Question

In isolated thylakoid membranes you measure, through the use of molecular probes, a transmembrane potential of delta psi = + 60 mV and a delta pH of 2- (inside acidic) across the thylakoid membrane. A) How much free energy is yielded by moving 1 mole of protons outward through the H+-ATPase under these conditions of delta psi and delta pH? B) If there are 10 c- subunits in the chloroplast ATPase (cFo), how much energy is available to synthesize each ATP?

Answer 1

Given-

Transmembrane potential of delta psi = + 60 mV

Delta pH of 2- (inside acidic)

A)

Free-energy change during solute movement across a voltage gradient-

H+out <==> H+in

ΔG = nFΔΨm

If proton pumping maintains a voltage gradient of 0.06V, positive outside, then ΔΨm is negative here.

DG = (1)(96.48 kJ/V-mol)(- 0.06 V) = - 5.79 kJ/mol

Free energy is available from the movement of protons down the concentration gradient created by electron transport-

ΔG = ΔG⁰ + RT lnQ

= ΔG⁰ + RT ln([H+in]/[H+out])

ΔG⁰ = 0 because Keq for the process is 1.0

So ΔG⁰ = - RT ln Keq)

ΔG = RT ln([H+in]/[H+out])

To express ΔG in terms of the pH gradient, change ln to log (that is, log10) and expand the log term

ΔG = 2.303 RT log([H+in]/[H+out])

ΔG = 2.303 RT (log[H+in] - log[H+out])

= - 2.303 RT (pHin - pHout)

ΔG = - 2.303 RT ΔpH

ΔG = - 2.303 (8.315 x 10-3 kJ/mol-K)(298K)(2) = -11.41 kJ/mol

The total free energy available from the movement of 1 mole of protons from outward through the H+-ATPase under these conditions of delta psi and delta pH) is the sum of the free energy changes calculated in above both processes.

ΔG = - 2.303 RT ΔPH + nFΔΨm = (-11.41 kJ/mol )+ (– 5.79 kJ/mol)

ΔG = -17.2 kJ/mol

B. there are 10 c- subunits in the chloroplast ATPase (cFo) and energy is available to synthesize each ATP

H+/ATP = (number of c-subunits) / 3

H+/ATP = 10/3

Estimated consumption of the proton gradient by ATP synthesis is about 3 moles protons per mole ATP. ΔG = 50 kJ/mol for ATP synthesis in mitochondria,

According to Hess's law, ΔG = 50 + 3(- 17.2) = - 1.6 kJ/mol, and the process of synthesis of ATP is spontaneous under mitochondrial conditions