Unit 1: Principles of biophysical chemistry and Carbohydrates

Biophysical chemistry applies the laws of physics and chemistry to biological molecules, explaining why macromolecules fold, how reactions proceed, and where cells obtain usable energy. This unit builds from the weak forces that stabilize structure, through the thermodynamics and kinetics that govern reactions, to carbohydrates as the first major biomolecule class.

• Governing principle: Living systems are open, non-equilibrium systems that obey thermodynamics; spontaneity is set by free energy, not by heat alone.
• Central quantities: Gibbs free energy (G), enthalpy (H), entropy (S), equilibrium constant (K), pH, and reaction rate constant (k).
• Structural basis: Biomolecular architecture is held together mostly by weak, reversible, non-covalent interactions acting in large numbers.
• Convention: Standard biochemical state is denoted with a prime (ΔG°′) and defined at 25 °C, 1 M solutes, pH 7.0, 55.5 M water.

II. Molecular Interactions and Acid–Base Environment

The physical forces and ionic conditions in which biomolecules exist.

A. Chemical bonds and stabilizing interactions

Covalent bonds define primary structure, while weak interactions dictate three-dimensional shape and reversibility.

• Covalent bonds: Shared electron pairs, ~200–500 kJ/mol; e.g. the C–C backbone and the peptide (amide) bond linking amino acids.
• Ionic (electrostatic) interactions: Attraction between opposite charges, energy scaling as 1/εr; salt bridges between –COO⁻ and –NH₃⁺ groups; weakened in high-dielectric water (ε ≈ 80).
• Hydrogen bonds: Sharing of an H between electronegative donor and acceptor (~10–30 kJ/mol); O–H···O in water, N–H···O=C in α-helices and β-sheets.
• Van der Waals forces: Weak, distance-dependent (~1/r⁶) transient dipole attractions; significant only at optimal contact distance (~0.3–0.4 nm).
• Hydrophobic effect: Not a bond but an entropy-driven clustering of nonpolar groups to minimize ordered water cages; the main driving force in protein folding and lipid bilayers.

B. pH and buffer

pH quantifies acidity and buffers resist its change, keeping enzymes and structures functional.

pH = -log[H⁺]
Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA])

• Symbols: [H⁺] = molar hydrogen-ion concentration; pKa = –log Ka, the pH at which [HA]=[A⁻].
• Buffer action: A weak acid/conjugate base pair neutralizes added acid or base; maximum buffering within pKa ± 1.
• Physiological buffers: Bicarbonate (H₂CO₃/HCO₃⁻, blood pH 7.4), phosphate (H₂PO₄⁻/HPO₄²⁻, intracellular), and protein histidine side chains (pKa ≈ 6).
• Worked example: For an acetate buffer, pKa 4.76, with [A⁻]/[HA] = 1, pH = 4.76 + log(1) = 4.76.

III. Thermodynamics and Energetics of Life

How cells account for energy and drive unfavourable reactions.

A. Bioenergetics

Bioenergetics is the quantitative study of energy transformations in living cells.

• First law: Energy is conserved; cells convert chemical bond energy into work and heat, never creating it.
• Second law: Total entropy of universe increases; cells stay ordered by exporting entropy (heat, disordered products) to surroundings.
• Energy currency: ATP hydrolysis (ATP → ADP + Pi) releases ΔG°′ ≈ –30.5 kJ/mol, linking exergonic and endergonic processes.

B. Free energy

Gibbs free energy predicts the direction and useful work of a reaction at constant temperature and pressure.

ΔG = ΔH - TΔS
ΔG = ΔG°′ + RT ln([products]/[reactants])
ΔG°′ = -RT ln K′eq

• Symbols: ΔH = enthalpy change; T = absolute temperature (K); ΔS = entropy change; R = 8.314 J/mol·K; K′eq = equilibrium constant.
• Interpretation:
  • ΔG < 0: Exergonic, spontaneous.
  • ΔG > 0: Endergonic, requires energy input.
  • ΔG = 0: System at equilibrium.
• Key point: ΔG°′ is fixed for a reaction, but actual ΔG depends on real concentrations, so cells drive reactions by keeping ratios far from equilibrium.

C. Group transfer and coupled reaction

Endergonic reactions become feasible when coupled to a strongly exergonic one, usually via transfer of a chemical group.

• Group transfer potential: The tendency of a compound to donate a group (e.g. phosphoryl from ATP, acyl from acetyl-CoA); measured by ΔG°′ of hydrolysis.
• Coupling rule: Two reactions sharing a common intermediate add their free energies: ΔG_total = ΔG₁ + ΔG₂.
• Example — glucose phosphorylation:
  • Glucose + Pi → glucose-6-P: ΔG°′ = +13.8 kJ/mol (unfavourable).
  • ATP → ADP + Pi: ΔG°′ = –30.5 kJ/mol.
  • Coupled: ΔG°′ = –16.7 kJ/mol, so the reaction proceeds.
• High-energy compounds: Phosphoenolpyruvate (–61.9 kJ/mol) and 1,3-bisphosphoglycerate (–49.3 kJ/mol) sit above ATP and can phosphorylate ADP.

D. Biological energy transducers

Energy transducers convert one energy form into another usable by the cell.

