Hill Analysis of Interactive Ligand Binding (lig)

In this exercise, the ligand binding interactions between the bivalent ligand binding sites of symmetrical dicarboxylic acid are examined using a Hill plot. When fully protonated ("saturated"), a dicarboxylic acid undergoes a two-step dissociation reaction with decreasing hydronium ion concentration. When completely deprotonated ("desaturated"), a dicarboxylate undergoes a two-step association reaction with increasing hydronium ion concentration.

For correct statistical analysis is it necessary to keep track of binding to the right and left sides of the molecule.

Two-step dissociation
kd1
HOOC-CH2-COOH
- H+
+H+
-OOC-CH2-COOH
kd1'ka2kd2
- H+

+ H+

ka2'

ka1

+ H+
- H+
ka1'
HOOC-CH2-COO-
+H+
- H+
-OOC-CH2-COO-
kd2'
Two-step association
kd1-cooh = [H+] * [-OOC-CH2-COOH] / [HOOC-CH2-COOH] (step d1)
kd1'-cooh = [H+] * [HOOC-CH2-COO-] / [HOOC-CH2-COOH] (step d1')
kd2-cooh = [H+] * [-OOC-CH2-COO-] / [-OOC-CH2-COOH] (step d2)
kd2'-cooh = [H+] * [-OOC-CH2-COO-] / [HOOC-CH2-COO-] (step d2')
kd1 = kd1' = 1/ka2 = 1/ka2'kd2 = kd2' =1/ka1 = 1/ka1'

ka1-cooh = [-OOC-CH2-COOH] / [ H+] * [-OOC-CH2-COO-] (step a1)
ka1'-cooh =[HOOC-CH2-COO-] / [H+] * [-OOC-CH2-COO-] (step a1')
ka2-cooh = [HOOC-CH2-COOH] / [H+] * [-OOC-CH2-COOH] (step a2)
ka2'-cooh = [HOOC-CH2-COOH] / [H+] * [HOOC-CH2-COO-] (step a2')
ka1 = ka1' = 1/kd2 = 1/kd2'ka2 = ka2' = 1/kd1 = 1/kd1'

Continue the acid-base titration analysis of dicarboxylic acid by opening the Excel spreadsheet below.

Dicarboxylic Acid Titration:

Hill Plot


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Duane W. Sears
Revised: August 10, 1998