- Explain the structure and function of the four classes of biomolecules
- Calculate enzyme reaction rates with the Michaelis–Menten equation
- Analyse reaction coupling to ATP hydrolysis using ΔG
A living cell is a tiny but very complex chemical factory: thousands of reactions per second run at just 37 °C, in a neutral medium, amazingly fast thanks to enzymes. In this lesson we apply earlier topics — thermodynamics, kinetics, acid–base equilibria and bonding — to biomolecules.
Carbohydrates
Monosaccharides — glucose (an aldohexose) and fructose (a ketohexose), both C₆H₁₂O₆ — exist in water mostly as rings. Two monosaccharides condense into a disaccharide through a glycosidic bond: C₆H₁₂O₆ + C₆H₁₂O₆ → C₁₂H₂₂O₁₁ + H₂O. Sucrose = glucose + fructose, maltose = 2 glucose, lactose = glucose + galactose. Polysaccharides (C₆H₁₀O₅)ₙ: starch (plant storage, α-1,4 and α-1,6 links), the more branched glycogen (animal storage) and cellulose (β-1,4 links, a structural material; humans lack an enzyme to break it down).
Photosynthesis (light, chlorophyll) and respiration — the same reaction in two directions
ΔfH°(C₆H₁₂O₆) = −1273.3 kJ/mol; the values for CO₂ and H₂O(l) are in the thermodynamics lesson table. Calculate ΔH° for the complete oxidation of glucose. How much heat does 1 g of glucose release?
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Per gram: 2802.5 / 180 ≈ 15.6 kJ/g (≈ 3.7 kcal/g) — the source of the roughly 4 kcal/g on food labels.
Lipids
Triglycerides are esters of glycerol with three fatty acids. Saturated acids (stearic C₁₇H₃₅COOH, palmitic C₁₅H₃₁COOH) have straight chains that pack tightly — animal fats are solid. In unsaturated acids (oleic C₁₇H₃₃COOH) a cis C=C bond kinks the chain — plant oils are liquid. Hydrogenation saturates the double bonds: C₁₇H₃₃COOH + H₂ → C₁₇H₃₅COOH (this is how margarine is made). Phospholipids have a hydrophilic “head” and two hydrophobic “tails”: in water they form the bilayer at the heart of cell membranes. Fats are the densest energy store: ≈ 9 kcal/g (≈ 37 kJ/g), against ≈ 4 kcal/g for carbohydrates and proteins.
Triolein, C₅₇H₁₀₄O₆, has 3 C=C bonds per molecule. How many grams of iodine (I₂, M = 253.8 g/mol) add to 100 g of triolein? This number measures how unsaturated a fat is.
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One I₂ per double bond: n(I₂) = 3 · 0.113 = 0.339 mol.
m(I₂) = 0.339 · 253.8 ≈ 86 g — the iodine value of triolein is ≈ 86.
Proteins and enzymes
Proteins are built from amino acids joined by peptide bonds and have four levels of structure. They transport (haemoglobin), build (collagen, keratin), defend (antibodies) and regulate (insulin), and most importantly act as enzymes. An enzyme binds its substrate at the active site (lock-and-key or induced-fit model) and lowers the activation energy. Every enzyme has an optimum temperature and pH: pepsin in the stomach works best at pH ≈ 2, trypsin in the intestine at pH ≈ 8.
Deriving the Michaelis–Menten equation. In E + S ⇌ ES → E + P, the concentration of the ES complex quickly becomes steady: k₁[E][S] = (k₋₁ + k₂)[ES]. Substituting [E]₀ = [E] + [ES] and v = k₂[ES] gives the formula below, with Vmax = k₂[E]₀ and Km = (k₋₁ + k₂) / k₁.
- vinitial rate of the enzyme reaction
- Vmaxmaximum rate, when all enzyme is saturated with substrate
- KmMichaelis constant: the [S] at which v = Vmax / 2; a small Km means high affinity
An enzyme has Km = 2.0 mmol/L and Vmax = 10 µmol/min. What is the rate at [S] = 2.0 and at 18 mmol/L?
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[S] = 18: v = 10 · 18 / (2.0 + 18) = 9.0 µmol/min — nine times more substrate raised the rate only 1.8-fold: the enzyme is close to saturation.
Nucleic acids
A nucleotide consists of a nitrogenous base, a pentose (deoxyribose in DNA, ribose in RNA) and a phosphate group. The two antiparallel strands of DNA are held together by complementary base pairs: A–T (2 hydrogen bonds) and G–C (3 hydrogen bonds). Hence Chargaff's rule: A = T and G = C. RNA has uracil (U) instead of thymine. Genetic information flows DNA → RNA → protein; each amino acid is encoded by a codon of three nucleotides (64 codons, 20 amino acids).
ATP — the cell's energy currency
ATP consists of adenine, ribose and three phosphate groups. Its hydrolysis releases energy: ATP + H₂O → ADP + Pᵢ, ΔG°′ ≈ −30.5 kJ/mol (more negative, about −50 kJ/mol, under cell conditions). A non-spontaneous reaction is coupled to ATP hydrolysis: the Gibbs energies add up and the total becomes negative. In respiration one glucose molecule yields about 30–32 ATP (older textbooks say 36–38), so roughly a third of the oxidation energy is stored in ATP.
Glucose + Pᵢ → glucose-6-phosphate + H₂O, ΔG°′ = +13.8 kJ/mol. The reaction is coupled to ATP hydrolysis. What is the overall ΔG°′?
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ΔG°′ = +13.8 + (−30.5) = −16.7 kJ/mol < 0 — the coupled reaction is spontaneous. This is Hess's law applied to Gibbs energy.
Key points
- Carbohydrates: monosaccharides join by glycosidic bonds; starch and glycogen store energy, cellulose is structural.
- Fats are glycerol esters, ≈ 9 kcal/g; phospholipids build the membrane bilayer.
- Enzymes lower Eₐ; v = Vmax[S] / (Km + [S]), and v = Vmax / 2 when [S] = Km.
- DNA: A–T (2 H bonds), G–C (3 H bonds); Chargaff's rule A = T, G = C.
- ATP + H₂O → ADP + Pᵢ, ΔG°′ ≈ −30.5 kJ/mol; in coupling the ΔG values add up.
Check yourself
10 questions. Every correct answer earns XP.