Improved strategy in analytic surface calculation for molecular systems: Handling of singularities and computational efficiency

Abstract Computer methods for analytic surface calculations of molecular systems suffer from numerical instabilities and are CPU time consuming. In this article, we present proposals toward the solution of both problems. Singularities arise when nearly collinear triples of neighboring atoms or multiple vertices are encountered during the calculation. Topological decisions in analytic surface calculation algorithms (accessibility of vertices and arcs) are based upon the comparison of distances or angles. If two such numbers are nearly equal, then currently used computer programs may not resolve this ambiguity correctly and can subsequently fail. In this article, modifications in the analytic surface calculation algorithm are described that recognize singularities automatically and treat them appropriately without restarting parts of the computation. The computing time required to execute these alterations is minimal. The basic modification consists in defining an accuracy limit within which two values may be assumed as equal. The search algorithm has been reformulated to reduce the computational effort. A new set of formulas makes it possible to avoid mostly the extraction of square roots. Tests for small‐and medium‐sized intersection circles and for pairs of vertices with small vertex height help recognize fully buried circles and vertex pairs at an early stage. The new program can compute the complete topology of the surface and accessible surface area of the protein crambin in 1.50–4.29 s (on a single R3000 processor of an SGI 4D/480) depending on the compactness of the conformation where the limits correspond to the fully extended or fully folded chain, respectively. The algorithm, implemented in a computer program, will be made available on request. © John Wiley & Sons, Inc.