Analysis of chorismate mutase catalysis by QM/MM modelling of enzyme-catalysed and uncatalysed reactions

Chorismate mutase is at the centre of current controversy about fundamental features of biological catalysts. Some recent studies have proposed that catalysis in this enzyme does not involve transition state (TS) stabilization but instead is due largely to the formation of a reactive conformation of the substrate. To understand the origins of catalysis, it is necessary to compare equivalent reactions in different environments. The pericyclic conversion of chorismate to prephenate catalysed by chorismate mutase also occurs (much more slowly) in aqueous solution. In this study we analyse the origins of catalysis by comparison of multiple quantum mechanics/molecular mechanics (QM/MM) reaction pathways at a reliable, well tested level of theory (B3LYP/6-31G(d)/CHARMM27) for the reaction (i) in Bacillus subtilis chorismate mutase (BsCM) and (ii) in aqueous solvent. The average calculated reaction (potential energy) barriers are 11.3 kcal mol(-1) in the enzyme and 17.4 kcal mol(-1) in water, both of which are in good agreement with experiment. Comparison of the two sets of reaction pathways shows that the reaction follows a slightly different reaction pathway in the enzyme than in it does in solution, because of a destabilization, or strain, of the substrate in the enzyme. The substrate strain energy within the enzyme remains constant throughout the reaction. There is no unique reactive conformation of the substrate common to both environments, and the transition state structures are also different in the enzyme and in water. Analysis of the barrier heights in each environment shows a clear correlation between TS stabilization and the barrier height. The average differential TS stabilization is 7.3 kcal mol(-1) in the enzyme. This is significantly higher than the small amount of TS stabilization in water (on average only 1.0 kcal mol(-1) relative to the substrate). The TS is stabilized mainly by electrostatic interactions with active site residues in the enzyme, with Arg90, Arg7 and Glu78 generally the most important. Conformational effects (e.g. strain of the substrate in the enzyme) do not contribute significantly to the lower barrier observed in the enzyme. The results show that catalysis is mainly due to better TS stabilization by the enzyme.     

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.     

A hybrid potential reaction path and free energy study of the chorismate mutase reaction.

We present a combination of two techniques--QM/MM statistical simulation methods and QM/MM internal energy minimizations--to get a deeper insight into the reaction catalyzed by the enzyme chorismate mutase. Structures, internal energies and free energies, taken from the paths of the reaction in solution and in the enzyme have been analyzed in order to estimate the relative importance of the reorganization and preorganization effects. The results we obtain for this reaction are in good agreement with experiment and show that chorismate mutase achieves its catalytic efficiency in two ways; first, it preferentially binds the active conformer of the substrate and, second, it reduces the free energy of activation for the reaction relative to that in solution by providing an environment which stabilizes the transition state.     

Multiple-steering QM-MM calculation of the free energy profile in chorismate mutase

A novel technique for computing free energy profiles in enzymatic reactions using the multiple steering molecular dynamics approach in the context of an efficient QM-MM density functional scheme is presented. The conversion reaction of chorismate to prephenate catalyzed by the Bacillus subtilis enzyme chorismate mutase has been chosen as an illustrative example.     

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.     

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.     

Theoretical study of the reaction mechanism and solvent effect on the regioselectivity of 1,3‐dipolar cycloaddition reaction between azide and acetylene derivatives

The reaction mechanism and solvent‐dependant regioselectivity of 1,3‐dipolar cycloaddition reactions between azide and acetylene derivatives have been studied using computational methods. The two possible reaction transition states were located. Geometry and NBO analysis found that the reactions take place along a synchronous and concerted mechanism for TS1 and an asynchronous and less concerted mechanism for TS2 . SCRF analysis found that TS2 is more sensitive to the polarity of solvent. In less polar solvent such as CCl₄, the difference of activation barriers of the two transition states is small. However, when the reactions were conducted in water, the activation barriers for TS2 increase which leads to the observed regioselectivity. © 2007 Wiley Periodicals, Inc. Heteroatom Chem 18:203–207, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20236     

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.     

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.     

