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Paul Bash* and L. Lawrence Ho
Center for Mechanistic Biology and Biotechnology,
Argonne National Laboratory
*current address: Northwestern University
Alexander Mackerell, Jr.
School of Pharmacy,
University of Maryland, Baltimore
Fig. 1: Proton transfer reaction in the enzyme malate hydrogenase
Fig. 2: Energy surface for the whole reeation in the enzyme
Scientists have long sought to understand how enzymes facilitate the wide variety of chemical reactions found in biological systems. 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 (QM/MM) methods.
We have now developed a systematized approach to calibrate and use our QM/MM method in complex heterogeneous molecular systems. Key to this approach are (1) the use of a genetic algorithm to optimize the parameters associated with the semiempirical QM method, and (2) adjustment of van der Waals parameters such that the interaction energies between QM and MM atoms emulate those determined from ab initio QM calculations or experimental data.
Using this optimized QM/MM approach, we calculated (1) a proton transfer from methanol to imidazole and (2) a hydride transfer from methoxide to nicotnamide. These molecular species were chosen because they are functional groups involved with proton transfers in many biochemical systems. We used free energy perturbation (FEP) theory to calculate the potential of mean force along a reaction coordinate to determine the free energy of transfer for a proton and hydride transfer reaction in aqueous solution. The free energy changes are calculated to be 15.1 and -6.3 kcal/mol for the proton and hydride transfers, respectively, which compare favorably with the corresponding experimental values of 12.9 and -7.4 kcal/mol.
Usin this approach, we have conducted a simulation and analysis of the reaction mechanism of the enzyme malate dehydrogenase (MDH). Encouraged by preliminary results of a computational simulation, we calculated the minimum energy surface and reaction pathway for the interconversion of malate and oxaloacetate catalyzed by MDH. Analysis of the energy profile shows that solvent effects due to the protein matrix dramatically alter the intrinsic reactivity of the functional groups involved in the MDH reactions. The enzyme effectively changes the reaction from an exothermic reaction in the gas phase to a nearly isoenergetic one in the protein-solvient environment of MDH. An energy decomposition analysis indicates that specific MDH residues in the vicinity of the substrate make significant energetic contributions to the stabilization of proton transfer and destabilization of hydride transfer. This data suggests that the amino acids play an important role in the catalytic properties of MDH, consistent with site-directed mutagensis experiments.
To determine the minimum energy profile, we conducted 675 separate energy minimizations, using Argonne's 128-processor IBM SP parallel computer. Each processor was assigned an MDH model with a different and independent set of distance parameters that define the reaction mechanism in the enzyme. Each simulation consisted of 1000 steps of Adopted Basis Newton-Raphson minimization method (CHARMM program). The energy convergence for all 675 calculations was 0.013+-0.03 kcal/mol. From these simulations we developed a detailed atomic description of the MDH reaction mechanism. Specifically, we showed that the MDH enzyme reaction is sequential, with the proton transfer preceding the hydride transfer.
In addition to giving a detailed atomic description of the MDH reaction, computer experiments with our QM/MM approach can also provide insights into the reasons that MDH is able to effectively catalyze the interconversion of malate and oxaloacetate. In particular, examination of the reaction profile shows that electrostatic effects in specific regions may enhance the transfer potential.
Additional simulations are in progress to determine the free energy profile and transition states for the MDH reaction. We anticipate that improved methods to solve Schroedinger's equation, coupled with 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 eventually will lead to the simulation of free energies of reaction for enzymes to chemical accuracy of less than 1 kcal/mol, which would result in estimates of rate constants to within one order of magnitude of experimental values.
The figures were produced by R. Gillilan at the Cornell Theory Center from data generated by P. Bash on the IBM SP at Argonne National Laboratory.
Paul Bash
Dept. of Molecular Pharmacology & Biological Chemistry
Northwestern University Medical School
Ward Bldg. Rm. 7-246
303 East Chicago Ave.
Chicago, IL 60611-3008
e-mail: pabash@nwu.edu
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