Question

The proton motive force

a. Write a simple chemical expression for proton movement from the cytoplasm into the matrix of the mitochondria. Calculate the free energy change due to this movement across a concentration gradient (Answer in terms of pH, no numbers are necessary).

When deriving this equation, you might find it helpful to remember that under Standard conditions: [reactants] =1M and [products] = 1M. If both the products and reactants are the same molecule, i.e. a proton, what is ΔG° ?

b. Define the membrane voltage gradient or membrane potential as ΔV=Vmatrix - Vout.

How much free energy is available from the movement of protons down the voltage gradient created by the electron transport if ΔG = -nFΔV° + nFΔV and the voltage gradient that is maintained is positive outside?

Hint: under standard conditions there will be 1M protons on each side of the membrane. What is ΔV° ?

c. Finally, calculate the 'proton motive force' (Δp) per mole of protons, which is the free energy change during a movement across a proton gradient, if ΔG = - nFΔp° + nFΔp

Hint: Recall again that under standard conditions the concentration of protons on each side of the membrane = 1M

Answer 1

1.Concentration Gradient

Under standard conditions when H⁺_in = 1M, H⁺_out = 1M

ln K_{eq = 0, so}

to express interms of pH,

If Del pH is 1.4 (when pH is lower outside)

= -2.303 x 8.314 x 10 ^-3 (kJ/mol -K) x 298 (K) x 1.4

= - 7.98 kJ/mol

2. Voltage gradient

for standard conditions.

if voltage gradient is - 0.14 V (positive outside)

= 1 x (96.48 kJ/V-mol) x (-0.14 V)

= -13.5 kJ/mol

3. Proton motive force = Concentration Gradient + Voltage Gradient

  under standard conditions

sum of contributions of voltage gradient and concentration gradient = proton motive force

so

= (sum of del G of concentration gradient + voltage gradient)/nF

= -13.5-7.98/(1 x 96.48)

= 0.222 V