Molecular dynamics and free energy perturbation study of hydride-ion transfer step in dihydrofolate reductase using combined quantum and molecular mechanical model

Hybrid Quantum and Classical Simulations of the Dihydrofolate Reductase Catalyzed Hydride Transfer Reaction on an Accurate Semi-Empirical Potential Energy Surface

Dihydrofolate reductase (DHFR) catalyzes the reduction of 7,8-dihydrofolate by nicotinamide adenine dinucleotide phosphate hydride (NADPH) to form 5,6,7,8-tetrahydrofolate and oxidized nicotinamide. DHFR is a small, flexible, monomeric protein with no metals or SS bonds and serves as one of the enzymes commonly used to examine basic aspects in enzymology. In the current work, we present extensive benchmark calculations for several model reactions in the gas phase that are relevant to the DHFR catalyzed hydride transfer. To this end, we employ G4MP2 and CBS-QB3 ab initio calculations as well as numerous density functional theory methods. Using these results, we develop two specific reaction parameter (SRP) Hamiltonians based on the semiempirical AM1 method. The first generation SRP Hamiltonian does not account for dispersion, while the second generation SRP accounts for dispersion implicitly via the AM1 core-repulsion functions. These SRP semiempirical Hamiltonians are subsequently used in hybrid quantum mechanics/molecular mechanics simulations of the DHFR catalyzed reaction. Finally, kinetic isotope effects are computed using a mass-perturbation-based path-integral approach.

Asymmetric synthesis of (S)-ethyl-4-chloro-3-hydroxy butanoate using a Saccharomyces cerevisiae reductase: enantioselectivity and enzyme-substrate docking studies

Ethyl (S)-4-chloro-3-hydroxy butanoate (ECHB) is a building block for the synthesis of hypercholesterolemia drugs. In this study, various microbial reductases have been cloned and expressed in Escherichia coli. Their reductase activities toward ethyl-4-chloro oxobutanoate (ECOB) have been assayed. Amidst them, Baker's yeast YDL124W, YOR120W, and YOL151W reductases showed high activities. YDL124W produced (S)-ECHB exclusively, whereas YOR120W and YOL151W made (R)-form alcohol. The homology models and docking models with ECOB and NADPH elucidated their substrate specificities and enantioselectivities. A glucose dehydrogenase-coupling reaction was used as NADPH recycling system to perform continuously the reduction reaction. Recombinant E. coli cell co-expressing YDL124W and Bacillus subtilis glucose dehydrogenase produced (S)-ECHB exclusively.

Charge-dependent model for many-body polarization, exchange, and dispersion interactions in hybrid quantum mechanical/molecular mechanical calculations

This work explores a new charge-dependent energy model consisting of van der Waals and polarization interactions between the quantum mechanical (QM) and molecular mechanical (MM) regions in a combined QMMM calculation. van der Waals interactions are commonly treated using empirical Lennard-Jones potentials, whose parameters are often chosen based on the QM atom type (e.g., based on hybridization or specific covalent bonding environment). This strategy for determination of QMMM nonbonding interactions becomes tedious to parametrize and lacks robust transferability. Problems occur in the study of chemical reactions where the "atom type" is a complex function of the reaction coordinate. This is particularly problematic for reactions, where atoms or localized functional groups undergo changes in charge state and hybridization. In the present work we propose a new model for nonelectrostatic nonbonded interactions in QMMM calculations that overcomes many of these problems. The model is based on a scaled overlap model for repulsive exchange and attractive dispersion interactions that is a function of atomic charge. The model is chemically significant since it properly correlates atomic size, softness, polarizability, and dispersion terms with minimal one-body parameters that are functions of the atomic charge. Tests of the model are examined for rare-gas interactions with neutral and charged atoms in order to demonstrate improved transferability. The present work provides a new framework for modeling QMMM interactions with improved accuracy and transferability.

