A network of coupled promoting motions in the enzyme dihydrofolate reductase is identified and characterized. The present identification is based on genomic analysis for sequence conservation, kinetic measurements of multiple mutations, and mixed quantum͞ classical molecular dynamics simulations of hydride transfer. The motions in this network span time scales of femtoseconds to milliseconds and are found on the exterior of the enzyme as well as in the active site. This type of network has broad implications for an expanded role of the protein fold in catalysis as well as ancillaries such as the engineering of altered protein function and the action of drugs distal to the active site.A relationship between the motion of protein structural elements and activity has been implicated in enzyme catalysis (1-3). Evidence for the existence of promoting vibrations or modes that augment catalytic activity has been sought for a number of enzymes. At the amino acid level, motions of residues both in and distal to the active site have been proposed to participate in catalysis. The identification, characterization, and clarification of the function of such proximal and distal promoting motions present a challenging task. Recently the importance of coupled motions sampled in differing time domains involving distal residues in the enzyme dihydrofolate reductase (DHFR; EC 1.5.1.3) has been suggested by a combination of NMR experiments (microsecond to picosecond) (4), classical molecular dynamics simulations (nanosecond) (5), and kinetic experiments for site-directed mutants (millisecond to second) (6, 7). Here we report the results of genomic analysis, kinetic measurements of multiple mutations, and mixed quantum͞classical molecular dynamics simulations (8) of the hydride transfer step in DHFR. Based on the crystal structure framework, these results provide a description of specific residue motions and their linkage to enzyme catalysis.DHFR is required for normal folate metabolism in prokaryotes and eukaryotes. It catalyzes the reduction of 7,8-dihydrofolate (DHF) to 5,6,7,8-tetrahydrofolate (THF) by using nicotinamide adenine dinucleotide phosphate (NADPH) as a coenzyme. Specifically, the pro-R hydride of NADPH is transferred to the C6 of the pterin with concurrent protonation at the N5 position. This reaction is essential to maintain necessary levels of THF needed to support the biosynthesis of purines, pyrimidines, and amino acids, fostering DHFR as a pharmacological target. As a result of its importance, DHFR has been studied extensively with a wide range of methodologies.X-ray crystallographic studies indicate that the Escherichia coli DHFR enzyme contains an eight-stranded ␤-sheet and four ␣-helices interspersed with flexible loop regions that connect these structural elements (ref. 9; see Fig. 1). Depending on the nature of the bound ligand, three different conformations have been observed for a surface loop formed by residues 9-24 (denoted the Met-20 loop). When the DHF substrate and NADPH coenzyme are bound, the Met-20...

Mixed quantum/classical molecular dynamics simulations of the hydride transfer reaction catalyzed by dihydrofolate reductase are presented. The nuclear quantum effects such as zero point energy and hydrogen tunneling, as well as the motion of the entire solvated enzyme, are included during the generation of the free energy profiles and the real-time dynamical trajectories. The calculated deuterium kinetic isotope effect agrees with the experimental value. The simulations elucidate the fundamental nature of the nuclear quantum effects and provide evidence of hydrogen tunneling in the direction along the donor−acceptor axis. The transmission coefficient was found to be 0.80 for hydrogen and 0.85 for deuterium, indicating the significance of dynamical barrier recrossings. Nonadiabatic transitions among the vibrational states were observed but did not strongly affect the transmission coefficient. A study of motions involving residues conserved over 36 diverse species from Escherichia coli to human implies that motions of residues both in the active site and distal to the active site impact the free energy of activation and the degree of barrier recrossing. This analysis resulted in the characterization of a network of coupled promoting motions that extends throughout the protein and involves motions spanning femtosecond to millisecond time scales. This type of network has broad implications for protein engineering and drug design.

