Accurate Boundary Integral Formulations for the Calculation of Electrostatic Forces with an Implicit-Solvent Model

Area of Science:

• Computational chemistry
• Molecular modeling
• Physical chemistry

Background:

• Accurate force calculations are crucial for molecular dynamics simulations.
• The Poisson-Boltzmann equation is widely used for solvation energy calculations.
• Calculating electric fields on molecular surfaces for force computations presents a significant challenge.

Purpose of the Study:

• To develop and evaluate methods for accurate electric field and force calculations using the Poisson-Boltzmann equation.
• To compare the boundary element method (BEM) with the finite difference method (FDM) for force calculations.
• To identify the most suitable BEM-based approach for realistic molecular systems.

Main Methods:

• Developed an exact calculation of the electric field on the solute-solvent interface for piecewise linear potential variations.
• Implemented and analyzed four distinct force calculation methods using the boundary element method.
• Performed verification using isolated and interacting molecular systems.
• Compared BEM with FDM, highlighting mesh requirements for accurate force calculations.

Main Results:

• The boundary element method (BEM) demonstrates superior accuracy compared to the finite difference method (FDM) for force calculations.
• BEM requires similar surface mesh density as used for solvation energy calculations, unlike FDM which needs a much finer mesh.
• The Maxwell stress tensor-based approach yields the highest accuracy among evaluated BEM methods.
• For practical applications like the barnase-barstar complex, energy functional variation methods provide comparable results to more accurate, albeit less practical, approaches.

Conclusions:

• The boundary element method provides an accurate and efficient approach for Poisson-Boltzmann force calculations.
• BEM is a viable alternative to FDM, offering better accuracy with less stringent meshing requirements.
• The choice of force calculation method should balance accuracy needs with computational feasibility for specific applications.
• This work facilitates the use of Poisson-Boltzmann equation-based forces in molecular dynamics and studies of large molecular assemblies.