Cellular Respiration

Glycolysis, Krebs cycle, and oxidative phosphorylation

🔋 Cellular Respiration

Overview

Cellular respiration: Process of breaking down glucose to produce ATP

Overall equation:

C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ~32 ATP

Three main stages:

Glycolysis (cytoplasm)
Krebs cycle (mitochondrial matrix)
Oxidative phosphorylation (inner membrane)

Stage 1: Glycolysis

Location: Cytoplasm

Process:

Glucose (6C) → 2 Pyruvate (3C each)
Does NOT require oxygen (anaerobic)
"Glucose splitting"

Energy yield:

2 ATP (net) - used 2, produced 4
2 NADH

Steps:

Energy investment phase (uses 2 ATP)
Energy payoff phase (makes 4 ATP, 2 NADH)

Stage 2: Krebs Cycle (Citric Acid Cycle)

Location: Mitochondrial matrix

Before Krebs:

Pyruvate → Acetyl CoA (by pyruvate dehydrogenase)
Releases CO₂, makes NADH

Process:

Acetyl CoA (2C) enters cycle
Combines with oxaloacetate (4C) → citrate (6C)
Series of redox reactions
Regenerates oxaloacetate

Energy yield (per glucose = 2 turns):

2 ATP (or GTP)
6 NADH
2 FADH₂
4 CO₂ released

Stage 3: Oxidative Phosphorylation

Two parts:

Electron Transport Chain (ETC)

Location: Inner mitochondrial membrane (cristae)

Process:

NADH and FADH₂ donate electrons
Electrons pass through protein complexes
Energy used to pump H⁺ into intermembrane space
Creates electrochemical gradient (proton-motive force)

Protein complexes:

Complex I: NADH → Q
Complex II: FADH₂ → Q
Complex III: Q → Cytochrome c
Complex IV: Cytochrome c → O₂

Final electron acceptor: O₂ → H₂O

Chemiosmosis

Process:

H⁺ gradient created by ETC
H⁺ flows back through ATP synthase
Flow drives ATP synthesis
~3 ATP per NADH
~2 ATP per FADH₂

Total ATP Yield

From one glucose:

Glycolysis: 2 ATP + 2 NADH
Pyruvate → Acetyl CoA: 2 NADH
Krebs cycle: 2 ATP + 6 NADH + 2 FADH₂
Oxidative phosphorylation: ~28 ATP

Total: ~32 ATP (varies by cell type)

Anaerobic Respiration (Fermentation)

When O₂ unavailable:

Lactic acid fermentation:

Pyruvate → Lactate
Regenerates NAD⁺ for glycolysis
Occurs in muscles during intense exercise

Alcohol fermentation:

Pyruvate → Ethanol + CO₂
Regenerates NAD⁺
Used by yeast

Energy yield: Only 2 ATP (from glycolysis)

Key Concepts

Glycolysis: glucose → 2 pyruvate (2 ATP, 2 NADH)
Krebs cycle: completes glucose oxidation (2 ATP, 8 NADH, 2 FADH₂)
ETC: electrons from NADH/FADH₂ pump H⁺
Chemiosmosis: H⁺ gradient drives ATP synthesis
O₂ is final electron acceptor in aerobic respiration
Fermentation: anaerobic, regenerates NAD⁺, only 2 ATP

📚 Practice Problems

1Problem 1easy

❓ Question:

Outline the four stages of cellular respiration: (a) name each stage, (b) state where each occurs in the cell, (c) identify the main products of each stage, and (d) calculate the total ATP yield from one glucose molecule.

💡 Show Solution

Cellular Respiration Overview:

$\text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} + \text{ATP}$

(a) Four stages:

Glycolysis
Pyruvate Oxidation (transition reaction)
Krebs Cycle (Citric Acid Cycle)
Electron Transport Chain + Oxidative Phosphorylation

(b) Locations:

1. Glycolysis:

Location: Cytoplasm (cytosol)
Anaerobic (doesn't require O₂)

2. Pyruvate Oxidation:

Location: Mitochondrial matrix
Entry into mitochondria

3. Krebs Cycle:

Location: Mitochondrial matrix
Aerobic (requires O₂ indirectly)

4. Electron Transport Chain:

Location: Inner mitochondrial membrane (cristae)
Requires O₂ as final electron acceptor

(c) Products of each stage:

