A new practical approach to studying enzyme reactions by combining ab initio QM/MM calculations with free energy perturbation is presented. An efficient iterative optimization procedure has been developed to determine optimized structures and minimum energy paths for a system with thousands of atoms on the ab initio QM/MM potential: the small QM sub-system is optimized using a quasi-Newton minimizer in redundant internal coordinates with ab initio QM/MM calculations, while the large MM sub-system is minimized by the truncated Newton method in Cartesian coordinates with only molecular mechanical calculations. The above two optimization procedures are performed iteratively until they converge. With the determined minimum energy paths, free energy perturbation calculations are carried out to determine the change in free energy along the reaction coordinate. Critical to the success of the iterative optimization procedure and the free energy calculations is the smooth connection between the QM and MM regions provided by a recently proposed pseudobond QM/MM approach [J. Chem. Phys. 110, 46 (1999)]. The methods have been demonstrated by studying the initial proton transfer step in the reaction catalyzed by the enzyme triosephosphate isomerase (TIM).

Drought is one of the most important environmental constraints limiting plant growth and agricultural productivity. To understand the underlying mechanism of drought tolerance and to identify genes for improving this important trait, we conducted a gain-of-function genetic screen for improved drought tolerance in Arabidopsis thaliana. One mutant with improved drought tolerance was isolated and designated as enhanced drought tolerance1. The mutant has a more extensive root system than the wild type, with deeper roots and more lateral roots, and shows a reduced leaf stomatal density. The mutant had higher levels of abscisic acid and Pro than the wild type and demonstrated an increased resistance to oxidative stress and high levels of superoxide dismutase. Molecular genetic analysis and recapitulation experiments showed that the enhanced drought tolerance is caused by the activated expression of a T-DNA tagged gene that encodes a putative homeodomain-START transcription factor. Moreover, overexpressing the cDNA of the transcription factor in transgenic tobacco also conferred drought tolerance associated with improved root architecture and reduced leaf stomatal density. Therefore, we have revealed functions of the homeodomain-START factor that were gained upon altering its expression pattern by activation tagging and provide a key regulator that may be used to improve drought tolerance in plants.

The mechanism for the reaction catalyzed by the 4-oxalocrotonate tautomerase (4-OT) enzyme has been studied using a quantum mechanical/molecular mechanical (QM/MM) method developed in our laboratory. Total free energy barriers were obtained for the two steps involved in this reaction. In the first step, Pro-1 acts as a general base to abstract a proton from the third carbon of the substrate, 2-oxo-4-hexenedioate, creating a negative charge on the oxygen at C-2 of this substrate. In the second step, the same hydrogen abstracted by the N-terminal Pro-1 is shuttled back to the fifth carbon of the substrate to form the product, 2-oxo-3-hexenedioate. The calculated total free energy barriers are 14.54 and 16.45 kcal/mol for the first and second steps, respectively. Our calculations clearly show that there is no general acid in the reaction. Arg-39' ', which is hydrogen bonded to the carboxylate group of the substrate, and an ordered water, which moves closer to the site of the charge formed in the transition state and intermediate, play the main role in transition state/intermediate stabilization without acting as general acids in the reaction.

We have investigated the feasibility of predicting free energy differences between a manifold of molecular states from a single simulation or ensemble representing one reference state. Two formulas that are based on the so-called λ- coupling parameter approach are analyzed and compared:  (i) expansion of the free energy F(λ) into a Taylor series around a reference state (λ = 0), and (ii) the so-called free energy perturbation formula. The results obtained by these extrapolation methods are compared to exact (target) values calculated by thermodynamic integration for mutations in two molecular systems:  a model dipolar diatomic molecule in water, and a series of para-substituted phenols in water. For moderate charge redistribution (≈0.5 e), both extrapolation methods reproduce the exact free energy differences. For free energy changes due to a change of atom type or size, the Taylor expansion method fails completely, while the perturbation formula yields moderately accurate predictions. Both extrapolation methods fail when a mutation involves the creation or deletion of atoms, due to the poor sampling in the reference state simulation of the configurations that are important in the end states of interest. To overcome this sampling difficulty, a procedure based on the perturbation formula and on biasing the sampling in the reference state is proposed, in which soft-core interaction sites are incorporated into the Hamiltonian of the reference state at positions where atoms are to be created or deleted. For mutations going from p-methylphenol to the other five differently para-substituted phenols, the differences in free energy are correctly predicted using extrapolation based on a single simulation of a biased, non-physical reference state. Since a large number of mutations can be investigated using a recorded trajectory of a single simulation, the proposed method is potentially viable in practical applications such as drug design.

