The signature molecular descriptor. 3. Inverse-quantitative structure-activity relationship of ICAM-1 inhibitory...

We present a methodology for solving the inverse-quantitative structure-activity relationship (QSAR) problem using the molecular descriptor called signature. This methodology is detailed in four parts. First, we create a QSAR equation that correlates the occurrence of a signature to the activity values using a stepwise multilinear regression technique. Second, we construct constraint equations, specifically the graphicality and consistency equations, which facilitate the reconstruction of the solution compounds directly from the signatures. Third, we solve the set of constraint equations, which are both linear and Diophantine in nature. Last, we reconstruct and enumerate the solution molecules and calculate their activity values from the QSAR equation. We apply this inverse-QSAR method to a small set of LFA-1/ICAM-1 peptide inhibitors to assist in the search and design of more-potent inhibitory compounds. Many novel inhibitors were predicted, a number of which are predicted to be more potent than the strongest inhibitor in the training set. Two of the more potent inhibitors were synthesized and tested in-vivo, confirming them to be the strongest inhibiting peptides to date. Some of these compounds can be recycled to train a new QSAR and develop a more focused library of lead compounds.