Conformational change of the methionine 20 loop of Escherichia coli dihydrofolate reductase modulates pKa of the bound dihydrofolate

We evaluate the pK(a) of dihydrofolate (H(2)F) at the N(5) position in three ternary complexes with Escherichia coli dihydrofolate reductase (ecDHFR), namely ecDHFR(NADP(+):H(2)F) in the closed form (1), and the Michaelis complexes ecDHFR(NADPH:H(2)F) in the closed (2) and occluded (3) forms, by performing free energy perturbation with molecular dynamics simulations (FEP/MD). Our simulations suggest that in the Michaelis complex the pK(a) is modulated by the Met20 loop fluctuations, providing the largest pK(a) shift in substates with a "tightly closed" loop conformation; in the "partially closed/open" substates, the pK(a) is similar to that in the occluded complex. Conducive to the protonation, tightly closing the Met20 loop enhances the interactions of the cofactor and the substrate with the Met20 side chain and aligns the nicotinamide ring of the cofactor coplanar with the pterin ring of the substrate. Overall, the present study favors the hypothesis that N(5) is protonated directly from solution and provides further insights into the mechanism of the substrate protonation.

Conformational heterogeneity and low-frequency vibrational modes of proteins

Molecular dynamics simulation and normal mode analysis are used to calculate the vibrational density of states of dihydrofolate reductase complexed with nicotinamide adenine dinucleotide phosphate at 120 K and the results are compared with the experimental spectrum derived from inelastic neutron scattering. The simulation results indicate that the experimental spectrum arises from an average over proteins trapped in different conformations with structural differences mainly in the loop regions, and that these conformations have significantly different low-frequency (<20 cm(-1)) spectra. Thus, the experimentally measured spectrum is an average over the vibrational modes of different protein conformations and is thus inhomogeneously broadened. The implications of this broadening for future neutron scattering experiments and ligand binding calculations are discussed.

Freezing a Single Distal Motion in Dihydrofolate Reductase

Constraining a single motion between distal residues separated by approximately 28 A in hybrid quantum/classical molecular dynamics simulations is found to increase the free energy barrier for hydride transfer in dihydrofolate reductase by approximately 3 kcal/mol. Our analysis indicates that a single distal constraint alters equilibrium motions throughout the enzyme on a wide range of time scales. This alteration of the conformational sampling of the entire system is sufficient to significantly increase the free energy barrier and decrease the rate of hydride transfer. Despite the changes in conformational sampling introduced by the constraint, the system assumes a similar transition state conformation with a donor-acceptor distance of approximately 2.72 A to enable the hydride transfer reaction. The modified thermal sampling leads to a substantial increase in the average donor-acceptor distance for the reactant state, however, thereby decreasing the probability of sampling the transition state conformations with the shorter distances required for hydride transfer. These simulations indicate that fast thermal fluctuations of the enzyme, substrate, and cofactor lead to conformational sampling of configurations that facilitate hydride transfer. The fast thermal motions are in equilibrium as the reaction progresses along the collective reaction coordinate, and the overall average equilibrium conformational changes occur on the slower time scale measured experimentally. Recent single molecule experiments suggest that at least some of these thermally averaged equilibrium conformational changes occur on the millisecond time scale of the hydride transfer reaction. Thus, introducing a constraint that modifies the conformational sampling of an enzyme could significantly impact its catalytic activity.

Reaction-path energetics and kinetics of the hydride transfer reaction catalyzed by dihydrofolate reductase

We have studied the hydride transfer reaction catalyzed by the enzyme dihydrofolate reductase (DHFR) and the coenzyme nicotinamide adenine dinucleotide phosphate (NADPH); the substrate is 5-protonated 7,8-dihydrofolate, and the product is tetrahydrofolate. The potential energy surface is modeled by a combined quantum mechanical-molecular mechanical (QM/MM) method employing Austin model 1 (AM1) and a simple valence bond potential for 69 QM atoms and employing the CHARMM22 and TIP3P molecular mechanics force fields for the other 21 399 atoms; the QM and MM regions are joined by two boundary atoms treated by the generalized hybrid orbital (GHO) method. All simulations are carried out using periodic boundary conditions at neutral pH and 298 K. In stage 1, a reaction coordinate is defined as the difference between the breaking and forming bond distances to the hydride ion, and a quasithermodynamic free energy profile is calculated along this reaction coordinate. This calculation includes quantization effects on bound vibrations but not on the reaction coordinate, and it is used to locate the variational transition state that defines a transition state ensemble. Then, the key interactions at the reactant, variational transition state, and product are analyzed in terms of both bond distances and electrostatic energies. The results of both analyses support the conclusion derived from previous mutational studies that the M20 loop of DHFR makes an important contribution to the electrostatic stabilization of the hydride transfer transition state. Third, transmission coefficients (including recrossing factors and multidimensional tunneling) are calculated and averaged over the transition state ensemble. These averaged transmission coefficients, combined with the quasithermodynamic free energy profile determined in stage 1, allow us to calculate rate constants, phenomenological free energies of activation, and primary and secondary kinetic isotope effects. A primary kinetic isotope effect (KIE) of 2.8 has been obtained, in good agreement with the experimentally determined value of 3.0 and with the value 3.2 calculated previously. The primary KIE is mainly a consequence of the quantization of bound vibrations. In contrast, the secondary KIE, with a value of 1.13, is almost entirely due to dynamical effects on the reaction coordinate, especially tunneling.

