BLASTing small molecules - statistics and extreme statistics of chemical similarity scores

Motivation: Small organic molecules, from nucleotides and amino acids to metabolites and drugs, play a fundamental role in chemistry, biology and medicine. As databases of small molecules continue to grow and become more open, it is important to develop the tools to search them efficiently. In order to develop a BLAST-like tool for small molecules, one must first understand the statistical behavior of molecular similarity scores. Results: We develop a new detailed theory of molecular similarity scores that can be applied to a variety of molecular representations and similarity measures. For concreteness, we focus on the most widely used measure - the Tanimoto measure applied to chem-ical fingerprints. In both the case of empirical fingerprints and fingerprints generated by several stochastic models, we derive accurate approximations for both the distribution and extreme value distribution of similarity scores. These approximation are derived using a ratio of correlated Gaussians approach. The theory enables the calculation of significance scores, such as Z-scores and P-values, and the estimation of the top hits list size. Empirical results obtained using both the random models and real data from the ChemDB database are given to corroborate the theory and show how it can be applied to mine chemical space.