Dielectric pressure in continuum electrostatic solvation of biomolecules

Continuum solvation representations based on the Poisson-Boltzmann equation have become widely accepted in biomolecular applications after years of basic research and development. Since analytical solution of the differential equation can be achieved only in a few specific cases with simple solute geometry, only numerical solution is possible for biomolecular applications. However, it is conceptually difficult to assign solvation forces in the numerical methods, limiting their applications into direct simulations of energy minimization and molecular dynamics. In this study a dielectric pressure formulation was derived from the general Maxwell stress tensor for continuum solvation of biomolecules modeled with the widely used abrupt-transitioned dielectrics. A charge-central strategy was then proposed to improve the numerical behavior of the computed pressure. An interesting observation is the highly similar charge-central formulations between the smooth-transition dielectric and the abrupt-transition dielectric models utilized in the biomolecular solvation treatments. The connections of the new formulation with both the Davis-McCammon and Gilson et al. approaches were further presented after applying the normal field approximation. The consistency was verified with the numerical tests on a realistic biomolecule. The numerical experiments on the tested biomolecule further indicate that the charge-central strategy combined with the normal field approximation not only improves the accuracy of the dielectric boundary force but also reduces its grid dependence for biomolecular applications.