Transition state stabilization and substrate strain in enzyme catalysis: ab initio QM/MM modelling of the chorismate mutase reaction

To investigate fundamental features of enzyme catalysis, there is a need for high-level calculations capable of modelling crucial, unstable species such as transition states as they are formed within enzymes. We have modelled an important model enzyme reaction, the Claisen rearrangement of chorismate to prephenate in chorismate mutase, by combined ab initio quantum mechanics/molecular mechanics (QM/MM) methods. The best estimates of the potential energy barrier in the enzyme are 7.4-11.0 kcal mol(-1)(MP2/6-31+G(d)//6-31G(d)/CHARMM22) and 12.7-16.1 kcal mol(-1)(B3LYP/6-311+G(2d,p)//6-31G(d)/CHARMM22), comparable to the experimental estimate of Delta H(++)= 12.7 +/- 0.4 kcal mol(-1). The results provide unequivocal evidence of transition state (TS) stabilization by the enzyme, with contributions from residues Arg90, Arg7, and Arg63. Glu78 stabilizes the prephenate product (relative to substrate), and can also stabilize the TS. Examination of the same pathway in solution (with a variety of continuum models), at the same ab initio levels, allows comparison of the catalyzed and uncatalyzed reactions. Calculated barriers in solution are 28.0 kcal mol(-1)(MP2/6-31+G(d)/PCM) and 24.6 kcal mol(-1)(B3LYP/6-311+G(2d,p)/PCM), comparable to the experimental finding of Delta G(++)= 25.4 kcal mol(-1) and consistent with the experimentally-deduced 10(6)-fold rate acceleration by the enzyme. The substrate is found to be significantly distorted in the enzyme, adopting a structure closer to the transition state, although the degree of compression is less than predicted by lower-level calculations. This apparent substrate strain, or compression, is potentially also catalytically relevant. Solution calculations, however, suggest that the catalytic contribution of this compression may be relatively small. Consideration of the same reaction pathway in solution and in the enzyme, involving reaction from a 'near-attack conformer' of the substrate, indicates that adoption of this conformation is not in itself a major contribution to catalysis. Transition state stabilization (by electrostatic interactions, including hydrogen bonds) is found to be central to catalysis by the enzyme. Several hydrogen bonds are observed to shorten at the TS. The active site is clearly complementary to the transition state for the reaction, stabilizing it more than the substrate, so reducing the barrier to reaction.     

Differential transition-state stabilization in enzyme catalysis: quantum chemical analysis of interactions in the chorismate mutase reaction and prediction of the optimal catalytic field

Chorismate mutase is a key model system in the development of theories of enzyme catalysis. To analyze the physical nature of catalytic interactions within the enzyme active site and to estimate the stabilization of the transition state (TS) relative to the substrate (differential transition state stabilization, DTSS), we have carried out nonempirical variation-perturbation analysis of the electrostatic, exchange, delocalization, and correlation interactions of the enzyme-bound substrate and transition-state structures derived from ab initio QM/MM modeling of Bacillus subtilis chorismate mutase. Significant TS stabilization by approximately -23 kcal/mol [MP2/6-31G(d)] relative to the bound substrate is in agreement with that of previous QM/MM modeling and contrasts with suggestions that catalysis by this enzyme arises purely from conformational selection effects. The most important contributions to DTSS come from the residues, Arg90, Arg7, Glu78, a crystallographic water molecule, Arg116, and Arg63, and are dominated by electrostatic effects. Analysis of the differential electrostatic potential of the TS and substrate allows calculation of the catalytic field, predicting the optimal location of charged groups to achieve maximal DTSS. Comparison with the active site of the enzyme from those of several species shows that the positions of charged active site residues correspond closely to the optimal catalytic field, showing that the enzyme has evolved specifically to stabilize the TS relative to the substrate.     

A comparative study of claisen and cope rearrangements catalyzed by chorismate mutase. An insight into enzymatic efficiency: transition state stabilization or substrate preorganization?

