Hemoglobin as a Nitrite Anhydrase: Modeling Methemoglobin-Mediated N₂O₃ Formation

Computational Details

(a) Some general remarks

The various isomerism and spin state possibilities lead to a formidable combinatorial space of reaction channels, which we have nonetheless explored quite thoroughly. Before presenting a systematic account of the different pathways considered, some additional remarks on these variables might be helpful. As mentioned above, we have taken into account the three linkage isomers of Fe³⁺-NO₂⁻ and different isomers of N₂O₃ (Figure 1). The asymmetric form of N₂O₃ (asym-N₂O₃) has a primarily ionic bond between the nitrogen centers and is the form observed in gas phase.^[37] The symmetric (sym-N₂O₃) and trans-cis forms have been observed in low temperature matrix.^[38] Theoretical studies show that the sym- and trans-cis-N₂O₃ forms are respectively ~1 and ~6 kcal mol⁻¹ less stable than asym-N₂O₃.^[39] While concentrating on the formation of the two more stable N₂O₃ isomers, asym- and sym-N₂O₃, we have not neglected to examine the formation of trans-cis-N₂O₃.

We have investigated the ‘Fe³⁺-heme-NO₂⁻ + NO’ pathway [equation (2)] suggested by Basu et al.^[12] with both five- and six-coordinate heme models (Models A and B, Figure 2). Although consideration of five-coordinate models might not seem absolutely required, the proximal histidine has been shown to be susceptible to dissociation in a number of heme proteins.^[40,41,42] We therefore examined both types of models. The coordination number is likely to affect the spin state of the iron center, which in turn should lead to different reaction channels. For low-spin Fe(III) (S = ½), reaction with free NO can occur on two different surfaces, depending on the relative alignment of the spins of the NO and of the iron center. Antiparallel alignment results in an open-shell M_S = 0 surface (denoted hereafter as S1, Figure 3, I), whereas parallel alignment produces an M_S = 1 surface (denoted T1, Figure 3, II). If the Fe(III) center is intermediate spin state (S = 3/2), reaction with NO would occur on a different M_S = 1 surface (hereafter referred to as T2, Figure 3, III). Studies of the S1 and T2 surfaces entailed rather challenging broken-symmetry transition state optimizations; to our considerable satisfaction, the vast majority of these were successful.

To keep track of the extensive combinatorial space of isomerism and spin variables, we will refer to each optimized geometry with a four-part subscript, indicating the overall coordination number, nitrite linkage isomerism, the spin surface, and the N₂O₃ isomer produced as shown below in Scheme 1:

(b) N₂O₃ formation from Fe³⁺-Por-NO₂⁻

Briefly stated, B3LYP/6-311G(d,p) calculations indicate an intermediate-spin state (S = 3/2) iron center for the five-coordinate Fe³⁺-Por-O-nitrito complex, which implies that N₂O₃ formation occurs on the T2 surface. Formation of asym-N₂O₃ on this surface is significantly lower in energy (by ~9 kcal mol⁻¹) than formation of sym-N₂O₃. Some additional details are as follows.

The reactant structures of the five-coordinate (S = 3/2) O-nitrito linkage isomers and free NO have similar relative energies (Table 1). The O-nitrito β isomer (Reac_A-Oβ-T2, Figure 4) was employed as the energy reference for all calculations on the five-coordinated system in this study. The O-nitrito a reactant is only 0.4 kcal mol⁻¹ higher in energy (Table 1 and Supporting Information Figure S1).^[43]

The preferred reaction pathway for formation of N₂O₃ from five-coordinate (S = 3/2) Fe³⁺-Por-NO₂⁻ involves generation of asym-N₂O₃ from the O-nitrito β isomer (Reac_A-Oβ-T2, Figure 4). At the transition state (TS_{A-Oβ-T2-asym}), the incipient N_NO-N_NO2 bond is about 1.90 Å. The displacement vector of the imaginary frequency (176i cm⁻¹) shows that bond formation occurs simultaneously with Fe-O dissociation, resulting in N₂O₃ release. The overall spin population on NO at the TS is −0.53, compared to −1.01 for the reactant, indicating significant bond formation between NO and NO₂⁻. Simultaneously with NO attack, an electron is transferred from the NO₂⁻ ligand to the iron center, resulting in formation of intermediate- spin (S = 1) Fe²⁺. The overall barrier for this reaction pathway is 11.6 kcal mol−1 (Figure 4, top), indicating a very feasible pathway. The reaction energy is positive (12.0 kcal mol⁻¹),^[44] making product formation endothermic. It is likely, however, that the displaced N₂O₃ molecule would be replaced by another ligand (such as NO or H₂O), which would reduce the reaction energy.

