Our forebears believed that living matter was imbued with a special essence, vitality, which distinguished it from ordinary matter. Modern science has stripped away much of the mystery of biological processes and we now understand the basic metabolic sequences to be a chain of relatively straightforward, albeit intricately coordinated, chemical reactions. The protein molecules known as enzymes are vital components of the biochemical machinery, serving as extraordinarily specific and highly efficient catalysts. It has been a longstanding goal of biochemists to understand the mechanisms employed by these enzymes to achieve their catalytic prowess and, thanks to increasingly more sophisticated experimental techniques, the mystery shrouding the function of these molecules is dissipating. Molecular biology methods provide information about the amino acid sequences which make up the protein and also provide the means to identify and modify key interacting groups. High-resolution three-dimensional enzyme structures can be obtained by x-ray crystallography methods, which yield further insights into the functioning of these remarkable chemical factories. Nonetheless, there remain a number of issues which are difficult to address with current experimental technology due to the fact that the key steps of the catalytic process are short-lived events.
The initial recognition and capture of the substrate molecule into what is termed the Michaelis complex occurs on a time scale of nanoseconds, due primarily to the diffusion of the substrate into the active site of the enzyme. The actual chemical events, the making and breaking of bonds, occur on an even shorter time scale: perhaps tens of femtoseconds. Present experimental methods are limited in their ability to yield much information on such rapid processes. This situation has stimulated our efforts to develop numerical tools which can analyze the details of molecular recognition and catalytic processes in enzymes that are difficult to ascertain via present biophysical and biochemical experimental methods.
The Schrodinger equation describes the quantum behaviour of atoms and molecules but generating a solution for an enzyme/substrate complex composed of thousands of atoms is problematic. High-level ab initio quantum mechanics calculations capable of chemical accuracy (1-2 kcal/mol) are limited in practice to molecules containing at most a dozen atoms, for which a single energy calculation requires several hours of supercomputer time. An alternative approach, suitable for large systems like enzymes, treats the atoms classically, like soft, charged balls coupled with springs to represent the bonds. The spring constants and atomic charge distributions used in these so-called molecular mechanics methods  are calibrated in small molecule systems to reproduce the known structures and infrared spectra in the gas phase and observed thermodynamic properties in the condensed phase. While, admittedly, the method provides only a rough approximation to the actual solutions of the Schrodinger equation, it has the significant advantage that calculations can be performed very rapidly, thus providing the means to study the time evolution of large systems.
We have recently used just such a method, coupled with a Laue x-ray diffraction experiment, to define the structure of the Miehaelis complex of the enzyme isocitrate dehydrogenase (IDH), its substrate isocitrate, cofactor nicotinamide adenine dinucleotide phosphate (NADP+) and magnesium . The Michaelis complex represents the initial step in the reaction which yields [Alpha]-ketoglutarate, carbon dioxide and NADPH. The key issue addressed by the molecular dynamics calculations was the position of the mobile nicotinamide ring of NADP+, which was not well-defined through standard crystallographic refinement. Using different starting configurations, a series of numerical experiments converged upon a single conformation which can be identified as the Michaelis complex and is consistent with the crystallographic data. To take the next step and monitor the chemical events is, unfortunately, not possible with molecular mechanics methods; to do so requires a more accurate description of the quantum mechanical processes involved in the reaction.
Using the observation that molecular mechanics provides a reasonable dynamical description of the protein, it is possible to formulate a hybrid method in which the bulk of the protein is treated classically and only a small number of atoms in the active region are treated quantum mechanically.  As we noted above, however, high-level ab initio quantum methods are too slow to be practical on even a reduced system. Instead, the hybrid method utilizes a semi-empirical, quantum Hamiltonian to approximate solutions to the Schrodinger equation.  The semi-empirical approach is orders of magnitude faster than ab initio methods but can be significantly less reliable. For our purposes, however, these semi-empirical models will be sufficient if they can be suitably calibrated for the specific reactions under study in a particular enzyme-substrate system.