• Mitochondria: Convert redox energy of NADH/FADH₂ into a proton gradient, then into ATP via oxidative phosphorylation.
• Chloroplasts: Transduce light energy into chemical energy (ATP, NADPH) during photosynthesis.
• ATP synthase: A rotary molecular motor using the proton-motive force (Δp) to synthesize ATP; couples electrochemical to chemical energy.
• Membrane pumps: Na⁺/K⁺-ATPase converts ATP energy into transmembrane ion gradients (electrical/osmotic work).

IV. Reaction Kinetics

The rates of reactions and factors controlling them.

A. Rate laws and order

Kinetics measures how fast reactions occur, independent of thermodynamic favourability.

Rate = k[A]^m[B]^n
First order: ln[A] = ln[A]₀ - kt

• Symbols: k = rate constant; m, n = reaction orders; [A]₀ = initial concentration; t = time.
• Order: Zero, first, or second order describes how rate depends on concentration; overall order = m + n.
• Activation energy (Ea): Energy barrier of the transition state; Arrhenius relation k = A·e^(–Ea/RT) shows rate rising with temperature and falling with Ea.

B. Enzyme catalysis

Enzymes accelerate reactions by lowering Ea without altering ΔG or equilibrium.

Michaelis–Menten: v = Vmax[S] / (Km + [S])

• Symbols: v = velocity; Vmax = maximum rate at saturating substrate; [S] = substrate concentration; Km = substrate concentration at half-Vmax.
• Km meaning: Low Km indicates high substrate affinity; catalytic efficiency = kcat/Km.
• Key distinction: Catalysts change kinetics (rate) only; they never make an endergonic reaction spontaneous.

V. Carbohydrates

Polyhydroxy aldehydes and ketones, the primary energy and structural sugars.

• General formula: (CH₂O)n for many monosaccharides.
• Functional groups: Aldehyde (aldoses) or ketone (ketoses) plus multiple hydroxyls.

A. Stereoisomerism in sugars

Sugars have chiral centres, producing multiple three-dimensional isomers with distinct biological roles.

• Chiral carbon: A carbon bearing four different groups; number of stereoisomers = 2ⁿ (n = chiral centres); glucose (4 centres) → 16 isomers.
• D and L forms: Assigned by the hydroxyl on the highest-numbered asymmetric carbon relative to D-glyceraldehyde; most natural sugars are D.
• Enantiomers vs diastereomers: Enantiomers are mirror images (D-/L-glucose); diastereomers differ at one or more but not all centres.
• Epimers: Diastereomers differing at a single carbon; glucose and galactose are C-4 epimers, glucose and mannose C-2 epimers.
• Anomers: α and β forms differing at the new anomeric carbon formed on cyclization; α-D-glucose and β-D-glucose interconvert by mutarotation.

B. Classification of carbohydrates

Carbohydrates are classified by the number of sugar units on hydrolysis.

• Monosaccharides: Single sugar units, non-hydrolysable; e.g. glucose, fructose.
• Oligosaccharides: 2–10 units; disaccharides are the commonest.
• Polysaccharides: Many units (hundreds–thousands); e.g. starch, cellulose.
• Further descriptors: By functional group (aldose/ketose) and by carbon number (triose, pentose, hexose).

C. Monosaccharides

Monosaccharides are the simplest sugars and the building blocks of all larger carbohydrates.

• Glucose (C₆H₁₂O₆): An aldohexose; primary blood sugar and metabolic fuel; cyclizes to a six-membered pyranose ring.
• Fructose: A ketohexose; forms a five-membered furanose ring; sweetest natural sugar.
• Ribose and deoxyribose: Aldopentoses forming the sugar backbone of RNA and DNA respectively.
• Ring formation: Intramolecular reaction of a hydroxyl with the carbonyl gives a hemiacetal (aldose) or hemiketal (ketose), creating the anomeric carbon.

D. Disaccharides

Disaccharides form when two monosaccharides join through a glycosidic bond with loss of water.

• Glycosidic bond: An O-linkage between the anomeric carbon of one sugar and a hydroxyl of another.
• Maltose: Glucose + glucose, α(1→4); reducing sugar with a free anomeric carbon.
• Lactose: Galactose + glucose, β(1→4); the reducing "milk sugar".
• Sucrose: Glucose + fructose, α,β(1→2); non-reducing because both anomeric carbons are engaged in the bond.

E. Polysaccharides

Polysaccharides are long polymers serving storage or structural roles, distinguished by monomer, linkage, and branching.

1. Storage polysaccharides:
   • Starch: Plant glucose store; amylose (linear α1→4) and amylopectin (branched α1→4 with α1→6 branches).
   • Glycogen: Animal glucose store; like amylopectin but more highly branched for rapid mobilization.
2. Structural polysaccharides:
   • Cellulose: Linear β(1→4) glucose chains; hydrogen-bonded into rigid fibrils; indigestible to humans lacking cellulase.
   • Chitin: β(1→4) N-acetylglucosamine; forms arthropod exoskeletons and fungal cell walls.
   • Linkage significance: The α versus β configuration alone determines whether glucose polymers become digestible fuel (starch) or rigid structure (cellulose).