Enthalpy-Entropy Compensation

Enthalpy-Entropy Compensation (EEC) is observed in many unrelated domains. It appears as a strong correlation of the variations ΔΔ H and ΔΔ S of enthalpy and entropy resulting from experiments performed either at different temperatures on a given system (e.g. the binding of a ligand on a macromolecule), or at the same temperature T on related systems (e.g. the binding of related ligands on a macromolecule). In both cases, EEC is characterized by the ‘compensation temperatures’ (ΔΔ H/ ΔΔ S ). When a continuous variable X (e.g. X = pH ) characterizes the related systems at constant temperature, Θ _T = ( ∂ Δ H/∂ Δ S ) _T may be used in lieu of the ratio of finite variations and when T is variable and X constant, one may always consider Θ _X = ( ∂ Δ H/∂ Δ S ) _X . Thermodynamics trivially imposes Θ _X ≡ T , but also Θ _T = T + δT ( X, T ), where the corrective term δT ( X, T ) only depends on Δ G ( X, T ). The quest for ‘molecular’ explanations of EEC is thus vain: only the value of Θ _T deserves such explanations. This is illustrated with the denaturation of globular proteins and with the dissociation of hydrophobic peptides from a specific protein. The theoretical estimate Θ _T = ( T − T *) /Ln ( T /T *) with T * ≃ 383 K being imposed by experiments, fits well experimental results. Considerations of molecular dynamics (MD) methods led to a theoretical estimate for Θ _T when no continuous variable X exists. One might obtain better MD estimates of Δ H and Δ S of binding by imposing the correct value of Θ _T .