Effect of mutation on enzyme motion in dihydrofolate reductase

Hybrid quantum-classical molecular dynamics simulations of a mutant Escherichia coli dihydrofolate reductase enzyme are presented. Although residue 121 is on the exterior of the enzyme, experimental studies have shown that the mutation of Gly-121 to valine reduces the rate of hydride transfer by a factor of 163. The simulations indicate that the decrease in the hydride transfer rate for the G121V mutant is due to an increase in the free energy barrier. The calculated free energy barrier is higher for the mutant than for the wild-type enzyme by an amount that is consistent with the experimentally observed rate reduction. The calculated transmission coefficients are comparable for the wild-type and mutant enzymes. The simulations suggest that this mutation may interrupt a network of coupled promoting motions proposed to play an important role in DHFR catalysis. This phenomenon has broad implications for protein engineering and drug design.

Importance of substrate and cofactor polarization in the active site of dihydrofolate reductase

By using a combined quantum-mechanical and molecular-mechanical potential in molecular dynamics simulations, we have investigated the effects of the enzyme electric field of dihydrofolate reductase on the electronic polarization of its 5-protonated dihydrofolate substrate at various stages of the catalyzed hydride transfer reaction. Energy decomposition of the total electrostatic interaction energy between the ligands and the enzyme shows that the polarization effect is 4% of the total electrostatic interaction energy, and, significantly, it accounts for 9kcal/mol of transition state stabilization relative to the reactant state. Therefore it is essential to take account of substrate polarization for quantitative interpretation of enzymatic function and for calculation of binding free energies of inhibitors to a protein. Atomic polarizations are calculated as the differences in the average atomic charges on the atoms in gas phase and in molecular simulations of the enzyme; this analysis shows that the glutamate tail and the pterin ring are the highly polarized regions of the substrate. Electron density difference plots of the reactant and product complexes at instantaneous configurations in the enzyme active center confirm the inferences made on the basis of partial atomic charges.

Comparison of linear-scaling semiempirical methods and combined quantum mechanical/molecular mechanical methods for enzymic reactions. II. An energy decomposition analysis

QM/MM methods have been developed as a computationally feasible solution to QM simulation of chemical processes, such as enzyme-catalyzed reactions, within a more approximate MM representation of the condensed-phase environment. However, there has been no independent method for checking the quality of this representation, especially for highly nonisotropic protein environments such as those surrounding enzyme active sites. Hence, the validity of QM/MM methods is largely untested. Here we use the possibility of performing all-QM calculations at the semiempirical PM3 level with a linear-scaling method (MOZYME) to assess the performance of a QM/MM method (PM3/AMBER94 force field). Using two model pathways for the hydride-ion transfer reaction of the enzyme dihydrofolate reductase studied previously (Titmuss et al., Chem Phys Lett 2000, 320, 169-176), we have analyzed the reaction energy contributions (QM, QM/MM, and MM) from the QM/MM results and compared them with analogous-region components calculated via an energy partitioning scheme implemented into MOZYME. This analysis further divided the MOZYME components into Coulomb, resonance and exchange energy terms. For the model in which the MM coordinates are kept fixed during the reaction, we find that the MOZYME and QM/MM total energy profiles agree very well, but that there are significant differences in the energy components. Most significantly there is a large change (approximately 16 kcal/mol) in the MOZYME MM component due to polarization of the MM region surrounding the active site, and which arises mostly from MM atoms close to (<10 A) the active-site QM region, which is not modelled explicitly by our QM/MM method. However, for the model where the MM coordinates are allowed to vary during the reaction, we find large differences in the MOZYME and QM/MM total energy profiles, with a discrepancy of 52 kcal/mol between the relative reaction (product-reactant) energies. This is largely due to a difference in the MM energies of 58 kcal/mol, of which we can attribute approximately 40 kcal/mol to geometry effects in the MM region and the remainder, as before, to MM region polarization. Contrary to the fixed-geometry model, there is no correlation of the MM energy changes with distance from the QM region, nor are they contributed by only a few residues. Overall, the results suggest that merely extending the size of the QM region in the QM/MM calculation is not a universal solution to the MOZYME- and QM/MM-method differences. They also suggest that attaching physical significance to MOZYME Coulomb, resonance and exchange components is problematic. Although we conclude that it would be possible to reparameterize the QM/MM force field to reproduce MOZYME energies, a better way to account for both the effects of the protein environment and known deficiencies in semiempirical methods would be to parameterize the force field based on data from DFT or ab initio QM linear-scaling calculations. Such a force field could be used efficiently in MD simulations to calculate free energies.

