The enzyme tetrahydrofolate synthetase has four identical and independent bindin

Question

The enzyme tetrahydrofolate synthetase has four identical and independent binding sites for its substrate ATP. For an equilibrium dialysis experiment, a solution of the enzyme was prepared. First the osmotic pressure of this solution was measured to be 2.4×103 bar at 20 C using an osmometer. Then the enzyme solution was placed in a dialysis bag, and the binding of ATP to the enzyme was measured by equilibrium dialysis at the same temperature. In one run, after the binding equilibrium was established, the concentration of free ATP outside the bag was found to be 1.00×104M, and the total ATP concentration inside the bag was found to be 3.00×104M.

A) On the basis of the information above, calculate K the equilibrium constant for the binding of ATP to the enzyme at 20C.

Explanation / Answer

Given osmotic pressure, P = 2.4×103 bar = 2.4E3 bar*×1E5Pa = 240 Pa
Gas constant, R = 8.314 J/mol K
Temperature, T = 20 + 273 = 293 K

Concentration of the enzyme, cM = n/V = P/(R*T) = 240/(8.314*293) = 0.0985 moles/m3 = 0.0985*0.001 moles/L = 0.985E-4 M

free ATP outside the bag, cout = 1.0E4 M
ATP inside the bag, cin = 3.0E4 M
ATP bound to the enzyme, cbound = cin - cout = 3E-4 - 1E-4 = 2.0E-4 M

n = cbound/cM = 2E-4/0.985E-4 = 2.03
L = ligand concentration = cout = 1E-4 M
n/L =2.03/1E-4 M = 20300 M-1.

K=(n/L)/(4-n) = 20300/(4-2.03) = 10305 M-1

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