The heat capacity paradox of ligand binding proteins: reconciling the microscopic and macroscopic world

Differential scanning microcalorimetry (DSC) is a superb method for the analysis of protein energetics. However, the relative simplicity of application has led astray many to assume that a proper analysis of the data was possible without a sound knowledge of the underlying statistical thermodynamic principles. In this study, the question is addressed of how to calculate properly the heat capacity signal of a protein in the presence of high affinity ligands. It is shown that the signal corresponds neither to grand canonic nor to canonic heat capacity. Statistical thermodynamic model calculations result only in the observed macroscopic heat capacity signal, if the protein in the calorimetric cell is assumed to form a grand canonic ensemble (T, p, mu controlled) which is, however, heated under constraints typical for a canonic ensemble (T, p, N controlled). As a consequence, the microscopic statistical thermodynamic heat capacity must be carefully distinguished from the macroscopically observable thermodynamic heat capacity in those cases where proteins unfold in the presence of high affinity ligands.