Calculating the electrostatic potential of molecules in solution: Method and error assessment

TLDR

The authors develop a numerical method based on the linearized Poisson–Boltzmann equation to compute electrostatic potentials of molecules in solution, with a focus on biological macromolecules. They evaluate the method by comparing it to analytic Tanford–Kirkwood solutions for a single charge in a dielectric sphere, incorporate algorithmic refinements, and implement the approach in the Del Phi software package that transforms PDB files into electrostatic field data. The method achieves generally 5 % accuracy, with errors rising to about 15 % near charges and dielectric boundaries, particularly at ion‑bonding distances 3 Å from a charge 1 Å inside the boundary.

Abstract

Abstract We present a numerical method for calculating the electrostatic potential of molecules in solution, using the linearized Poisson‐Boltzmann equation. The emphasis in this work is on applications to biological macromolecules. The accuracy of the method is assessed by comparisons with analytic solutions for the case of a single charge in a dielectric sphere (Tanford‐Kirkwood theory), which serves as a model for a macromolecule. We find that the solutions are generally accurate to within 5%. Larger errors occur close to the charge and the dielectric boundary, but the maximum error found at ion‐bonding distance (3 Å) from a charge close to the boundary (1 Å deep) is only ∼15%. Several algorithmic improvements, described here, contribute to the accuracy of the method. The programs involved compose a coherent software package, called Del Phi, which goes from a Brookhaven Protein Data Bank format file to calculated electrostatic fields.