## 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.

Original language | English (US) |
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Title of host publication | Methods in Enzymology |

Editors | Gregory A. Voth |

Publisher | Academic Press Inc. |

Pages | 359-388 |

Number of pages | 30 |

DOIs | |

State | Published - 2016 |

### Publication series

Name | Methods in Enzymology |
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Volume | 577 |

ISSN (Print) | 0076-6879 |

ISSN (Electronic) | 1557-7988 |

### Bibliographical note

Funding Information:This work has been supported by the National Institutes of Health. The author wishes to thank his coworkers whose name are shown in references cited.

## Keywords

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