# Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

## Abstract

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a method for quantifying this uncertainty in solvation energies using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space required compressed sensing combined with an iterative rotation method to enhance problem sparsity. We present results for the uncertainty in small molecule solvation energies based on these approaches. Additionally, we explore the correlation between uncertainties due to radii and charges which motivates the need for future work in uncertainty quantification methods for high-dimensional parameter spaces.

- Authors:

- Department of Pharmaceutical Sciences, University of California Irvine, Irvine, California 92697, United States
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, United States

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1437548

- Report Number(s):
- PNNL-SA-126404

Journal ID: ISSN 1549-9618; KJ0401000

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Theory and Computation; Journal Volume: 14; Journal Issue: 2

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Yang, Xiu, Lei, Huan, Gao, Peiyuan, Thomas, Dennis G., Mobley, David L., and Baker, Nathan A.
```*Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations*. United States: N. p., 2018.
Web. doi:10.1021/acs.jctc.7b00905.

```
Yang, Xiu, Lei, Huan, Gao, Peiyuan, Thomas, Dennis G., Mobley, David L., & Baker, Nathan A.
```*Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations*. United States. doi:10.1021/acs.jctc.7b00905.

```
Yang, Xiu, Lei, Huan, Gao, Peiyuan, Thomas, Dennis G., Mobley, David L., and Baker, Nathan A. Tue .
"Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations". United States.
doi:10.1021/acs.jctc.7b00905.
```

```
@article{osti_1437548,
```

title = {Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations},

author = {Yang, Xiu and Lei, Huan and Gao, Peiyuan and Thomas, Dennis G. and Mobley, David L. and Baker, Nathan A.},

abstractNote = {Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a method for quantifying this uncertainty in solvation energies using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space required compressed sensing combined with an iterative rotation method to enhance problem sparsity. We present results for the uncertainty in small molecule solvation energies based on these approaches. Additionally, we explore the correlation between uncertainties due to radii and charges which motivates the need for future work in uncertainty quantification methods for high-dimensional parameter spaces.},

doi = {10.1021/acs.jctc.7b00905},

journal = {Journal of Chemical Theory and Computation},

number = 2,

volume = 14,

place = {United States},

year = {Tue Jan 16 00:00:00 EST 2018},

month = {Tue Jan 16 00:00:00 EST 2018}

}