Cooperative Interactions of the Catalytic Nucleophile and the Catalytic Acid in the Inhibition of β‐Glycosidases. Calculations and their validation by comparative kinetic and structural studies of the inhibition of glycogen phosphorylase b

Abstract

AbstractThe difference between the strong inhibition of retaining β‐glucosidases by the tetrazole 1 and the weak inhibition by the triazole 3 has been explained by the protonation by the enzymic catalytic acid of N(3) of 1, replaced by CH in 3. One also expects a contribution to the inhibition from the charge‐dipole interaction between the enzymic catalytic nucleophile and the azole ring. The extent of this contribution was estimated from the calculated, distance‐dependent heats of formation of the acetate‐azole complexes. The calculations were validated by comparison of the charge‐dipole interaction between phosphate and the inhibitors 1 and 3 in the glycogen phosphorylase b (GPb)‐azole‐phosphate complexes, as derived from differences in the Ki values for 1 and 3, while the structural invariance of the complexes was demonstrated by X‐ray analysis. The difference between the charge‐dipole interactions of (dihydrogen) phosphate and 1 or 3 as derived from Δ Ki is 1.1 kcal mol−1, while the calculated difference is 1.3 kcal mol−1. The calculated difference for the interaction of 1 or 3 with acetate, representing the catalytic nucleophile in β‐glycosidases, is 2.0 kcal mol−1, while the differences of the binding energies as derived from the Ki values for the inhibition by 1 or 3 of different β‐glycosidases range from 2.4 to 5.3 5 kcal mol−1. The calculated difference for 1 and the imidazole 6 is 2.5 kcal mol−1 in favour of 1, whereas the Ki‐derived difference is 3.7 kcal mol−1 in favour of 6, equal to the calculated difference between 1 and the protonated imidazole 6. Thus, protonation by the catalytic acid and the charge‐dipole interaction with the catalytic nucleophile contribute cooperatively to the binding of inhibitors possessing a trigonal anomeric centre bonded to a heteroatom.