A comparative theoretical study of a bimolecular reaction in aqueous solution and catalyzed by the enzyme catechol O-methyltransferase (COMT) has been carried out by a combination of two hybrid QM/MM techniques: statistical simulation methods and internal energy minimizations. In contrast to previous studies by other workers, we have located and characterized transition structures for the reaction in the enzyme active site, in water and in a vacuum, and our potential of mean force calculations are based upon reaction coordinates obtained from features of the potential energy surfaces in the condensed media, not from the gas phase. The AM1/CHARMM calculated free energy of activation for the reaction of S-adenosyl methionine (SAM) with catecholate catalyzed by COMT is 15 kcal mol(-1) lower the AM1/TIP3P free-energy barrier for the reaction of the trimethylsulfonium cation with the catecholate anion in water at 300 K, in agreement with previous estimates. The thermodynamically preferred form of the reactants in the uncatalyzed model reaction in water is a solvent-separated ion pair (SSIP). Conversion of the SSIP into a contact ion pair, with a structure resembling that of the Michaelis complex (MC) for the reaction in the COMT active site, is unfavorable by 7 kcal mol(-1), largely due to reorganization of the solvent. We have considered alternative ways to estimate the so-called "cratic" free energy for bringing the reactant species together in the correct orientation for reaction but conclude that direct evaluation of the free energy of association by means of molecular dynamics simulation with a simple standard-state correction is probably the best approach. The latter correction allows for the fact that the size of the unit cell employed with the periodic boundary simulations does not correspond to the standard state concentration of 1 M. Consideration of MC-like species allows a helpful decomposition of the catalytic effect into preorganization and reorganization phases. In the preorganization phase, the substrates are brought together into the MC-like species, either in water or in the enzyme active site. In the reorganization phase, the roles of the enzymic and aqueous environments may be compared directly because reorganization of the substrate is about the same in both cases. Analysis of the electric field along the reaction coordinate demonstrates that in water the TS is destabilized with respect to the MC-like species because the polarity of the solute diminishes and consequently the reaction field is also decreased. In the enzyme, the electric field is mainly a permanent field and consequently there is only a small reorganization of the environment. Therefore, destabilization of the TS is lower than in solution, and the activation barrier is smaller.

In recent years, the temperature dependence of primary kinetic isotope effects (KIE) has been used as indicator for the physical nature of enzyme catalyzed H-transfer reactions. An interactive study where experimental data and calculations examine the same chemical transformation is a critical means to interpret more properly temperature dependence of KIEs. Here, the rate limiting step of the thymidylate synthase catalyzed reaction has been studied by means of hybrid Quantum Mechanics/ Molecular Mechanics (QM/MM) simulations in the theoretical framework of the ensemble-averaged variational transition state theory with multidimensional tunneling (EA-VTST/MT) combined with Grote-Hynes theory. The KIEs were calculated across the same temperature range examined experimentally, revealing a temperature independent behaviour, in agreement with experimental findings. The calculations show that the H-transfer proceeds with ca. 91 % by tunneling in the case of protium and ca. 80% when the transferred protium is replaced by tritium. Dynamic recrossing coefficients are almost invariant with temperature and in all cases far from unity, showing significant coupling between protein motions and the reaction coordinate. In particular, the relative movement of a conserved arginine (Arg166 in E. coli) promotes the departure of a conserved cysteine (Cys146 in E. coli) from the dUMP by polarizing the thioether bond thus facilitating this bond breaking that takes place concomitantly with the hydride transfer. These promoting vibrations of the enzyme, which represent some of the dimensions of the real reaction coordinate, would limit the search through configurational space to efficiently find those decreasing both barrier height and width, thereby enhancing the probability of H-transfer by either tunneling (through barrier) or classical (over-the-barrier) mechanisms. In other words, the thermal fluctuations that are coupled to the reaction coordinate, together with transition state geometries and tunneling, are the same in different bath temperatures (within the limited experimental range examined). All these terms contribute to the observed temperature independent KIEs in thymidylate synthase.