In this work we present a detailed analysis of the activation free energies and averaged interactions for the Claisen and Cope rearrangements of chorismate and carbachorismate catalyzed by Bacillus subtilischorismate mutase (BsCM) using quantum mechanics/molecular mechanics (QM/MM) simulation methods. In gas phase, both reactions are described as concerted processes, with the activation free energy for carbachorismate being about 10-15 kcal mol(-)(1) larger than for chorismate, at the AM1 and B3LYP/6-31G levels. Aqueous solution and BsCM active site environments reduce the free energy barriers for both reactions, due to the fact that in these media the two carboxylate groups can be approached more easily than in the gas phase. The enzyme specifically reduces the activation free energy of the Claisen rearrangement about 3 kcal mol(-)(1) more than that for the Cope reaction. This result is due to a larger transition state stabilization associated to the formation of a hydrogen bond between Arg90 and the ether oxygen. When this oxygen atom is changed by a methylene group, the interaction is lost and Arg90 moves inside the active site establishing stronger interactions with one of the carboxylate groups. This fact yields a more intense rearrangement of the substrate structure. Comparing two reactions in the same enzyme, we have been able to obtain conclusions about the relative magnitude of the substrate preorganization and transition state stabilization effects. Transition state stabilization seems to be the dominant effect in this case.     

Multiple high-level QM/MM reaction paths demonstrate transition-state stabilization in chorismate mutase: correlation of barrier height with transition-state stabilization

Multiple profiles for the reaction from chorismate to prephenate in the enzyme chorismate mutase calculated with hybrid density functional combined quantum mechanics/molecular mechanics methods (B3LYP/6-31G(d)-CHARMM27) agree well with experiment, and provide direct evidence of transition-state stabilization by this important enzyme, which is at the centre of current debates about the nature of enzyme catalysis.     

Entropic and enthalpic components of catalysis in the mutase and lyase activities of Pseudomonas aeruginosa PchB

The isochorismate-pyruvate lyase from Pseudomonas aeruginosa (PchB) catalyzes two pericyclic reactions, demonstrating the eponymous activity and also chorismate mutase activity. The thermodynamic parameters for these enzyme-catalyzed activities, as well as the uncatalyzed isochorismate decomposition, are reported from temperature dependence of k(cat) and k(uncat) data. The entropic effects do not contribute to enzyme catalysis as expected from previously reported chorismate mutase data. Indeed, an entropic penalty for the enzyme-catalyzed mutase reaction (ΔS(++) = -12.1 ± 0.6 cal/(mol K)) is comparable to that of the previously reported uncatalyzed reaction, whereas that of the enzyme-catalyzed lyase reaction (ΔS(++) = -24.3 ± 0.2 cal/(mol K)) is larger than that of the uncatalyzed lyase reaction (-15.77 ± 0.02 cal/(mol K)) documented here. With the assumption that chemistry is rate-limiting, we propose that a reactive substrate conformation is formed upon loop closure of the active site and that ordering of the loop contributes to the entropic penalty for converting the enzyme substrate complex to the transition state.     

Just a near attack conformer for catalysis (chorismate to prephenate rearrangements in water,antibody, enzymes,and their mutants)

Standard free energies for formation of ground-state reactive conformers (DeltaGN degrees ) and transition states (DeltaG) in the conversion of chorismate to prephenate in water, B. subtilis mutase, E. coli mutase, and their mutants, as well as a catalytic antibody, are related by DeltaG = DeltaGN degrees + 16 kcal/mol. Thus, the differences in the rate constants for the water reaction and catalysts reactions reside in the mole fraction of substrate present as reactive conformers (NACs). These results, and knowledge of the importance of transition state stabilization in other cases, suggest a proposal that enzymes utilize both NAC and transition state stabilization in the mix required for the most efficient catalysis.     

Comparison of formation of reactive conformers (NACs) for the Claisen rearrangement of chorismate to prephenate in water and in the E. coli mutase: the efficiency of the enzyme catalysis

