Folding energetics of ligand binding proteins. I. Theoretical model

Heat capacity curves as obtained from differential scanning calorimetry are an outstanding source for molecular information on protein folding and lig and-binding energetics. However, deconvolution of C-p data of proteins in t he presence of ligands can be compromised by indeterminacies concerning the correct choice of the statistical thermodynamic ensemble. By convent, the assumption of constant free ligand concentration has been used to derive fo rmulae for the enthalpy. Unless the ligand occurs at large excess, this ass umption is incorrect. Still the relevant ensemble is the grand canonical en semble. We derive formulae for both constraints, constancy of total or free ligand concentration and illustrate the equations by application to the ty pical equilibrium Nx=N+x=D+x. It is demonstrated that as long as the thermo dynamic properties of the ligand can be completely corrected for by perform ing a reference measurement, the grand canonical approach provides the prop er and mathematically significantly simpler choice. We demonstrate on the t wo cases of sequential or independent ligand-binding the fact, that similar binding mechanisms result in different and distinguishable heat capacity e quations. Finally, we propose adequate strategies for DSC experiments as we ll as for obtaining first estimates of the characteristic thermodynamic par ameters, which can be used as starting values in a global fit of DSC data. (C) 2001 Academic Press.