An analytical approach to computing biomolecular electrostatic potential. I. Derivation and analysis.

Area of Science:

• Computational chemistry
• Theoretical physics
• Molecular modeling

Background:

• Continuum electrostatics are essential for understanding molecular interactions.
• Analytical approximations to fundamental equations can simplify electrostatic calculations.
• Accurate electrostatic potential calculations are vital for molecular modeling.

Purpose of the Study:

• To derive a closed-form analytical approximation to the Poisson equation for electrostatic potential.
• To develop a parameter-free formula for continuous electrostatic potential around spherical dielectric boundaries.
• To assess the accuracy of the approximation against exact solutions.

Main Methods:

• Derivation of a closed-form analytical approximation to the Poisson equation.
• Utilizing an approximate summation method on the exact infinite-series (Kirkwood) solution.
• Assessing accuracy by comparing with the exact solution for two unit charges within a spherical dielectric boundary.

Main Results:

• A simple, parameter-free formula for continuous electrostatic potential was derived.
• The approximation shows controllable accuracy, especially when all terms are retained.
• For charges near the boundary, the root-mean-square error was < 0.1 kcal/mol/mR, with a maximum error of 0.4 kcal/mol/mR.

Conclusions:

• The derived analytical approximation provides a computationally inexpensive and accurate method for calculating electrostatic properties.
• The method is particularly effective for spherical dielectric boundaries and can be extended to realistic biomolecular shapes.
• This approach offers a valuable tool for molecular modeling and understanding electrostatic interactions in complex systems.