The Claisen rearrangements of chorismate (CHOR) in water and at the active site of E. coli chorismate mutase (EcCM) have been compared. From a total of 33 ns molecular dynamics simulation of chorismate in water solvent, seven diaxial conformers I-VII were identified. Most of the time (approximately 99%), the side chain carboxylate of the chorismate is positioned away from the ring due to the electrostatic repulsion from the carboxylate in the ring. Proximity of the two carboxylates, as seen in conformer I, is a requirement for the formation of a near attack conformer (NAC) that can proceed to the transition state (TS). In the EcCM.CHOR complex, the two carboxylates of CHOR are tightly held by Arg28 of one subunit and Arg11* of the other subunit, resulting in the side chain C16 being positioned adjacent to C5 with their motions restricted by van der Waals contacts with methyl groups of Val35 and Ile81. With the definition of NAC as the C5...C16 distance < or =3.7 A and the attack angle < or =30 degrees, it was estimated from our MD trajectories that the free energy of NAC formation is approximately 8.4 kcal/mol above the total ground state in water, whereas in the enzyme it is only 0.6 kcal/mol above the average of the Michaelis complex EcCM.CHOR. The experimentally measured difference in the activation free energies of the water and enzymatic reactions (Delta Delta G(++)) is 9 kcal/mol. It follows that the efficiency of formation of NAC (7.8 kcal/mol) at the active site provides approximately 90% of the kinetic advantage of the enzymatic reaction as compared to the water reaction. Comparison of the EcCM.TSA (transition state analogue) and EcCM.NAC simulations suggests that the experimentally measured 100 fold tighter binding of TSA compared to CHOR does not originate from the difference between NAC and the TS binding affinities, but might be due to the free energy cost to bring the two carboxylates of CHOR together to interact with Arg28 and Arg11* at the active site. The two carboxylates of TSA are fixed by a bicyclic structure. The remaining approximately 10% of Delta Delta G(++) may be attributed to a preferential interaction of Lys39-NH(3)(+) with O13 ether oxygen in the TS.     

Conformational effects in enzyme catalysis: QM/MM free energy calculation of the 'NAC' contribution in chorismate mutase

The controversial 'near attack conformation'(NAC) effect in the important model enzyme chorismate mutase is calculated to be 3.8-4.6 kcal mol(-1) by QM/MM free energy perturbation molecular dynamics methods, showing that the NAC effect by itself does not account for catalysis in this enzyme.     

All electron quantum chemical calculation of the entire enzyme system confirms a collective catalytic device in the chorismate mutase reaction

To elucidate the catalytic power of enzymes, we analyzed the reaction profile of Claisen rearrangement of Bacillus subtilis chorismate mutase (BsCM) by all electron quantum chemical calculations using the fragment molecular orbital (FMO) method. To the best of our knowledge, this is the first report of ab initio-based quantum chemical calculations of the entire enzyme system, where we provide a detailed analysis of the catalytic factors that accomplish transition-state stabilization (TSS). FMO calculations deliver an ab initio-level estimate of the intermolecular interaction between the substrate and the amino acid residues of the enzyme. To clarify the catalytic role of Arg90, we calculated the reaction profile of the wild-type BsCM as well as Lys90 and Cit90 mutant BsCMs. Structural refinement and the reaction path determination were performed at the ab initio QM/MM level, and FMO calculations were applied to the QM/MM refined structures. Comparison between three types of reactions established two collective catalytic factors in the BsCM reaction: (1) the hydrogen bonds connecting the Glu78-Arg90-substrate cooperatively control the stability of TS relative to the ES complex and (2) the positive charge on Arg90 polarizes the substrate in the TS region to gain more electrostatic stabilization.     

Enzymes do what is expected (chalcone isomerase versus chorismate mutase)

Madicago sativa chalcone isomerase (CI) catalyzes the isomerization of chalcone to flavanone, whereas E. coli chorismate mutase (CM) catalyzes the pericyclic rearrangement of chorismate to prephenate. Covalent intermediates are not formed in either of the enzyme-catalyzed reactions, K(M) and k(cat) are virtually the same for both enzymes, and the rate constants (k(o)) for the noncatalyzed reactions in water are also the same. This kinetic identity of both the enzymatic and the nonenzymatic reactions is not shared by a similarity in driving forces. The efficiency (DeltaG(o)() - DeltaG(cat)()) for the CI mechanism involves transition-state stabilization through general-acid catalysis and freeing of three water molecules trapped in the E.S species. The contribution to lowering DeltaG(cat)() by an increase in near attack conformer (NAC) formation in E.S as compared to S in water is not so important. In the CM reaction, the standard free energy for NAC formation in water is 8.4 kcal/mol as compared to 0.6 kcal/mol in E.S. Because the value of (DeltaG(o)() - DeltaG(cat)()) is 9 kcal/mol, the greater percentage of NACs accounts for approximately 90% of the kinetic advantage of the CM reaction. There is no discernible transition-state stabilization in the CM reaction. These results are discussed. In anthropomorphic terms, each enzyme has had to do what it must to have a biologically relevant rate of reaction.     

