A quantitative structure-activity relationship and pharmacophore modeling investigation of aryl-X and heterocyclic bisphosphonates as bone resorption agents

We have used quantitative structure-activity relationship (QSAR) techniques, together with pharmacophore modeling, to investigate the relationships between the structures of a wide variety of geminal bisphosphonates and their activity in inhibiting osteoclastic bone resorption. For aryl-X (X = alkyl, oxyalkyl, and sulfanylalkyl) derivatives of pamidronate and one alendronate, a molecular field analysis (MFA) yielded an R-2 value of 0.900 and an F-test of 54 for a training set of 29 compounds. Using reduced training sets, the activities of 20 such compounds were predicted with an average error of 2.1 over a 4000x range in activity. Such good results were only obtained when using the X-ray crystallographic structure of farnesyl pyrophosphate (FPP) bound to the target enzyme, farnesyl pyrophosphate synthase (FPP synthase), to guide the initial molecular alignment. For a series of heterocyclic bisphosphonates, use of the MFA method yielded an R-2 of 0.873 and an F-test of 36 for a training set of 26 compounds. Using a reduced training set, the activities of 20 compounds were predicted with an average error of 2.5 over a 2000x range in activity. With the heterocyclic compounds, test calculations indicated the importance of correct choice of protonation of the heterocyclic rings. For example, thiazoles, pyrazoles, and triazoles have low (similar to2-3) pK(a) values and the derived bisphosphonates are inactive in bone resorption since they cannot readily be side chain protonated and are thus poor carbocation reactive intermediate analogues. On the other hand, aminothiazoles, imidazoles, pyridyl, and aminopyridyl species typically have pKa values in the range similar to5-9 and, in the absence of unfavorable steric interactions, the corresponding bisphosphonates are generally good inhibitors. However, aminoimidazole bisphosphonates are generally less active, since their pK(a)s (similar to11) are so high, due to guanidinium-like resonance, that they cannot readily be deprotonated, which we propose results in poor cellular uptake. The results of pharmacophore modeling using the Catalyst program revealed the importance of two negative ionizable and one positive charge feature for both aryl-X and heterocyclic pharmacophores, together with the presence of a distal. hydrophobic feature in the aryl bisphosphonate and a more proximal aromatic feature in the heterocyclic bisphosphonate pharmacophores. When taken together, these results show that it is now possible to predict the activity, within a factor of about 2.3, of a wide range of aryl-X and heterocyclic bisphosphonates. The results emphasize the importance of utilizing crystallographic structural information to guide the initial alignment of extended bisphosphonates, and in the case of heterocyclic bisphosphonates, the importance of side chain protonation state. These simple ideas may facilitate the design of other, novel hisphosphonates, of use in bone resorption therapy, and as antiparasitic and immunotherapeutic agents.