Strong Nonadditivity as a Key Structure–Activity Relationship Feature: Distinguishing Structural Changes from Assay Artifacts

Nonadditivity in protein-ligand affinity data represents highly instructive structure-activity relationship (SAR) features that indicate structural changes and have the potential to guide rational drug design. At the same time, nonadditivity is a challenge for both basic SAR analysis as well as many ligand-based data analysis techniques such as Free-Wilson Analysis and Matched Molecular Pair analysis, since linear substituent contribution models inherently assume additivity and thus do not work in such cases. While structural causes for nonadditivity have been analyzed anecdotally, no systematic approaches to interpret and use nonadditivity prospectively have been developed yet. In this contribution, we lay the statistical framework for systematic analysis of nonadditivity in a SAR series. First, we develop a general metric to quantify nonadditivity. Then, we demonstrate the non-negligible impact of experimental uncertainty that creates apparent nonadditivity, and we introduce techniques to handle experimental uncertainty. Finally, we analyze public SAR data sets for strong nonadditivity and use recourse to the original publications and available X-ray structures to find structural explanations for the nonadditivity observed. We find that all cases of strong nonadditivity (ΔΔpKi and ΔΔpIC50 > 2.0 log units) with sufficient structural information to generate reasonable hypothesis involve changes in binding mode. With the appropriate statistical basis, nonadditivity analysis offers a variety of new attempts for various areas in computer-aided drug design, including the validation of scoring functions and free energy perturbation approaches, binding pocket classification, and novel features in SAR analysis tools.