Unit 3: Thermodynamics of biomolecules

Biomolecular structure and function are governed by the drive toward minimum Gibbs free energy under the near-constant temperature and pressure of the cell. This unit treats the macromolecule as a thermodynamic system whose folded, functional state is a delicate balance of large, opposing enthalpic and entropic contributions.

• Governing relation: the sign of ΔG = ΔH − TΔS decides spontaneity; a process proceeds when ΔG < 0.
• Marginal stability convention: native proteins sit at ΔG_fold ≈ −20 to −60 kJ/mol, small differences between huge (~1000s kJ/mol) enthalpic and entropic terms.
• Reference state: the unfolded (denatured) ensemble is taken as the baseline against which the folded state is measured.
• Weak-force premise: stability arises from many non-covalent interactions (H-bonds, van der Waals, electrostatics, hydrophobic effect), each of order a few kJ/mol.
• Water is a participant: solvent entropy, not just solute enthalpy, drives folding — the hydrophobic effect is fundamentally entropic.
• Two-state assumption: many small proteins fold cooperatively, populating only Native (N) and Unfolded (U) states at equilibrium.

II. Thermodynamics of Biomolecular Structures

Energetics that stabilise nucleic acids and folded macromolecules

Biomolecular architecture is the macroscopic expression of free-energy minimisation across many weak interactions and solvent reorganisation.

A. Free energy, enthalpy and entropy of structure

The stable conformation is the one minimising total system free energy including solvent.

• Enthalpic stabilisation (ΔH < 0): formation of hydrogen bonds and van der Waals contacts releases heat; e.g. each backbone H-bond contributes ~4–8 kJ/mol in a folded context.
• Conformational entropy (ΔS_conf < 0 on folding): ordering the chain into one geometry costs ~−2 to −4 kJ/mol per residue, opposing structure.
• Solvent entropy (ΔS_solv > 0): burying non-polar groups releases ordered water, the dominant favourable term.
• Electrostatics: governed by Coulomb's law screened by dielectric,
  
  TEXT

  E = q1·q2 / (4π·ε0·εr·r)

  
  where εr ≈ 2–4 in a protein core versus ~80 in water, so buried salt bridges are strong but desolvation-costly.

B. The hydrophobic effect

Non-polar sequestration is the primary organising force of folded structures and membranes.

• Origin: water forms a low-entropy clathrate cage around non-polar surfaces; aggregation of these surfaces frees that water.
• Sign of terms: near room temperature ΔH ≈ 0, ΔS > 0, so ΔG_transfer < 0 is entropy-driven.
• Quantitation: burial scales with surface area, ~−0.1 to −0.2 kJ/mol per Ų of buried non-polar surface.
• Structural consequence: hydrophobic residues (Leu, Ile, Val, Phe) partition to the interior; polar residues face solvent.

C. Nucleic acid stability

Base stacking and pairing set the free energy of duplex DNA/RNA.

• Stacking: van der Waals and hydrophobic stacking of bases, not just pairing, dominates duplex enthalpy.
• Pairing: G·C (three H-bonds) is more stable than A·T (two), raising melting temperature Tm.
• Melting: at Tm, ΔG = 0 so Tm = ΔH / ΔS; higher G+C content and salt raise Tm.
• Electrostatics: the phosphate backbone's negative charge is screened by counter-ions (Na⁺, Mg²⁺); low salt destabilises the duplex.

III. Protein Folding: Thermodynamics and Kinetics

How the sequence reaches, and how fast it reaches, the native fold

Folding is described both by the equilibrium free-energy difference between states and by the rate of interconversion along the folding pathway.

A. Thermodynamics of folding

The native fold is the global free-energy minimum encoded by the sequence.

• Anfinsen's principle: native structure is thermodynamically determined by the amino-acid sequence (ribonuclease refolding, 1961).
• Two-state equilibrium:
  
  TEXT

  U ⇌ N ,  K = [N]/[U] ,  ΔG_fold = −RT ln K

  
  R = 8.314 J·mol⁻¹·K⁻¹, T in kelvin.
• Marginal stability: net ΔG_fold is small because large ΔH and TΔS nearly cancel — proteins are only ~20–60 kJ/mol more stable than unfolded.
• Heat capacity change: folding gives ΔCp > 0 (buried non-polar surface exposed on unfolding); this makes ΔG_fold(T) a downward-curving parabola.
• Cold and heat denaturation: because of ΔCp, stability peaks near ~25 °C and falls at both high and low temperature.
• Denaturants: urea and guanidinium chloride shift ΔG linearly:
  
  TEXT

  ΔG(D) = ΔG(water) − m·[D]

  
  m measures surface exposed on unfolding.

