Achieving Energy Conservation in Poisson-Boltzmann Molecular Dynamics: Accuracy and Precision with Finite-Difference Algorithms

Abstract

Violation of energy conservation in Poisson-Boltzmann molecular dynamics, due to the limited accuracy and precision of numerical methods, is a major bottleneck preventing its wide adoption in biomolecular simulations. We explored the ideas of enforcing interface conditions by the immerse interface method and of removing charge singularity to improve the finite-difference methods. Our analysis of these ideas on an analytical test system shows significant improvement in both energies and forces. Our analysis further indicates the need for more accurate force calculation, especially the boundary force calculation.

Figure 1

A single dielectric sphere with radius R=2Å. The inside dielectric is ε⁻ and outside dielectric is ε⁺ . A single point charge (Q=+e) is positioned d away from the center.

Figure 2

Comparison of errors of potential and electric field on inside grid points near the interface and those of interpolated potential and field on the interface (left). Analytical potential on the interface is shown on the right.

Figure 3

Convergence of numerical db forces with respect to the number of numerical surface elements (N) for the charge placed at d=1.0 Å.

Figure 4

Standard deviations (upper) and maximum errors (lower) of reaction field energies, qE forces, and db forces versus decreasing h.