−6 However, theoretical modeling studies have suggested that four preactivation steps are needed before catalysis starts. 8That suggestion implies that E 4 is obtained, not by four, but by eight reductions of the ground state.With eight reductions, the redox state of E 4 instead is (Mo 3+ 7Fe 2+ ), which is the lowest possible stable redox state for the cofactor.With the eight reductions, four more positions to place the protons, always accompanied by the reductions, are needed than those for the experimental mechanism.For that reason, it was initially suggested that the carbide should be protonated three times. 9However, it was later shown by a modeling study that with a release of a sulfide from the cofactor, the carbide would only be protonated once. 10ecently, it was found experimentally that the carbide is not protonated at all. 11 mechanism for nitrogen activation in E 4 without carbide protonation has recently been suggested by model calculations. 12That mechanism agrees with all of the above experimental findings for the E 4 state.Point 4 above is particularly significant since it means that several independent requirements on the mechanism are fulfilled.
The experimentally suggested mechanism for nitrogen activation in the E 4 state is quite different from the theoretically suggested one since it is built on the premise that E 4 in the catalytic cycle is reached after only four reductions of the ground state, 4−6 instead of the eight reductions required in the theoretical mechanism.In the present modeling study, the experimental mechanism will be investigated by the same methods as were used recently for the theoretical mechanism. 12he purpose of the study is to investigate if the experimentally suggested structure fulfills the requirements set by the EPR experiments for E 4 .
There are many theoretical studies of the E 4 state of nitrogenase.The most abundant ones are the ones by Cao and Ryde, 13 Pang and Bjornsson, 14 and Dance. 15However, none of them discuss the energetics of H 2 release in E 4 , which is the subject of this paper, and they will therefore not be discussed further here.

METHODS
The methods used in the present study are exactly the same as those used in the recent study of the theoretical mechanism of the E 4 state. 12−18 In particular, the mechanism of seven redox enzymes has been compared to available experiments with errors of usually less than 3 kcal/ mol. 18Those enzymes were photosystem II, cytochrome c oxidase, NiFe and FeFe hydrogenases, NiFe-CO dehydrogenase, multicopper oxidase, and acetyl-CoA synthase.The electronic structure method is built on the DFT functional B3LYP 19 but with the fraction of exact exchange changed from 20 to 15%.Geometries were optimized with the rather small lacvp* basis set, and the final energies were obtained with a large cc-pvtz(-f) basis.For zero-point effects and determination of transition states, Hessians were computed by using B3LYP with lacvp*.Dispersion effects were obtained with the empirical D2 correction. 20Cluster modeling of the enzyme active site was used, 21 with a model of about 170 atoms, essentially the same as in the previous study. 12Solvation effects were included with a dielectric constant of 4.0. 22The spin-coupling used for all states studied here was (−2,−3,−4), where the nomenclature shows the irons that have negative spins.The experimental numbering of the irons is used.The spin state is a doublet.The Jaguar and Gaussian programs were used. 22,23Since the BP86 functional 24 was used in the theoretical part of the experimental paper on the mechanism, 25 it was also used here for comparisons.

