Anomeric specificity and kinetics of glucokinase: theoretical unsuitability of the Hill equation

The kinetics of the low-Km hexokinase isoenzymes, which obey the Michaelis-Menten equation, can be established from the Km (Michaelis constant) and Vmax (maximal velocity) values for either equilibrated D-glucose or its alpha- and beta-anomers. In the case of the high-Km glucokinase isoenzyme, however, the sigmoidal substrate dependency and the competition between the two anomers of D-glucose do not allow, theoretically, to assign any meaningful value to either the Km, Vmax or n (Hill number) constants for equilibrated D-glucose. Thus, with equilibrated D-glucose, the concentration dependency fails to display a rectilinear relationship in the Hill plot. These observations illustrate the shortcomings of current biochemical studies in which the anomeric heterogeneity of D-glucose is ignored.