A simple mathematical approach to the analysis of polypharmacology and polyspecificity data.

There many possible types of drug-target interactions, because there are a surprising number of ways in which drugs and their targets can associate with one another.  These relationships are expressed as polypharmacology and polyspecificity.  Polypharmacology is the capability of a given drug to exhibit activity with respect to multiple drug targets, which are not necessarily in the same activity class. Adverse drug reactions ('side effects') are its principal manifestation, but polypharmacology is also playing a role in the repositioning of existing drugs for new therapeutic indications.  Polyspecificity, on the other hand, is the capability of a given target to exhibit activity with respect to multiple, structurally dissimilar drugs.  That these concepts are closely related to one another is, surprisingly, not well known.  It will be shown in this work that they are, in fact, mathematically related to one another and are in essence 'two sides of the same coin'.  Hence, information on polypharmacology provides equivalent information on polyspecificity, and vice versa. Networks are playing an increasingly important role in biological research. Drug-target networks, in particular, are made up of drug nodes that are linked to specific target nodes if a given drug is active with respect to that target.  Such networks provide a graphic depiction of polypharmacology and polyspecificity.  However, by their very nature they can obscure information that may be useful in their interpretation and analysis.  This work will show how such latent information can be used to determine bounds for the degrees of polypharmacology and polyspecificity, and how to estimate other useful features associated with the lack of completeness of most drug-target datasets.