A REVIEW AND EXAMINATION OF THE MATHEMATICAL SPACES UNDERLYING MOLECULAR SIMILARITY ANALYSIS

As an intuitive concept, molecular similarity has played a fundamental role in chemistry. It is implicit in Hammond's postulate, in the principle of minimum structure change, and in the assumption that similar structures tend to have similar properties. With the advent of large computers, computable definitions of similarity are being used in the pharmaceutical industry for similarity searching, dissimilarity selection, molecular superpositioning, structure generation, and quantitative structure-activity analysis. The diversity of applications of computable definitions of molecular similarity has of ten obscured important mathematical commonalities underlying these definitions. The broadest commonalities are relationships based on equivalence, matching, partial ordering, and proximity. A mathematical space suitable for molecular similarity analysis consists of a set of mathematicaI structures and one or more of these similarity relationships defined on that set. This report surveys the mathematical spaces used in molecular similarity analysis. The survey covers the types of chemical information, similarity relationships, and applications associated with the use of each mathematical space in a molecular similarity context.