Proton-coupled electron transfer of the phenoxyl/phenol couple: effect of Hartree-Fock exchange on transition structures

Proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) reactions of the phenoxyl/phenol couple are studied theoretically by using wave function theory (WFT) as well as DFT methods. At the complete active space self-consistent field (CASSCF) level, geometry optimization is found to give two transition states (TSs); one is the PCET type with two benzene rings being nearly coplanar, and the other is the HAT type with two benzene rings taking a stacking structure. Geometry optimization at the (semilocal) DFT level, on the other hand, is found to give only one transition state (i.e., the PCET-type one) and fail to obtain the stacking TS structure. By comparing various levels of theories (including long-range corrected DFT functionals), we demonstrate that the Hartree-Fock exchange at long range plays a critical role in obtaining the sufficient stacking stabilization of the present open-shell system, and that the sole addition of empirical dispersion correction to semilocal DFT functionals may not be adequate for describing such a stacking interaction. Next, we investigate the solvent effect on the PCET and HAT TS thus obtained using the reference interaction site model self-consistent field (RISM-SCF) method. The results suggest that the free energy barrier increases with increasing polarity of the solvent, and that the solvent effects are stronger for the PCET TS than the stacking HAT TS pathway. The reason for this is discussed based on the dipole moment of different TS structures in solution.     

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.     

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.     

Investigation of solvent effects for the Claisen rearrangement of chorismate to prephenate: mechanistic interpretation via near attack conformations

Solvent effects on the rate of the Claisen rearrangement of chorismate to prephenate have been examined in water and methanol. The preequilibrium free-energy differences between diaxial and diequatorial conformers of chorismate, which had previously been implicated as the sole basis for the observed 100-fold rate increase in water over methanol, have been reframed using the near attack conformation (NAC) concept of Bruice and co-workers. Using a combined QM/MM Monte Carlo/free-energy perturbation (MC/FEP) method, 82%, 57%, and 1% of chorismate conformers were found to be NAC structures (NACs) in water, methanol, and the gas phase, respectively. As a consequence, the conversion of non-NACs to NACs provides no free-energy contributions to the overall relative reaction rates in water versus methanol. Free-energy perturbation calculations yielded differences in free energies of activation for the two polar protic solvents and the gas phase. The rate enhancement in water over the gas phase arises from preferential hydration of the transition state (TS) relative to the reactants via increased hydrogen bonding and long-range electrostatic interactions, which accompany bringing the two negatively charged carboxylates into closer proximity. More specifically, there is an increase of 1.3 and 0.6 hydrogen bonds to the carboxylate groups and the ether oxygen, respectively, in going from the reactant to the TS in water. In methanol, the corresponding changes in hydrogen bonding with first shell solvent molecules are small; the rate enhancement arises primarily from the enhanced long-range interactions with solvent molecules. Thus, the reaction occurs faster in water than in methanol due to greater stabilization of the TS in water by specific interactions with first shell solvent molecules.     

On the mechanism of hydrolysis of phosphate monoesters dianions in solutions and proteins

The nature of the hydrolysis of phosphate monoester dianions in solutions and in proteins is a problem of significant current interest. The present work explores this problem by systematic calculations of the potential surfaces of the reactions of a series of phosphate monoesters with different leaving groups. These calculations involve computational studies ranging from ab initio calculations with implicit solvent models to ab initio QM/MM free energy calculations. The calculations reproduce the observed linear free energy relationship (LFER) for the solution reaction and thus are consistent with the overall experimental trend and can be used to explore the nature of the transition state (TS) region, which is not accessible to direct experimental studies. It is found that the potential surface for the associative and dissociative paths is very flat and that the relative height of the associative and dissociative TS is different in different systems. In general, the character of the TS changes from associative to dissociative upon decrease in the pKa of the leaving group. It is also demonstrated that traditional experimental markers such as isotope effects and the LFER slope cannot be used in a conclusive way to distinguish between the two classes of transition states. In addition it is found that the effective charges of the TS do not follow the previously assumed simple rule. Armed with that experience we explore the free energy surface for the GTPase reaction of the RasGap system. In this case it is found that the surface is flat but that the lowest TS is associative. The present study indicates that the nature of the potential surfaces for the phosphoryl transfer reactions in solution and proteins is quite complicated and cannot be determined in a conclusive way without the use of careful theoretical studies that should, of course, reproduce the available experimental information.     