Investigation of the enzymatic and nonenzymatic cope rearrangement of carbaprephenate to carbachorismate

The dimethyl esters of carbaprephenate and 4-epi-carbaprephenate were prepared by modification of published procedures. In methanol these compounds are converted quantitatively to isomeric 6-hydroxytricyclo[3.3.1.0(2,7)]non-3-en-1,3-dimethyl esters via a two-step sequence involving an initial Cope rearrangement, followed by intramolecular Diels-Alder reaction of the dimethyl carbachorismate or 4-epi-carbachorismate intermediates. Carbaprephenate and its epimer were obtained by alkaline hydrolysis of the corresponding dimethyl esters. These compounds, in contrast to their ester precursors, undergo spontaneous acid-catalyzed decarboxylation in aqueous solution. Only at high pH does the Cope rearrangement compete with decarboxylation. At pH 12 and 90 degrees C, carbaprephenate slowly rearranges to carbachorismate, which rapidly loses water to give 3-(2-carboxyallyl)benzoic acid as the major product. A small amount of the intramolecular Diels-Alder adduct derived from carbachorismate is also observed by NMR as a minor product. Carbaprephenate is not a substrate for the enzyme chorismate mutase from Bacillus subtilis (BsCM), nor does carbaprephenate inhibit the normal chorismate mutase activity of this enzyme, even when present in 200-fold excess over chorismate. Its low affinity for the enzyme-active site is presumably a consequence of placing a methylene group rather than an oxygen atom proximal to the essential cationic residue Arg90. Nevertheless, BsCM variants that lack this cation (R90G and R90A) do not accelerate the Cope rearrangement of carbaprephenate either, and a catalytic antibody 1F7, which exhibits modest chorismate mutase activity, is similarly inactive. Poor substrate binding and the relatively high barrier for the Cope compared to the Claisen rearrangement presumably account for the lack of detectable catalysis. Acceleration of this sigmatropic rearrangement apparently requires more than an active site that is complementary in shape to the reactive substrate conformer.     

Selective stabilization of the chorismate mutase transition state by a positively charged hydrogen bond donor

Citrulline was incorporated via chemical semisynthesis at position 90 in the active site of the AroH chorismate mutase from Bacillus subtilis. The wild-type arginine at this position makes hydrogen-bonding interactions with the ether oxygen of chorismate. Replacement of the positively charged guanidinium group with the isosteric but neutral urea has a dramatic effect on the ability of the enzyme to convert chorismate into prephenate. The Arg90Cit variant exhibits a >104-fold decrease in the catalytic rate constant kcat with a 2.7-fold increase in the Michaelis constant Km. In contrast, its affinity for a conformationally constrained inhibitor molecule that effectively mimics the geometry but not the dissociative character of the transition state is only reduced by a factor of approximately 6. These results show that an active site merely complementary to the reactive conformation of chorismate is insufficient for catalysis of the mutase reaction. Instead, electrostatic stabilization of the polarized transition state by provision of a cationic hydrogen bond donor proximal to the oxygen in the breaking C-O bond is essential for high catalytic efficiency.     

Charge optimization increases the potency and selectivity of a chorismate mutase inhibitor

The highest affinity inhibitor for chorismate mutases, a conformationally constrained oxabicyclic dicarboxylate transition state analogue, was modified as suggested by computational charge optimization methods. As predicted, replacement of the C10 carboxylate in this molecule with a nitro group yields an even more potent inhibitor of a chorismate mutase from Bacillus subtilis (BsCM), but the magnitude of the improvement (roughly 3-fold, corresponding to a DeltaDeltaG of -0.7 kcal/mol) is substantially lower than the gain of 2-3 kcal/mol binding free energy anticipated for the reduced desolvation penalty upon binding. Experiments with a truncated version of the enzyme show that the flexible C terminus, which was only partially resolved in the crystal structure and hence omitted from the calculations, provides favorable interactions with the C10 group that partially compensate for its desolvation. Although truncation diminishes the affinity of the enzyme for both inhibitors, the nitro derivative binds 1.7 kcal/mol more tightly than the dicarboxylate, in reasonable agreement with the calculations. Significantly, substitution of the C10 carboxylate with a nitro group also enhances the selectivity of inhibition of BsCM relative to a chorismate mutase from Escherichia coli (EcCM), which has a completely different fold and binding pocket, by 10-fold. These results experimentally verify the utility of charge optimization methods for improving interactions between proteins and low-molecular weight ligands.     

