Software →FOx

FOx uses a transformation invariant approach to compare the shape of a given molecule with the query molecule. The component is constructed using a variation of the MaP descriptor method introduced by Steifl and Baumann [1, 2]. The MaP descriptor is based on radial distribution functions (RDF) using distance dependent count statistics. For each pair of atoms, the distance is calculated and the occurrence of the distance is added to the descriptor vector. This distance vector is then used to compare its shape with the shape of the query molecule. Cut-off values for the comparison were manually generated with an exhaustive test over a range of values to determine its optimal value.

The operation of this component is as follows: given a query molecule Q and an evaluation molecule M, FOx initially calculates the array RDF(Q) and RDF(M) using Eq. (1). Here, d_ij represents the distance between atom i and atom j, and l represents a parameter which denotes the evaluation radius of a particular RDF calculation.

NoA∑tomsNoA∑toms 1 2 RDFl = e2((l+1)-d(i,j)) i=1j=1

(1)

The mean square RDF (MSRDF) of the two molecules is then calculated using Eq. (2), where RDF(Q) represents the RDF value of the query molecule, whereas RDF(M) represents the RDF value of the evaluation molecule, and L is a user-defined maximum evaluation radius. A user-defined cut-off is then used to filter the MSRDF value to determine shape similarity.

L M SRDF = ∑ (RDF Q - RDF M )2 l=0 l l

(2)

References

[1] Daniel Baum and Hans-Christian Hege. (2006) "A point-matching based algorithm for 3D surface alignment of drug-sized molecules". In M.R. Berthold, R. Glen, and I. Fischer, editors, Computational Life Sciences II, Second International Symposium, CompLife 2006, Cambridge (UK), Sept. 2006, Volume 4216 of Lecture Notes in Bioinformatics, pages 183–193. Springer.

[2] N. Stiefl and K. Baumann. (2003) "Mapping property distributions of molecular surfaces: Algorithm and evaluation of a novel 3D quantitative structure-activity relationship technique." Journal of Medicinal Chemistry, 46(8):1390–1407.