Inclusion of quantum-mechanical vibrational energy in reactive potentials of mean force

Abstract

Classical molecular dynamics and Monte Carlo simulations typically exclude quantum effects on the vibrations of reactants and transition states, and this may lead to significant errors in the computed potential of mean force. To correct this deficiency, a simple approximate procedure is proposed for the inclusion of quantum-mechanical vibrational energy in the computation of reactive potentials of mean force in condensed phases. The method is illustrated by a hydrogen atom transfer and a proton transfer reaction in water, in particular, the 1,5-sigmatropic shift in malonaldehyde and the intermolecular proton shift between ammonium ion and ammonia in an encounter complex. In both cases, quantum-mechanical vibrational energy makes significant contributions by reducing the free energy of activation by 2 to 3 kcal/mol. This finding has important implications in developing empirical potential functions for the study of enzyme reactions, and it is essential to quantize vibrational energy in the computed potential of mean force and free energy of activation in order to compare simulations quantitatively with experiment.

Unraveling the role of protein dynamics in dihydrofolate reductase catalysis

“…The findings from the QM/MM MD simulations are consistent with the kinetic fits, which found « LE and « HE to be very similar at each pH and within 1.2 kcal·mol −1 of V TS (Table S4). The magnitude of these corrections is similar to those found in previous studies on hydride transfer reactions in other NAD(P)H-dependent enzymes (52)(53)(54). The 300-K rate constants obtained from MD simulations, which result directly from the simulations without any fitting to the experimental data, are in excellent agreement with the experimental values (which are of course themselves subject to some uncertainty) ( Table 1).…”

Anticorrelated motions as a driving force in enzyme catalysis: The dehydrogenase reaction

“…Thorpe and Brooks (15), we used the analytical barrierdistributions approach (15) and estimated the thermally averaged effective hydride-transfer barrier to be 18.4 kcal͞mol. It is generally appreciated that AM1-calculated values of energy barriers overestimate the barrier heights in comparison with ab initio and density functional results (21). By inclusion of the quantum-mechanical corrections to the vibration energy (21) (Ϸ2.8 kcal͞mol) to the calculated hydride-transfer barrier height, our calculated energy value (15.6 kcal͞mol) may be compared to the experimentally simulated tunneling value of Ϸ16 kcal͞mol (22,23).…”

“…They noted that the steric demand of the bulky distal substituents induces the formation of one of two quasi-boat conformers of NAD(P)H in which the axial H of NAD(P)H is pointed to the substrate carbonyl carbon and at times at van der Waals distance. The quasi-boat conformation contributes to the energetic advantage of enzymatic catalysis and is required geometry along the pathway to the transition state (21). Recently, an ab initio electronic-structure calculation (31) for NADH in the enzyme TDP-D-glucose dehydrogenase has shown that the hydride donor ability of NADH is influenced by the degree of bending in the dihydronicotinamide ring, and in this enzyme complex, the ring is profoundly puckered.…”

An Integrated Path Integral and Free-Energy Perturbation−Umbrella Sampling Method for Computing Kinetic Isotope Effects of Chemical Reactions in Solution and in Enzymes

“…We note that the overall barrier reduction is identical to that estimated previously using the EA-VTST-QM/MM method. 34 In addition, to dissect the specific contributing factors of the nuclear quantum effects, we have used the multidimensional tunneling algorithms developed by Truhlar and co-workers, 8 extended to enzyme applications, [1][2][3] to determine the average tunneling transmission factor, yielding a value of 〈κ〉 ) 1.3. 34 This suggests that that tunneling only makes minor contributions in the present case for the aqueous reaction.…”