Preorganization and reorganization as related factors in enzyme catalysis: the chorismate mutase case

In this paper a deeper insight into the chorismate-to prephenate-rearrangement, catalyzed by Bacillus subtilis chorismate mutase, is provided by means of a combination of statistical quantum mechanics/molecular mechanics simulation methods and hybrid potential energy surface exploration techniques. The main aim of this work is to present an estimation of the preorganization and reorganization terms of the enzyme catalytic rate enhancement. To analyze the first of these, we have studied different conformational equilibria of chorismate in aqueous solution and in the enzyme active site. Our conclusion is that chorismate mutase preferentially binds the reactive conformer of the substrate--that presenting a structure similar to the transition state of the reaction to be catalyzed--with shorter distances between the carbon atoms to be bonded and more diaxial character. With respect to the reorganization effect, an energy decomposition analysis of the potential energies of the reactive reactant and of the reaction transition state in aqueous solution and in the enzyme shows that the enzyme structure is better adapted to the transition structure. This means not only a more negative electrostatic interaction energy with the transition state but also a low enzyme deformation contribution to the energy barrier. Our calculations reveal that the structure of the enzyme is responsible for stabilizing the transition state structure of the reaction, with concomitant selection of the reactive form of the reactants. This is, the same enzymatic pattern that stabilizes the transition structure also promotes those reactant structures closer to the transition structure (i.e., the reactive reactants). In fact, both reorganization and preorganization effects have to be considered as the two faces of the same coin, having a common origin in the effect of the enzyme structure on the energy surface of the substrate.     

Contributions of conformational compression and preferential transition state stabilization to the rate enhancement by chorismate mutase

The rate enhancement provided by the chorismate mutase (CM) enzyme for the Claisen rearrangement of chorismate to prephenate has been investigated by application of the concept of near attack conformations (NACs). Using a combined QM/MM Monte Carlo/free-energy perturbation (MC/FEP) method, 82% and 100% of chorismate conformers were found to be NAC structures in water and in the CM active site, respectively. Consequently, the conversion of non-NACs to NACs does not contribute to the free energy of activation from preorganization of the substrate into NACs. The FEP calculations yielded differences in free energies of activation that well reproduce the experimental data. Additional calculations indicate that the rate enhancement by CM over the aqueous phase results primarily from conformational compression of NACs by the enzyme and that this process is enthalpically controlled. This suggests that preferential stabilization of the transition state in the enzyme environment relative to water plays a secondary role in the catalysis by CM.     

Effect of electrostatic interaction on the mechanism of dehalogenation catalyzed by haloalkane dehalogenase

Theoretical calculation has been carried out for the nucleophilic displacement reaction of 1,2‐dichloroethane catalyzed by haloalkane dehalogenase. The results indicate that different hydrogen bond patterns of the oxyanion hole and the halide‐stabilizing residues play an important role in the dehalogenation reaction. They cause concertedly an earlier transition state (TS) with the activation barrier of 16.60 kcal/mol. The stabilization effect of Trp125 and Trp175 on chlorine atom in the TS is larger than that of the reactant complex by 15.67 kcal/mol so that, they make contribution to the stabilization of the TS. Moreover, the reaction shows the enzymatic action can be attributed to a combination of reactant‐state destabilization and transition‐state electrostatic stabilization. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Mechanism of the tyrosine ammonia lyase reaction-tandem nucleophilic and electrophilic enhancement by a proton transfer

