# Atomic radius and charge parameter uncertainty in biomolecular solvation energy calculations

## TL;DR

This paper introduces a novel method using surrogate models and generalized polynomial chaos to quantify uncertainty in atomic radii and charges, improving the reliability of solvation energy calculations in biomolecular modeling.

## Contribution

It presents a new approach combining surrogate models, least-squares fitting, and compressed sensing to efficiently quantify parameter uncertainty in implicit solvation energy calculations.

## Key findings

- Surrogate models effectively quantify uncertainty in small molecule solvation energies.
- The method enhances understanding of parameter sensitivity in force field development.
- Application demonstrates improved uncertainty estimation in biomolecular simulations.

## 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 new method for quantifying this uncertainty in implicit solvation calculations of small molecules 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 requires compressed sensing combined with an iterative rotation method to enhance problem sparsity. We demonstrate the application of the method by presenting results for the uncertainties in small molecule solvation energies based on these approaches. The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parameterization problems, including those beyond continuum solvation calculations.The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters.