Search

The aim of present paper is to derive the generating functions for the generalized hyperge-ometric polynomials [image omitted]  by using the representation of the Lie group SL(2,C) (the complex special linear group). In order to derive the elements of Lie algebra, a suitable interpretation to the index n is given. These generating functions, in turn yield, as special cases, a number of bilateral (bilinear) generating functions to the various classical orthogonal polynomials; namely the Laguerre, Meixner, Gottlieb, Krawtchouk and Meixner-Pollaczek polynomials. Many results obtained as special cases are known but some of them are believed to be new.

A series of heteroaryl modified 1,2-diarylimidazoles has been synthesized and found to be potent and highly selective (1000−9000-fold) inhibitors of the human COX-2. 3-Pyridyl derived COX-2 selective inhibitor (25) exhibited excellent activity in acute (carrageenan induced paw edema, ED50 = 5.4 mg/kg) and chronic (adjuvant induced arthritis, ED50 = 0.25 mg/kg) models of inflammation. The relatively long half-life of 25 in rat and dog prompted investigation of the pyridyl and other heteroaromatic systems containing potential metabolic functionalities. A number of substituted pyridyl and thiazole containing compounds (e.g., 44, 46, 54, 76, and 78) demonstrated excellent oral activity in every efficacy model evaluated. Several orally active diarylimidazoles exhibited desirable pharmacokinetics profiles and showed no GI toxicity in the rat up to 100 mg/kg in both acute and chronic models. The paper describes facile and practical syntheses of the targeted diarylimidazoles. The structure−activity relationships and antiinflammatory properties of a series of diarylimidazoles are discussed.

Series of 1,2-diarylpyrroles has been synthesized and found to contain very potent and selective inhibitors of the human cyclooxygenase-2 (COX-2) enzyme. The paper describes short and practical syntheses of the target molecules utilizing the Paal−Knorr reaction. Electrophilic substitution on 1 proceeds in a regioselective fashion, and the method was used to generate a number of tetrasubstituted pyrroles. Detailed SAR on the series has been studied by modifications of the aryl rings and the substituents in the pyrrole ring. Diarylpyrrole 1 is a very potent (COX-2, IC50 = 60 nm) and selective (COX-1/COX-2 = >1700) inhibitor whereas the isomeric 2 is completely inactive against COX-2. Modifications of the substituents on the fluorophenyl ring in 1 yields very potent inhibitors of COX-2 (IC50 = 40−80 nm) with excellent selectivity (1200 to >2500) vs COX-1. Analog 20 containing a sulfonamide group is an excellent inhibitor of COX-2 with an IC50 of 14 nm. Tetrasubstituted pyrroles containing groups such as COCF3, SO2CF3, or CH2OAr at position 3 in the pyrrole ring give excellent inhibitors (COX-2, IC50 = 30−120 nm). In vivo testing in the carrageenan-induced paw edema model in the rat establishes that the 1,2-diarylpyrroles are orally active antiinflammatory agents. Compound 3 is the most potent inhibitor of edema with an ED50 of 4.7 mpk.

Series of 1,2-diarylimidazoles has been synthesized and found to contain highly potent and selective inhibitors of the human COX-2 enzyme. The paper describes a short synthesis of the target 1,2-diarylimidazoles starting with aryl nitriles. Different portions of the diarylimidazole (I) were modified to establish SAR. Systematic variations of the substituents in the aryl ring B have yielded very potent (IC50 = 10−100 nm) and selective (1000−12500) inhibitors of the COX-2 enzyme. The study on the influence of substituents in the imidazole ring established that a CF3 group at position 4 gives the optimum oral activity. A number of the diarylimidazoles showed excellent inhibition in the adjuvant induced arthritis model (e.g., ED50 = 0.02 mpk for 22 and 34). The diarylimidazoles are also potent inhibitors of carrageenan-induced edema (ED50 = 9−30 mpk) and hyperalgesia (ED50 = 11−40 mpk). Several orally active diarylimidazoles show no GI toxicity in the rat and mouse up to 200 mpk.