Formation of asym-N₂O₃ from the O-nitrito a isomer of intermediate-spin Fe³⁺-Por-NO₂⁻ occurs analogously to the O-nitrito β isomer and displays similar reactivity (TS_{A-Oα-T2-asym}, ΔG^sol = 12.4 kcal mol⁻¹, ΔH^sol = 7.5 kcal mol⁻¹, ΔE = 7.3 kcal mol⁻¹, Supporting Information Figure S2A). For the N-nitrito isomer, asym-N₂O₃ formation is not possible, as it would require dissociation of the nitrite ligand from the iron ion to allow for N_NO-N_NO2 bond formation. Instead of an N_NO-N_NO2 interaction, N_NO-O_NO2 bond formation can occur, leading to generation of sym-N₂O₃. The optimized transition states for formation of sym-N₂O₃ from the three nitrite linkage isomers of intermediate-spin Fe³⁺-Por-NO₂⁻ display barriers of 20.0 to 20.8 kcal mol⁻¹, which is ~9 kcal mol⁻¹ higher than for formation of asym-N₂O₃ (Figure 4, top). At the optimized geometry for the O-nitrito β TS, the incipient N_NO-O_NO2 bond is 1.75 Å (TS_{A-Oβ-T2-sym,} imaginary frequency = 306i cm⁻¹, Figure 4 bottom, right). The NO radical has an overall spin of only −0.23, and the iron center is partially reduced with a spin population of 2.35. The optimized product (Prod_A-sym) indicates an endothermic reaction energy (14.5 kcal mol⁻¹), which is slightly higher than that for asym-N₂O₃. The O-nitrito a isomer shows a similar spin density profile and reactivity (TS_{A-Oα-T2-sym,} ΔG^sol = 20.0 kcal mol⁻¹, ΔH^sol = 16.0 kcal mol⁻¹, ΔE = 14.0 kcal mol⁻¹, Supporting Information Figure S2B). Formation of sym-N₂O₃ from the N-nitrito isomer entails slightly different bond distances (TS_A-N-T2-sym, Supporting Information Figure S3), but a similar barrier of 20.3 kcal mol⁻¹ (ΔH^sol = 15.3 kcal mol⁻¹, ΔE = 14.0 kcal mol⁻¹).

The results for the five-coordinate complexes show facile formation of asym-N₂O₃ from the intermediate-spin O-nitrito linkage isomers. If the five-coordinate Fe(III) center instead adopts a low-spin state (S = 1/2, S1 and T1 surface, Figure 3), the reaction barriers are increased by several kcal mol⁻¹. The low-spin reactant states of three nitrite-linkage isomers display energies of ~5 to 11 kcal mol⁻¹ relative to the intermediate-spin reactant complexes (Table S1, Supporting information), underlining the preference for an intermediate-spin state at the five-coordinated iron-center (for optimized geometries, see Supporting Information Figure S4–S6). Formation of asym-N₂O₃ from the low-spin O-nitrito-β isomer has a barrier of 14.7 kcal mol⁻¹ (T1 surface, Figure 5, top), compared with 11.6 kcal mol⁻¹ for the intermediate-spin complex. At the TS (TS_{A-Oβ-T1-asym,} Figure 5), the incipient N_NO-N_NO2 bond distance is 2.49 Å, which is much longer than that on the T2 surface (1.90 Å, TS_A-Oβ-T2-asym, Figure 4). The iron center is essentially reduced to Fe²⁺ (spin population of 1.97), which results in significant radical character of the NO₂ ligand (spin population of −0.58, Figure 5). This allows N_NO-N_NO2 bond formation to occur earlier on the T1 surface than on the T2 surface. Formation of sym-N₂O₃ from the low-spin N-nitrito isomer has a barrier of 23.0 kcal mol⁻¹ (ΔH^sol = 17.4 kcal mol⁻¹, ΔE = 16.6 kcal mol⁻¹, Supporting Information Figure S6C), which is also a few kcal mol⁻¹ higher than that on the T1 surface (20.0 kcal mol⁻¹).

