Protein Stability─Analysis of Heat and Cold Denaturation without and with Unfolding Models

Protein stability is important in many areas of life sciences. Thermal protein unfolding is investigated extensively with various spectroscopic techniques. The extraction of thermodynamic properties from these measurements requires the application of models. Differential scanning calorimetry (DSC) is less common, but is unique as it measures directly a thermodynamic property, that is, the heat capacity; C; p; (; T; ). The analysis of; C; p; (; T; ) is usually performed with the chemical equilibrium two-state model. This is not necessary and leads to incorrect thermodynamic consequences. Here we demonstrate a straightforward model-independent evaluation of heat capacity experiments in terms of protein unfolding enthalpy Δ; H; (; T; ), entropy Δ; S; (; T; ), and free energy Δ; G; (; T; )). This now allows the comparison of the experimental thermodynamic data with the predictions of different models. We critically examined the standard chemical equilibrium two-state model, which predicts a positive free energy for the native protein, and diverges distinctly from the experimental temperature profiles. We propose two new models which are equally applicable to spectroscopy and calorimetry. The Θ; U; (; T; )-weighted chemical equilibrium model and the statistical-mechanical two-state model provide excellent fits of the experimental data. They predict sigmoidal temperature profiles for enthalpy and entropy, and a trapezoidal temperature profile for the free energy. This is illustrated with experimental examples for heat and cold denaturation of lysozyme and β-lactoglobulin. We then show that the free energy is not a good criterion to judge protein stability. More useful parameters are discussed, including protein cooperativity. The new parameters are embedded in a well-defined thermodynamic context and are amenable to molecular dynamics calculations.