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.     

Transition structure selectivity in enzyme catalysis: a QM/MM study of chorismate mutase

Two different transition structures (TSs) have been located and characterized for the chorismate conversion to prephenate in Bacillus subtilis chorismate mutase by means of hybrid quantum-mechanical/molecular-mechanical (QM/MM) calculations. GRACE software, combined with an AM1/CHARMM24/TIP3P potential, has been used involving full gradient relaxation of the position of ca. 3300 atoms. These TSs have been connected with their respective reactants and products by the intrinsic reaction coordinate (IRC) procedure carried out in the presence of the protein environment, thus obtaining for the first time a realistic enzymatic reaction path for this reaction. Similar QM/MM computational schemes have been applied to study the chemical reaction solvated by ca. 500 water molecules. Comparison of these results together with gas phase calculations has allowed understanding of the catalytic efficiency of the protein. The enzyme stabilizes one of the TSs (TS_OHout) by means of specific hydrogen bond interactions, while the other TS (TS_OHin) is the preferred one in vacuum and in water. The enzyme TS is effectively more polarized but less dissociative than the corresponding solvent and gas phase TSs. Electrostatic stabilization and an intramolecular charge-transfer process can explain this enzymatically induced change. Our theoretical results provide new information on an important enzymatic transformation and the key factors responsible for efficient selectivity are clarified. Received: 25 March 2000 / Accepted: 7 August 2000 / Published online: 23 November 2000     

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.     

Can Enantioselectivity be Computed in Enthalpic Barrierless Reactions? The Case of CuI‐Catalyzed Cyclopropanation of Alkenes

An extensive computational study has been carried out on different catalytic systems for cyclopropanation reactions based on copper. Most DFT schemes used present drawbacks that preclude the calculation of accurate absolute kinetic properties (energy barriers) of such systems, excepting the M05 and M06 suites of density functionals. On the other hand, there is a wide range of DFT methods capable of reproducing relative energy values, which can be easily translated into selectivities. Most of the theoretical levels used tend to overestimate activation barriers, allowing the location of the transition state (TS) on the potential-energy surface (PES) of the most reactive systems, which are probably artifacts of the method. However, after a thorough analysis of the calculated PES, and the origin of the energy differences obtained for the different alkene approaches in chiral systems, it is found that energy differences are almost constant over a wide range of geometries covering the reaction channel zone in which the true TS on the Gibbs free-energy surface (GFES) lies. Therefore, many computational schemes can still be used confidently to explain and predict enantioselectivities in these systems.     

Quantitative evaluation of noncovalent chorismate mutase-inhibitor binding by ESI-MS

Electrospray time-of-flight mass spectrometry was used to quantitatively determine the dissociation constant of chorismate mutase and a transition state analogue inhibitor. This system presents a fairly complex stoichiometry because the native protein is a homotrimer with three equal and independent substrate binding sites. We can detect the chorismate mutase trimer as well as chorismate mutase-inhibitor complexes by choosing appropriate conditions in the ESI source. To verify that the protein-inhibitor complexes are specific, titration experiments with different enzyme variants and different inhibitors were performed. A plot of the number of bound inhibitors versus added inhibitor concentration revealed saturation behavior with 3:1 (inhibitor:functional trimer) stoichiometry for the TSA. The soft ESI conditions, the relatively high protein mass of 43.5 kDa, and the low charge state (high m/z) result in broad peaks, a typical problem in analyzing noncovalent protein complexes. Due to the low molecular weight of the TSA (226 Da) the peaks of the free protein and the protein with one, two or three inhibitors bound cannot be clearly resolved. For data analysis, relative peak areas of the deconvoluted spectra of chorismate mutase-inhibitor complexes were obtained by fitting appropriate peak shapes to the signals corresponding to the free enzyme and its complexes with one, two, or three inhibitor molecules. From the relative peak areas we were able to calculate a dissociation constant that agreed well with known solution-phase data. This method may be generally useful for interpreting mass spectra of noncovalent complexes that exhibit broad peaks in the high m/z range.