Given a protein, analyzing the geometric structure of protein is fundamental for the study of a protein folding, docking, interactions between proteins, and so on. One of the important geometric analyses is computing the molecular surface of protein. Discussed in this paper is an efficient algorithm to compute such a molecular surface of protein via the concept of blending operation among atoms constituting the protein. To facilitate the decision for the existence of blending surface among atoms, we take advantage of the proximity information of Euclidean Voronoi diagram of atoms. The proposed algorithm initially detects topological locations where blending surface exist via both edge accessibility and face accessibility of Euclidean Voronoi diagram.
Protein consists of a set of atoms. Given a protein, the molecular surface of the protein is defined with respect to a probe approximating a solvent molecule. This paper presents an efficient, as efficient as the realtime, algorithm to triangulate the blending surfaces which is the most critical subset of a molecular surface. For the quick evaluation of points on the surface, the proposed algorithm uses masks which are similar in their concepts to those in subdivision surfaces. More fundamentally, the proposed algorithm takes advantage of the concise representation of topology among atoms stored in the β-shape which is indeed used in the computation of the blending surface itself. Given blending surfaces and the corresponding β-shape, the proposed algorithm triangulates the blending surfaces in O(c • m) time in the worst case, where m is the number of boundary atoms in the protein and c is the number of point evaluations on a patch in the blending surface.
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