“Cooperative collapse” of the denatured state revealed through Clausius-Clapeyron analysis of protein denaturation phase diagrams

Alexander Tischer, Venkata R. Machha, Jörg Rösgen, Matthew Auton

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Protein phase diagrams have a unique potential to identify the presence of additional thermodynamic states even when non-2-state character is not readily apparent from the experimental observables used to follow protein unfolding transitions. Two-state analysis of the von Willebrand factor A3 domain has previously revealed a discrepancy in the calorimetric enthalpy obtained from thermal unfolding transitions as compared with Gibbs-Helmholtz analysis of free energies obtained from the Linear Extrapolation Method (Tischer and Auton, Prot Sci 2013; 22(9):1147-60). We resolve this thermodynamic conundrum using a Clausius-Clapeyron analysis of the urea-temperature phase diagram that defines how ΔH and the urea m-value interconvert through the slope of cm versus T, ∂cm/∂T=ΔH/(mT). This relationship permits the calculation of ΔH at low temperature from m-values obtained through iso-thermal urea denaturation and high temperature m-values from ΔH obtained through iso-urea thermal denaturation. Application of this equation uncovers sigmoid transitions in both cooperativity parameters as temperature is increased. Such residual thermal cooperativity of ΔH and the m-value confirms the presence of an additional state which is verified to result from a cooperative phase transition between urea-expanded and thermally-compact denatured states. Comparison of the equilibria between expanded and compact denatured ensembles of disulfide-intact and carboxyamidated A3 domains reveals that introducing a single disulfide crosslink does not affect the presence of the additional denatured state. It does, however, make a small thermodynamically favorable free energy (∼–13 ± 1 kJ/mol) contribution to the cooperative denatured state collapse transition as temperature is raised and urea concentration is lowered. The thermodynamics of this “cooperative collapse” of the denatured state retain significant compensations between the enthalpy and entropy contributions to the overall free energy.

Original languageEnglish (US)
Article numbere23106
Issue number8
StatePublished - Aug 2018


  • Clausius-Clapeyron equation
  • denatured state collapse
  • disulfide bond
  • urea-temperature phase diagram
  • von Willebrand factor

ASJC Scopus subject areas

  • Biophysics
  • Biochemistry
  • Biomaterials
  • Organic Chemistry


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