We apply "molecular dynamics with quantum transitions" (MDQT), a surface-hopping method previously used only for electronic transitions, to proton transfer in solution, where the quantum particle is an atom. We use full classical mechanical molecular dynamics for the heavy atom degrees of freedom. including the solvent molecules, and treat the hydrogen motion quantum mechanically. We identify new obstacles that arise in this application of MDQT and present methods for overcoming them. We implement these new methods to demonstrate that application of MDQT to proton transfer in solution is computationally feasible and appears capable of accurately incorporating quantum mechanical phenomena such as tunneling and isotope effects. As an initial application of the method, we employ a model used previously by Azzouz and Borgis to represent the proton transfer reaction AH-B-.=.A --H+B in liquid methyl chloride, where the AH-B complex corresponds to a typical phenol-amine complex. We have chosen this model, in part, because it exhibits both adiabatic and diabatic behavior, thereby offering a stringent test of the theory. MDQT proves capable of treating both limits, as well as the intermediate regime. Up to four quantum states were included in this simulation, and the method can easily be extended to include additional excited states, so it can be applied to a wide range of processes, such as photoassisted tunneling. In addition, this method is not perturbative, so trajectories can be continued after the barrier is crossed to follow the subsequent dynamics.

The seminal hypotheses proposed over the years for enzymatic catalysis are scrutinized. The historical record is explored from both biochemical and theoretical perspectives. Particular attention is given to the impact of molecular motions within the protein on the enzyme's catalytic properties. A case study for the enzyme dihydrofolate reductase provides evidence for coupled networks of predominantly conserved residues that influence the protein structure and motion. Such coupled networks have important implications for the origin and evolution of enzymes, as well as for protein engineering.

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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...