Theoretical evaluation of the hydrogen kinetic isotope effect on the first step of the methylmalonyl-CoA mutase reaction

Nonequilibrium Relaxation of Conformational Dynamics Facilitates Catalytic Reaction in an Elastic Network Model of T7 DNA Polymerase

Nucleotide-induced conformational closing of the finger domain of DNA polymerase is crucial for its catalytic action during DNA replication. Such large-amplitude molecular motion is often not fully accessible to either direct experimental monitoring or molecular dynamics simulations. However, a coarse-grained model can offer an informative alternative, especially for probing the relationship between conformational dynamics and catalysis. Here we investigate the dynamics of T7 DNA polymerase catalysis using a Langevin-type elastic network model incorporating detailed structural information on the open conformation without the substrate bound. Such a single-parameter model remarkably captures the induced conformational dynamics of DNA polymerase upon dNTP binding, and reveals its close coupling to the advancement toward transition state along the coordinate of the target reaction, which contributes to significant lowering of the activation energy barrier. Furthermore, analysis of stochastic catalytic rates suggests that when the activation energy barrier has already been significantly lowered and nonequilibrium relaxation toward the closed form dominates the catalytic rate, one must appeal to a picture of two-dimensional free energy surface in order to account for the full spectrum of catalytic modes. Our semiquantitative study illustrates the general role of conformational dynamics in achieving transition-state stabilization, and suggests that such an elastic network model, albeit simplified, possesses the potential to furnish significant mechanistic insights into the functioning of a variety of enzymatic systems.

Co-C dissociation of adenosylcobalamin (coenzyme B12): role of dispersion, induction effects, solvent polarity, and relativistic and thermal corrections

Quantum-chemical cluster modeling is challenged in the limit of large, soft systems by the effects of dispersion and solvent, and well as other physical interactions. Adenosylcobalamin (AdoCbl, coenzyme B12), as one of the most complex cofactors in life, constitutes such a challenge. The cleavage of its unique organometallic Co-C bond has inspired multiple studies of this cofactor. This paper reports the fully relaxed potential energy surface of Co-C cleavage of AdoCbl, including for the first time all side-chain interactions with the dissociating Ado group. Various methods and corrections for dispersion, relativistic effects, solvent polarity, basis set superposition error, and thermal and vibrational effects were investigated, totaling more than 550 single-point energies for the large model. The results show immense variability depending on method, including solvation, functional type, and dispersion, challenging the conceived accuracy of methods used for such systems. In particular, B3LYP-D3 seems to severely underestimate the Co-C bond strength, consistent with previous results, and BP86 remains accurate for cobalamins when dispersion interactions are accounted for.

DFT and ONIOM(DFT:MM) studies on Co-C bond cleavage and hydrogen transfer in B12-dependent methylmalonyl-CoA mutase. Stepwise or concerted mechanism?

The considerable protein effect on the homolytic Co-C bond cleavage to form the 5'-deoxyadenosyl (Ado) radical and cob(II)alamin and the subsequent hydrogen transfer from the methylmalonyl-CoA substrate to the Ado radical in the methylmalonyl-CoA mutase (MMCM) have been extensively studied by DFT and ONIOM(DFT/MM) methods. Several quantum models have been used to systematically study the protein effect. The calculations have shown that the Co-C bond dissociation energy is very much reduced in the protein, compared to that in the gas phase. The large protein effect can be decomposed into the cage effect, the effect of coenzyme geometrical distortion, and the protein MM effect. The largest contributor is the MM effect, which mainly consists of the interaction of the QM part of the coenzyme with the MM part of the coenzyme and the surrounding residues. In particular, Glu370 plays an important role in the Co-C bond cleavage process. These effects tremendously enhance the stability of the Co-C bond cleavage state in the protein. The initial Co-C bond cleavage and the subsequent hydrogen transfer were found to occur in a stepwise manner in the protein, although the concerted pathway for the Co-C bond cleavage coupled with the hydrogen transfer is more favored in the gas phase. The assumed concerted transition state in the protein has more deformation of the coenzyme and the substrate and has less interaction with the protein than the stepwise route. Key factors and residues in promoting the enzymatic reaction rate have been discussed in detail.

Coupling of hydrogenic tunneling to active-site motion in the hydrogen radical transfer catalyzed by a coenzyme B12-dependent mutase

Hydrogen transfer reactions catalyzed by coenzyme B(12)-dependent methylmalonyl-CoA mutase have very large kinetic isotope effects, indicating that they proceed by a highly quantal tunneling mechanism. We explain the kinetic isotope effect by using a combined quantum mechanical/molecular mechanical potential and semiclassical quantum dynamics calculations. Multidimensional tunneling increases the magnitude of the calculated intrinsic hydrogen kinetic isotope effect by a factor of 3.6 from 14 to 51, in excellent agreement with experimental results. These calculations confirm that tunneling contributions can be large enough to explain even a kinetic isotope effect >50, not because the barrier is unusually thin but because corner-cutting tunneling decreases the distance over which the system tunnels without a comparable increase in either the effective potential barrier or the effective mass for tunneling.

