Zippier zaps: faster electrostatics calculations

Abstract

Macromolecular modeling techniques have contributed enormously to our understanding of macromolecular structures and their relationships to biological function. As computers become more and more powerful, modeling should become a truly predictive science, offering insights into structurefunction relationships in systems where a single, static structure is an insufficient description, and providing guidance for the rational design of drugs and engineered macromolecules. For modeling methods to realize their full potential as predictive tools, they must be as accurate as possible. In this issue, Oberoi and Allewell (1) present a method that offers significant improvements in the speed and accuracy of the treatment of molecular electrostatics, which is currently the largest source of error in the most common quantitative modeling algorithms (energy minimization, molecular dynamics, and Monte Carlo). The independent development of this same approach was recently reported by Holst and Saied (2). Electrostatic interactions are often modeled with a modified Coulombic approximation. Coulomb's law is the solution to Poisson's equation around a point charge in the case of a homogeneous system with a uniform dielectric constant. This is inappropriate for a macromolecule under physiological conditions, because the macromolecule has a low dielectric constant (-2-4), and it is surrounded by a solution with a high dielectric constant (-80) and containing mobile ions. In this case, the proper mathematical treatment of electrostatic interactions requires the solution of the Poisson-Boltzmann equation (PBE). The PBE does not have analytical solutions except for very simple geometries, so numerical methods are reuses the finite difference method, pioneered by Warwicker and Watson (3) and extended and improved by efforts in many laboratories over the past decade. Finite differences have been applied to both the complete nonlinear form of the PBE and the linearized PBE, a frequently used approximation. (The linearized PBE makes the approximation sinh(x) = x, x being the ratio of the electrostatic energy of a unit test charge to the thermal energy,