Relations between the dissociation constants of dibasic acids

Solvent kinetic isotope effects of human placental alkaline phosphatase in reverse micelles

Human placental alkaline phosphatase was embedded in a reverse micellar system prepared by dissolving the surfactant sodium bis(2-ethylhexyl) sulphosuccinate (Aerosol-OT) in 2,2, 4-trimethylpentane. This microemulsion system provides a convenient instrumental tool to study the possible kinetic properties of the membranous enzyme in an immobilized form. The pL (pH/p2H) dependence of hydrolysis of 4-nitrophenyl phosphate has been examined over a pL range of 8.5-12.5 in both aqueous and reverse micellar systems. Profiles of log V versus pL were Ha-bell shaped in the acidic region but reached a plateau in the basic region in which two pKa values of 9.01-9.71 and 9.86-10.48, respectively, were observed in reverse micelles. However, only one pKa value of 9.78-10.27 in aqueous solution was detected. Profiles of log V/K versus pL were bell-shaped in the acidic region. However, they were wave-shaped in the basic region in which a residue of pKa 9.10-9.44 in aqueous solution and 8.07-8.78 in reverse micelles must be dehydronated for the reaction to reach an optimum. The V/K value shifted to a lower value upon dehydronation of a pKa value of 9.80-10.62 in aqueous solution and 11.23-12.17 in reverse micelles. Solvent kinetic isotope effects were measured at three pL values. At pL 9.5, the observed isotope effect was a product of equilibrium isotope effect and a kinetic isotope effect; at pL 10.4, the log V/K value was identical in water and deuterium. The deuterium kinetic isotope effect on V/K was 1.14 in an aqueous solution and 1.16 in reverse micelles. At pL 11.0 at which the log V values reached a plateau in either solvent system, the deuterium kinetic isotope effect on V was 2.08 in an aqueous solution and 0.62 in reverse micelles. Results from a proton inventory experiment suggested that a hydron transfer step is involved in the transition state of the catalytic reaction. The isotopic fractionation factor (pi) for deuterium for the transition state (piT) increased when the pH of the solution was raised. At pL 11.0, the piT was 1.07 in reverse micelles, which corresponds to the inverse-isotope effect of the reaction in this solvent system. Normal viscosity effects on kcat and kcat/Km were observed in aqueous solution, corresponding to a diffusional controlled physical step as the rate-limiting step. We propose that the rate-limiting step of the hydrolytic reaction changes from phosphate releasing in aqueous solution to a covalent phosphorylation or dephosphorylation step in reverse micelles.

Sulphate-activated phosphorylase b: the pH-dependence of catalytic activity

The pH-dependence of sulphate-activated phosphorylase b has been studied in the direction of glycogen synthesis. The bell-shaped curve of the pH-dependence of the catalytic constant for the AMP-activated enzyme showed pK values of 6.1 and 7.3, but the curve for the enzyme activated by 0.9 M ammonium sulphate showed a drop of activity on the acid side at much higher pH values. Its bell was centred at pH 7.8 but it was too narrow to be characterized by only two pK values. The narrowness of the curve could be explained by positive co-operativity, but not its unusually steep acid side. We suggest that the fall on the acid side is due to more than one hydronation (addition of H+). The points can be fitted by a curve with two de-activating hydronations and a de-activating dehydronation having identical titration pK values of 7.5, and hence molecular values of 7.0, 7.5 and 8.0. If both 0.9 M ammonium sulphate and 5 mM AMP are added, the bell is as broad as with AMP alone, but is somewhat raised in pH optimum. The results are discussed in the light of new structural data from crystallographic studies on binary complexes of the enzyme.

The origin of multiply sigmoid curves of pH-dependence. The partitioning of groups among titration pK values

An acid, HnA, with n ionizing groups is known to have the same titration curve as an equimolar mixture of n hypothetical monobasic acids, whose dissociation constants are known as the 'titration constants' of the real acid. We show that the pH-dependence of any property of HnA is also represented by the sum of one-site titration curves, characterized by these same titration constants. Since one such property is the degree of dissociation of one of the dissociating groups, a fraction of each group shows each of the various titration pK values, so that the group partitions among them. The n groups therefore share the same n titration pK values but differ in the fractions belonging to each. The one H+ ion per molecule that titrates with each pK is thus made up of the fractions, one from each group, that share this pK value. A group may possess a single pK value, in that it contributes virtually all of this pK and almost nothing to the others, only if either (1) in titrates in a different pH range from the other groups or (2) its affinity for H+ is unaffected by their ionization state.