The Centroid Approximation for Mixtures:  Calculating Similarity and Deriving Structure−Activity Relationships

Compounds are often synthesized and tested as mixtures. We propose the idea that the descriptor representation of a mixture may be approximated as the descriptor average of its individual component molecules. This centroid approximation has several potential advantages: the representation is very compact, calculating similarities and deriving structure-activity relationships (SARs) of mixtures involves very little computation, and existing software can be directly applied to mixtures as if they were single molecules. Here we use the atom pair and topological torsion descriptors. We run several types of simulations using mixtures composed of druglike molecules from the MDL Drug Data Report database. We show that similarity searches using mixtures as queries and/or database entries yield reasonable results, with the caveat that a correction is necessary for mixture-mixture comparisons where at least one of the mixtures contains very diverse molecules. We also show that predictive SARs in the form of trend vectors can be derived from mixtures.