Dielectric Boundary Forces in Numerical Poisson-Boltzmann Methods: Theory and Numerical Strategies

Abstract

Continuum modeling of electrostatic interactions based upon the numerical solutions of the Poisson-Boltzmann equation has been widely adopted in biomolecular applications. To extend their applications to molecular dynamics and energy minimization, robust and efficient methodologies to compute solvation forces must be developed. In this study, we have first reviewed the theory for the computation of dielectric boundary forces based on the definition of the Maxwell stress tensor. This is followed by a new formulation of the dielectric boundary force suitable for the finite-difference Poisson-Boltzmann methods. We have validated the new formulation with idealized analytical systems and realistic molecular systems.

Figure 1

Correlations between atomic dielectric boundary forces (kcal/(mol Å)) computed at the grid spacings of 1/2 Å, 1/4 Å, and 1/8 Å, respectively, and those at the grid spacing of 1/16 Å for the GC dimer and AT dimer.

Figure 2

Total nonbonded force (kcal/(mol Å)) on base G of the GC dimer with respect to the N-N distance (the distance between N-1 of guanine and N-3 of cytosine). The results of this work are shown in red triangle, and the results of the virtual work method are shown in blue star. The error bar means the standard error of the means. The data were collected with the grid spacings of 1/4 Å (top) and 1/16 Å (bottom).