One of the discussion questions for lesson 4 concerned Paul Boyer\'s 180 exchang

Question

One of the discussion questions for lesson 4 concerned Paul Boyer's 180 exchange experiment. As you discovered, his experiments unexpectedly concluded that the energy-requiring step for the synthesis of ATP is not the bond formation but the release of ATP from the enzyme. Given that the AGo for the synthesis of ATRP in solution is +30.5 kJ/mol, it is clear that it is counter-intuitive for the formation of the bond between ADP and Pi to be completely reversible in the active site of the ATP Synthase. How can that be? What provides the energy to make that possible? Let's do some calculations to unearth the answer. 5. a) Keq for the synthesis of ATP from ADP P bound to ATP Synthase has been determined to be 0.42. Calculate the ?Go, for this reaction. Compare this to the AGo, for the synthesis of ATP in solution. Enzyme-(ADP + Pi) + Enzyme-(ATP) b) Kd, the binding constant, is usually expressed as the dissociation constant for the binding of a ligand to an enzyme. Therefore, the smaller the constant, the tighter the binding. The binding constants for FiFo (i.e., the ATP Synthase) with ATP or ADP Pi were determined to be 10-12 and 10-5, respectively. Enzyme-ATP Enzyme ATP Kd 10-12 1012 eSpectits for Enzyme (ADP + P) EnzymeADP P Kd 10-5

Explanation / Answer

Answer 5: (a)

DG°' for the reaction can be calculated by the following eq.

DG°' = -RT ln K'eq

Given K'eq =0.42 , R (gas constant) = 8.314 J/mol.K , T (temp. in kelvin) = 298 K

DG°' = -(8.314 J/mol.K)(298) ln0.42

         = 2149.29 J/mol = 2.149 KJ/mol

(b) Kd, binding constant, for F1 F0 with ATP is very low i.e. F1 F0 binds ATP with very high affinity. While Kd, binding constant, for F1 F0 with ADP is high i.e. F1 F0 binds ADP with low affinity. This difference in Kd corresponds to difference in binding energy, which derives the equilibrium to the formation of ATP.

DG°' = -RT ln K'eq

Given K'eq =0.42 , R (gas constant) = 8.314 J/mol.K , T (temp. in kelvin) = 298 K

DG°' = -(8.314 J/mol.K)(298) ln0.42

         = 2149.29 J/mol = 2.149 KJ/mol

• Standard free energy change is positive but much smaller than the DG°' (+30.5 KJ/mol) for the synthesis of ATP in solution.

(b) Kd, binding constant, for F1 F0 with ATP is very low i.e. F1 F0 binds ATP with very high affinity. While Kd, binding constant, for F1 F0 with ADP is high i.e. F1 F0 binds ADP with low affinity. This difference in Kd corresponds to difference in binding energy, which derives the equilibrium to the formation of ATP.

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