### Abstract

Free energy calculation is an efficient way for studying rare event dynamics. For a complex rare event dynamics, multiple reaction coordinates may be required to describe the transition path between equilibrium states. Theoretically, a one-dimensional sampling along the transition path can provide sufficient information to calculate the potential of mean force (PMF) along the transition path. In the widely used free energy analysis method Wham, the sample data are divided into a series of bins to calculate PMF. However, bin segmentation in Wham is coupled with the umbrella potentials applied in each window, because each umbrella potential is assumed to have a close value for all sample points in each bin. This coupling makes it difficult to perform one-dimensional bin segmentation along the transition path when multivariable umbrella potentials are used in sampling. Here, we develop a weighted least square analysis method (Welsam) to take the place of Wham for free energy analysis. In the new method Welsam, bin segmentation is decoupled from application of umbrella potentials. As a result, it becomes very convenient to perform one-dimensional bin segmentation and calculate one-dimensional PMF along the transition path. Our simulation results suggest that Welsam has a comparable statistical error with Wham. Furthermore, Welsam can be used to reduce waste of sample data obtained during exploration of reaction coordinates.

Original language | English (US) |
---|---|

Pages (from-to) | 2397-2404 |

Number of pages | 8 |

Journal | Journal of Computational Chemistry |

Volume | 39 |

Issue number | 28 |

DOIs | |

State | Published - Oct 30 2018 |

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### Keywords

- free energy
- rare event
- umbrella sampling
- weighted least square
- Welsam

### ASJC Scopus subject areas

- Chemistry(all)
- Computational Mathematics

### Cite this

*Journal of Computational Chemistry*,

*39*(28), 2397-2404. https://doi.org/10.1002/jcc.25580

**Weighted least square analysis method for free energy calculations.** / Hu, Dan; Guan, Xiaoqing; Wang, Yukun.

Research output: Contribution to journal › Article

*Journal of Computational Chemistry*, vol. 39, no. 28, pp. 2397-2404. https://doi.org/10.1002/jcc.25580

}

TY - JOUR

T1 - Weighted least square analysis method for free energy calculations

AU - Hu, Dan

AU - Guan, Xiaoqing

AU - Wang, Yukun

PY - 2018/10/30

Y1 - 2018/10/30

N2 - Free energy calculation is an efficient way for studying rare event dynamics. For a complex rare event dynamics, multiple reaction coordinates may be required to describe the transition path between equilibrium states. Theoretically, a one-dimensional sampling along the transition path can provide sufficient information to calculate the potential of mean force (PMF) along the transition path. In the widely used free energy analysis method Wham, the sample data are divided into a series of bins to calculate PMF. However, bin segmentation in Wham is coupled with the umbrella potentials applied in each window, because each umbrella potential is assumed to have a close value for all sample points in each bin. This coupling makes it difficult to perform one-dimensional bin segmentation along the transition path when multivariable umbrella potentials are used in sampling. Here, we develop a weighted least square analysis method (Welsam) to take the place of Wham for free energy analysis. In the new method Welsam, bin segmentation is decoupled from application of umbrella potentials. As a result, it becomes very convenient to perform one-dimensional bin segmentation and calculate one-dimensional PMF along the transition path. Our simulation results suggest that Welsam has a comparable statistical error with Wham. Furthermore, Welsam can be used to reduce waste of sample data obtained during exploration of reaction coordinates.

AB - Free energy calculation is an efficient way for studying rare event dynamics. For a complex rare event dynamics, multiple reaction coordinates may be required to describe the transition path between equilibrium states. Theoretically, a one-dimensional sampling along the transition path can provide sufficient information to calculate the potential of mean force (PMF) along the transition path. In the widely used free energy analysis method Wham, the sample data are divided into a series of bins to calculate PMF. However, bin segmentation in Wham is coupled with the umbrella potentials applied in each window, because each umbrella potential is assumed to have a close value for all sample points in each bin. This coupling makes it difficult to perform one-dimensional bin segmentation along the transition path when multivariable umbrella potentials are used in sampling. Here, we develop a weighted least square analysis method (Welsam) to take the place of Wham for free energy analysis. In the new method Welsam, bin segmentation is decoupled from application of umbrella potentials. As a result, it becomes very convenient to perform one-dimensional bin segmentation and calculate one-dimensional PMF along the transition path. Our simulation results suggest that Welsam has a comparable statistical error with Wham. Furthermore, Welsam can be used to reduce waste of sample data obtained during exploration of reaction coordinates.

KW - free energy

KW - rare event

KW - umbrella sampling

KW - weighted least square

KW - Welsam

UR - http://www.scopus.com/inward/record.url?scp=85055696748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055696748&partnerID=8YFLogxK

U2 - 10.1002/jcc.25580

DO - 10.1002/jcc.25580

M3 - Article

C2 - 30374999

AN - SCOPUS:85055696748

VL - 39

SP - 2397

EP - 2404

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

SN - 0192-8651

IS - 28

ER -