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 alone, 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.