Introduction to Bivalent Ligand Binding: Considerations for Interactive Binding Sites

Length-Dependent Titration Properties of Symmetrical (Diprotic) Dicarboxylic Acids

Symmetrical dicarboxylic acids provide good examples of anti-cooperative ligand binding behavior caused by the repulsive interactions between the negatively-charged carboxyl groups when both are ionized on the same molecule. This "negative" interaction shifts the equilibrium dissociation or association constants of the carboxyl groups in proportion to the strength of the electrostatic repulsion between the two carboxylate ions when the acid is fully desaturated.

STEP 1 association rxn, k1_an= 1/k1_dn:^-OOC-(CH2)X-COO^- + H⁺ Û HOOC-(CH₂)_X-COO^- or ^-OOC-(CH₂)_X-COOH STEP 2 association rxn, k2_an= 1/k2_dn:HOOC-(CH₂)_X-COO^- or ^-OOC-(CH₂)_X-COOH + H⁺ Û HOOC-(CH₂)_X-COOH
Acetate	Malonate (X = 1)	Succinate (X = 2)	Adipate (X = 4)

pK_dn = 4.70	pk1_dn = 5.85, pk2_dn = 3.55 Dpk_dn = 2.3	pk1_dn = 5.05, pk2_dn = 4.35 Dpk_dn = 1.7	pk1_dn = 4.90, pk2_dn = 4.50 Dpk_dn = 2.4

HOOC-(CH₂)_X-COOH (X >> 1)

pk1_dn = 4.70, pk1_dn = 4.70 Dpk_dn = 0

Click here for a comprehensive Excel spreadsheet analysis of dicarboxylate titrations as a function of the methylene carbon spacer.