Substrate- and alkali-metal-ion-induced pK shifts in intestinal brush-border sucrase, according to the three-protons model

Abstract

To define adequately enzyme activation/inhibition mechanisms as a function of pH, it is necessary to characterize the effector-induced pK shifts on both the free enzyme and on the enzyme-substrate complex. On the basis of our recent three-protons model for sucrase [Vasseur, van Melle, Frangne & Alvarado (1988) Biochem. J. 251, 667-675], we show how the 'fundamental' pK values, deduced from the classical double-logarithmic transformations, are insufficient to generate the required information. This insufficiency derives from the fact that, for sucrase, the acid ionization constant, K1, is a molecular constant that involves complex, V-type plus K-type, activatory and inhibitory kinetic effects. As a consequence, substrate-induced pK shifts cannot be interpreted correctly only by using the fundamental pK approach, because an unequal number of key protons is involved, depending on whether the free enzyme or the enzyme-substrate complex is considered. We demonstrate how this problem can be solved by using the 'theoretical' pK values, derived from the reciprocals of the Michaelis pH functions, i.e. Cha's fractional concentration factors. The procedure we propose, which is general, has the advantage of yielding all the macroscopic pK values for any given model, as calculated from the microscopic pK values. Furthermore, it permits predicting pK shifts as a function of [S] and/or [A] (where S is the substrate and A is the allosteric modifier), an objective that cannot be attained by using the double-logarithmic plot approach. Finally, we describe the relation existing between the fundamental and the theoretical pK values.