The quantum dynamics of the hydride transfer reaction catalyzed by liver alcohol dehydrogenase (LADH) are studied with real-time dynamical simulations including the motion of the entire solvated enzyme. The electronic quantum effects are incorporated with an empirical valence bond potential, and the nuclear quantum effects of the transferring hydrogen are incorporated with a mixed quantum/classical molecular dynamics method in which the transferring hydrogen nucleus is represented by a three-dimensional vibrational wave function. The equilibrium transition state theory rate constants are determined from the adiabatic quantum free energy profiles, which include the free energy of the zero point motion for the transferring nucleus. The nonequilibrium dynamical effects are determined by calculating the transmission coefficients with a reactive flux scheme based on real-time molecular dynamics with quantum transitions (MDQT) surface hopping trajectories. The values of nearly unity for these transmission coefficients imply that nonequilibrium dynamical effects such as barrier recrossings are not dominant for this reaction. The calculated deuterium and tritium kinetic isotope effects for the overall rate agree with experimental results. These simulations elucidate the fundamental nature of the nuclear quantum effects and provide evidence of hydrogen tunneling in the direction along the donor-acceptor axis. An analysis of the geometrical parameters during the equilibrium and nonequilibrium simulations provides insight into the relation between specific enzyme motions and enzyme activity. The donor-acceptor distance, the catalytic zinc-substrate oxygen distance, and the coenzyme (NAD(+)/NADH) ring angles are found to strongly impact the activation free energy barrier, while the donor-acceptor distance and one of the coenzyme ring angles are found to be correlated to the degree of barrier recrossing. The distance between VAL-203 and the reactive center is found to significantly impact the activation free energy but not the degree of barrier recrossing. This result indicates that the experimentally observed effect of mutating VAL-203 on the enzyme activity is due to the alteration of the equilibrium free energy difference between the transition state and the reactant rather than nonequilibrium dynamical factors. The promoting motion of VAL-203 is characterized in terms of steric interactions involving THR-178 and the coenzyme.

An integrated view of protein structure, dynamics, and function is emerging, where proteins are considered as dynamically active assemblies and internal motions are closely linked to function such as enzyme catalysis. Further, the motion of solvent bound to external regions of protein impacts internal motions and, therefore, protein function. Recently, we discovered a network of protein vibrations in enzyme cyclophilin A, coupled to its catalytic activity of peptidyl-prolyl cis-trans isomerization. Detailed studies suggest that this network, extending from surface regions to active site, is a conserved part of enzyme structure and has a role in promoting catalysis. In this report, theoretical investigations of concerted conformational fluctuations occurring on microsecond and longer time scales within the discovered network are presented. Using a new technique, kinetic energy was added to protein vibrational modes corresponding to conformational fluctuations in the network. The results reveal that protein dynamics promotes catalysis by altering transition state barrier crossing behavior of reaction trajectories. An increase in transmission coefficient and number of productive trajectories with increasing amounts of kinetic energy in vibrational modes is observed. Variations in active site enzyme-substrate interactions near transition state are found to be correlated with barrier recrossings. Simulations also showed that energy transferred from first solvation shell to surface residues impacts catalysis through network fluctuations. The detailed characterization of network presented here indicates that protein dynamics plays a role in rate enhancement by enzymes. Therefore, coupled networks in enzymes have wide implications in understanding allostericity and cooperative effects, as well as protein engineering and drug design.

A hybrid approach for simulating proton and hydride transfer reactions in enzymes is presented. The electronic quantum effects are incorporated with an empirical valence bond approach. The nuclear quantum effects of the transferring hydrogen are included with a mixed quantum/classical molecular dynamics method in which the hydrogen nucleus is described as a multidimensional vibrational wave function. The free energy profiles are obtained as functions of a collective reaction coordinate. A perturbation formula is derived to incorporate the vibrationally adiabatic nuclear quantum effects into the free energy profiles. The dynamical effects are studied with the molecular dynamics with quantum transitions (MDQT) surface hopping method, which incorporates nonadiabatic transitions among the adiabatic hydrogen vibrational states. The MDQT method is combined with a reactive flux approach to calculate the transmission coefficient and to investigate the real-time dynamics of reactive trajectories. This hybrid approach includes nuclear quantum effects such as zero point energy, hydrogen tunneling, and excited vibrational states, as well as the dynamics of the complete enzyme and solvent. The nuclear quantum effects are incorporated during the generation of the free energy profiles and dynamical trajectories rather than subsequently added as corrections. Moreover, this methodology provides detailed mechanistic information at the molecular level and allows the calculation of rates and kinetic isotope effects. An initial application of this approach to the enzyme liver alcohol dehydrogenase is also presented.