2. The free energy of ATP synthesis from ATP synthase under cellular conditions

Question

2. The free energy of ATP synthesis from ATP synthase under cellular conditions is +45 kJ/mol.

a. Where does the energy come from?

b. If the pH of the matrix is 7.84, the intermembrane space is 7.16 and the membrane potential is 0.15 V at 37 °C, how much energy can be produced from this gradient per mol of protons?

c. How many moles of protons moving across this gradient would be required to produce enough energy for one mole of ATP to be synthesized?

d. To generate a proton gradient the mitochondria use the energy of electron transport. How much energy is produced in the oxidation of NADH by oxygen (under standard biochemical conditions)?

e. Using your answer from b, how many moles of protons could be transported out of the matrix with this oxidation energy (d)?

f. How many moles of protons are actually transported in the oxidation of NADH through the ETC?

Explanation / Answer

a. The electron transport chain is a series of proteins and organic molecules on the inner membrane of mitochondria. As the electron passes from one member of ETC to another a series of redox reactions takes place. The energy released in these redox reactions is harnessed as a proton gradient which in turn is used in the synthesis of ATP. This process is called chemiosmosis. Therefore, ETC together with chemiosmosis leads to oxidative phosphorylation or ATP synthesis.

b. G or Gibb’s energy = -2.303 RT pH

R = Gas constant 8.315 * 10-3 kJ / mol- K

T is the Absolute temperature

= -2.303 (8.315 * 10-3 * 298)(7.84)

= -2.303 (.24)*(7.84)

= -2.303 * 1.93

=- 4.46 kj/mol

G = nF m

= (1) (96.48 kJ / V-mol Faraday’s constant) (0.15)

= 14.17 kJ/mol

The total free energy available for the movement of 1 mole of protons under cellular conditions (pH = 7.84 and m = 0.15 )is the sum of energy changes calculated above;

G or Gibb’s energy = -2.303 RT pH + nF m

= -4.46 kJ/mol + 14.17 kJ/mol

= 10.01 kJ /mol

c. Estimated consumption of the proton gradient for ATP synthesis is about 3 moles of protons per mole of ATP.

If G = 45 kJ /mol for ATP synthesis in mitochondria, then by Hess’s law

G = 45 + 3(10.01)

= 75.03 kJ/mol

d and e. The estimated pumping associated with electron transport chain is 10 protons per electron pair from NADH to Oxygen.

We now know that 3 protons are consumed per ATP molecule synthesized and one proton is spent in transporting ATP to the cytoplasm. So the yield of cytoplasmic ATP per electron pair is:-

1 ATP / 4 H+ ) / (10 H+ / electron pair)

= 2.5 ATP / electron pair

6 protons are pumped for each electron pair passed from FADH2 to Oxygen, so the ATP yield is;

(1 ATP / 4 H+) / (6 H+ / electron pair)

= 1.5 ATP / electron pair

f. The electron transport from NADH to oxygen is coupled by the proton transport across the membrane. During ETC from NADH to oxygen protons translocate from the matrix to inter membrane space. The pH of the outside of the membrane is lowered. The pH change indicates that 10 protons are transported out of the matrix for the transfer of every electron pair from NADH to oxygen.

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