In summary, the computational results suggest that five-coordinate Fe³⁺-Por-NO₂⁻ prefers an intermediate-spin (S = 3/2) iron center (T2 surface) over a low-spin one (S = ½). Attack of nitric oxide on the coordinated nitrite ion preferably leads to formation of asym-N₂O₃ (with a computed barrier of 11.6 kcal mol⁻¹ on the T2 surface).

(c) N₂O₃ formation from Fe³⁺-Por-Im-NO₂⁻

Our studies of N₂O₃ formation from six-coordinate Fe³⁺-Por-Im-NO₂⁻, which are very possibly more faithful mimics of methemoglobin, may be summarized as follows. Low-spin Fe(III) (S1 and T1) surfaces are most relevant for this model. Formation of a T2 species with intermediate-spin Fe(III) center requires partial loss of the imidazole ligand so the complex would no longer be truly 6-coordinate. N-nitrito coordination of NO₂⁻ is slightly favored over O-nitrito coordination. For the O-nitrito models, asym-N₂O₃ formation is ~9 kcal mol⁻¹ lower in activation-barrier than sym-N₂O₃ formation. Both sym- and asym-N₂O₃ initially remain coordinated to the iron complex, displaying a noninnocent electronic structure. For the N-nitrito isomer, the results indicate a preference for formation of trans-cis-N₂O₃ over sym-N₂O₃. Some details of our findings are discussed below.

Six-coordinate Fe³⁺-Por-Im-NO₂⁻ has an unambiguous low-spin Fe(III) center (S = ½), so the S1 and T1 surfaces (Figure 3) are expected to be most relevant (however, the T2 surface has been considered as well). On the low-spin surface, N-nitrito coordination is favored by 1.3 kcal mol⁻¹ over O-nitrito coordination. Parallel (T1) or antiparallel (S1), alignment of the spin on NO results in similar relative energies (Table 2 and Supporting Information Figure S7 and S8). Our results are in line with previous theoretical calculations on Fe³⁺-Por-L-NO₂⁻ complexes (L = DMS,^[28] His,^[12] NO,^[29] Im^[23]), where the N-nitrito form was favored over the O-nitrito isomers by 1.9 to ~10 kcal mol⁻¹ (electronic energies only). Experimental results by Kurtikyan et al. have shown that whereas five-coordinate Fe³⁺-Por-NO₂⁻ complexes prefer O-nitrito coordination, the stable form of the six-coordinate complexes is the N-nitrito bound form, in agreement with our results.^[45]

N_NO-N_NO2 bond formation and generation of asym-N₂O₃ from the low-spin O-nitrito α-isomer of Fe³⁺-Por-Im-NO₂⁻ on the T1 surface has a barrier of 19.4 kcal mol⁻¹ (TS_{B-Oα-T1-asym}, Figure 6, top). For the S1 surface, a similar barrier is obtained (ΔG^sol =20.2 kcal mol⁻¹, ΔH^sol = 14.6 kcal mol⁻¹, ΔE = 14.2 kcal mol⁻¹, Supporting Information Figure S9). The spin population on NO at the TS is reduced to 0.6 (TS_{B-Oα-T1-asym}, Figure 6) showing significant electron pairing with NO₂⁻. In contrast to five-coordinate Fe³⁺-Por-NO₂⁻, the unpaired electron generated on NO₂⁻ at the TS is not transferred to the iron, which therefore remains low-spin Fe(III). The displacement vector of the imaginary frequency of the optimized TS (258i cm⁻¹) reveals that bond formation between NO and NO₂⁻ is not accompanied with Fe-O bond breakage, i.e. the asym-N₂O₃ product remains coordinated to iron (Figure 6). The bound-product states display a noninnocent electronic structure, with a spin-population of 0.94 on the asym-N₂O₃ ligand. The N-N bond length is rather short, 1.49 Å (compared to 1.89 Å in free N₂O₃), which is a consequence of radical character of the non-innocent ligand.