Theoretical evaluation of the hydrogen kinetic isotope effect on the first step of the methylmalonyl-CoA mutase reaction

We have calculated hydrogen kinetic isotope effects (KIEs) for the first step of the methylmalonyl-CoA mutase reaction, including multidimensional tunneling correction at the zero curvature (ZCT) level, and compared them with the experimental values. Both alternative mechanisms of this step, concerted and stepwise, can be accommodated. It turned out to be essential to include Arg207 hydrogen-bonded to the reactant in the mechanism predicting simultaneous breaking of the Co-C bond of AdoCbl and hydrogen atom transfer. The consequence of the stepwise mechanism is a much larger facilitation of the homolytic dissociation of the carbon-cobalt bond by the enzyme than currently appreciated; our results suggest lowering of the activation energy by about 23 kcal mol(-1). We have also shown that large hydrogen KIEs of tunneling origin do not necessarily break the Swain-Schaad equation. Furthermore, when this equation does not hold, the exponent may be smaller in the presence of tunneling than it is at the semi-classical limit, indicating that nonclassical behavior may be a more common phenomenon than expected.

Biomolecular simulations: recent developments in force fields, simulations of enzyme catalysis, protein-ligand, protein-protein, and protein-nucleic acid noncovalent interactions

Computer modeling has been developed and widely applied in studying molecules of biological interest. The force field is the cornerstone of computer simulations, and many force fields have been developed and successfully applied in these simulations. Two interesting areas are (a) studying enzyme catalytic mechanisms using a combination of quantum mechanics and molecular mechanics, and (b) studying macromolecular dynamics and interactions using molecular dynamics (MD) and free energy (FE) calculation methods. Enzyme catalysis involves forming and breaking of covalent bonds and requires the use of quantum mechanics. Noncovalent interactions appear ubiquitously in biology, but here we confine ourselves to review only noncovalent interactions between protein and protein, protein and ligand, and protein and nucleic acids.

Chlorine kinetic isotope effects on the haloalkane dehalogenase reaction

We have found chlorine kinetic isotope effects on the dehalogenation catalyzed by haloalkane dehalogenase from Xanthobacter autotrophicus GJ10 to be 1.0045 +/- 0.0004 for 1,2-dichloroethane and 1.0066 +/- 0.0004 for 1-chlorobutane. The latter isotope effect approaches the intrinsic chlorine kinetic isotope effect for the dehalogenation step. The intrinsic isotope effect has been modeled using semiempirical and DFT theory levels using the ONIOM QM/QM scheme. Our results indicate that the dehalogenation step is reversible; the overall irreversibility of the enzyme-catalyzed reaction is brought about by a step following the dehalogenation.

