Duodenal alkaline phosphatase of juvenile (11-day-old) mice, like other non-specific alkaline phosphatases, has the ability to hydrolyse PP(i). When a constant Mg(2+)/PP(i) concentration ratio is maintained, plots of velocity as a function of PP(i) concentration are consistent with Michaelis-Menten kinetics. Mg(2+) activates pyrophosphate hydrolysis and maximal activity is obtained at a constant Mg(2+)/PP(i) concentration ratio of 0.66. At higher ratios there is strong inhibition. At constant concentrations of Mg(2+) and increasing concentrations of PP(i), the velocity-substrate (PP(i)) concentration plots show sigmoidal dependence. By assuming that the true substrate is MgP(2)O(7) (2-) complex, and using complexity constants, the concentrations of free Mg(2+), Mg(2)P(2)O(7) and MgP(2)O(7) (2-) were calculated in assay mixtures ranging in PP(i) concentration from 0.1 to 2.5mm and in total Mg(2+) concentration from 0.6 to 2.6mm. From these data, the concentrations of added Mg(2+) and PP(i) in the assay mixtures were selected so that the velocity could be measured (1) at three fixed concentrations of free Mg(2+) ions with varied concentrations of MgP(2)O(7) (2-) and (2) at four fixed concentrations of Mg(2)P(2)O(7) with varied concentrations of MgP(2)O(7) (2-). Lineweaver-Burk and Hill plots from these data showed that the inhibition is caused by free Mg(2+) ions, of a mixed type and consistent with Michaelis-Menten kinetics. The sigmoidal dependence observed between velocity and PP(i) concentration at constant concentration of total Mg(2+) is therefore not due to allosteric inhibition. It is due to a combined effect of (1) inhibition by free Mg(2+) ions, (2) depletion of the true substrate, MgP(2)O(7) (2-), owing to the formation of Mg(2)P(2)O(7) and (3) the manner in which the concentrations of these three molecular or ionic species change when PP(i) concentration is increased maintaining the total Mg(2+) concentration constant.