Combinatorial preferences affect molecular similarity/diversity calculations using binary fingerprints and Tanimoto coefficients

A combinatorial method was developed to calculate complete distributions of the Tanimoto coefficient (Tc) for binary fingerprint (FP) representations of specified length, regardless of the chemical parameters they reflect. Theoretical Tc distributions were calculated for FPs consisting of up to 67 bit positions which revealed significant statistical preferences of certain Tc values. Calculation of Tc distributions in a large compound database using different FPs mirrored the effects identified by our general analysis. On the basis of these findings, an average Tc is biased by statistically preferred values.