B. Kinetics of folding

Folding rate is set by the height of the free-energy barrier, independent of final stability.

• Levinthal's paradox: random search of ~3^100 conformations would take longer than the universe, yet folding takes µs–s; therefore folding follows directed pathways, not random search.
• Energy landscape ("folding funnel"): a rugged funnel biases the ensemble downhill toward N; width = entropy, depth = energy.
• Transition state (‡): the rate-limiting ensemble; rate follows
  
  TEXT

  k = A·exp(−ΔG‡ / RT)

• Intermediates: molten globule states — compact, native-like secondary structure but fluid side chains — populate many folding routes.
• Φ-value analysis: mutations probe how native-like the transition state is; Φ ≈ 1 means that region is folded at ‡, Φ ≈ 0 means unfolded.
• Chaperones: GroEL/GroES and Hsp70 lower kinetic traps and prevent aggregation without changing the native ΔG.

Worked example (stability): if K = 100 at 310 K, then ΔG_fold = −(8.314)(310)ln(100) = −11.9 kJ/mol, confirming marginal stability.

C. Thermodynamics versus kinetics contrasted

The two frameworks answer different questions about the same reaction.

1. Thermodynamic control: compares only U and N; predicts which state is favoured via ΔG_fold; path-independent.
2. Kinetic control: compares U and ‡; predicts how fast and by what route; can trap a protein in a metastable, non-native state (e.g. amyloid) that is kinetically accessible though thermodynamically off-pathway.

IV. Functional Design of Proteins

How thermodynamic principles are tuned to produce biological function

Function requires more than a stable fold: sequences are selected so that structure, dynamics and binding energetics deliver activity.

A. Structure–stability trade-off for function

Proteins are only marginally stable because function demands flexibility.

• Reason for marginality: a too-rigid, over-stable protein cannot undergo the conformational changes that catalysis and signalling require.
• Local instability: active-site loops are often the least stable regions, poised to move.
• Turnover: marginal stability lets cells degrade and regulate proteins on physiological timescales.

B. Binding energetics and specificity

Function is realised through the free energy of ligand binding.

• Binding free energy:
  
  TEXT

  ΔG_bind = −RT ln Ka ,  Ka = [PL]/([P][L])

• Enthalpy–entropy compensation: tighter enthalpic contacts often incur greater entropic cost (loss of motion, ordered water), so ΔG changes less than either term.
• Induced fit vs lock-and-key: binding may pay a conformational cost (ΔG_conf > 0) recovered by strong interface contacts.
• Electrostatic complementarity: charged pockets match ligand charge, with desolvation penalties built into the design.

C. Catalytic design

Enzymes are engineered to stabilise the transition state, not the substrate.

• Rate enhancement: enzymes lower ΔG‡; stabilising ‡ by ~30 kJ/mol gives ~10⁵-fold rate increase.
• Preorganisation: the active site is pre-arranged so binding the transition state costs little reorganisation entropy.
• Proximity and orientation: substrates are held so as to reduce the entropic cost of reaching ‡.

D. Cooperativity and allostery

Multi-subunit proteins couple binding events thermodynamically for regulation.

• Cooperative binding: ligand at one site alters affinity at another (haemoglobin O₂ binding, Hill coefficient ~2.8).
• MWC two-state model: proteins interconvert between low-affinity (T) and high-affinity (R) states; ligand shifts the T⇌R equilibrium.
• Allosteric coupling: effector binding at a distant site changes ΔG at the active site, tuning activity without covalent change.

E. Design principles summarised through folding energetics

Natural selection tunes the same weak forces that drive folding to encode function.

• Sequence-encoded specificity: the interior packing and surface charge pattern jointly set both fold and binding partners.
• Robustness with adaptability: conserved core residues maintain the fold while variable surface residues evolve new functions.
• Frustration: local energetic conflicts left in the design are not defects but the seats of dynamics, catalysis and allostery.