Differential scanning calorimetry of proteins and Zimm–Bragg model in water

Differential Scanning Calorimetry (DSC) is a regular and powerful tool to measure the specific heat profile of various materials. Hydrogen bonds play a crucial role in stabilizing the three-dimensional structure of proteins. Naturally, information about the strength of hydrogen bonds is contained in the measured DSC profiles. Despite its obvious importance, there is no approach that would allow the extraction of such information from the heat capacity measurements. In order to connect the measured profile to microscopic properties of a polypeptide chain, a proper model is required to fit. Using recent advances in the Zimm–Bragg (ZB) theory of protein folding in water, we propose a new and efficient algorithm to process the DSC experimental data and to extract the H-bonding energy among other relevant constants. Thus, for the randomly picked set of 33 proteins, we have found a quite narrow distribution of hydrogen bonding energies from 1 to 8 kJ/mol with the average energy of intra-protein hydrogen bonds $\overline{h}=4.2\pm 1.5$ kJ/mol and the average energy of water–protein bonds as $\overline{h_{ps}}=3.8\pm 1.5$ kJ/mol. This is an important illustration of a tiny disbalance between the water–protein and intraprotein hydrogen bonds. Fitted values of the nucleation parameter $\sigma$ belong to the range from 0.001 to 0.01, as expected. The reported method can be considered as complementary to the classical two-state approach and together with other parameters provides the protein–water and intraprotein H-bonding energies, not accessible within the two-state paradigm.