Theoretical study on the relative energies of cationic pterin tautomers

Introduction

Pterins are heterocyclic compounds that have wide and important roles in various biological systems. Some pterins exist as enzymes [1–3], coenzymes [4, 5], sensitizers [6–8], pigments [9], and inhibitors [10]. The chemical behavior and function of pterins depend on a wide variety of other conditions such as the availability of molecular oxygen, redox environment, and pH [11–16]. Understanding the relative acidity and basicity of the various atoms within a pterin is an important step in understanding the chemistry with regard to not only acid/base chemistry but also will help to explain binding and other noncovalent interactions. Theoretical calculations can help to determine the relative energies of pterin structures, both as neutral tautomers as well as ionic species that would be found in acidic or alkaline media.

Back in the mid-1980s, there was quite a bit of activity in the chemical literature using theoretical calculations to investigate various electronic and structural properties of various pterins. These reports include topics such as the substrates of dihydropterin reductase [17–20], pterin ring basicities [17], and general pterin geometries [18, 19, 21]. These studies often used the SCF/STO, SCF/3-21, and CNDO/2 levels of theory, ignored solvent effects, and tried to compare several related pterins, pteridines, and quinazolines in various oxidation states. In the 1990s, Reibnegger reported several studies using Hatrree Fock calculations that investigated the geometries and charge densities of several pterins [22–24]. These studies mainly focused on the 5,8 reduced form of the pterins. Despite the various reduced and oxidized forms, the fundamental pterin structure consists of a fused heterocyclic system consisting of several nitrogen atoms (Figure 1).

Figure 1

Pterin numbering scheme.

Recently, the density functional theory (DFT) has been used in more focused studies investigating the relative stabilities of both the uncharged pterin tautomers found in aqueous solution as well as the possible anionic pterins formed in alkaline media through the use of PCM, polarizable continuum model. These reports [25, 26] indicate that the lactam and the lactim form of pterin, 1–3, commonly presented and discussed in the literature as the only predominant forms, are only some of six structures that should be considered, 1–6 [25] (Figure 2). The two lactim forms (owing to two hydroxyl rotamers, 2 and 3) are actually the least stable of the six structures and are calculated to be approximately 6 kcal/mol higher in energy than the lactam, 1. The lactim exists in two distinct conformations with the hydroxyl group aligned with either N3, 2, or N5, 3. In addition to the commonly accepted lactam and lactim forms, an α,β-unsaturated lactam, 4, and two exocyclic imine (guanidinyl) structures, 5 and 6, should also be considered as possible tautomers as they are calculated to be lower in energy than the (generally accepted) lactim forms.

Figure 2

Calculated relative energies of neutral pterin structures [22] (B3LYP/6-21G** level of theory and PCM water dielectric).

In alkaline media, the pterin will be deprotonated resulting in an anion. Previously reported results using DFT calculations of all the possible pterin anions present in alkaline media reveal that two main isomers exist [27] (Figure 3). The most stable anion structure, the enolate of the lactim, 7, is the most thermodynamically stable structure according to theoretical calculations. However, anilinic depronation of the lactam, 1, (or alternatively deprotonation at N1 from the corresponding guanidinyl lactam, 5) produces a structure, 8, that is only 1.9 kcal/mol higher in energy and, therefore, may play a significant role in the chemistry of pterins in alkaline media. All other anion structures reported in this study were >7 kcal/mol higher in energy than the pterin enolate, 7, and were considered to not be significant contributors.

Figure 3

Calculated relative energies of anionic pterin structures [23] (B3LYP/6-31+G*//B3LYP/3-21G* level of theory and PCM water dielectric).

In the current work, we report a DFT study of cationic pterins resulting from protonation in acidic aqueous media. The relative energies of the various possible protonated isomers will lend insight into the basicities of the numerous pterin positions. To remain consistent with the earlier reported studies, DFT calculations were performed using the PCM to represent the dielectric constant of water. Although calculations with the addition of discrete water molecules at selected hydrogen-bonding sites would produce more accurate energies, the numerous binding sites and various solvent orientations would have resulted in the number of structures and calculations to become very large. Protonation at the various oxygen or nitrogen positions of the six neutral pterin structures, 1–6, resulted in the generation of 32 different cationic structures, 9–40. Protonation of each neutral pterin can occur at one of the four ring nitrogen atoms (N1, N3, N5, or N8), on the anilinic nitrogen atom (N2′), or on the phenolic oxygen atom (O4′). Therefore, the resulting structures are organized and discussed based on the neutral pterin by which it is derived (1–6) and the location of protonation (ring or non-ring atoms). The charge densities of four of the parent neutral 6-methylpterin tautomers, 1–4, are also analyzed. High negative charge density should be an indication of sites of high proton affinity and should support the thermodynamic stability of the protonated products.