Quantum mechanics/molecular mechanics calculations in tyrosine ammonia lyase (TAL) ruled out the hypothetical Friedel-Crafts (FC) route for ammonia elimination from L-tyrosine due to the high energy of FC intermediates. The calculated pathway from the zwitterionic L-tyrosine-binding state (0.0?kcal mol(-1)) to the product-binding state ((E)-coumarate+H(2)N-MIO; -24.0?kcal mol(-1); MIO = 3,5-dihydro-5-methylidene-4H-imidazol-4-one) involves an intermediate (IS, -19.9?kcal mol(-1)), which has a covalent bond between the N atom of the substrate and MIO, as well as two transition states (TS1 and TS2). TS1 (14.4?kcal mol(-1)) corresponds to a proton transfer from the substrate to the N1 atom of MIO by Tyr300-OH. Thus, a tandem nucleophilic activation of the substrate and electrophilic activation of MIO happens. TS2 (5.2?kcal mol(-1)) indicates a concerted C-N bond breaking of the N-MIO intermediate and deprotonation of the pro-S β position by Tyr60. Calculations elucidate the role of enzymic bases (Tyr60 and Tyr300) and other catalytically relevant residues (Asn203, Arg303, and Asn333, Asn435), which are fully conserved in the amino acid sequences and in 3D structures of all known MIO-containing ammonia lyases and 2,3-aminomutases.     

How much do enzymes really gain by restraining their reacting fragments?

The steric effect, exerted by enzymes on their reacting substrates, has been considered as a major factor in enzyme catalysis. In particular, it has been proposed that enzymes catalyze their reactions by pushing their reacting fragments to a catalytic configuration which is sometimes called near attack configuration (NAC). This work uses computer simulation approaches to determine the relative importance of the steric contribution to enzyme catalysis. The steric proposal is expressed in terms of well defined thermodynamic cycles that compare the reaction in the enzyme to the corresponding reaction in water. The S(N)2 reaction of haloalkane dehalogenase from Xanthobacter autotrophicus GJ10, which was used in previous studies to support the strain concept is chosen as a test case for this proposal. The empirical valence bond (EVB) method provides the reaction potential surfaces in our studies. The reliability and efficiency of this method make it possible to obtain stable results for the steric free energy. Two independent strategies are used to evaluate the actual magnitude of the steric effect. The first applies restraints on the substrate coordinates in water in a way that mimics the steric effect of the protein active site. These restraints are then released and the free energy associated with the release process provides the desired estimate of the steric effect. The second approach eliminates the electrostatic interactions between the substrate and the surrounding in the enzyme and in water, and compares the corresponding reaction profiles. The difference between the resulting profiles provides a direct estimate of the nonelectrostatic contribution to catalysis and the corresponding steric effect. It is found that the nonelectrostatic contribution is about -0.7 kcal/mol while the full "apparent steric contribution" is about -2.2 kcal/mol. The apparent steric effect includes about -1.5 kcal/mol electrostatic contribution. The total electrostatic contribution is found to account for almost all the observed catalytic effect ( approximately -6.1 kcal/mol of the -6.8 calculated total catalytic effect). Thus, it is concluded that the steric effect is not the major source of the catalytic power of haloalkane dehalogenase. Furthermore, it is found that the largest component of the apparent steric effect is associated with the solvent reorganization energy. This solvent-induced effect is quite different from the traditional picture of balance between the repulsive interaction of the reactive fragments and the steric force of the protein.     

Theoretical insights in enzyme catalysis

In this tutorial review we show how the methods and techniques of computational chemistry have been applied to the understanding of the physical basis of the rate enhancement of chemical reactions by enzymes. This is to answer the question: Why is the activation free energy in enzyme catalysed reactions smaller than the activation free energy observed in solution? Two important points of view are presented: Transition State (TS) theories and Michaelis Complex (MC) theories. After reviewing some of the most popular computational methods employed, we analyse two particular enzymatic reactions: the conversion of chorismate to prephenate catalysed by Bacillus subtilis chorismate mutase, and a methyl transfer from S-adenosylmethionine to catecholate catalysed by catechol O-methyltransferase. The results and conclusions obtained by different authors on these two systems, supporting either TS stabilisation or substrate preorganization, are presented and compared. Finally we try to give a unified view, where a preorganized enzyme active site, prepared to stabilise the TS, also favours those reactive conformations geometrically closer to the TS.