Modeling the reactions catalyzed by coenzyme B12-dependent enzymes

Enzymes accelerate chemical reactions with an exceptional selectivity that makes life itself possible. Understanding the factors responsible for this efficient catalysis is of utmost importance in our quest to harness the tremendous power of enzymes. Computational chemistry has emerged as an important adjunct to experimental chemistry and biochemistry in this regard, because it provides detailed insights into the relationship between structure and function in a systematic and straightforward manner. In this Account, we highlight our recent high-level theoretical investigations toward this end in studying the radical-based reactions catalyzed by enzymes dependent on coenzyme B(12) (or adenosylcobalamin, AdoCbl). In addition to their fundamental position in biology, the AdoCbl-dependent enzymes represent a valuable framework within which to understand Nature's method of efficiently handling high-energy species to execute very specific reactions. The AdoCbl-mediated reactions are characterized by the interchange of a hydrogen atom and a functional group on adjacent carbon atoms. Our calculations are consistent with the conclusion that the main role of AdoCbl is to provide a source of radicals, thus moving the 1,2-rearrangements onto the radical potential energy surface. Our studies also show that the radical rearrangement step is facilitated by partial proton transfer involving the substrate. Specifically, we observe that the energy requirements for radical rearrangement are reduced dramatically with appropriate partial protonation or partial deprotonation or sometimes (synergistically) both. Such interactions are particularly relevant to enzyme catalysis, because it is likely that the local amino acid environment in the active site of an enzyme can function in this capacity through hydrogen bonding. Finally, our calculations indicate that the intervention of a very stable radical along the reaction pathway may inactivate the enzyme, demonstrating that sustained catalysis depends on a delicate energy balance. Radical-based enzyme reactions are often difficult to probe experimentally, so theoretical investigations have a particularly valuable role to play in their study. Our research demonstrates that a small-model approach can provide important and revealing insights into the mechanism of action of AdoCbl-dependent enzymes.

On the importance of ribose orientation in the substrate activation of the coenzyme B12-dependent mutases

The degree to which the corrin ring portion of coenzyme B(12) can facilitate the H-atom-abstraction step in the glutamate mutase (GM)-catalyzed reaction of (S)-glutamate has been investigated with density functional theory. The crystal structure of GM identifies two possible orientations of the ribose portion of coenzyme B(12). In one orientation (A), the OH groups of the ribose extend away from the corrin ring, whereas in the other orientation (B) the OH groups, especially that involving O3', are instead directed towards the corrin ring. Our calculations identify a sizable stabilization amounting to about 30 kJ mol(-1) in the transition structure (TS) complex corresponding to orientation B (TS(B)CorIm). In the TS complex where the ribose instead is positioned in orientation A, no such effect is manifested. The observed stabilization in TS(B)CorIm appears to be the result of favorable interactions involving O3' and the corrin ring, including a C-HO hydrogen bond. We find that the degree of stabilization is not particularly sensitive to the Co-C distance. Our calculations show that any potential stabilization afforded to the H-atom-abstraction step by coenzyme B(12) is sensitive to the orientation of the ribose moiety.

Ab initio investigation of the fragmentation of 5,5-diamino-substituted 1,4,2-oxathiazoles

The mechanism for the fragmentation of 5,5-diamino-1,4,2-oxathiazole derivatives has been studied at the CCSD(T)/6-311+G(3df,2p)//MP2/6-31+G(2df,p) level of theory. The calculations suggest that the fragmentation occurs via a stepwise process involving the formation of polar intermediates that lie in shallow potential wells. We find a large thermodynamic driving force for fragmentation, which together with a weakening of the C-S bond through electron donation by the amino substituents provides the impetus for a low-barrier fragmentation.

