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.
Dixon
H B
HB
Department of Biochemistry, University of Cambridge, U.K.
Clarke
S D
SD
Smith
G A
GA
Carne
T K
TK
D000143:Acids / Q000737:chemistry*; D055598:Chemical Phenomena; D002627:Chemistry, Physical; D003545:Cysteine / Q000737:chemistry; D006863:Hydrogen-Ion Concentration; D008433:Mathematics; D011522:Protons
D000143:Acids; D011522:Protons; D003545:Cysteine