Measures for Distance-Based 3D Similarity Searching

Local Measures for Distance-Based 3D Similarity Searching 

The atom-mapping method provides a quantitative measure of the similarity between a pair of 3D molecules, A and B, that are represented by their interatomic distance matrices. The measure is calculated in two stages. First, the geometric environment of each atom in A is compared with the corresponding environment of each atom in B to determine the similarity between each possible pair of atoms. The resulting interatomic similarities are then used to identify pairs of geometrically related atoms, and these equivalences allow the calculation of the overall intermolecular similarity. 

Assume that the molecule A contains N(A) nonhydrogen atoms. The distance matrix for A, DA is then an N(A) x N(A) matrix such that the I th element, DA(I, J), contains the distance between the /th and Jth atoms in A (and similarly for the matrix DB representing the N(B)-atom molecule B). The first stage of the procedure compares each atom from A with each atom from B. Consider the /th atom in A, A(I) then the /th row of the distance matrix DA contains the distances from / to all of the other atoms in A. This set of distances is compared with each of the rows, J, from the distance matrix DB to identify the matching distances. These common distances are used to calculate a Tani-moto coefficient, S(I, J), that measures the similarity between A(I) and B(J). S(I, J) is the //th element of an N(A) x N(B) atom-match matrix, S, that contains the similarities between all pairs of atoms, A(I) and B(J), from A and B. The 

Van Geerestein et al. discuss the use of SPERM to search a 30,000-structure subset of the Cambridge Structural Database for molecules that are similar to the antitumor antibiotics netropsin and daunomycin, which bind to DNA and which have also been studied by Nilakantan et al. as discussed in 

The description above has assumed that the property that is stored at the vertices of the tessellated icosahedron describing a molecule is either the minimal or the radial distance to the molecular surface. However, it is equally possible to store at each vertex any sort of property that can be calculated for that point in 3D space, such as the molecular electrostatic potential. Thus SPERM, like atom-mapping, allows local, property-based 3D similarity searching. 

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