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 -7.40 kJ/mol , what is the equilibrium constant, K, of the first reactions at 30 C ? The G for the hydrolysis of ATP to AMP is 31.6 kJ/mol.

Explanation / Answer

The given reaction is:

Luciferin+O2ATPoxyluciferin +lightAMP +PPi

The overall G of the coupled reaction is -7.40 kJ/mol

The G for the hydrolysis of ATP to AMP is 31.6 kJ/mol.

T = 300C = 30 +273 = 303K

Step1.

To calculate G of the first reaction

G of the first reaction = G of the coupled reaction - G for the hydrolysis of ATP to AMP

G0 of first reaction = -7.40kJ/mol - (31.6 kJ/mol)

G0 of first reaction = -7.40kJ/mol + 31.6 kJ/mol

G0 of first reaction = 24.20kJ/mol

G0 of first reaction = 24200J/mol

Step2.

To calculate the equilibrium constant, K, of the first reaction

G0 = RT lnK

R is 8.314J/(molK)

Thus K = e^- G0/RT

         K = e^- 24200J/mol/ 8.314J/(molK) x 303K

         K = e^-9.6018

        K = 0.0000676069

        K = 6.76069 x 105h

The equilibrium constant, K, of the first reaction is 6.76069 x 105

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