Accuracy of the numerical solution of the Poisson–Boltzmann equation

Abstract

Electrostatic interactions and solvation play a relevant role in protein–protein association. The electrostatic solvation free energy can be calculated by solving the Poisson–Boltzmann equation, and new fields of applications of the Poisson–Boltzmann calculations have emerged namely the MMPB/SA (molecular mechanics/Poisson–Boltzmann surface area) methodology to probe protein–protein interactions by calculating free energies. However, the differentiation of the Poisson–Boltzmann equation is only possible, in most cases, using numerical methods, whose accuracy depends on the input parameter set. The study presented here is due to the great importance of a deeper knowledge concerning the influence of parameter variation in solvation free energy. We have investigated the variation of the electrostatic solvation free energy, as well as the computational cost involved, as a function of the variation of key parameters for the numerical differentiation of the Poisson–Boltzmann equation as implemented in DelPhi.