Double hydrogen tunneling revisited: the breakdown of experimental tunneling criteria

Formic acid dimer was chosen as a model system to investigate synchronous double proton transfer by means of variational transition state theory (VTST) for various isotopically modified hydrogen species. The electronic barrier for the double proton transfer was evaluated to be 7.9 kcal/mol, thus being significantly lower than it was determined in previous studies. The tunneling probabilities were evaluated at temperatures from 100 up to 400 K and typical Arrhenius behavior with enhancement by tunneling is observed. When comparing the transmission factors kappa in dependence of the mass of the tunneling hydrogen, it was found that there are two maxima, one at very low masses (e.g., 0.114 amu, corresponding to the muonium entity) and one maximum at around 2 amu (corresponding to deuterium). With the knowledge of the VTST-hydrogen transfer rates and the corresponding tunneling corrections, various tunneling criteria were tested (e.g., Swain-Schaad exponents) and were shown to fail in this reaction in predicting the extent of tunneling. This finding adds another aspect in the ongoing "Tunneling-Enhancement by Enzymes" discussion, as the used tunneling criteria based on experimental reaction rates may fail to predict tunneling behavior correctly.

Alternative pathways for radical dissipation in an active site mutant of B12-dependent methylmalonyl-CoA mutase

Methylmalonyl-CoA mutase catalyzes the adenosylcobalamin-dependent rearrangement of (2R)-methylmalonyl-CoA to succinyl-CoA. The crystal structure of the enzyme reveals that Y243 is in van der Waals contact with the methyl group of the substrate and suggests a possible role for it in the stereochemical control of the reaction. This hypothesis was tested by designing a molecular hole by replacing the phenolic side chain of Y243 with the methyl group of alanine. The Y243A mutation lowered the catalytic efficiency >(4 x 10(4))-fold compared to wild-type enzyme, the K(M)app for the cofactor approximately 4-fold, and the cob(II)alamin concentration under steady-state turnover conditions approximately 2-fold. However, the mutation did not appear to lead to loss of the stereochemical preference for the substrate. The Y243A mutation is expected to create a cavity and should, in principle, allow accommodation of bulkier substrates. To test this, we used ethylmalonyl-CoA and allylmalonyl-CoA as alternate substrates. Surprisingly, both analogues resulted in suicidal inactivation, albeit in an O(2)-dependent and O(2)-independent fashion, respectively. The inactivation by allylmalonyl-CoA was further investigated, and revealed formation of cob(II)alamin at an approximately 1.5-fold higher rate than with wild-type mutase under single-turnover conditions. Product analysis revealed a stoichiometric mixture of 5'-deoxyadenosine, aquocobalamin, and allylmalonyl-CoA. Taken together, these results are consistent with an internal electron transfer from cob(II)alamin to the substrate analogue radical. These studies serve to emphasize the fine control exerted by Y243 in the vicinity of the substrate to minimize radical extinction in side reactions.

Validation of semiempirical methods for modeling of corrinoid systems

Several semiempirical methods (MNDO-d, PM3tm, PM3-d, PM5, PM6, and AM1-d) have been tested against experimental data and density functional theory (DFT) results in search for the best methods that can be used for quantum-mechanical-molecular mechanics (QM/MM) modeling of corrinoid systems of vitamin B(12) co-factor. It has been found that the PM6 parametrization in its present form gives results closest to hybrid DFT calculations that are most widely used thus far. In comparison with pure DFT and experimental data the best agreement is obtained for PM3tm parametrization, while PM6 yields slightly worse results. AM1-d yields bad geometry of the corrin moiety. The worst performance was observed for MNDO-d, which has severe problem with position and orientation of the alpha-ligands.

How enzymes work: analysis by modern rate theory and computer simulations

Advances in transition state theory and computer simulations are providing new insights into the sources of enzyme catalysis. Both lowering of the activation free energy and changes in the generalized transmission coefficient (recrossing of the transition state, tunneling, and nonequilibrium contributions) can play a role. A framework for understanding these effects is presented, and the contributions of the different factors, as illustrated by specific enzymes, are identified and quantified by computer simulations. The resulting understanding of enzyme catalysis is used to comment on alternative proposals of how enzymes work.

