TY - JOUR

T1 - Weighted least square analysis method for free energy calculations

AU - Hu, Dan

AU - Guan, Xiaoqing

AU - Wang, Yukun

N1 - Funding Information:
[a] D. Hu School of Mathematical Sciences, Institute of Natural Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China E-mail: [email protected] [b] X. Guan, Y. Wang Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China Contract Grant sponsor: National Natural Science Foundation of China; Contract Grant number: 91630208, 11471213
Funding Information:
The work was supported by NSFC grants 11471213 and 91630208, and supported by Center for High Performance Computing, Shanghai Jiao Tong University.
Publisher Copyright:
© 2018 Wiley Periodicals, Inc.

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 - Welsam

KW - free energy

KW - rare event

KW - umbrella sampling

KW - weighted least square

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

SN - 0192-8651

VL - 39

SP - 2397

EP - 2404

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

IS - 28

ER -