An analytical approach to computing biomolecular electrostatic potential. I. Derivation and analysis.
Analytical approximations to fundamental equations of continuum electrostatics on simple shapes can lead to computationally inexpensive prescriptions for calculating electrostatic properties of realistic molecules. Here, we derive a closed-form analytical approximation to the Poisson equation for an arbitrary distribution of point charges and a spherical dielectric boundary. The simple, parameter-free formula defines continuous electrostatic potential everywhere in space and is obtained from the exact infinite-series (Kirkwood) solution by an approximate summation method that avoids truncating the infinite series. We show that keeping all the terms proves critical for the accuracy of this approximation, which is fully controllable for the sphere. The accuracy is assessed by comparisons with the exact solution for two unit charges placed inside a spherical boundary separating the solute of dielectric 1 and the solvent of dielectric 80. The largest errors occur when the source charges are closest to the dielectric boundary and the test charge is closest to either of the sources. For the source charges placed within 2 A from the boundary, and the test surface located on the boundary, the root-mean-square error of the approximate potential is less than 0.1 kcal/mol/mid R:emid R: (per unit test charge). The maximum error is 0.4 kcal/mol/mid R:emid R:. These results correspond to the simplest first-order formula. A strategy for adopting the proposed method for realistic biomolecular shapes is detailed. An extensive testing and performance analysis on real molecular structures are described in Part II that immediately follows this work as a separate publication. Part II also contains an application example.
Fenley
Andrew T
AT
Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA. afenley@vt.edu
Gordon
John C
JC
Onufriev
Alexey
A
D000465:Algorithms; D001665:Binding Sites; D001704:Biopolymers / Q000032:analysis* / Q000737:chemistry; D036022:Capsid Proteins / Q000032:analysis* / Q000737:chemistry; D003198:Computer Simulation; D008956:Models, Chemical; D016012:Poisson Distribution; D012313:RNA / Q000378:metabolism; D055672:Static Electricity
D001704:Biopolymers; D036022:Capsid Proteins; D012313:RNA