Pairwise and Multiple Identification of Three-Dimensional Common Substructures in Proteins

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Abstract
In this paper, we present an algorithm to find three-dimensional substructures common to two or more molecules. The basic algorithm is devoted to pairwise structural comparison. Given two sets of atomic coordinates, it finds the largest subsets of atoms which are "similar" in the sense that all internal distances are approximately conserved. The basic idea of the algorithm is to recursively build subsets of increasing sizes, combining two sets of size k to build a set of size k + 1. The algorithm can be used "as is" for small molecules or local parts of proteins (about 30 atoms). When a high number of atoms is involved, we use a two step procedure. First we look for common "local" fragments by using the previous algorithm, and then we gather these fragments by using a Branch and Bound technique. We also extend the basic algorithm to perform multiple comparisons, by using one of the structures as a reference point (pivot) to which all other structures are compared. The solution is the largest subsets of atoms common to the pivot and at least q other structures. Although both algorithms are theoretically exponential in the number of atoms, experiments performed on biological data and using realistic parameters show that the solution is obtained within a few minutes. Finally, an application to the determination of the structural core of seven globins is presented.