Formation of asym-N₂O₃ from the O-nitrito β-isomer of low-spin Fe³⁺-Por-Im-NO₂⁻ occurs as from the O-nitrito α-isomer, but involves a slightly lower barrier of 17.7 kcal mol⁻¹ (TS_{B-Oβ-T1-asym}, T1 surface, ΔH^sol = 14.3 kcal mol⁻¹, ΔE = 15.7 kcal mol⁻¹, Supporting information Figure S10). The geometry parameters and spin profiles are similar for O-nitrito a and β, supporting a similar reactivity towards N₂O₃ formation for the two six-coordinate low-spin O-nitrito isomers.

Analysis of the alternative N_NO-O_NO2 bond formation pathways show that sym-N₂O₃ formation is less feasible than asym-N₂O₃ formation, as also observed for the five-coordinate complex. Similar results were obtained for both low-spin surfaces, S1 and T1, with barriers of 25.8 kcal mol⁻¹ kcal mol⁻¹ (TS_{B-Oα-S1-sym,} Supporting Information Figure S11) and 30.1 kcal mol⁻¹ (TS_B-Oα-T1-sym Figure 7, top), respectively. The sym-N₂O₃ product (Prod_B-Oα-T1-sym) displays noninnocent character (spin population of 0.54, Figure 7, bottom), while remaining coordinated to the iron center. Release of the product is accompanied by reduction of the iron to intermediate-spin (S = 1) Fe(II) (Figure 7).

The reaction pathway for formation of sym-N₂O₃ from low-spin N-nitrito Fe³⁺-Por-Im-NO₂-proceeds as for the O-nitrito complexes and has a barrier of 24.5 kcal mol⁻¹ (TS_B-N-S1-sym, S1 surface, ΔH^sol = 18.5 kcal mol⁻¹, ΔE = 17.2 kcal mol⁻¹, Supporting Information Figure S12). An alternative and more feasible route to N₂O₃ formation was obtained for the N-nitrito linkage isomer when N-O bond formation leads to trans-cis-N₂O₃; this process has a barrier of 19.8 kcal mol⁻¹ (Figure 8, top). The trans-cis product also exhibits noninnocent character (Figure 8, bottom). The spin population on iron decreases from 1.11 at the reactant (Reac_B-N-S1) to 0.39 at the bound product geometry (Prod_{B-N-S1-trans-cis}), indicating that the iron center is partially reduced. The spin density on the trans-cis-N₂O₃ ligand is −0.45, which is centered on the iron-bound oxygen and the adjacent nitrogen. The electronic structure of the product is thus intermediate between Fe³⁺-N₂O₃^·− and Fe²⁺-N₂O₃. The results indicate that formation of trans-cis-N₂O₃ and asym-N₂O₃ is approximately equally feasible, despite the significant energy difference between the free forms of the two N₂O₃ isomers. Following release of trans-cis-N₂O₃, it is likely to isomerize to sym- or asym-N₂O₃, which are calculated to be 5 to 6 kcal mol⁻¹ more stable.^[39] The computed transition state for isomerization of free trans-cis-N₂O₃ to sym-N₂O₃ has a barrier of only 4.1 kcal mol⁻¹ (Supporting Information Figure S13). The computational results show that N₂O₃ formation from the six-coordinate low-spin (S = ½) complex occurs in two steps: in the first step, N-N or N-O bond formation occurs, resulting in formation of a coordinated one-electron-reduced N₂O₃ form, followed by electron transfer to the iron center in the second step and release of free N₂O₃. Product dissociation involves formation of an intermediate-spin electronic structure (S = 1) at the iron center. This observation led us to also examine N₂O₃ formation from an intermediate-spin Fe³⁺-Por-Im-NO₂⁻ reactant structure (T2 surface), from which N₂O₃ formation and release can occur in a single step (Figure 9). Formation of an intermediate-spin reactant complex of Fe³⁺-Por-Im-NO₂⁻ is accompanied by a lengthening of the Fe-N_Im bond to 2.44 Å (Supporting Information S14A), highlighting the importance of the proximal histidine in modulating the spin state of the iron center. The resulting complex has a relative energy of 0.8 kcal mol⁻¹, making it energetically accessible. The optimized transition state for sym-N₂O₃ formation on the T2 surface exhibits an elongated Fe-O_NO2 bond, implying that product release occurs concertedly with N_NO-O_NO2 bond formation (TS_B-Oα-T2-sym, Supporting Information S14B). The incipient N_NO-O_NO2 bond is very short, 1.57 Å. The barrier for this transition state is 22.1 kcal mol⁻¹ (Figure 9). The products consist of a dissociated closed-shell N₂O₃ molecule and an intermediate-spin Fe(III)-Im complex (Figure 9). Similar results were also obtained for the N-nitrito isomer, for which the formation of sym-N₂O₃ on the T2 surface has a barrier of 21.2 kcal mol⁻¹ (ΔH^sol =20.0 kcal mol⁻¹, ΔE = 19.1 kcal mol⁻¹, TS_B-N-T2-sym, Supporting Information Figure S15).

