Quantitative pharmacophore models with inductive logic programming

Three-dimensional models, or pharmacophores, describing Euclidean constraints on the location on small molecules of functional groups (like hydrophobic groups, hydrogen acceptors and donors, etc.), are often used in drug design to describe the medicinal activity of potential drugs (or ‘ligands’). This medicinal activity is produced by interaction of the functional groups on the ligand with a binding site on a target protein. In identifying structure-activity relations of this kind there are three principal issues: (1) It is often difficult to “align” the ligands in order to identify common structural properties that may be responsible for activity; (2) Ligands in solution can adopt different shapes (or `conformations’) arising from torsional rotations about bonds. The 3-D molecular substructure is typically sought on one or more low-energy conformers; and (3) Pharmacophore models must, ideally, predict medicinal activity on some quantitative scale. It has been shown that the logical representation adopted by Inductive Logic Programming (ILP) naturally resolves many of the difficulties associated with the alignment and multi-conformation issues. However, the predictions of models constructed by ILP have hitherto only been nominal, predicting medicinal activity to be present or absent. In this paper, we investigate the construction of two kinds of quantitative pharmacophoric models with ILP: (a) Models that predict the probability that a ligand is “active”; and (b) Models that predict the actual medicinal activity of a ligand. Quantitative predictions are obtained by the utilising the following statistical procedures as background knowledge: logistic regression and naive Bayes, for probability prediction; linear and kernel regression, for activity prediction. The multi-conformation issue and, more generally, the relational representation used by ILP results in some special difficulties in the use of any statistical procedure. We present the principal issues and some solutions. Specifically, using data on the inhibition of the protease Thermolysin, we demonstrate that it is possible for an ILP program to construct good quantitative structure-activity models. We also comment on the relationship of this work to other recent developments in statistical relational learning. Editors: Tamás Horváth and Akihiro Yamamoto