A protein has a single site for the binding of ligand A. The binding of A is lin

Question

A protein has a single site for the binding of ligand A. The binding of A is linked to the ionization of an aspartate side-chain located near the binding site for A, so that the apparent association binding constant for A depends on pH. Both the protonated (EH) and deprotonated protein (E) can bind ligand A to give the species EHA and EA, respectively.
a. Derive an expression for the apparent association binding constant for the binding of A to the protein.
b. The pKa value of the aspartate side chain in the free protein (EH) is 3.52. The apparent association binding constant for the binding of A to the protein is
4.02 x 105 at pH 3.00 and 1.11 x 105 at pH 4.50. What are the values of the
association constants for the binding of A to the protein when the aspartate side chain is protonated and when it is deprotonated? Show all calculations.

Explanation / Answer

free protein + A = protein bounded A

The expression is as follows :

binding constant = [bounded complex]/[free protein][A]

The protein can be either in E or EH form and bound ligand can therefore be in EA or EHA form

A + N = NA = D + A where D was denatured protein and N was natured (and only natured protein could bind A), and the Kd = [D][A]/[NA]

A can bind to both forms of the protein.

So 256500 = 3.52 [A] / 1

Association constant = [A] = 72869.3182

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