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Fatty Acids &
Energy Density

Explore the structure of fatty acids and triacylglycerols, understand why fats store more energy per gram than carbohydrates, and master the biochemistry of lipid energy.

Biochemistry

What Are Fatty Acids?

A fatty acid is a long hydrocarbon chain with a carboxyl group (\( \text{-COOH} \)) at one end. They are the building blocks of more complex lipids and a major source of metabolic fuel.

Hydrophobic Tail
Long chain of \( \text{-CH}_2\text{-} \) groups: nonpolar, insoluble in water
Carboxyl Head
\( \text{-COOH} \) group: polar, ionizable at physiological pH

Saturated vs Unsaturated

Saturated
\( \text{-COOH} \)
\( \text{CH}_3 \)
 No double bonds Straight chain Unsaturated cis
\( \text{-COOH} \)
\( \text{CH}_3 \)
 1+ double bonds Kinked chain

Common Fatty Acid Examples

Palmitic Acid
\( \text{C}_{16}\text{H}_{32}\text{O}_2 \) : 16 carbons, saturated, found in palm oil and animal fats
Oleic Acid
\( \text{C}_{18}\text{H}_{34}\text{O}_2 \) : 18 carbons, one double bond (mono-unsaturated), found in olive oil
Linoleic Acid
\( \text{C}_{18}\text{H}_{32}\text{O}_2 \) : 18 carbons, two double bonds (poly-unsaturated), essential fatty acid

What Are Triacylglycerols?

A triacylglycerol (TAG, also called triglyceride) is formed when three fatty acid chains are esterified to a single glycerol backbone. This is the primary storage form of fat in the body.

Glycerol Fatty Acid 1 (e.g., Palmitic) Fatty Acid 2 (e.g., Oleic) Fatty Acid 3 (e.g., Linoleic) ester ester ester
3 Ester bonds release 3 \( \text{H}_2\text{O} \) molecules

The Esterification Reaction

1
Hydroxyl groups on glycerol (\( \text{-OH} \)) react with carboxyl groups (\( \text{-COOH} \)) on each fatty acid.
2
An ester bond (\( \text{-COO-} \)) forms between glycerol and each fatty acid chain.
3
One molecule of water (\( \text{H}_2\text{O} \)) is released per bond: 3 bonds = 3 water molecules.

Why Fats Have Higher Energy Density

Energy density is the amount of energy stored per gram of fuel. Fats yield approximately \( 9 \text{ kcal/g} \) while carbohydrates and proteins yield only \( 4 \text{ kcal/g} \). This means fats store over twice as much energy per gram.

0 2 4 6 8 10
\( \text{kcal/g} \)
 9 Fat 4 Carbs 4 Protein

Three Reasons for Higher Energy

1
More C-H bonds: Fatty acids are highly reduced (rich in hydrogen). Each \( \text{C-H} \) bond releases energy when oxidized. Fats have far more \( \text{C-H} \) bonds per carbon than carbohydrates.
2
Lower oxidation state: Carbons in fatty acids have an average oxidation state near \( -2 \), while carbons in glucose average \( 0 \). More electrons are available for transfer to \( \text{O}_2 \).
3
Anhydrous storage: Fats are hydrophobic and stored without water. Glycogen binds ~2 g water per gram, effectively halving its energy density by weight.

Saturated vs Unsaturated Energy

Saturated fatty acids yield slightly more energy per gram than unsaturated ones because they have more \( \text{C-H} \) bonds (no double bonds replacing them). However, the difference is small.

Fatty Acid Carbons Double Bonds \( \Delta H_{\text{combustion}} \) (kJ/mol)
Stearic (C18:0) 18 0 11,290
Oleic (C18:1) 18 1 11,180
Linoleic (C18:2) 18 2 11,050

\( \beta \)-Oxidation Pathway

\( \beta \)-Oxidation is the metabolic process that breaks fatty acids into 2-carbon acetyl-CoA units in the mitochondrial matrix. Each cycle produces reducing equivalents that feed the electron transport chain.

Fatty Acyl-CoA
One Cycle of \( \beta \)-Oxidation
Oxidation \( \rightarrow \) \( \text{FADH}_2 \)
Hydration \( \rightarrow \) Oxidation \( \rightarrow \) \( \text{NADH} \)
Thiolysis \( \rightarrow \) Acetyl-CoA
\( \text{FADH}_2 \)
\( \text{NADH} \)
 Acetyl-CoA Shortened chain repeats
\( \rightarrow \) TCA Cycle

Calculating ATP Yield

For a 16-carbon saturated fatty acid (palmitate), \( \beta \)-oxidation runs 7 cycles, producing 8 acetyl-CoA units:

