The use of Hasse diagrams as a potential approach for inverse QSAR

Quantitative structure-activity relationships are often based on standard multidimensional statistical analyses and sophisticated local and global molecular descriptors. Here, the aim is to develop a tool helpful to define a molecule or a class of molecules which fulfills pre-described properties, i.e., an Inverse QSAR approach. If highly sophisticated descriptors are used in QSAR, the structure and then the synthesis recipe may be hard to derive. Thus, descriptors, from which the synthesis recipe can be easily derived, seem appropriate to be included within this study. However, if descriptors simple enough to be useful for defining syntheses recipes of chemicals were used, the accuracy of a numeric expression may fail. This paper suggests a method, based on very simple elements of the theory of partially ordered sets, to find a qualitative basis for the relationship between such fairly simple descriptors on the one side and a series of ecotoxicological properties, on the other side. The partial order ranking method assumes neither linearity nor certain statistical distribution properties. Therefore the method may be more general compared to many standard statistical techniques. A series of chlorinated aliphatic compounds has been used as an illustrative example and a comparison with more sophisticated descriptors derived from quantum chemistry and graph theory is given. Among the results, it was disclosed that only for algae lethal concentration, as one of the four ecotoxicological properties, the synthesis specific predictors seem to be good estimators. For all other ecotoxicological properties quantum chemical descriptors appear as the more suitable estimators.