1. Glycolysis (glucose → 2 pyruvate):

ATP: 2 net (4 produced - 2 invested)
NADH: 2
Pyruvate: 2

2. Pyruvate Oxidation (2 pyruvate → 2 acetyl-CoA):

NADH: 2
CO₂: 2
Acetyl-CoA: 2

3. Krebs Cycle (2 turns, one per acetyl-CoA):

ATP (GTP): 2
NADH: 6
FADH₂: 2
CO₂: 4

4. Electron Transport Chain:

ATP: ~34 (from NADH and FADH₂)
H₂O: 6 (O₂ reduced)

(d) Total ATP yield:

From NADH:

Glycolysis: 2 NADH × 2.5 ATP = 5 ATP
Pyruvate oxidation: 2 NADH × 2.5 ATP = 5 ATP
Krebs: 6 NADH × 2.5 ATP = 15 ATP
Subtotal: 25 ATP

(Note: Glycolysis NADH may yield only 1.5 ATP each if using glycerol phosphate shuttle = 3 ATP total)

From FADH₂:

Krebs: 2 FADH₂ × 1.5 ATP = 3 ATP

From substrate-level phosphorylation:

Glycolysis: 2 ATP
Krebs: 2 ATP (or GTP)
Subtotal: 4 ATP

Total (using malate-aspartate shuttle): $\text{Total} = 25 + 3 + 4 = 32 \text{ ATP}$

Total (using glycerol phosphate shuttle): $\text{Total} = 23 + 3 + 4 = 30 \text{ ATP}$

$\boxed{\text{Total ATP: 30-32 per glucose (most commonly cited: 30-38)}}$

Note: Older textbooks cite 36-38 ATP using 3 ATP/NADH and 2 ATP/FADH₂. Modern estimates (accounting for proton leak and ATP/ADP transport) are lower: ~30-32 ATP.

Summary Table:

| Stage | Location | ATP | NADH | FADH₂ | CO₂ | |-------|----------|-----|------|-------|-----| | Glycolysis | Cytoplasm | 2 | 2 | 0 | 0 | | Pyruvate ox. | Matrix | 0 | 2 | 0 | 2 | | Krebs | Matrix | 2 | 6 | 2 | 4 | | ETC | Inner membrane | ~26 | 0 | 0 | 0 | | TOTAL | | ~30 | | | 6 |

Efficiency:

Glucose: 686 kcal/mol
ATP: 7.3 kcal/mol
Efficiency: (30 × 7.3) / 686 = ~32%
Rest lost as heat (maintains body temperature)

2Problem 2easy

❓ Question:

💡 Show Solution

Cellular Respiration Overview:

$\text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} + \text{ATP}$

(a) Four stages:

Glycolysis
Pyruvate Oxidation (transition reaction)
Krebs Cycle (Citric Acid Cycle)
Electron Transport Chain + Oxidative Phosphorylation

(b) Locations:

1. Glycolysis:

Location: Cytoplasm (cytosol)
Anaerobic (doesn't require O₂)

2. Pyruvate Oxidation:

Location: Mitochondrial matrix
Entry into mitochondria

3. Krebs Cycle:

Location: Mitochondrial matrix
Aerobic (requires O₂ indirectly)

4. Electron Transport Chain:

Location: Inner mitochondrial membrane (cristae)
Requires O₂ as final electron acceptor

(c) Products of each stage:

1. Glycolysis (glucose → 2 pyruvate):

ATP: 2 net (4 produced - 2 invested)
NADH: 2
Pyruvate: 2

2. Pyruvate Oxidation (2 pyruvate → 2 acetyl-CoA):

NADH: 2
CO₂: 2
Acetyl-CoA: 2

3. Krebs Cycle (2 turns, one per acetyl-CoA):

ATP (GTP): 2
NADH: 6
FADH₂: 2
CO₂: 4

4. Electron Transport Chain:

ATP: ~34 (from NADH and FADH₂)
H₂O: 6 (O₂ reduced)

(d) Total ATP yield:

From NADH:

Glycolysis: 2 NADH × 2.5 ATP = 5 ATP
Pyruvate oxidation: 2 NADH × 2.5 ATP = 5 ATP
Krebs: 6 NADH × 2.5 ATP = 15 ATP
Subtotal: 25 ATP

(Note: Glycolysis NADH may yield only 1.5 ATP each if using glycerol phosphate shuttle = 3 ATP total)

From FADH₂:

