Chemiosmotic Theory (Peter Mitchell, 1961):

(a) Electron Transport Chain - Creating the gradient:

Overview: ETC pumps H⁺ from matrix to intermembrane space, creating electrochemical gradient

Four protein complexes + 2 mobile carriers:

Complex I (NADH dehydrogenase):

• Accepts: 2e⁻ from NADH
• Passes to: Ubiquinone (CoQ)
• Pumps: 4 H⁺ out
• NADH → NAD⁺ + H⁺ + 2e⁻

Complex II (Succinate dehydrogenase):

• Accepts: 2e⁻ from FADH₂ (from Krebs cycle)
• Passes to: CoQ
• Pumps: 0 H⁺ (no pumping!)
• Lower entry point → less ATP

Ubiquinone (CoQ):

• Mobile carrier in membrane
• Carries electrons from Complex I/II to Complex III
• Also picks up H⁺ from matrix

Complex III (Cytochrome bc₁ complex):

• Accepts: 2e⁻ from CoQ
• Passes to: Cytochrome c
• Pumps: 4 H⁺ out
• Q-cycle mechanism

Cytochrome c:

• Mobile carrier (peripheral protein)
• Carries electrons from Complex III to Complex IV

Complex IV (Cytochrome oxidase):

• Accepts: 2e⁻ from cytochrome c
• Passes to: O₂ (final electron acceptor)
• Pumps: 2 H⁺ out
• Reaction: ½O₂ + 2H⁺ + 2e⁻ → H₂O

Total H⁺ pumped:

• Per NADH: 4 + 4 + 2 = 10 H⁺
• Per FADH₂: 0 + 4 + 2 = 6 H⁺

Electrochemical gradient created:

• Chemical gradient (ΔpH): ~0.5-1 pH units
  • Matrix pH ~8, intermembrane space pH ~7
• Electrical gradient (ΔΨ): ~180 mV (matrix negative)
• Proton-motive force (PMF):

$\Delta p = \Delta\Psi - \frac{2.3RT}{F}\Delta pH$

At 37°C: $\Delta p \approx 180 - 60(1) = 220 \text{ mV}$

(b) ATP Synthase - Using the gradient:

Structure:

F₀ portion (membrane-embedded):

• c-ring: 8-15 subunits forming rotor
• Proton channel through a-subunit
• Anchored in membrane

F₁ portion (matrix-facing):

• 3α and 3β subunits (catalytic)
• γ-subunit (central stalk/rotor)
• Extends into matrix

Mechanism (rotary catalysis):

Step 1: H⁺ enters channel in F₀

• H⁺ binds to c-ring subunit
• Neutralizes negative charge (Asp/Glu residue)

Step 2: Rotation

• Binding of H⁺ causes c-ring to rotate
• Each H⁺ binding causes ~30° rotation (for 12-subunit c-ring)

Step 3: H⁺ release

• c-ring rotation brings H⁺ to exit channel
• H⁺ released into matrix
• c-ring subunit returns to start

Step 4: Mechanical energy → chemical energy

• γ-subunit (connected to c-ring) rotates

• Rotation changes conformation of β-subunits

• 3 β-subunits cycle through 3 states:

  1. Open (O): ADP + Pi bind
  2. Loose (L): Binding stimulated
  3. Tight (T): ATP formed and released

Binding change mechanism:

• All three β-subunits in different states simultaneously
• 120° rotation changes: O → L → T → O
• ATP formed spontaneously when in T state
• Energy used to RELEASE ATP, not form it!

(c) H⁺ per ATP calculation:

Depends on c-ring size:

Most organisms: c-ring with 8-15 subunits

Complete rotation (360°):

• c-ring: 10 subunits (common in mitochondria)
• 1 full rotation = 10 H⁺ through F₀
• 1 full rotation = 3 ATP made (3 β-subunits × 1 ATP each)

$\frac{\text{H}^+}{\text{ATP}} = \frac{10}{3} \approx 3.3 \text{ H}^+\text{/ATP}$

For different c-ring sizes:

• 8 subunits: 8/3 = 2.7 H⁺/ATP
• 10 subunits: 10/3 = 3.3 H⁺/ATP
• 12 subunits: 12/3 = 4.0 H⁺/ATP
• 15 subunits: 15/3 = 5.0 H⁺/ATP

$\boxed{\text{Approximately 3-4 H}^+ \text{ per ATP (depends on organism)}}$

ATP yield from NADH:

NADH → 10 H⁺ pumped

At 3.3 H⁺/ATP: $\text{ATP} = \frac{10}{3.3} \approx 3 \text{ ATP/NADH}$

Modern estimates (accounting for ATP/ADP translocase): $\text{ATP} \approx 2.5 \text{ ATP/NADH}$

FADH₂: $\text{ATP} = \frac{6}{3.3} \approx 1.8 \approx 1.5 \text{ ATP/FADH}_2$

Energy coupling: $\Delta G_{pmf} = n\Delta p = (3.3)(220 \text{ mV}) = 726 \text{ mV}$

Enough to drive ATP synthesis: $\text{ADP} + \text{P}_i \rightarrow \text{ATP} + \text{H}_2\text{O} \quad \Delta G = +30.5 \text{ kJ/mol}$

Uncouplers:

• DNP (2,4-dinitrophenol): carries H⁺ across membrane
• Bypasses ATP synthase
• Energy dissipated as heat (thermogenesis)
• Brown fat uses UCP1 (uncoupling protein) naturally