Indeed, we find that the key elements required to realistically simulate enzyme-substrate systems with such a hybrid method are as follows:
* Good experimental data about the enzyme crystal structure. Our simulations require three-dimensional structural information about the enzyme as input; protein folding is an entirely separate issue which we do not address.
* Calibration of the semi-empirical quantum mechanics model for the specific reactions which can occur in the enzyme-substrate complex against ab initio quantum mechanical calculations for small-molecule analogs and available experimental data for related reactions in the gas phase and aqueous solution.
* Calibration of the interactions between atoms described quantum mechanically and those described with molecular mechanics, again by comparison with ab initio quantum mechanical calculations for small-molecule analogs. This step ensures that the effects of the protein environment on the reaction dynamics is handled realistically.
Once suitably tailored for an enzyme/substrate system, the hybrid approach allows us to simulate the enzymatic process, including the changes in electronic structure that occur as the chemical events unfold.
We have recently employed this method in a study of the enzyme malate dehydrogenase, which interconverts malate and oxaloacetate by means of a proton and a hydride transfer.
Figure 1 is an illustration of the minimum energy surface associated with the two primary reaction coordinates of the system: d(O2-H2) represents the proton transfer and d(C2-H21) represents the hydride transfer. The minimum energy pathway from the initial malate state (reactant) to the final oxaloacetate state (product), along with the location of intermediate transition states, can be obtained by inspection of Figure 1. We infer that the proton transfer precedes the hydride transfer due to the large potential barrier facing an initial hydride transfer event. Recent experiments by John Burgner's group at Purdue have yielded results which are consistent with our proposed reaction sequence.
Unlike the static charge model utilized in molecular mechanics methods, electronic structure is directly computed in the hybrid model, for atoms treated quantum mechanically. Figure 2 illustrates the electron density at the proton-transfer transition state identified in Figure 1; the H2 proton is equidistant (1.3 [Angstrom]) between the NE2 nitrogen of the histidine residue (pentagonal ring) in MDH and the O2 oxygen of the malate substrate. Analysis of the changes in electronic structure for states along the minimum-energy reaction pathway allow us to ascertain the effects of the enzyme environment during the reaction process.
A century ago, scientists had to invoke the existence of a vital essence to account for biological activity. Biochemists have since isolated enzymes, deduced their composition and determined their structure. The long-sought goal of understanding enzyme function in terms of atomic composition and three-dimensional structure is within reach, at least for some systems. Numerical simulations can supply key information about reaction mechanisms and complement experimental investigations. Additionally, as the methods grow more sophisticated and robust, their predictive power will improve, opening the way to the design of novel enzymatic systems for industrial applications.
1. Brooks, C.L., Karplus, M. and Pettit, BM, Proteins: A Theoretical Perspective of Dynamics, Structure and Thermodynamics, Advances in Chemical Physics, LXXI, John Wiley and Sons, New York, 1988.
2. Stoddard, B.L., Dean, A. and Bash, P.A., Combining Laue diffraction and molecular dynamics to study enzyme intermediates, Nature Struc. Biol. 3: 590-595, 1996.
3. Field, M.J., Bash, P.A., and Karplus, M., A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulation, J. Comp. Chem. 11:700-733, 1990.
4. Dewar, M.J.S., Zoebisch, E.G., Healy, E.F. and Stewart, J.J.P., AM1: A new general purpose quantum mechanical molecular model, J. Am. Chem. Soc. 107:3902-3909, 1985.
Mark Cunningham is a Research Associate at the Center for Mechanistic Biology and Biotechnology, Argonne National Laboratory, where Paul Bash is a Research Scientist. Richard Gillilan is a Visualization Specialist at the Cornell Theory Center, Cornell University.
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|Author:||Cunningham, Mark A.; Gillilan, Richard E.; Bash, Paul A.|
|Publication:||Canadian Chemical News|
|Date:||Apr 1, 1997|
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