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 -5.80 kJ/mol , what is the equilibrium constant, K, of the first reactions at 22 C ? The G for the hydrolysis of ATP to AMP is 31.6 kJ/mol.

Explanation / Answer

we know that

for a series of reactions

dG = dG1 + dG2

given

overall dG = -5.80

dG2 = -31.6

so

we get

-5.80 = dG1 - 31.6

dG1 = 25.8 kJ/mol

now

we know that

dG= -RT lnK

given

temp = 22 C

T = 22 + 273

T = 295 K

so

we get

25.8 x 1000 = -8.314 x 295 x lnk

k = 2.7 x 10-5

so

the equilibrium constant of the first reaction is 2.7 x 10-5

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