Firefly luciferase is the enzyme that allows fireflies to illuminate their abdom

Question

Firefly luciferase is the enzyme that allows fireflies to illuminate their abdomens. Because this light generation is an ATP-requiring reaction, firefly luciferase can be used to test for the presence of ATP. In this way, luciferase can test for the presence of life. The coupled reactions are luciferin+O2ATPoxyluciferin+lightAMP+PPi If the overall G of the coupled reaction is -4.70 kJ/mol , what is the equilibrium constant, K, of the first reactions at 13 C ? The G for the hydrolysis of ATP to AMP is 31.6 kJ/mol. Express your answer numerically.

Explanation / Answer

The overall reaction being, ---> luciferin+O2 + ATPoxyluciferin+light + AMP+PPi

it can be considered as a combination of following these two reactions

luciferin+O2 oxyluciferin+light --------------(i) ----related standard free energy change = G1

ATP AMP+PPi ----------------------(ii)---------related standard free energy change = G2

The standard free energy change G for the coupled reaction = G1 +  G2

G = -4.70 kJ/mol , G2 = 31.6 kJ/mol

Hence, G1 = G - G2 = -4.70 kJ/mol -(31.6 kJ/mol) = 26.9 kJ/mol

Now, G1 = -RTlnK [K=equilibrium constant of equation (i)]

i.e. 26.9 * 10^3 J/mol = -8.314 J mol^-1 K^-1 * (273+13) K * ln K

i.e. ln K = - 11.313

Hence, K = 1.22 * 10^-5

So, the equilbrium constant for the first reaction at 13 C will be 1.22 * 10^-5

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