1
7 \( \text{FADH}_2 \) \( \times 1.5 \) ATP each = 10.5 ATP
2
\( 7 \text{ NADH} \) \( \times 2.5 \) ATP each = 17.5 ATP
3
8 Acetyl-CoA \( \times 10 \) ATP each (via TCA + ETC) = 80 ATP
4
Activation cost: \( -2 \) ATP equivalents (fatty acid activation to acyl-CoA)

How to Calculate Energy Yield

1
Count carbons in the fatty acid chain: \( n \)
2
Number of \( \beta \)-oxidation cycles: \( \frac{n}{2} - 1 \)
3
Acetyl-CoA produced: \( \frac{n}{2} \)
4
Total \( \text{FADH}_2 \): \( \frac{n}{2} - 1 \); Total NADH: \( \frac{n}{2} - 1 \)
5
Calculate ATP: \( (\text{FADH}_2 \times 1.5) + (\text{NADH} \times 2.5) + (\text{Acetyl-CoA} \times 10) - 2 \)

Example: Lauric Acid (\( \text{C}_{12} \))

Lauric acid has 12 carbons and is fully saturated. Let us calculate its ATP yield:

1
\( \beta \)-oxidation cycles: \( \frac{12}{2} - 1 = \) 5 cycles
2
Acetyl-CoA: \( \frac{12}{2} = \) 6 units
3
From \( \beta \)-oxidation: \( 5 \times 1.5 + 5 \times 2.5 = 7.5 + 12.5 = \) 20 ATP
4
From TCA cycle: \( 6 \times 10 = \) 60 ATP
5
Net: \( 20 + 60 - 2 = \) 78 ATP

Example: Palmitate vs Glucose

Compare the energy per gram from palmitate (\( \text{C}_{16}\text{H}_{32}\text{O}_2 \), MW = 256 g/mol) and glucose (\( \text{C}_6\text{H}_{12}\text{O}_6 \), MW = 180 g/mol):

Property Palmitate Glucose
ATP per molecule 106 ~32
Molecular weight (g/mol) 256 180
ATP per gram \( \frac{106}{256} \approx 0.41 \) \( \frac{32}{180} \approx 0.18 \)
Ratio \( \frac{0.41}{0.18} \approx 2.3\times \) more ATP per gram from fat

Example: Oleic Acid (Unsaturated)

Oleic acid (\( \text{C}_{18:1} \)): 18 carbons with 1 double bond.

1
Cycles: \( \frac{18}{2} - 1 = 8 \); Acetyl-CoA: \( \frac{18}{2} = 9 \)
2
\( \beta \)-oxidation: \( 8 \times 1.5 + 8 \times 2.5 = 12 + 20 = \) 32 ATP
3
TCA: \( 9 \times 10 = \) 90 ATP
4
Double bond penalty: \( -1.5 \) ATP (one existing double bond skips one \( \text{FADH}_2 \))
5
Net: \( 32 + 90 - 2 - 1.5 = \) 118.5 ATP

Common Mistakes

✕ Forgetting Activation Cost
The initial conversion of fatty acid to acyl-CoA costs 2 ATP equivalents. Always subtract 2 from your final answer.
✕ Wrong Cycle Count
A \( \text{C}_n \) fatty acid undergoes \( \frac{n}{2} - 1 \) cycles, not \( \frac{n}{2} \). The last thiolysis produces the final two acetyl-CoA units simultaneously.
✕ Ignoring Unsaturation
Each pre-existing double bond bypasses one \( \text{FADH}_2 \) step, so subtract 1.5 ATP per double bond from the total.

Summary Comparison

Feature Triacylglycerols Glycogen (Carbs)
Energy density ~9 kcal/g ~4 kcal/g
Water of hydration None (hydrophobic) ~2 g water per g glycogen
Oxidation state of C Highly reduced (~\(-2\)) Partially oxidized (~\(0\))
Primary storage site Adipose tissue Liver, skeletal muscle
Mobilization speed Slow (lipolysis) Fast (glycogenolysis)
ATP per gram ~0.41 ~0.18

Question 1 of 5

Fats yield approximately \( 9 \text{ kcal/g} \) while carbohydrates yield \( 4 \text{ kcal/g} \). Which is NOT a reason for this difference?

Question 2 of 5

How many cycles of \( \beta \)-oxidation are needed to completely oxidize a 14-carbon saturated fatty acid?

Question 3 of 5

A triacylglycerol is formed by the esterification of glycerol with three fatty acids. How many water molecules are released?

Question 4 of 5

What is the approximate net ATP yield from the complete oxidation of one molecule of palmitate (\( \text{C}_{16} \))?

Question 5 of 5

Compared to a saturated \( \text{C}_{18} \) fatty acid, an unsaturated \( \text{C}_{18} \) fatty acid with two double bonds would produce how much less ATP?