QM/MM and SCRF studies of the ionization state of 8-methylpterin substrate bound to dihydrofolate reductase: existence of a low-barrier hydrogen bond

Using combined semiempirical quantum mechanics and molecular mechanics (QM/MM) and ab initio self-consistent reaction field (SCRF) calculations, we determined that a low-barrier hydrogen bond (LBHB) is formed when the mechanism-based substrate 8-methylpterin binds to dihydrofolate reductase (DHFR). The substrate initially was assumed bound either in the ion-pair form corresponding to N3-protonated substrate hydrogen (H) bonded to the unprotonated (carboxylate) of the conserved Glu30 residue in the active site, or in the neutral-pair form corresponding to unprotonated substrate H bonded to the neutral (carboxylic acid) from of Glu30. The free energy of interaction of these H-bonded systems with the protein/solvent surroundings was computed using a coordinate-coupled free energy perturbation (FEP) method implemented within the molecular dynamics (MD) simulation scheme and using a semiempirical (PM3) QM/MM force field. The free energy obtained from the QM/MM force-field simulations corresponds most closely with the corresponding free energy component obtained from HF/6-31G* SCRF calculations using a value of 2 for the dielectric constant (epsilon) for the solvated protein. Calculations were performed at levels ranging from HF/6-31G to MP2/6-31G* to B3LYP/6-31 + G**, with varying dielectric constants. The energy-minimized path for motion of the proton in the H bond along a one-dimensional reaction coordinate was calculated at HF/6-31G, HF/6-31G* (epsilon = 1) and B3LYP/6-31G* (epsilon = 2) levels. These calculations identified a second neutral-pair complex, involving the 2-amino group of substrate, which also interacts with Glu30, which is lower in energy than the ion-pair form. A harmonic vibrational analysis shows that the first vibrational state appears to lie near or above the TS connecting potential energy minima corresponding to the two neutral-pair configurations, thus indicating an LBHB. Consequently, the H-bonded system will have a significant probability of being found in the ion-pair form, in agreement with experimental spectral studies indicating an enzyme-bound cation and suggesting that the LBHB would activate substrate towards hydride-ion transfer from NADPH.

Towards a better description and understanding of biomolecular solvation

We introduce a flexible framework for the correct description of the solvation of biological macromolecules, the dielectric field equation (DFE). The formalism permits the use of any combination of quantum mechanical (QM), molecular mechanical (MM) and continuum electrostatic (CE) based techniques. For the CE region a method that yields the electric field rather than the potential is outlined. The DFE formalism makes clear the need to consider and to calibrate a dielectric boundary region surrounding the simulation system. The details of how to do this are presented for the case of the Ewald summation method; the effects are demonstrated by calculations of the dielectric properties and the spatially resolved Kirkwood G-factor, G(K)(r), of TIP3P water. Computing the dielectric properties of a multi-component system provides a sensitive method to better understand the solvation of biological macromolecules. Towards this goal a rigorous analysis of the dielectric properties of solvated biomolecules based on a decomposition of the frequency-dependent dielectric constant (or susceptibility) of the full system is presented. The meaning of our approach is investigated, and the results of a first application are reported. Using the method of Voronoi polyhedra, the dielectric properties of the first two solvation shells and bulk water are compared by re-analyzing a 12-ns trajectory of a zinc finger peptide in water [Löffler et al. J. Mol. Biol. 270 (1997) 520]. It is found that the first shell behaves considerably different; in addition, there is a non-negligible contribution to the total susceptibility of the system from coupling between the protein and the bulk water phase, i.e. the water molecules not in the immediate vicinity of the solute.

Quantum chemical analysis of the enolization of ribulose bisphosphate: the first hurdle in the fixation of CO2 by Rubisco

A study, using ab initio quantum chemical methods, of the first step in the reaction mechanism of Rubisco, the enolization of the substrate, ribulose bisphosphate, is reported. This is the first such study that takes into account the likely roles of critical features within the active site. On the basis of molecular dynamics relaxation of the complex between activated enzyme and substrate using X-ray crystallographic structures as starting coordinates, a 29-atom fragment that mimicked the active site was constructed. States along a proposed reaction pathway were calculated using density functional theory and Moller-Plesset second-order perturbation theory. The results are consistent with the postulate that the base that abstracts the C3 proton of ribulose bisphosphate is the metal-stabilized carbamate of Lys-201 formed during the activation process. The calculations suggest that the active-site residue, Lys-175, is charged before enolization commences and they indicate a possible means by which the enzyme directs the incoming CO2 to attack the C2 carbon atom of the enediol, rather than the chemically very similar C3 atom.