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.