Fast Analytical Methods for Macroscopic Electrostatic Models in Biomolecular Simulations

Abstract

We review recent developments of fast analytical methods for macroscopic electrostatic calculations in biological applications, including the Poisson–Boltzmann (PB) and the generalized Born models for electrostatic solvation energy. The focus is on analytical approaches for hybrid solvation models, especially the image charge method for a spherical cavity, and also the generalized Born theory as an approximation to the PB model. This review places much emphasis on the mathematical details behind these methods.

Comparison of efficient techniques for the simulation of dielectric objects in electrolytes

“…In certain cases, it is possible to avoid the evaluation of harmonic series via an image-charge representation of the closed-form Green's functions [26][27][28][29][30]. Recently, this image-charge method (ICM) has been extended to the treatment of multiple spheres via recursive reflections [31].…”

Competitive effects between stationary chemical reaction centres: A theory based on off-center monopoles

“…11,17,[26][27][28][29][30][31][32][33][34] At first sight, it would seem highly improbable that anything novel can be added to such a well-established subject. Indeed, strictly speaking, we do not believe that we have added anything really new to the subject that was not known already to experts in the field, in the sense that everything that we have presented is somehow implicitly contained in earlier work.…”

“…In recent years, it has again become the subject of intense research activity following the seminal work of Greengard and co-workers on so-called fast multipole moments. This theory has now been developed for conductors, 11,[26][27][28] for dielectric media, [29][30][31][32] for the steady-state 33 and the time-dependent heat equation, 34 for molecular dynamics, 26,35 and in numerous other applications. It is remarkable that the recent flurry of activity in applying image-charge concepts to dielectric media [29][30][31][32] comes more than 130 years after the basic ideas were originally published.…”

Treecode-based generalized Born method

“…[1][2][3][4][5][6] Due to its long-range nature, an accurate but efficient treatment of electrostatics is the key in fast computer simulations of biological systems. [7][8][9][10][11] The Possion-Boltzmann (PB) model 12,13 is one of the most widely used implicit solvation models that describe electrostatic interactions of biological systems in aqueous solutions under a mean field approximation. PB treats the solvent as a high dielectric continuum medium and thus eliminates the degrees of freedom of the explicit solvent molecules;…”