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Figure 4 Schematic diagram of the first step of the reaction catalyzed by bovine protein tyrosine phosphatase (BPTP): formation of the cysteinyl phosophate intermediate.

determination of reaction activation parameters and the dynamics of active site residues to be followed along the trajectory of the reaction. This enabled the determination of a free energy of activation of 14 kcal/mol, which was in excellent agreement with the results from stopped-flow studies [30]. In addition, the dynamics of the hydrogen-bonding network of the active site could be followed throughout the reaction.

A free energy study of malate dehydrogenase [29] using semiempirical QM–MM methods has also been reported, and that study also attributes many of the benefits to simulation of enzyme reactions found in the BPTP study.

C. Citrate Synthase

The final application considered in this chapter is chosen to illustrate the application of a QM–MM study of an enzyme reaction that employs an ab initio Hamiltonian in the quantum region [67]. Because of the computational intensity of such calculations there are currently very few examples in the literature of QM–MM studies that use a quantum mechanical technique that is more sophisticated than a semiempirical method. Mulholland et al. [67] recently reported a study of part of the reaction catalyzed by citrate synthase (CS) in which the quantum region is treated by Hartree–Fock and MP2 methods [10,51],

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and this serves as a useful illustration of the current state of the art in the field of QM– MM applications to enzyme catalysis.

Citrate synthase catalyzes the metabolically important formation of citrate from ace- tyl-CoA and oxaloacetate [68]. Asp-375 (numbering for pig CS) has been shown to be the base for the rate-limiting deprotonation of acetyl-CoA (Fig. 5) [69]. An intermediate (which subsequently attacks the second substrate, oxaloacetate) is believed to be formed in this step; the intermediate is thought to be stabilized by a hydrogen bond with His274. It is uncertain from the experimental data whether this intermediate is the enolate or enol of acetyl-CoA; related questions arise in several similar enzymatic reactions such as that catalyzed by triosephosphate isomerase. From the relative pKa values of Asp-375

Figure 5 A suggested mechanism for the enolization of acetyl-CoA by the enzyme citrate synthase (CS). The keto, enolate, and enol forms of the substrate are shown.

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and acetyl-CoA, it appears that the enolate (or enol) can be an intermediate in the enzymatic reaction only if it is stabilized by the enzyme. It has been proposed that the necessary stabilization is provided by a low barrier hydrogen bond (LBHB) in this and other enzymes [70,71]. A low barrier hydrogen bond is a covalent interaction between a hydrogen bond donor and the transition state of an enzymatic reaction, and it is believed to be the main source of catalysis. The hydrogen in an LBHB is almost equidistant from the heavy atoms, and the donor and acceptor are closer to each other than in normal hydrogen bonds. The potential energy surface for the transfer of the hydrogen between the donor and acceptor atoms is very small, leading to the appearance of a single broad energy well. For normal hydrogen bonds the potential energy for hydrogen transfer is characterized by two energy wells corresponding to the hydrogen being bonded to either of the heavy atoms. The suggested LBHB is betwen His-274, which is neutral, and an ‘‘enolic’’ acetyl-CoA intermediate [71,72]. To resolve the question of the nautre of the intermediate and its stabilization by the enzyme, the first reaction step in CS was investigated by ab initio QM–MM calculations with the CHARMM program.

˚

The system contained all residues within 17 A of the terminal carbon of acetylCoA, the R-malate substrate, and 23 crystallographic water molecules (the active site of CS is buried in the protein). All ab initio QM–MM calculations were performed using the CHARMM program interfaced to GAMESS [10]. Current computational resources preclude the use of molecular dynamics methods with an ab initio QM–MM potential, so the reaction pathway was followed by using the adiabatic mapping technique used previously for TIM and other enzymes. Even with this energy minimization approach, care is needed to avoid excessively long computational run times in calculating the reaction path. The approach used by Mulholland et al. [67] was to perform a series of calculations, beginning with a computationally inexpensive method and progressively increasing the level of calculation used in the quantum region. This is analogous to the approach often used in pure quantum mechanical studies that initially use a low level basis set to get a rough estimate of the potential energy surface and then refine this with a more accurate higher level basis set. The quantum region included the side chains of Asp-375, His-274, the thioester portion of acetyl-CoA, and the substrate.

For CS the reaction profile was initially extensively studied by QM–MM with an AM1 Hamiltonian [28]. The points along the reaction pathway were subsequently subjected to QM–MM minimization using RHF/3-21G* for the quantum region, and finally the minimization of the reaction points on the pathway was completed with RHF/6-31G* in the quantum region. This reaction pathway was further refined by performing singlepoint QM–MM calculations at the MP2/6-31G*level for the quantum region. This allowed the system to be fully minimized without incurring the large computational cost that would have resulted had the quantum region been treated at the RHF/6-31G* level from the start.

The study found that the enolate of acetyl-CoA is the intermediate in the rate-limiting step of the reaction, in agreement with previous experimental studies. The reaction catalyzed by CS has previously proposed to employ a mechanism that uses low barrier hydrogen bonds. Such bonds can be exceptionally strong in the gas phase and have been proposed to have energies of up to 20 kcal/mol in enzymes. However, the debate about their role in enzyme catalysis is controversial. A characteristic of low barrier hydrogen bonds is that the hydrogen is shared between atoms of approximately equal pKa. In CS it has been proposed that the hydrogen bond between His-274 and an enolic (the proton is shared equally) intermediate is responsible for stabilizing the intermediate. The calculations on

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CS indicated that the enolate of acetyl-CoA is significantly more stable than the enol or a proton-sharing enolic form and thus do not support the proposal that a low barrier hydrogen bond is involved in catalysis in CS. This study demonstrates the practial application of high level QM–MM studies to the elucidation of mechanistic details of an enzymatic reaction that are otherwise unclear.

IV. CONCLUSIONS

The field of QM–MM simulations of chemical reactions has grown considerably from the initial proposals of Warshel and Levitt [6] in the 1970s to a technique that can now deliver quantitatively accurate reaction pathways for reactions in the active sites of enzymes. Currently, the computational chemist has several options for treatment of the quantum region. Which method is employed in any given situation is dependent on a number of factors. The computational expense of the density functional and ab initio methods dictate studies using these methods need to be carried out on parallel computers. Naturally, these methods are more accurate for studying the chemistry of the process under consideration, and in the case of metalloenzymes with transition metals it is almost essential to use density functional methods. Nonetheless, it is possible to get quantitative accuracy with semiempirical QM–MM studies, particularly when the quantum atoms and the van der Waals parameters are parametrized for the specific reaction at hand. Additionally, semiempirical QM–MM methods allow a dynamic study of the chemical reaction, which is currently beyond the higher level methods, even with parallel computers. The field continues to expand, and it is to be expected that advances in the speed of the quantum calculations, the accuracy of the treatment of the quantum/classical boundary region, and computational speed will come over the next decade and enable further insight to be gained into the mechanisms of biochemical processes.

ACKNOWLEDGMENT

We are grateful to the Wellcome Trust for financial support.

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