The first experimental test of the hypothesis that enzymes have evolved to enhance hydrogen tunneling

The literature hypothesis that "the optimization of enzyme catalysis may entail the evolutionary implementation of chemical strategies that increase the probability of quantum-mechanical tunneling" is experimentally tested herein for the first time. The system employed is the key to being able to provide this first experimental test of the "enhanced hydrogen tunneling" hypothesis, one that requires a comparison of the three criteria diagnostic of tunneling (vide infra) for the same, or nearly the same, reaction with and without the enzyme. Specifically, studied herein are the adenosylcobalamin (AdoCbl, also known as coenzyme B(12))-dependent diol dehydratase model reactions of (i). H(D)(*) atom abstraction from ethylene glycol-d(0) and ethylene glycol-d(4) solvent by 5'-deoxyadenosyl radical (Ado(*)) and (ii.) the same H(*) abstraction reactions by the 8-methoxy-5'-deoxyadenosyl radical (8-MeOAdo(*)). The Ado(*) and 8-MeOAdo(*) radicals are generated by Co-C thermolysis of their respective precursors, AdoCbl and 8-MeOAdoCbl. Deuterium kinetic isotope effects (KIEs) of the H(*)(D(*)) abstraction reactions from ethylene glycol have been measured over a temperature range of 80-120 degrees C: KIE = 12.4 +/- 1.1 at 80 degrees C for Ado(*) and KIE = 12.5 +/- 0.9 at 80 degrees C for 8-MeOAdo(*) (values ca. 2-fold that of the predicted maximum primary times secondary ground-state zero-point energy (GS-ZPE) KIE of 6.4 at 80 degrees C). From the temperature dependence of the KIEs, zero-point activation energy differences ([E(D) - E(H)]) of 3.0 +/- 0.3 kcal mol(-)(1) for Ado(*) and 2.1 +/- 0.6 kcal mol(-)(1) for 8-MeOAdo(*) have been obtained, both of which are significantly larger than the nontunneling, zero-point energy only maximum of 1.2 kcal mol(-)(1). Pre-exponential factor ratios (A(H)/A(D)) of 0.16 +/- 0.07 for Ado(*) and 0.5 +/- 0.4 for 8-MeOAdo(*) are observed, both of which are significantly less than the 0.7 minimum for nontunneling behavior. The data provide strong evidence for the expected quantum mechanical tunneling in the Ado(*) and 8-MeOAdo(*)-mediated H(*) abstraction reactions from ethylene glycol. More importantly, a comparison of these enzyme-free tunneling data to the same KIE, (E(D) - E(H)) and A(H)/A(D) data for a closely related, Ado(*)-mediated H(*) abstraction reaction from a primary CH(3)- group in AdoCbl-dependent methylmalonyl-CoA mutase shows the enzymic and enzyme-free data sets are identical within experimental error. The Occam's Razor conclusion is that at least this adenosylcobalamin-dependent enzyme has not evolved to enhance quantum mechanical tunneling, at least within the present error bars. Instead, this B(12)-dependent enzyme simply exploits the identical level of quantum mechanical tunneling that is available in the enzyme-free, solution-based H(*) abstraction reaction. The results also require a similar, if not identical, barrier width and height within experimental error for the H(*) abstraction both within, and outside of, the enzyme.

A compelling experimental test of the hypothesis that enzymes have evolved to enhance quantum mechanical tunneling in hydrogen transfer reactions: the beta-neopentylcobalamin system combined with prior adocobalamin data

