A Charge Central Interpretation of the Full Nonlinear PB Equation: Implications to Accurate and Scalable Modeling of Solvation Interactions

摘要

Continuum solvation modeling based upon the Poisson-Boltzmann equation (PBE) is widely used in structural and functional analysis of biomolecules. In this work we proposed a charge-central interpretation of the full nonlinear PBE electrostatic interactions. The validity of the charge-central framework, as formulated as a vacuum Poisson equation with effective charges, was first demonstrated by reproducing both electrostatic potentials and energies from the original solvated full nonlinear PBE. There are at least two benefits when the charge-central framework is applied. Firstly the convergence analyses show that the use of polarization charges allows a much faster converging numerical procedure for electrostatic energy and forces calculation for the full nonlinear PBE. Secondly the formulation of the solvated electrostatic interactions as effective charges in vacuum allows scalable algorithms to be deployed for large biomolecular systems. Here we exploited the charge-central interpretation and developed a particle-particle particle-mesh (P3M) strategy for the full nonlinear PB systems. We also studied the accuracy and convergence of solvation forces with the charge-view and the P3M methods. It is interesting to note that the convergences of both the charge-view and the P3M methods are more rapid than the original full nonlinear PB method. Given the developments and validations documented here, we are working to adapt the P3M treatment of the full nonlinear PB model to molecular dynamics simulations.