Thermodynamics & Gibbs Free Energy

Introduction to Biological Thermodynamics

Thermodynamics is the study of energy transformations. In biological systems, every chemical reaction — from ATP synthesis to protein folding — is governed by thermodynamic principles. Understanding these principles allows us to predict whether reactions will occur spontaneously and how they can be coupled to drive otherwise unfavourable processes.

The Laws of Thermodynamics

The first law states that energy is conserved: it can be converted from one form to another but cannot be created or destroyed. In biology, chemical energy (stored in covalent bonds) is converted to mechanical work, heat, or electrochemical gradients.

The second law states that in any spontaneous process, the total entropy of the universe increases (ΔS_universe > 0). Entropy (S) is a measure of disorder or the number of available microstates. Biological organisms are highly ordered, but they maintain this order by increasing entropy in their surroundings — by releasing heat.

Gibbs Free Energy: The Biological Currency of Spontaneity

The Gibbs free energy (G) combines enthalpy and entropy into a single function that predicts spontaneity at constant temperature and pressure — the conditions of most biological reactions:

ΔG = ΔH − TΔS

Where:

• ΔH = change in enthalpy (heat content; negative if heat is released — exothermic)
• T = absolute temperature in Kelvin
• ΔS = change in entropy (positive if disorder increases)
• ΔG = change in Gibbs free energy

Interpretation:

• ΔG < 0: reaction is exergonic (spontaneous, releases free energy)
• ΔG > 0: reaction is endergonic (non-spontaneous, requires energy input)
• ΔG = 0: reaction is at equilibrium

It is critical to distinguish spontaneity from rate: a reaction may be thermodynamically spontaneous (ΔG < 0) yet occur extremely slowly in the absence of a catalyst. Thermodynamics predicts the direction; kinetics determines the rate.

Standard Free Energy Change (ΔG°)

The standard free energy change (ΔG°) is defined at standard conditions: 298 K (25°C), 1 M concentrations of all reactants and products, 1 atm pressure, pH 7.0 for biological systems (written ΔG°').

The relationship between ΔG°' and the equilibrium constant K_eq:

ΔG°' = −RT ln K_eq

Where R = 8.314 J mol⁻¹ K⁻¹ and T = 298 K. This means:

• If K_eq > 1 (products favoured at equilibrium), ΔG°' < 0
• If K_eq < 1 (reactants favoured), ΔG°' > 0

The actual free energy change under cellular conditions differs from ΔG°':

ΔG = ΔG°' + RT ln ([Products]/[Reactants])

This is vital: a reaction with a positive ΔG°' can be driven forward if the product-to-reactant ratio is kept very low (mass action).

ATP: The Universal Energy Currency

Adenosine triphosphate (ATP) is the primary energy currency of the cell. Its hydrolysis to ADP and inorganic phosphate (Pi) releases substantial free energy:

ATP + H₂O → ADP + Pi ΔG°' = −30.5 kJ/mol

Under cellular conditions (where [ATP]/[ADP][Pi] is maintained far from equilibrium by metabolism), the actual ΔG is more negative, typically −50 to −60 kJ/mol.

Why is ATP hydrolysis so exergonic?

1. Electrostatic repulsion: the three closely spaced phosphate groups carry multiple negative charges; hydrolysis relieves this repulsion
2. Resonance stabilisation: Pi and ADP are more resonance-stabilised than ATP
3. Hydration: water molecules stabilise the products

ATP occupies a unique intermediate position in the phosphoryl-transfer hierarchy. Compounds with higher phosphoryl-transfer potential than ATP (e.g., phosphoenolpyruvate, creatine phosphate) can donate their phosphoryl group to ADP to regenerate ATP. Compounds with lower potential (e.g., glucose-6-phosphate) accept phosphoryl groups from ATP.

Coupling Exergonic and Endergonic Reactions

Cells drive thermodynamically unfavourable (endergonic, ΔG > 0) reactions by coupling them to exergonic reactions so that the overall ΔG of the coupled process is negative.

Example: Glucose activation

Glucose + Pi → Glucose-6-phosphate + H₂O ΔG°' = +13.8 kJ/mol (unfavourable alone)

ATP + H₂O → ADP + Pi ΔG°' = −30.5 kJ/mol

Sum: Glucose + ATP → Glucose-6-phosphate + ADP ΔG°' = −16.7 kJ/mol (spontaneous)

The enzyme hexokinase catalyses this coupled reaction, which does not proceed as two separate steps but as a single concerted phosphoryl transfer. The key principle: the reactions must share a common intermediate (here, the phosphoryl group).

ATP Driving Biosynthesis

Biosynthetic reactions (anabolism) are generally endergonic — building complex molecules from simple precursors requires energy input. The cell couples these reactions to ATP hydrolysis.

Glutamine synthesis:

Glutamate + NH₄⁺ → Glutamine + H₂O ΔG°' = +14.2 kJ/mol (unfavourable)

Coupled with ATP hydrolysis → net ΔG°' ≈ −16 kJ/mol (favourable)

Protein synthesis requires hydrolysis of 4 high-energy bonds per peptide bond formed (2 ATP equivalents for aminoacyl-tRNA formation, and GTP hydrolysis during elongation).

Active transport: the Na⁺/K⁺-ATPase uses ATP hydrolysis to pump 3 Na⁺ out and 2 K⁺ in against their concentration gradients, maintaining the resting membrane potential. This consumes approximately 25–40% of cellular ATP.

Thermodynamic Control vs Kinetic Control

It is essential to distinguish thermodynamic and kinetic control of reactions:

• Thermodynamic control: the most stable product (lowest G) predominates; requires conditions where reversibility is possible
• Kinetic control: the product formed fastest (lowest activation energy pathway) predominates; common when reactions are irreversible or activation energies differ greatly

Most biological reactions are under kinetic control via enzyme catalysis — enzymes lower the activation energy (ΔG‡) without changing the thermodynamic driving force (ΔG).

Entropy in Biological Systems

Entropy contributions are central to many biological phenomena:

• Protein folding: the hydrophobic effect is entropy-driven. Burying hydrophobic residues releases ordered water molecules from the hydration shell, dramatically increasing system entropy (ΔS_system > 0), even though the protein itself becomes more ordered
• Membrane formation: lipid bilayer self-assembly is driven by the entropic gain of releasing water molecules from hydrophobic alkyl chains
• Receptor-ligand binding: conformational entropy loss in the receptor or ligand upon binding opposes binding; this is why rigid ligands often have higher affinity

Clinical Relevance: Thermodynamics in Metabolic Disease

Metabolic uncoupling: brown adipose tissue expresses uncoupling protein 1 (UCP1/thermogenin), which dissipates the proton gradient across the inner mitochondrial membrane as heat rather than driving ATP synthesis. This is thermogenic and important in neonatal heat production and cold adaptation. Pharmacological uncouplers (e.g., 2,4-dinitrophenol, historically misused as a weight-loss drug) can be lethal due to hyperthermia.

Phosphofructokinase deficiency: PFK catalyses a key irreversible step in glycolysis (ΔG°' ≈ −14 kJ/mol). Deficiency impairs glycolytic flux, causing exercise intolerance and haemolytic anaemia.

Thermodynamics of hypoxia: when O₂ is absent, cells cannot complete oxidative phosphorylation and ATP production falls dramatically. The cell shifts to anaerobic glycolysis (net 2 ATP/glucose vs ~30 ATP aerobically). The resulting ATP deficit and lactate accumulation underlie ischaemic injury.