The double cubic lattice method: Efficient approaches to numerical integration of surface area and volume and to dot surface contouring of molecular assemblies

Abstract

The double cubic lattice method (DCLM) is an accurate and rapid approach for computing numerically molecular surface areas (such as the solvent accessible or van der Waals surface) and the volume and compactness of molecular assemblies and for generating dot surfaces. The algorithm has no special memory requirements and can be easily implemented. The computation speed is extremely high, making interactive calculation of surfaces, volumes, and dot surfaces for systems of 1000 and more atoms possible on single‐processor workstations. The algorithm can be easily parallelized. The DCLM is an algorithmic variant of the approach proposed by Shrake and Rupley (J. Mol. Biol., 79, 351–371, 1973). However, the application of two cubic lattices—one for grouping neighboring atomic centers and the other for grouping neighboring surface dots of an atom—results in a drastic reduction of central processing unit (CPU) time consumption by avoiding redundant distance checks. This is most noticeable for compact conformations. For instance, the calculation of the solvent accessible surface area of the crystal conformation of bovine pancreatic trypsin inhibitor (entry 4PTI of the Brookhaven Protein Data Bank, 362‐point sphere for all 454 nonhydrogen atoms) takes less than 1 second (on a single R3000 processor of an SGI 4D/480, about 5 MFLOP). The DCLM does not depend on the spherical point distribution applied. The quality of unit sphere tesselations is discussed. We propose new ways of subdivision based on the icosahedron and dodecahedron, which achieve constantly low ratios of longest to shortest arcs over the whole frequency range. The DCLM is the method of choice, especially for large molecular complexes and high point densities. Its speed has been compared to the fastest techniques known to the authors, and it was found to be superior, especially when also taking into account the small memory requirement and the flexibility of the algorithm. The program text may be obtained on request. © 1995 by John Wiley & Sons, Inc.