Calculation of a Complete Enzymic Reaction Surface: Reaction and Activation Free Energies for Hydride-Ion Transfer in Dihydrofolate Reductase

Abstract

We present a two-dimensional grid method for the calculation of complete free-energy surfaces for enzyme reactions using a hybrid quantum mechanical/molecular mechanical (QM/MM) potential within the semiempirical (PM3) QM approximation. This implementation is novel in that parallel processing with multiple trajectories (replica-exchange molecular dynamics simulations) is used to sample configuration space. The free energies at each grid point are computed using the thermodynamic integration formalism. From the free-energy surface, the minimum free-energy pathway for the reaction can be defined, and the computed activation and reaction energies can be compared with experimental values. We illustrate its use in a study of the hydride-transfer step in the reduction of dihydrofolate to tetrahydrofolate catalyzed by Escherichia coli dihydrofolate reductase with bound nicotinamide adenine dinucleotide phosphate cofactor. We investigated the effects of changing the QM region, ionization state of the conserved active-site Asp27 residue, and polarization contributions to the activation and reaction free energy. The results clearly show the necessity for including the complete substrate and cofactor molecules in the QM region, and the importance of the overall protein (MM) electrostatic environment in determining the free energy of the transition state (TS) and products relative to reactants. For the model with ionized Asp27, its inclusion in the QM region is essential. We found that the reported [Garcia-Viloca, M.; Truhlar, D. G.; Gao, J. J. Mol. Biol. 2003, 327, 549] stabilization of the TS due to polarization is an artifact that can be attributed to truncation of the electrostatic interactions between the QM and MM atoms. For neutral (protonated) Asp27, our calculated reaction free energy of -4 ± 2 kcal/mol agrees well with the experimental value of -4.4 kcal/mol, although the corresponding activation free-energy estimate is still high at 21 ± 2 kcal/mol compared with the experimental value of 13.4 kcal/mol. The results are less supportive of the ionized Asp27 model, which gives rise to a much higher activation barrier and favors the reverse reaction.