How can you calualte the free enerygy withe Kd reversed? b) Kd, the binding cons

Question

How can you calualte the free enerygy withe Kd reversed?

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 F?Fo (i.e., the ATP Synthase) with ATP or ADP Pt were determined to be 10-12 and 10-5, respectively. Enzyme ATPEnzyme ATP Enzyme-(ADP + Pi) Enzyme + ADP + Pi Kd 10-12 Kd 10-5 Use the inverse of these binding constants (which would give the strength of the binding directly) to calculate the free energy for the binding of ATP by the synthase, and then the free energy for the binding of ADP P by the synthase. What is the difference in the binding energy of ATP versus ADP + Pi? (Note: the relationship between Kd and the free energy is the same as the relationship between Keq and the free energy.) c) So why is the reaction reversible on the enzyme surface when it is not reversible in solution?

Explanation / Answer

Free energy is calculated for a reaction in equilibrium from the following formula,

dG = - R T ln Keq

where dG is the free energy change, R is universal gas constant, T the temperature and Keq the corresponding equilibrium constant. For the reverse reaction for the given ones, the keq = 1/kd. Thus for reaction 1,

dG = -8.314 * 310 * ln (1012) = - 71.2 kJ / mol

for reaction 2,

dG = -8.314 * 310 * ln (105) = - 29.6 kJ / mol.

Difference in these free energies = - 41 kJ / mol.

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