Geometry-guided computation of 3D electrostatics for large biomolecules

TitleGeometry-guided computation of 3D electrostatics for large biomolecules
Publication TypeJournal Articles
Year of Publication2006
AuthorsHao X, Varshney A
JournalComputer Aided Geometric Design
Pagination545 - 557
Date Published2006/08//
ISBN Number0167-8396
KeywordsFinite difference methods, Iso-surface generation, Level-of-detail of hierarchy, Poisson–Boltzmann equation, Scalar field, Tetrahedron decomposition

Electrostatic interactions play a central role in biological processes. Development of fast computational methods to solve the underlying Poisson–Boltzmann equation (PBE) is vital for biomolecular modeling and simulation package. In this paper, we propose new methods for efficiently computing the electrostatic potentials for large molecules by using the geometry of the molecular shapes to guide the computation. The accuracy and stability of the solution to the PBE is quite sensitive to the boundary layer between the solvent and the solute which defines the molecular surface. In this paper, we present a new interface-layer-focused PBE solver. First, we analytically construct the molecular surface of the molecule and compute a distance field from the surface. We then construct nested iso-surface layers outwards and inwards from the surface using the distance field. We have developed a volume simplification algorithm to adaptively adjust the density of the irregular grid based on the importance to the PBE solution. We have generalized the finite difference methods using Taylor series expansion on the irregular grids. Our algorithm achieves about three times speedup in the iterative solution process of PBE, with more accurate results on an analytical solvable testing case, compared with the popular optimized DelPhi program.