Computational Enzymology

P. Bash and L. Ho
Center for Mechanistic Biology and Biotechnology
Argonne National Laboratory

Introduction and Motivation:

A fundamental property of biological organisms is their ability to facilitate the transformation of organic matter into unique biochemical components that are essential for the viability of life. The primary biological molecules responsible for such transformations are enzymes. These molecules have extraordinary molecular recognition and catalytic properties that are dependent on specific atomic interactions. A long-standing goal of enzymology has been to understand how enzymes facilitate the wide variety of chemical reactions found in biological systems in terms of their atomic structures and molecular compositions. Important insights into the mechanisms of several enzymes have been obtained through the combined use of x-ray crystallography and kinetic, thermodynamic, and genetic engineering experiments. However, the complexity of biological macromolecules makes it difficult to ascertain all the atomic, electronic, and energetic characteristics of enzyme-catalyzed reactions using only traditional biophysical and biochemical experimental methods. A complete understanding of the nature of enzyme systems requires the additional use of an approach that is based on fundamental physical and chemical principles and relies only on a knowledge of the chemical composition and the three-dimensional atomic structure of an enzyme-substrate complex. In our research, we have developed a first-principles approach that combines quantum and classical mechanics methods. We demonstrate its utility through a computational simulation of the proton and hydride transfer reactions catalyzed by the enzyme malate dehydrogenase (MDH). Specifically, we calculate (1) the minimum energy surface with respect to relevant reaction coordinates; (2) the minimum energy pathway for proton and hydride transfers; and (3) the transition states along the reaction pathway. From these simulations, we propose a detailed reaction mechanism that can, in principle, be tested by experimental methods, but may require the development and use of innovative biophysical methods such as time-resolved x-ray crystallography or NMR spectroscopy.

MDH catalyzes the interconversion of malate and oxaloacetate in the citric acid cycle. The arrangement of the key catalytic groups in the active site are shown in Figure 1, which is derived from a 1.9 resolution structure of Escherichia coli MDH complexed with the substrate analogue citrate and the co-factor nicotinamide adenine dinucleotide (NAD). This crystal structure and other biochemical data indicate that a proton (H2) is transferred between the substrate (O2) and His-177 (NE2) in the enzyme, and a hydride anion (H21) is transferred between the substrate (C2) and NAD (C4N). However, the details of the MDH mechanism, which includes the order of the reaction (i.e., proton followed by hydride, hydride followed by proton, or concerted) and quantitative information about the structures and energetics of the transition state(s), cannot be determined from the crystal structure or enzyme kinetics experiments. Furthermore, site-directed mutagenesis experiments on MDH and a related enzyme, lactate dehydrogenase (LDH), give results that are difficult to interpret from x-ray structures and kinetic data alone. This inability of traditional biochemical and biophysical techniques to completely characterize MDH and other enzyme reaction mechanisms, and the general problem of using chemical intuition alone to guide protein design experiments, provide the motivation for the development and use of novel analytic and predictive tools to augment and direct enzymology and genetic engineering experiments.

Computational Enzymology:

In principle, one can simulate the structural and energetic properties of enzyme reactions to chemical accuracy (1.0 kcal/mol) through the use of high level ab initio quantum mechanical (QM) methods on an entire enzyme system consisting of several thousand atoms. This is impossible to accomplish in practice becasue of the computational demands of current ab initio QM techniques. For many enzymes and other condensed phase systems, the electronic structure changes associated with bond-breaking and -making events are localized to within a few atomic diameters of the bond that is changing. In these cases, it is reasonable to hypothesize that one may treat different parts of a system at levels of theory commensurate with the accuracy required to simulate the salient properties in each subdomain. This reasoning led us to develop a combined QM (Austin Model 1, AM1 semiempirical) and classical molecular mechanics (MM) approach (QM/MM) for the study of condensed phase reactions.

