Cooperative protein unfolding. A statistical-mechanical model for the action of denaturants

Biophys Chem. 2018 Feb;233:19-25. doi: 10.1016/j.bpc.2017.12.001. Epub 2017 Dec 5.


Knowledge of protein stability is of utmost importance in various fields of biotechnology. Protein stability can be assessed in solution by increasing the concentration of denaturant and recording the structural changes with spectroscopic or thermodynamic methods. The standard interpretation of the experimental data is to assume a 2-state equilibrium between completely folded and completely unfolded protein molecules. Here we propose a cooperative model based on the statistical-mechanical Zimm-Bragg theory. In this model protein unfolding is driven by the weak binding of a rather small number of denaturant molecules, inducing the cooperative unfolding with multiple dynamic intermediates. The modified Zimm-Bragg theory is applied to published thermodynamic and spectroscopic data leading to the following conclusions. (i) The binding constant KD is correlated with the midpoint concentration, c0, of the unfolding reaction according to c0≅1/KD. The better the binding of denaturant the lower is the concentration to achieve unfolding. (ii) The binding constant KD agrees with direct thermodynamic measurements. A rather small number of bound denaturants suffices to induce the cooperative unfolding of the whole protein. (iii) Chemical unfolding occurs in the concentration range ΔcD=cend-cini. The theory predicts the unfolding energy per amino acid residue as gnu=RTKD(cend-cini). The Gibbs free energy of an osmotic gradient of the same size is ΔGDiff=-RTln(cend/cini). In all examples investigated ΔGDiff exactly balances the unfolding energy gnu. The total unfolding energy is thus close to zero. (iv) Protein cooperativity in chemical unfolding is rather low with cooperativity parameters σ≥3x10-3. As a consequence, the theory predicts a dynamic mixture of conformations during the unfolding reaction. The probabilities of individual conformations are easily accessible via the partition function Z(cD,σ).

Keywords: 2-state model; Chemical denaturation; Cooperativity; Osmotic gradient; Protein unfolding; Zimm-Bragg theory.

MeSH terms

  • Bacterial Proteins / chemistry
  • Chymotrypsin / chemistry
  • Hydrochloric Acid / chemistry
  • Hydrochloric Acid / pharmacology
  • Models, Statistical*
  • Muramidase / chemistry
  • Phosphoenolpyruvate Sugar Phosphotransferase System / chemistry
  • Protein Denaturation / drug effects*
  • Protein Unfolding / drug effects*
  • Thermodynamics*
  • Urea / chemistry
  • Urea / pharmacology


  • Bacterial Proteins
  • Urea
  • Phosphoenolpyruvate Sugar Phosphotransferase System
  • phosphocarrier protein HPr
  • Muramidase
  • Chymotrypsin
  • alpha-chymotrypsin
  • Hydrochloric Acid