An intriguing but controversial hypothesis has appeared that "The optimization of enzyme catalysis may entail the evolutionary implementation of chemical strategies that increase the probability of tunneling and thereby accelerate the reaction rate" (Kohen, A.; Klinman, J. P. Acc. Chem. Res. 1998, 31, 397). Restated, enzymes may have evolved to enhance quantum mechanical tunneling by coupling to protein low nu modes that squeeze the reacting centers together in, for example, their H(*) atom abstraction reactions. Such a putative "protein squeezing" mechanism would enhance hydrogen quantum mechanical tunneling by reducing the barrier width. An alternative hypothesis is that enzymes do not enhance tunneling, but simply exploit the same amount of tunneling present in their enzyme-free solution reactions, if those reactions occur. A third, conceivable hypothesis is that enzymes might even inadvertently decrease the amount of tunneling as an undesired result of increasing the barrier width while reducing the barrier height. Testing these hypotheses experimentally requires the extremely rare event of being able to measure the amount of tunneling both in the enzyme system and in a very similar if not identical reaction in enzyme-free solution. This has been accomplished experimentally in only one prior case, our recent study of AdoCbl (coenzyme B(12)) and 8-Meo-AdoCbl undergoing enzyme-like H(*) abstraction reactions (Doll, K. M.; Bender, B. R.; Finke, R. G. to J. Am. Chem. Soc. 2003, in press). The data there reveal no change in the level of tunneling within or outside of the enzyme in comparison to the best literature data for an AdoCbl-dependent enzyme, methylmalonyl-CoA mutase. However, that first system suffers from two limitations: the measurement of the KIE (kinetic isotope effect) data in a nonenzymic 80-110 degrees C temperature range; and lower precision data than desired due to the HPLC-MS method required for one of the KIE analyses. These limitations have now been overcome by the synthesis, then thermolysis and KIE study vs temperature of the H(*) abstraction reaction of beta-neopentylcobalamin (beta-NpCbl) in ethylene glycol-d(0) and ethylene glycol-d(4). This is the first experimental test of Klinman's hypothesis using KIE data obtained at enzyme-relevant temperatures. The key data obtained are as follows: deuterium KIEs of 23.1 +/- 3.0 at 40 degrees C to 39.0 +/- 2.3 at 10 degrees C; an activation energy difference E(D) - E(H) of 3.1 +/- 0.3 kcal mol(-)(1); and a pre-exponential factor ratio A(H)/A(D) of 0.14 +/- 0.07. Moreover, our now three sets of data (NpCbl; AdoCbl; 8-MeOAdoCbl) are shown to lie on the same ln KIE vs 1/T linear plot yielding a set of enzyme-temperature-relevant, high-precision KIE, E(D) - E(H), and A(H)/A(D) data over a relatively large, 110 degrees C temperature range. Significantly, the enzyme-free solution KIE, E(D) - E(H), and A(H)/A(D) are identical within experimental error to those for methylmalonyl-CoA mutase. This finding leads to the conclusion that there is no enzymic enhancement of the tunneling in at least this B(12)-dependent enzyme. This B(12) enzyme does, however, exploit the same (unchanged) level of tunneling measured for the nonenzymic, Ado(*) solution H(*) abstraction reaction. A discussion is presented of the still open question of if this first experimental finding, of "no enzymic enhancement of tunneling" in one B(12)-dependent enzymic system, is likely to prove more general or not.

Kinetic results implicating a polar radical reaction pathway in the rearrangement catalyzed by alpha-methyleneglutarate mutase

alpha-Methyleneglutarate mutase (MGM) catalyzes the rearrangement of 2-methyleneglutarate to 3-methylitaconate (2-methylene-3-methylsuccinate). A putative mechanism for the MGM-catalyzed reaction involves 3-exo cyclization of the 2-methyleneglutaric acid-4-yl radical to a cyclopropylcarbinyl radical intermediate that ring opens to the 3-hydroxycarbonyl-2-methylenebutanoic acid-4-yl radical (3-methylitaconic acid radical). Model reactions for this mechanism were studied by laser flash photolysis kinetic methods. alpha-Ester radicals were produced by 266 nm photolysis of alpha-phenylselenyl ester derivatives. Rate constants for cyclizations of the (Z)-1-ethoxycarbonyl-4-(2,2-diphenylcyclopropyl)-3-buten-1-yl radical ((Z)-8a) and (E)- and (Z)-1,3-di(ethoxycarbonyl)-4-(2,2-diphenylcyclopropyl)-3-buten-1-yl radicals ((E)- and (Z)-8b) were determined. The ester group in (Z)-8a accelerates the 3-exo cyclization in comparison to the parent radical lacking an ester group by a factor of 3, an effect ascribed to a polarized transition state. The ester groups at C3 in radicals 8b slow the 3-exo cyclization reaction by a factor of 50. The rate constant for cyclization of the 2-methyleneglutaric acid-4-yl radical is estimated to be k approximately 2000 s(-1) at ambient temperature. When coupled with the estimated partitioning of the intermediate cyclopropylcarbinyl radical, the overall rate constant for the conversion is estimated to be k approximately equal to 1 x 10(-3) s(-1), which is much too small for any radical reaction and several orders of magnitude too small for kinetic competence for the MGM-catalyzed process. The possibility that the radical reaction in nature involves an unusual mechanism in which polar effects are important is discussed.

Energetic and stereochemical effects of the protein environment on substrate: a theoretical study of methylmalonyl-CoA mutase

QM/MM methods were used to study the isomerization step from (2R)-methylmalonyl-CoA to succinyl-CoA. A pathway via a "fragmentation-recombination" mechanism is ruled out on energetic grounds. For the other radicalic pathway, involving an addition recombination step, geometries and vibrational contributions have been determined, and a barrier height of 11.70 kcal/mol was found. The effect of adjacent hydrogen-donating groups was found to reduce the energy barrier by 1-2 kcal/mol each and thus to provide a significant catalytic effect for this reaction. By means of molecular dynamics studies, the stereochemistry of the methylmalonyl-CoA mutase catalyzed reaction was examined. It is shown that TYR89 is essential for maintaining stereoselectivity of the abstraction of a hydrogen in the backreaction. The subsequent selective formation of one isomer of methylmalonyl-CoA is probably due to the presence of a bulky side chain.