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Protein structure and dynamics are the keys to a wide range of problems in biology. In principle, both can be fully understood by using quantum mechanics as the ultimate tool to unveil the molecular interactions involved. Indeed, quantum mechanics of atoms and molecules have come to play a central role in chemistry and physics. In practice, however, direct application of quantum mechanics to protein systems has been prohibited by the large molecular size of proteins. As a consequence, there is no general quantum mechanical treatment that not only exceeds the accuracy of state-of-the-art empirical models for proteins but also maintains the efficiency needed for extensive sampling in the conformational space, a requirement mandated by the complexity of protein systems. Here we show that, given recent developments in methods, a general quantum mechanical-based treatment can be constructed. We report a molecular dynamics simulation of a protein, crambin, in solution for 350 ps in which we combine a semiempirical quantum-mechanical description of the entire protein with a description of the surrounding solvent, and solvent-protein interactions based on a molecular mechanics force field. Comparison with a recent very high-resolution crystal structure of crambin (Jelsch et al., Proc Natl Acad Sci USA 2000;102:2246-2251) shows that geometrical detail is better reproduced in this simulation than when several alternate molecular mechanics force fields are used to describe the entire system of protein and solvent, even though the structure is no less flexible. Individual atomic charges deviate in both directions from "canonical" values, and some charge transfer is found between the N and C-termini. The capability of simulating protein dynamics on and beyond the few hundred ps timescale with a demonstrably accurate quantum mechanical model will bring new opportunities to extend our understanding of a range of basic processes in biology such as molecular recognition and enzyme catalysis.

A polarizable model for simulation of liquid methanol, compatible with the COS/G2 water model, has been developed using the Charge-on-Spring (COS) technique. The model consists of three point charges, with one polarizable center on the oxygen atom. The Lennard-Jones parameters on the oxygen atom together with the molecular polarizability were varied to reproduce the experimental heat of vaporization and density of liquid methanol at ambient conditions. We examined the energies of various methanol dimers in the gas phase and compared them with values obtained from ab initio calculations. The model was then used to study the thermodynamic, dynamic, structural, and dielectric properties of liquid methanol as well as of a methanol-water mixture. A microscopic picture of the structure of pure liquid methanol and of the methanol-water mixture is provided. Good agreement was found between the results from our model simulations and available experimental and ab initio calculation data. In particular, the experimental dielectric permittivity of 32 could be reproduced, which had been shown to be difficult when using nonpolarizable models.

Using a combined ab initio quantum mechanical/molecular mechanical approach developed in our laboratory, we obtained the reaction paths and free energy barriers for the two steps of the reaction catalyzed by enolase. In the first step, the R-proton of the substrate, 2-phospho-D-glycerate (PGA), is removed by Lys345, resulting in an enolic intermediate. In the second step, the -hydroxyl group leaves the enolic intermediate with the assistance of a general acid, Glu211. The calculated free energies of activation are 13.1 and 9.4 kcal mol -1 for the first and the second step, respectively. The barrier heights are consistent with the reaction rates measured from experiments. The calculations indicate that the electrostatic interactions between the substrate and two divalent metal cations at the active site strongly favor the first step. However, the same metal cations strongly disfavor the second step because the change in charge of the substrate is of an opposite sign compared with that in the first step. We conclude that the enzyme environment (excluding Lys345, Glu211, and the metal cations) forms an essential part of the reaction mechanism. It counterbalances the disfavoring effects of the metal cations in the second step without interfering with the first step despite the reversed charge changes of the substrate in the two steps. This capability of the enzyme originates from the three-dimensional organization of polar and charged groups in the active site of enolase, as indicated by correlations between the threedimensional structure and energetic analyses based on our calculations. To achieve overall catalytic efficiency, the structure of the enolase active site takes advantage of the fact that the charge reorganization procedures accompanying the two reaction steps take place in two different directions in space.