Materials and methods

Theoretical calculations were performed using Gaussian 09 on Abe Linux 64 cluster located at Carnegie Mellon University and on the Blacklight cluster located at the Pittsburgh Supercomputing Center [28]. All cationic structures, 9–40, were optimized at the B3LYP/6-31+G** level of theory, and all minima were confirmed by frequency analyses [26, 29–31]. All calculations were performed at 298.15 K and 1.0 atm. The calculated sum of the electronic and the thermal correction to the Gibbs free energies were compared, ΔG. The six most stable structures were also optimized using the MP2/6-31+G** for comparison [32]. All B3LYP thermal corrections were scaled by 0.9804, and all MP2 thermal corrections were scaled by 0.9646. All calculations were treated with the PCM water solvation model [33]. The most stable neutral pterin tautomers, 1–4, were minimized with the B3LYP/6-31+G** and MP2/6-31+G** levels of theory and a natural population analysis (NPA) was performed on each structure to produce the natural charge density [34].

Results and discussion

The relative energies of the 32 possible cationic pterins, 9–40, as calculated by DFT are shown in Table 1. An analysis of the results based on the neutral pterins, 1–6, from which the protonated product originates, is presented.

Table 1

Relative energies of various protonated pterins (B3LYP/6-31+G**, PCM solvation model with water dielectric).

Protonation of pterin tautomers at ring nitrogens

Protonation of lactam (1)

As neutral pterin 1 is the most stable neutral pterin tautomer, it is predicted that this structure will be the most prevalent structure in neutral aqueous media in free solution. Protonation of the ring nitrogen atoms produce the structures shown in Figure 4. Structure 9 is the most stable protonated pterin calculated and will, therefore, be the dominant form in acidic media. As N1 is the most basic atom, it will most likely be the site of protonation or reaction with another Lewis acid in free solution. Structure 12 is very close in energy to 9, and therefore, N8 and N1 are similar in their basicities. The pterin derived from protonation at N5, 11, is slightly higher in energy at 3.7 kcal/mol above structure 9. Protonation of ring nitrogen N3, 10, results in a very unstable product as this effectively removes that atom from participation in aromaticity. Therefore, structures 9, 11, and 12 will contribute to the distribution of pterins in acidic media where structure 10 will not contribute to any significant extent.

Figure 4

Relative calculated energies of pterins resulting from the ring nitrogen protonation of the lactam structure, 1.

Protonation of lactims (2 and 3)

Although the phenolic tautomers of the neutral pterin, 2 and 3, are calculated to be less stable compared to 1 by approximately 6 kcal/mol, these are still listed in many published reports and should, therefore, still be considered. Protonation of the ring nitrogen atoms reveal that N1 is again the most basic ring atom in the structure of all the protonated lactims (Figure 5). These structures, 13 and 17, are more than 4 kcal/mol higher in energy than the most stable pterin cation tautomer, 9, but are approximately 4 kcal/mol more stable than protonation on N8, 16 and 20. This differs from the results reported earlier that originated from 1 as the difference in energy from protonation at N1 and N8 was negligible at 0.2 kcal/mol. The pterin cations resulting from protonation at N3 and N5 (14, 15, 18, and 19) are all more than 12 kcal/mol higher in energy than 9 due to electronic factors and are an additional 5–7 kcal/mol higher when the phenolic hydrogen is aligned with the hydrogen atom in question due to steric interactions.

Figure 5

Relative calculated energies of pterins resulting from the ring nitrogen protonation of the two lactim structures, 2 (top) and 3 (bottom).

Protonation of α,β-unsaturated lactam (4)

Our previous reports indicate that the α,β-unsaturated lactam, 4, is <1 kcal/mol higher in energy than the most stable structure, lactam 1. Although this is not represented as a major contributing structure in other literature reports, we, nevertheless, believe that this will serve as a major contributor in free solution. Ring protonation of 4 produces four possible tautomers 9, 21–23 (Figure 6). Structure 9, resulting from protonation of 4 at N3, is identical to the most stable structure resulting from protonation of 1 at N1. As 9 can be derived from the two most stable neutral pterin structures, 1 and 4, it further supports that this structure will be the most predominant pterin cation in acidic aqueous solution. Protonation at N1 results in a very unstable structure as the aromaticity from that ring is effectively lost, similar to that observed in 10. Cation 22 is over 6 kcal/mol higher in energy than the most stable structure and may contribute somewhat. Structure 23 is less stable than 9 by 13.4 kcal/mol and is not predicted to contribute significantly.

Figure 6

Relative calculated energies of pterins resulting from the ring nitrogen protonation of the α,β-unsaturated lactam structure, 4.