The carbon-skeleton rearrangement in tropane alkaloid biosynthesis

High-level quantum chemistry calculations have been performed to examine the carbon-skeleton rearrangement of the tropane alkaloid littorine to hyoscyamine. Two pathways involving radical and carbocation intermediates have been investigated in this regard, namely, stepwise (or fragmentation-recombination) and concerted. The fragmentation products are calculated to be of high energy for both the radical- and carbocation-based mechanisms (136.3 and 170.9 kJ mol(-1), respectively). Similarly, the rearrangement barrier for the radical-based concerted pathway is calculated to be quite high (135.6 kJ mol(-1)). In contrast, the carbocation-based concerted pathway is found to be associated with a relatively low barrier (47.4 kJ mol(-1)). The ionization energy of the substrate-derived radical 3a is calculated to be 7.01 eV, suggesting that its oxidation to generate the substrate-derived carbocation 3b ought to be facile. In an attempt to investigate how an enzyme might modulate the rearrangement barriers, the separate and combined influences of partially protonating the migrating group and partially deprotonating the spectator OH group of the substrate were investigated. Such interactions can lead to significant reductions in the rearrangement barrier for both the radical- and carbocation-based concerted pathways, although the carbocation pathway continues to have significantly lower energy requirements. Also, the relatively high (gas-phase) acidity of the OH group of the product-related carbocation 4b indicates that the direct formation of hyoscyamine aldehyde (6) is a highly exothermic process. Although we would not wish to rule out alternative possibilities, our calculations suggest that a concerted rearrangement mechanism involving carbocations constitutes a viable low-energy pathway for the carbon-skeleton rearrangement in tropane alkaloid biosynthesis.

An evaluation of harmonic vibrational frequency scale factors

Scale factors for obtaining fundamental vibrational frequencies, low-frequency vibrational frequencies, zero-point vibrational energies (ZPVEs), and thermal contributions to enthalpy and entropy have been derived through a least-squares approach from harmonic frequencies determined at more than 100 levels of theory. Wave function procedures (HF, MP2, QCISD, QCISD(T), CCSD, and CCSD(T)) and a large and representative range of density functional theory (DFT) approaches (B3-LYP, BMK, EDF2, M05-2X, MPWB1K, O3-LYP, PBE, TPSS, etc.) have been examined in conjunction with basis sets such as 6-31G(d), 6-31+G(d,p), 6-31G(2df,p), 6-311+G(d,p), and 6-311+G(2df,p). The vibrational frequency scale factors were determined by a comparison of theoretical harmonic frequencies with the corresponding experimental fundamentals utilizing a standard set of 1066 individual vibrations. ZPVE scale factors were generally obtained from a comparison of the computed ZPVEs with experimental ZPVEs for a smaller standard set of 39 molecules, though the effect of expansion to a 48 molecule data set was also examined. In addition to evaluating the scale factors for a wide range of levels of theory, we have also probed the effect on scale factors of varying the percentage of incorporated exact exchange in hybrid DFT calculations using a modified B3-LYP functional. This has revealed a near-linear relationship between the magnitude of the scale factor and the proportion of exact exchange. Finally, we have investigated the effect of basis set size on HF, MP2, B3-LYP, and BMK scale factors by deriving values with basis sets ranging from 6-31G(d) up to 6-311++G(3df,3pd) as well as with basis sets in the cc-pVnZ and aug-cc-pVnZ series and with the TZV2P basis.

Proton-Bound Homodimers: How Are the Binding Energies Related to Proton Affinities?

High-level quantum chemical calculations [G3(MP2)-RAD//MP2/6-31+G(d,p)] have been employed to investigate the relationship between the binding energy (BE) of a substrate (X) and its protonated form [H-X]+ with the proton affinity (PA) of the substrate (X) in several series of protonated homodimers ([X...H-X]+). We find that for each series of closely related substrates, the binding energy (BE) is correlated with the proton affinity (PA) in an approximately quadratic manner. Thus, for a given series, the BE initially increases in magnitude with increasing PA, reaches a point of maximum binding, and then becomes smaller as the PA increases further. This behavior can be attributed to the competing effects of the exothermic partial protonation of the substrate and the endothermic partial deprotonation of the protonated substrate. As the PA increases, protonation of X contributes to increased binding but the penalty for partial deprotonation of [H-X]+ also increases. Once the PA becomes sufficiently high, the penalty for the partial deprotonation of [H-X]+ dominates, leading to maximum binding occurring at intermediate PA.

