A comprehensive analysis of the network of coupled motions correlated to hydride transfer in dihydrofolate reductase is presented. Hybrid quantum/classical molecular dynamics simulations are combined with a rank correlation analysis method to extract thermally averaged properties that vary along the collective reaction coordinate according to a prescribed target model. Coupled motions correlated to hydride transfer are identified throughout the enzyme. Calculations for wild-type dihydrofolate reductase and a triple mutant, along with the associated single and double mutants, indicate that each enzyme system samples a unique distribution of coupled motions correlated to hydride transfer. These coupled motions provide an explanation for the experimentally measured nonadditivity effects in the hydride transfer rates for these mutants. This analysis illustrates that mutations distal to the active site can introduce nonlocal structural perturbations and significantly impact the catalytic rate by altering the conformational motions of the entire enzyme and the probability of sampling conformations conducive to the catalyzed reaction.