Molecular Understanding of Calorimetric Protein Unfolding Experiments

Protein unfolding is a dynamic cooperative equilibrium between short lived protein conformations. The Zimm-Bragg theory is an ideal algorithm to handle cooperative processes. Here, we extend the analytical capabilities of the Zimm-Bragg theory in two directions. First, we combine the Zimm-Bragg partition function Z(T) with statistical-mechanical thermodynamics, explaining the thermodynamic system properties enthalpy, entropy and free energy with molecular parameters only. Second, the molecular enthalpy h0 to unfold a single amino acid residue is made temperature-dependent. The addition of a heat capacity term cv allows predicting not only heat denaturation, but also cold denaturation. Moreover, it predicts the heat capacity increase ΔC0p in protein unfolding. The theory is successfully applied to differential scanning calorimetry experiments of proteins of different size and structure, that is, gpW62 (62aa), ubiquitin (74aa), lysozyme (129aa), metmyoglobin (153aa) and mAb monoclonal antibody (1290aa). Particular attention was given to the free energy, which can easily be obtained from the heat capacity Cp(T). The DSC experiments reveal a zero free energy for the native protein with an immediate decrease to negative free energies upon cold and heat denaturation. This trapezoidal shape is precisely reproduced by the Zimm-Bragg theory, whereas the so far applied non-cooperative 2-state model predicts a parabolic shape with a positive free energy maximum of the native protein. We demonstrate that the molecular parameters of the Zimm-Bragg theory have a well-defined physical meaning. In addition to predicting protein stability, independent of protein size, they yield estimates of unfolding kinetics and can be connected to molecular dynamics calculations.