Enzyme Model:

The x-ray structure of the E. coli MDH ternary complex with malate is used as the basic input data for our simulations. Since the electronic and structural changes that occur during the chemical transformations in MDH are expected to be localized to a region near the substrate, we constructed a model about the active site (18 angstroms from the C2 atom of malate) (see Fig. 2). This includes (1) the key functional groups directly involved in the reaction (malate, imidazole of His-177, and nicotinamide of NAD), (2) enough of the enzyme to include longe-range electrostatic interactions that may contribute to the stabilization of intermediates along the reaction pathway; and (3) the structural features of the enzyme that are necessary to keep the catalytic groups in a geometry competent for the reaction.

Minimum Energy Reaction Surface:

Using our QM/MM method on the enzyme model, we calculated the minimum energy surface for the hydride and proton transfer reactions in the MDH enzyme. The resultant surface provides insights into the details of the minimum energy pathway and transition states for the reaction, i.e. the mechanism of the enzyme, which is difficult to determine experimentally. We carried out a systematic search over the relevant portions of conformational space associated with the transfer of the proton, H2, from O2 to NE2 and the hydride, H21, from C2 to C4N. This was a four-dimensional search over the distances d(O2-H2), d(H2-NE2), d(C2-H21), and d(H21-C4N) that constitutes a physically reasonable ensemble of possible conformations for the interconversion of malate and oxaloacetate. This is a parameter search problem that required a total of 675 energy calculations. This was an ideal application for the 128 node IBM SP parallel computer system, which could calculate the energy of 128 different configurations simultaneously.

A minimum energy surface was obtained by projecting out the two degrees of freedom, d(O2-H2) and d(C2-H21), that are natural coordinates for the MDH reaction in the direction from malate to oxaloacetate. The result is a minimum energy surface for the MDH reaction, which is shown in Figure 3. Figure 3 also displays the contour map for the reaction surface, where 2 transition states (saddle points on the energy surface) for the proton and hydride transfers can be clearly seen (molecular structure of the hydride transition state is displayed in Fig. 4).

Discussion:

Figure 3 provide a description of the minimum reaction pathway, energy barriers, and transition states for the MDH enzyme reaction. The energy barriers for the conversion of malate to oxaloacetate via a hydride/proton or a proton/hydride sequence are about 60 and 25 kcal/mol, respectively. This suggested that the reaction is sequential, with the proton transfer preceding the hydride transfer. Additional simulations are in progress to determine the free energy profile and transition states for the MDH reaction.

The approach outlined in this report, which is based on first principles of quantum and classical mechanics, is a general procedure that can be used to simulate the properties of any condensed phase reaction. Calculations on the enzyme malate dehydrogenase demonstrate the utility of our approach to gain insights into the behavior of a chemical reaction in a complex heterogeneous environment, where traditional experimental methods provide minimal information. The primary limitation of our procedure is the accurate and efficient determination of the electronic structure, using quantum mechanics, for the parts of a system where chemical bonds are made and broken. We are in a watershed period with respect to these kinds of physical and chemical simulations. It is anticipated that over the next few years the development of improved methods to solve Schrodinger's equation coupled with expected dramatic advances in computer technology will provide the means to simulate the electronic properties of complex systems at unprecedented levels of accuracy and reliability. The use of such advances in our QM/MM scheme will eventually lead to the calculation of enzymatic rate constants to chemical accuracy of less than 1 kcal/mol.

Although an accurate first-principles calculation of a rate constant, which can be measured experimentally, for an enzyme reaction would be a noteworthy accomplishment, the real power of computer simulation methods are their ability to provide essential information and insights into the behavior and properties of physical systems, which are difficult or impossible to obtain from traditional experiments. The fundamental property of enzymes is their ability to alter the relative stabilities of reactants, intermediates, and products, which can result in dramatic catalytic efficiency. This property is due to the unique solvent environment of an enzyme, which consists of amino acids and specific organic and inorganic co-factors. Our QM/MM method can be used to carry out a simulation analysis to determine the contribution of the protein matrix in general and specific amino acids in particular to the realization of the energetic characteristics of the entire reaction surface of an enzyme. This kind of analysis can be done only with a first-principles approach. When it is used to augment structural, kinetic, and genetic engineering experiments, the fundamental question of enzymology -- "Why an enzyme is an enzyme?" -- can finally be effectively addressed.