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Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory - PubMed

Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory

J Gao. Methods Enzymol. 2016.

Abstract

Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects.

Keywords: Combined QM/MM; Dual-level potential; Enzyme kinetics; Kinetic isotope effects; Nuclear quantum effects; PI-FEP; Path-integral simulation.

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Figures

**Fig. 1**
Computed nuclear quantum effects along the potential of mean force for the decarboxylation reaction of N-methyl picolinate ion in water. ¹³C denotes isotope substitution at the carboxyl carbon position.

**Fig. 2**
Computed ratio of quantum partition function between ¹²C and ¹³C isotope substitutions at the carboxyl carbon position along the centroid reaction coordinate for the decarboxylation of N-methyl picolinate in water.

**Fig. 3**
Classical (*blue*) and quantum mechanical potential of mean force for the proton (*red*) and deuteron (*green*) transfer from nitroethane to acetate ion in water (*dashed curves*), and to Asp402 (*solid curves*) in the active site of nitroalkane oxidase.

**Fig. 4**
Superposition comparison of snapshots of the Michaelis complex (*blue*) and transition state (*brown*) structures for the wild-type enzyme dihydrofolate reductase (*left*) and the M42W/G121V double mutant (*right*).

**Fig. 5**
Computed and experimental H/D primary kinetic isotope effects for the hydride transfer process catalyzed by wild-type and M42W/G121V mutant dihydrofolate reductase at different temperatures.

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Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory - PubMed