Uncatalyzed transfer hydrogenation of quinones and related systems: a theoretical mechanistic study

Quantum chemistry calculations have been used to study the uncatalyzed transfer hydrogenation between a range of hydrogen donors and acceptors, in the gas phase and in solution. Our study shows in the first place that in order to obtain reliable condensed-phase transition structures, it is necessary to perform geometry optimization in the presence of a continuum. In addition, the use of a free energy of solvation obtained with the UB3-LYP/6-31+G(d,p)/IEF-PCM/UA0 combination, in conjunction with UMPWB1K/6-311+G(3df,2p)//B3-LYP/6-31+G(d,p) gas-phase energies, gives the best agreement with experimental barriers. In condensed phases, the geometries and energies of the transition structures are found to relate to one another in a manner consistent with the Hammond postulate. There is also a correlation between the barriers and the energies of the radical intermediates in accord with the Bell-Evans-Polanyi principle. We find that in the gas phase, all the transfer-hydrogenation reactions examined proceed via a radical pathway. In condensed phases, some of the reactions follow a radical mechanism regardless of the solvent. However, for some reactions there is a change from a radical mechanism to an ionic mechanism as the solvent becomes more polar. Our calculations indicate that the detection of radical adducts by EPR does not necessarily indicate a predominant radical mechanism, because of the possibility of a concurrent ionic reaction. We also find that the transition structures for these reactions do not necessarily have a strong resemblance to the intermediates, and therefore one should be cautious in utilizing the influence of polar effects on the rate of reaction as a means of determining the mechanism.

Toward an Improved Understanding of the Glutamate Mutase System

High-level quantum chemistry calculations have been used to examine the catalytic reactions of adenosylcobalamin-dependent glutamate mutase (GM) with the natural substrate (S)-glutamic acid. We have also examined the rearrangement of (S)-2-hydroxyglutaric acid, (S)-2-thiolglutaric acid, and 2-ketoglutaric acid, all of which have previously been shown to react as substrates or inhibitors of the enzyme. Our calculations support the notion that the 100-fold difference in kcat between glutamate and 2-hydroxyglutarate is associated with the relatively high energy of the glycolyl radical intermediate compared with the glycyl radical. More generally, calculations of radical stabilization energies for a variety of substituted glycyl radical analogues indicate that modifications at the radical center can profoundly affect the relative stability of the resulting radical, leading to important mechanistic consequences. We find that the formation of a thioglycolyl radical, derived from (S)-2-thiolglutaric acid, is highly dependent on the protonation state of sulfur. The neutral radical is found to be of stability similar to that of the glycolyl radical, whereas the S- form of the thioglycolyl radical is much more stable, thus providing a rationalization for the inhibition of the enzyme by the substrate analogue 2-thiolglutarate. Two possible rearrangement pathways have been examined for the reaction of GM with 2-ketoglutaric acid, for which previous experiments had suggested no rearrangement took place. The fragmentation-recombination pathway is associated with a fragmentation step that is very endothermic (by 102.2 kJ mol-1). In contrast, the addition-elimination pathway has significantly lower energy requirements. An alternative possibility, namely, that 2-ketoglutaric acid is bound in its hydrated form, 2,2-dihydroxyglutaric acid, also leads to a pathway with relatively low energy requirements, suggesting that some rearrangement might be expected under such circumstances.