RESULTS
−6 Following that suggestion, the activation of N 2 takes place after four reductions of the ground state E 0 , in a state commonly referred to as E 4 .In the EPR study, it was found that there are two hydrides in E 4 .With four reductions, it means that two groups are protonated in E 4 , which are suggested to be the belt sulfides S2B and S3A, see Figures 1 and 2. 25 The two hydrides were found to disappear from the cluster as N 2 was activated, suggesting a concerted process.The structure in Figure 1 was obtained using BP86, while that in Figure 2 was found using B3LYP following the experimental suggestion for the structure.The structures are quite similar and the spin states are doublets.It is important to note that the B3LYP structure in the figure is much higher in energy by +14.7 kcal/mol than the one with only one hydride and three protonated sulfides using that functional. 17,26he first part of the present study reports the results using the B3LYP functional with 15% exact exchange.For details of the methods, see Section 2. The first step in the N 2 activation should be the formation of H 2 from the two hydrides.To obtain the reaction energy, the two hydrides were removed from the cluster and placed at a long distance away as H 2 .The reaction was found to be exergonic by −47.9 kcal/mol, including a gain of −8.4 kcal/mol for the translational entropy of free H 2 .The result is in line with previous studies using this functional. 17,26In the EPR study, the process should be reversible by varying the pressures of H 2 and N 2 .For the binding of N 2 , see further below.
The release pathway for H 2 was studied by varying the H−H distance in steps of 0.1−0.2Å.As the distance was decreased between the hydrogens, the hydride originally bound between Fe2 and Fe6 moved toward S2A and the energy goes down by −6.4 kcal/mol.That result agrees with the previous ones showing that a structure with three protonated sulfides and one hydride is lower in energy than one with two hydrides. 17It should be added that the protonation of S2A does not give the lowest energy structure.As the H−H distance was shortened further, a TS for H 2 formation was reached.A full TS optimization was performed, and the H−H distance was found to be 1.16 Å; see Figure 3.The imaginary frequency is 1177 cm −1 .There is a small barrier of 4.4 kcal/mol counted from To complete the picture, the binding of N 2 was investigated for the structure where H 2 has been released.Binding to Fe6 has been favored experimentally, but no binding was found when the translational entropy loss of +9.9 kcal/mol was included.A similar result was obtained for the binding on Fe4.
As mentioned above, the B3LYP functional with 15% exact exchange has been tested for the mechanisms of seven enzyme redox reactions, actually all the ones studied so far. 18The results show errors of usually 3 kcal/mol or less compared with available experiments.In contrast, the BP86 functional 24 used in the combined experimental and theoretical study of the nitrogenase mechanism 25 has not been tested on any enzyme redox mechanism.However, for completeness, the nitrogenase mechanism in E 4 has here been studied by also using BP86.
The E 4 structure obtained using the BP86 functional is shown in Figure 1.It is very similar to the B3LYP structure.It can be noted that the hydride bound between Fe2 and Fe6 points in a different direction for the lowest energy structure than for the one in the previous study. 25The energy difference is small (−3.5 kcal/mol) and is not significant for the present study.
When the two hydrides are removed from the BP86 structure, forming a free H 2 , the energy goes down by −32.5 kcal/mol, including the translational entropy gain of −8.4 kcal/mol.This exergonicity is smaller than for B3LYP with −47.9 kcal/mol, see above but still very different from what was suggested by the EPR experiments, which indicate a reversible release of H 2 and binding of N 2 .In the previous study, 25 no energies for this process were given, but only a sketch of the results was shown in a figure .From that figure, it is clear that very different results were obtained there than the ones obtained here, even though the BP86 functional was used in both studies and the E 4 structures are very similar.
For locating an approximate TS for H 2 formation, the H−H bond was varied in steps, just as for B3LYP, described above.A linear scan was done and the highest point was found for a distance of 1.10 Å.The approximate barrier is +9.1 kcal/mol compared to +10.8 kcal/mol for B3LYP.
An important feature of the suggested mechanism in the previous study 25 was that a big barrier was found for the loss of H 2 .As described above, with the B3LYP functional, there is no barrier for the release after the TS has been passed.The question is whether there is a barrier using BP86.A very large barrier of almost 20 kcal/mol is required in the suggested mechanism, in order to prevent the release for a sufficiently long time to allow a quite strong bond formation of N 2 .To investigate this question, the H−H bond is shortened from 1.10 Å in the TS to 0.90 Å and then to 0.70 Å.Just as for the B3LYP functional, no additional barrier was found.At the end point, the nearest distance to sulfur is 4.0 Å, and to the nearest iron is 4.1 Å.A difference between the results for BP86 and B3LYP is that with BP86 the protonated S2A is not lower in energy than the dihydride starting point.
In the suggested mechanism, 25 a strong binding of N 2 is required to the cluster, where H 2 has been removed.In the present study, no binding at all is found, using either B3LYP, see above, or BP86.Binding on Fe6 and Fe4 was investigated also for BP86.The lack of binding of N 2 to the type of experimentally suggested structure in Figures 1 and 2, is in line with another recent theoretical study. 27In that study, it was concluded that for the type of structure suggested experimentally, no functional gives favorable binding to any E n (n = 0,4) state.Several DFT functionals were used.
The best structure obtained after only four reductions in the previous study has only one hydride. 10The state was termed A 4 .An important feature of that A 4 structure is that it is preceded (in A 4 ) by a loss of a sulfide, leading to a large structural change.It was investigated here whether N 2 could bind to that structure.Indeed, a weak binding to Fe4 was found, see Figure 4.It is the same position that was found to bind and activate N 2 four reductions later in E 4 . 12The enthalpic binding energy is calculated to be −9.8 kcal/mol.In the case of a strong binding, the entire translational entropy of +9.9 kcal/mol is assumed to be lost upon the binding.In the present case of a very weak binding, it is reasonable to assume that some of that entropy is kept.A free energy of binding of about 5 kcal/mol appears reasonable.It is here speculated that it is the structure in Figure 4 that has been considered as an activated N 2 structure in the investigation by Lowe and Thorneley.

CONCLUSIONS
The key step in the nitrogenase mechanism is the nitrogen activation in the E 4 state of the catalytic cycle.EPR experiments have outlined the main features of the activation, see Section 1. 4−6 In combination with other experimental results, 3 a structure for E 4 with two hydrides and two protonated sulfides was suggested.In a combined theoretical and experimental study, the details of the mechanism were studied. 25In another theoretical paper, 12 a different mechanism has recently been suggested, which agrees with all experimental findings for E 4 .In that mechanism, four preactivation steps were suggested.No such preactivation is included in the experimentally suggested  The Journal of Physical Chemistry B mechanism, where N 2 should be activated after only four reductions of the ground state.
In the present study, an investigation has been performed for the experimentally suggested mechanism using the same methods as used for the theoretical mechanism based on B3LYP with 15% exact exchange. 12In contrast, the BP86 functional was used in the previous combined theoretical and experimental study. 25Therefore, also the results for the BP86 functional were obtained in the present study.
−6 Experimentally, the release of H 2 and binding of N 2 occurs in a concerted step in E 4 , which can be reversed by changing the pressures of H 2 and N 2 .In contrast, the calculations on the A 4 state with two hydrides give a very exergonic release of H 2 by −47.9 kcal/mol using B3LYP (15%), and N 2 does not bind at all in the product.Possible errors in the calculations of this order of magnitude can safely be ruled out. 18he conclusion drawn here is that the A 4 state obtained after four reductions of the ground state is not the same structure as the one observed by EPR for E 4 in the catalytic cycle.Instead, it is here suggested that the structure that binds N 2 after only four reductions 3 is the one in Figure 4 with only one hydride.
Coordinates for all structures (PDF)

Figure 2 .
Figure 2. B3LYP optimized structure obtained after four reductions from the ground state.It follows as closely as possible the experimentally suggested structure, 25 as described in the text.It has two hydrides and two protonated sulfides.The numbering of the irons follows that of the X-ray.

Figure 3 .
Figure 3. Optimized TS for H 2 formation from the two hydrides.

Figure 4 .
Figure 4. Optimized A 4 structure with bound N 2 .There is only one hydride in this structure.
NotesThe author declares no competing financial interest.■ACKNOWLEDGMENTS