Krebs: 2 FADH₂ × 1.5 ATP = 3 ATP

From substrate-level phosphorylation:

Glycolysis: 2 ATP
Krebs: 2 ATP (or GTP)
Subtotal: 4 ATP

Total (using malate-aspartate shuttle): $\text{Total} = 25 + 3 + 4 = 32 \text{ ATP}$

Total (using glycerol phosphate shuttle): $\text{Total} = 23 + 3 + 4 = 30 \text{ ATP}$

$\boxed{\text{Total ATP: 30-32 per glucose (most commonly cited: 30-38)}}$

Note: Older textbooks cite 36-38 ATP using 3 ATP/NADH and 2 ATP/FADH₂. Modern estimates (accounting for proton leak and ATP/ADP transport) are lower: ~30-32 ATP.

Summary Table:

Efficiency:

Glucose: 686 kcal/mol
ATP: 7.3 kcal/mol
Efficiency: (30 × 7.3) / 686 = ~32%
Rest lost as heat (maintains body temperature)

3Problem 3easy

❓ Question:

💡 Show Solution

Cellular Respiration Overview:

$\text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} + \text{ATP}$

(a) Four stages:

Glycolysis
Pyruvate Oxidation (transition reaction)
Krebs Cycle (Citric Acid Cycle)
Electron Transport Chain + Oxidative Phosphorylation

(b) Locations:

1. Glycolysis:

Location: Cytoplasm (cytosol)
Anaerobic (doesn't require O₂)

2. Pyruvate Oxidation:

Location: Mitochondrial matrix
Entry into mitochondria

3. Krebs Cycle:

Location: Mitochondrial matrix
Aerobic (requires O₂ indirectly)

4. Electron Transport Chain:

Location: Inner mitochondrial membrane (cristae)
Requires O₂ as final electron acceptor

(c) Products of each stage:

1. Glycolysis (glucose → 2 pyruvate):

ATP: 2 net (4 produced - 2 invested)
NADH: 2
Pyruvate: 2

2. Pyruvate Oxidation (2 pyruvate → 2 acetyl-CoA):

NADH: 2
CO₂: 2
Acetyl-CoA: 2

3. Krebs Cycle (2 turns, one per acetyl-CoA):

ATP (GTP): 2
NADH: 6
FADH₂: 2
CO₂: 4

4. Electron Transport Chain:

ATP: ~34 (from NADH and FADH₂)
H₂O: 6 (O₂ reduced)

(d) Total ATP yield:

From NADH:

Glycolysis: 2 NADH × 2.5 ATP = 5 ATP
Pyruvate oxidation: 2 NADH × 2.5 ATP = 5 ATP
Krebs: 6 NADH × 2.5 ATP = 15 ATP
Subtotal: 25 ATP

(Note: Glycolysis NADH may yield only 1.5 ATP each if using glycerol phosphate shuttle = 3 ATP total)

From FADH₂:

Krebs: 2 FADH₂ × 1.5 ATP = 3 ATP

From substrate-level phosphorylation:

Glycolysis: 2 ATP
Krebs: 2 ATP (or GTP)
Subtotal: 4 ATP

Total (using malate-aspartate shuttle): $\text{Total} = 25 + 3 + 4 = 32 \text{ ATP}$

Total (using glycerol phosphate shuttle): $\text{Total} = 23 + 3 + 4 = 30 \text{ ATP}$

$\boxed{\text{Total ATP: 30-32 per glucose (most commonly cited: 30-38)}}$

Note: Older textbooks cite 36-38 ATP using 3 ATP/NADH and 2 ATP/FADH₂. Modern estimates (accounting for proton leak and ATP/ADP transport) are lower: ~30-32 ATP.

Summary Table:

Efficiency:

Glucose: 686 kcal/mol
ATP: 7.3 kcal/mol
Efficiency: (30 × 7.3) / 686 = ~32%
Rest lost as heat (maintains body temperature)

4Problem 4hard

❓ Question:

Explain the chemiosmotic theory of ATP synthesis: (a) describe how the electron transport chain creates a proton gradient, (b) explain how ATP synthase uses this gradient to make ATP, and (c) calculate how many H⁺ must flow through ATP synthase to make one ATP.

💡 Show Solution

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

5Problem 5hard

❓ Question:

💡 Show Solution

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

6Problem 6hard

❓ Question:

💡 Show Solution

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

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