Hydrogenation of Simple Aromatic Molecules: A Computational Study of the Mechanism

Quantum chemistry calculations have been used to study the metal-free hydrogenation reactions of a variety of simple aromatic, heteroaromatic, and related linear conjugated systems. We find that the barrier for uncatalyzed 1,4-hydrogenation is always substantially lower (by approximately 200 kJ mol-1) than that for 1,2-hydrogenation, despite similar reaction enthalpies. The presence of hydrogen fluoride as a catalyst is found to decrease the 1,2-hydrogenation barriers but, in most cases, to slightly increase the 1,4-hydrogenation barriers when a constrained geometric arrangement is employed. These qualitative observations are consistent with orbital symmetry considerations, which show that both the uncatalyzed 1,4-hydrogenation and the catalyzed 1,2-hydrogenation are formally symmetry-allowed processes. An extreme example of the catalyzed 1,2-hydrogenation of benzene is provided by the involvement of a second molecule of hydrogen, which leads to a substantial lowering of the barrier. The effect of catalysis was further investigated by applying a selection of additional catalysts to the 1,2- and 1,4-hydrogenation of benzene. A decreasing barrier with increasing catalyst acidity is generally observed for the catalytic 1,2-hydrogenation, but the situation is more complex for catalytic 1,4-hydrogenation. For the uncatalyzed 1,4-hydrogenation of aromatic systems containing one or more nitrogen heteroatoms, the barriers for [C,C], [C,N], and [N,N] hydrogenations are individually related to the reaction enthalpies by the Bell-Evans-Polanyi principle. In addition, for a given reaction enthalpy, the barriers for [C,C] hydrogenation are generally lower than those for [C,N] or [N,N] hydrogenation. Finally, we find that the distortion experienced by the reactants in forming the transition structure represents a secondary factor that influences the reaction barrier. The correlation between these quantities allows the 1,4-hydrogenation barriers to be predicted from a ground-state property.

Thermochemistry and Kinetics of Hydrogen Abstraction by Methyl Radical from Polycyclic Aromatic Hydrocarbons

Thermodynamic and kinetic properties relating to hydrogen abstraction by methyl radical from various sites in polycyclic aromatic hydrocarbons (PAHs) have been investigated. The reaction enthalpies (298 K), barriers (0 K), and activation energies and pre-exponential factors (700-1100 K), have been calculated by means of density functional theory, specifically with B3-LYP/6-311G(d,p) geometries, followed by BMK/6-311+G(3df,2p) single-point energy calculations. For uncongested sites in the PAHs, a reasonable correlation is obtained between reactivities (as characterized by the reaction barriers) and reaction enthalpies. This is reflected in a Bell-Evans-Polanyi (BEP) relationship. However, for congested sites, abstraction is accompanied both by lower reaction enthalpies (due to relief of steric strain) and also by reduced reactivities (due to significantly increased steric hindrance effects in the transition structures), so that the BEP relationship does not hold. In addition, the reaction enthalpies and kinetic parameters for the series of linear acenes indicate that abstraction is more difficult from the central rings.

In Search of Radical Intermediates in the Reactions Catalyzed by Lysine 2,3-Aminomutase and Lysine 5,6-Aminomutase

High-level ab initio calculations have been used to study radical intermediates in the reactions catalyzed by lysine 2,3-aminomutase (2,3-LAM) and lysine 5,6-aminomutase (5,6-LAM). The reactions of these enzymes with the substrate analogues 4-oxalysine (4-OL), 4-thialysine (4-TL), or trans-4,5-dehydrolysine (t-4,5-DL) are rationalized in terms of stabilization provided by the substituent to the adjacent radical center. Large changes in the exothermicity accompanying the initial H-abstraction are observed relative to the lysine reference values that follow the series 4-OL < 4-TL < t-4,5-DL. These changes have the primary effect of increasing the endothermicity for subsequent ring-closure to form the putative aziridinylcarbinyl radical intermediate. Such stabilization is consistent with experimental observations of the substrate-derived radical (S*) in the reaction of 2,3-LAM with 4-TL as well as the ability of t-4,5-DL to act as an irreversible inhibitor of 2,3-LAM. Our calculations suggest that 4-TL and trans-3,4-dehydrolysine may also permit experimental characterization of S* radicals in the reactions catalyzed by 5,6-LAM. Strategies for modifying PLP are presented that might lead to the first observation of the aziridinylcarbinyl radical intermediate (I*) in the aminomutase-catalyzed reactions.