The results for intermediate-spin Fe³⁺-Por-Im-NO₂⁻ are thus analogous to the five-coordinate complex, with product formation and release occurring in the same step. It therefore appears that N₂O₃ formation from six-coordinate heme-nitrite complexes would be more facile if the trans ligand would be weakened, for example, via hydrogen-bond interactions with other residues.

(d) N₂O₃ formation from Fe³⁺-NO

Ford and coworkers have suggested that N₂O₃ formation from methemoglobin might occur via an alternative pathway in which an NO-coordinated heme reacts with free NO₂⁻ (eq. 3).^[19] Two variants of this pathway have been proposed, a direct attack of the nitrite anion on Fe³⁺-heme-NO ({FeNO}⁶),^[19] or a two-step pathway, involving electron transfer from NO₂⁻ to the heme complex in the first step (yielding Fe²⁺-heme-NO or {FeNO}⁷), followed by attack of the NO₂ radical so produced on NO.[19] We have analyzed the proposed pathways computationally and the results may be summarized as follows: Electron transfer from free NO₂⁻ to the porphyrin complex is exothermic, indicating that the initial step involves formation of an NO₂ radical. Reaction of the NO₂ radical with Fe²⁺-Por-Im-NO ({FeNO}⁷) to give N₂O₃ has a low barrier, indicating that this could provide a very facile way for N₂O₃ formation. Details of our findings are given below.

We have evaluated whether a diradical reactant state (originating from electron transfer from NO₂⁻ to the Fe³⁺-Por-Im-NO complex, Figure 10) is uphill or downhill from the charge-separated reactant by computing the ionization potential (IP) of NO₂⁻ and comparing it to the electron affinity (EA) of Fe²⁺-Por-Im-NO⁺. The computed EA of Fe²⁺-Por-Im-NO⁺ is −118.1 kcal mol⁻¹, compared to a computed IP for NO₂⁻ of 103.9 kcal mol⁻¹ (ΔG^sol). Transfer of an electron from NO₂⁻ to the iron-NO complex is thus favorable by 14.2 kcal mol⁻¹. The results indicate that N₂O₃ formation is more likely to occur via a diradical reactant complex (Fe²⁺-Por-Im-NO with NO₂·) rather than directly from a charge-separated complex (Fe²⁺-Por-Im-NO⁺ and NO₂⁻).

The NO₂ radical can react with the Fe²⁺-Por-Im-NO ({FeNO}⁷) center to yield N₂O₃. The reaction has to occur on an open-shell M_S = 1 surface (S1) to allow bond formation between the radicals. At the optimized reactant state, the spin population on NO₂ is exactly 1, aligned antiparallel to the unpaired electron on Fe²⁺-Por-Im-NO (Reac_C-S1, Figure 11, bottom). The spin density of the {FeNO}⁷ complex resides primarily on the NO ligand (0.79), with only a small amount on the iron. Although formation of different isomers of N₂O₃ might be anticipated, only the transition state for formation of trans-cis-N₂O₃ was successfully located (TS_{C-S1-trans-cis}, imaginary frequency 214i cm⁻¹, Figure 11). At the TS, the incipient N_NO-O_NO2 bond is 2.17 Å. The spin density on the NO₂ radical is reduced to −0.33, indicating strong electron pairing pairing with the coordinated NO. The barrier for this transition state is 8.1 kcal mol⁻¹ (solvent corrections not included^[46]) relative to the reactant complex, implying a very facile pathway for N₂O₃ formation. The closed-shell N₂O₃ generated remains coordinated to the iron center and has a relative energy of 7.3 kcal mo1⁻¹ (Figure 11).