Because of its computational cost, QM/MM simulations are usually carried out using low-quality Hamiltonians, such as semiempirical, which are not always able to provide an accurate potential energy surface. We here propose a simple but efficient way to obtain corrected quantum mechanics/molecular mechanics (QM/MM) potentials of mean force (PMF) for chemical processes in condensed media. By means of dual-level calculations on the QM subsystem, we evaluate a correction energy term by employing either the polarized or the unpolarized wave functions. This energy term is evaluated as a function of the distinguished reaction coordinate biased in the calculation of the PMF. Using a mapping coordinate and splines under tension, its derivatives can be readily included to perform molecular dynamics simulations. The structures selected to evaluate the energy correction are chosen from a reaction path obtained in the condensed media, ensuring then that they are representative of the ensemble of structures sampled during the simulation. We have tested the proposed scheme with two prototypical examples:  the Menshutkin reaction in aqueous solution and the chorismate rearrangement to prephenate catalyzed by Bacillus subtilis chorismate mutase. In both cases the use of interpolated corrections clearly improves the quality of the results.

Isotopic substitution (15N, 13C, 2H) of a catalytically compromised variant of Escherichia coli dihydrofolate reductase, EcDHFR-N23PP/S148A, has been used to investigate the effect of these mutations on catalysis. The reduction of the rate constant of the chemical step in the EcDHFR-N23PP/S148A catalyzed reaction is essentially a consequence of an increase of the quasi-classical free energy barrier and to a minor extent of an increased number of recrossing trajectories on the transition state dividing surface. Since the variant enzyme is less well set up to catalyze the reaction, a higher degree of active site reorganization is needed to reach the TS. Although millisecond active site motions are lost in the variant, there is greater flexibility on the femtosecond time scale. The “dynamic knockout” EcDHFR-N23PP/S148A is therefore a “dynamic knock-in” at the level of the chemical step, and the increased dynamic coupling to the chemical coordinate is in fact detrimental to catalysis. This finding is most likely applicable not just to hydrogen transfer in EcDHFR but also to other enzymatic systems.

Potential energy surfaces are fundamental tools for the analysis of reaction mechanisms. The accuracy of these surfaces for reactions in very large systems is often limited by the size of the system even if hybrid quantum mechanics/molecular mechanics (QM/MM) strategies are employed. The large number of degrees of freedom of the system requires hundreds or even thousands of optimization steps to reach convergence. Reactions in condensed media (such as enzymes or solutions) are thus usually restricted to be analyzed using low level quantum mechanical methods, thus introducing a source of error in the description of the QM region. In this paper, an alternative method is proposed, coupled to the use of a micro/macroiteration algorithm during the optimization. In these algorithms, the number of microsteps involved in the QM region optimization is usually much smaller than the number of macrosteps required to optimize the MM region. Thus, we define a new potential energy surface in which the gas-phase energy of the QM subsystem and the interaction energy with the MM subsystem are calculated at different computational levels. The high computational level is restricted to the gas-phase energy, which is only requested during the microsteps. The dual level strategy is tested for two reactions in solution (the Menshutkin and the oxy-Cope reactions) and an enzymatic one (the nucleophilic substitution of 1,2-dichloroethane in DhlA). The performance of the proposed computational scheme seems to be quite promising for future applications in other systems.

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.

Registro de acceso restringido Este recurso no está disponible en acceso abierto por política de la editorial. No obstante, se puede acceder al texto completo desde la Universitat Jaume I o si el usuario cuenta con suscripción. Registre d'accés restringit Aquest recurs no està disponible en accés obert per política de l'editorial. No obstant això, es pot accedir al text complet des de la Universitat Jaume I o si l'usuari compta amb subscripció. Restricted access item This item isn't open access because of publisher's policy. The full--text version is only available from Jaume I University or if the user has a running suscription to the publisher's contents.

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.