Protonation of guanidinyl lactams (5 and 6)

The guanidinyl lactams, 5 and 6, possess an exocyclic imine and are only about 4 kcal/mol less stable than 1. Ring protonation of these structures reveal that reactions at N1 or N3 (24, 25, 28, 29) are over 40 kcal/mol less stable than 9 owing to the loss of aromaticity (Figure 7). Protonation at N5 and N8 produce tautomers with relative calculated energies approximately 14 and 17 kcal/mol, respectively. What is interesting about these structures is how much less stable protonation at these sites is in the guanidinyl lactam compared to the lactam. As 5 and 6 are about 4 kcal/mol higher in energy than 1, it was expected that protonation at N5 and N8 would produce structures that are about 4 kcal/mol higher than the corresponding tautomers derived from 1, specifically 11 and 12. Instead, these structures are 10–13 kcal/mol less stable than would be predicted. This observed decrease in stability is attributed to the removal of the amine resonance contribution seen in 1 that is absent in the imines 5 and 6.

Figure 7

Relative calculated energies of pterins resulting from the ring nitrogen protonation of the guanidinyl lactam structures, 5 (top) and 6 (bottom).

Protonation of pterin tautomers at non-ring nitrogens

Protonation of lactam (1)

Protonation at the non-ring atoms of 1 produces three structures (14, 18, 32) that are all quite high in energy compared to 9 (Figure 8). Oxygen protonation results in phenol-like cations that are 12–17 kcal/mol less stable than 9. while amine protonation at N2′ results in a structure that is less stable by over 20 kcal/mol. None of these are predicted to contribute significantly to the distribution of pterin cations in acidic media.

Figure 8

Relative calculated energies of pterins resulting from the non-ring protonation of the lactam structure, 1.

Protonation of lactims (2 and 3)

When the popular lactim structures are protonated on the non-ring heteroatoms, structures 33–35 are produced (Figure 9). Protonation on N2′ result in structures that are over 20 kcal/mol less stable than 9 and adding a second hydrogen to O4′ produces a cation that is over 50 kcal/mol less stable. None of these structures are anticipated to significantly contribute in aqueous solution.

Figure 9

Relative calculated energies of pterins resulting from the non-ring protonation of the two lactim structures, 2 and 3.

Protonation of α,β-unsaturated lactam (4)

Non-ring atom protonation of the α,β-unsaturated lactam structure produces three cationic tautomers, 13, 17, and 36 (Figure 10). As observed with other structures, protonation at N2′ results in a relatively unstable ammonium ion that is over 20 kcal/mol higher in energy than the most stable structure, 9. Interestingly, protonation at O4′ results in the same structures, 13 and 17, as protonation of the two neutral lactim rotamers at the most basic ring nitrogen, N1. These structures are <5 kcal/mol above 9 and produce some of the most stable non-ring protonation cations calculated.

Figure 10

Relative calculated energies of pterins resulting from the non-ring protonation of the α,β-unsaturated lactam structure, 4.

Protonation of guanidinyl lactams (5 and 6)

Finally, protonation of the exocyclic imines at either N2′ or O4′ results in five possible tautomeric structures, 9 and 37–40 (Figure 11). Protonation of N2′ on either 5 or 6 results in 9 and is the most stable structure of pterin cations. The addition of the proton at O4′ results in a relatively unstable structure that is >20 kcal/mol in all the possible configurations of imines and rotamers of the lactim.

Figure 11

Relative calculated energies of pterins resulting from the non-ring protonation of the two guanidinyl lactam structures, 5 (top) and 6 (bottom).

Comparison of B3LYP and MP2 calculated energies of the most stable cations

The six most stable structures were also analyzed using the MP2/6-31+G** level of theory. These represent the tautomers of protonated 6-methylpterin that are within approximately 6 kcal/mol of the most stable structure, 9. The addition of the ab initio MP2 method to the semi-empirical DFT calculations provides additional support to the results reported here. All of the MP2 results agree very well with the B3LYP data (Figure 12). Both levels of theory predict that structure 9 is the most stable tautomer. All the calculated relative energies using the two levels of theory are within 1.5 kcal/mol.

Figure 12

Relative calculated energies of the most stable protonated pterin cations (top: B3LYP/6-31+G**; bottom: MP2/6-31+G**, bold).

Conclusions

Six structures exist that have been calculated using B3LYP (and MP2) to be 6 kcal/mol or less away from the most stable pterin cation tautomer, 9 (Figure 12). These can be categorized into two groups. The first group is produced by protonation of the lactam, 1, on N1, N5, or N8 that results in the most stable structures, 9, 12, and 11. The second group is derived from the protonation of the α,β-unsaturated lactam, 4, on N3, N5, or O4′ (two rotamers) forming structures 9, 17, 13, and 22. Although some of these structures can be generated by protonation of other neutral pterins (i.e., 13 and 17 from the lactim structures), it is clear that all of the most stable protonated pterin cations can be derived from the two most stable neutral pterin tautomers, 1 and 4. We believe that this only adds importance for consideration of the α,β-unsaturated lactam, 4, as a major contributing form in aqueous solution of pterins. Calculations of the charge densities on the neutral 6-methylpterin structures, 1–4, support the general trends for the thermodynamic stabilities of the protonated pterin products.