Beware of ligand efficiency (LE): understanding LE data in modeling structure-activity and structure-economy relationships

Background: On the one hand, ligand efficiency (LE) and the binding efficiency index (BEI), which are binding properties (B) averaged versus the heavy atom count (HAC: LE) or molecular weight (MW: BEI), have recently been declared a novel universal tool for drug design. On the other hand, questions have been raised about the mathematical validity of the LE approach. Results: In fact, neither the critics nor the advocates are precise enough to provide a generally understandable and accepted chemistry of the LE metrics. In particular, this refers to the puzzle of the LE trends for small and large molecules. In this paper, we explain the chemistry and mathematics of the LE type of data. Because LE is a weight metrics related to binding per gram, its hyperbolic decrease with an increasing number of heavy atoms can be easily understood by its 1/MW dependency. Accordingly, we analyzed how this influences the LE trends for ligand-target binding, economic big data or molecular descriptor data. In particular, we compared the trends for the thermodynamic Delta G data of a series of ligands that interact with 14 different target classes, which were extracted from the BindingDB database with the market prices of a commercial compound library of ca. 2.5 mln synthetic building blocks. Conclusions: An interpretation of LE and BEI that clearly explains the observed trends for these parameters are presented here for the first time. Accordingly, we show that the main misunderstanding of the chemical meaning of the BEI and LE parameters is their interpretation as molecular descriptors that are connected with a single molecule, while binding is a statistical effect in which a population of ligands limits the formation of ligand-receptor complexes. Therefore, LE (BEI) should not be interpreted as a molecular (physicochemical) descriptor that is connected with a single molecule but as a property (binding per gram). Accordingly, the puzzle of the surprising behavior of LE is explained by the 1/ MW dependency. This effect clearly explains the hyperbolic LE trend not as a real increase in binding potency but as a physical limitation due to the different population of ligands with different MWs in a 1 g sample available for the formation of ligand-receptor complexes.