Data from differential scanning calorimetry (DSC) may be used to estimate very large binding constants that cannot be conveniently measured by more conventional equilibrium techniques. Thermodynamic models have been formulated to describe interacting systems that involve either one thermal transition (protein-ligand) or two thermal transitions (protein-protein) and either 1:1 or higher binding stoichiometry. Methods are described for obtaining binding constants and heats of binding by two different methods: calculation or simulation fitting of data. Extensive DSC data on 2′CMP binding to RNase are presented and analyzed by the two methods. It is found that the methods agree when binding sites are completely saturated, but substantial errors arise in the calculation method when site saturation is incomplete and the transition of liganded molecules overlaps that of unliganded molecules. This arises primarily from an inability to determine TM (i.e., the temperature where concentrations of folded and unfolded protein are equal) under weak-binding conditions. Results from simulation show that the binding constants and heats of binding from the DSC method agree quantitatively with corresponding estimates obtained from equilibrium methods when extrapolated to the same temperature. It was also found from the DSC data that the binding constant decreases with increasing concentration of ligand, which might arise from nonideality effects associated with dimerization of 2′CMP. Simulations show that the DSC method is capable of estimating binding constants for ultratight interactions up to perhaps 1040 M−1 or higher, while most equilibrium methods fail well below 1010 M−1. DSC data from the literature on a number of interacting systems (trypsin-soybean trypsin inhibitor, trypsin-ovomucoid, trypsin-pancreatic trypsin inhibitor, chymotrypsin-subtilisin inhibitor, subtilisin BPN-subtilisin inhibitor, RNase S protein-RNase S peptide, avidin-biotin, ovotransferrin-Fe3+, superoxide dismutase-Zn2+, alkaline phosphatase-Zn2+, and assembly of regulatory and catalytic subunits of aspartate transcarbamoylase) were analyzed by simulation fitting or by calculation. Apparent single-site binding constants ranged from ca. 105 to 1020 M−1, while the interaction constant for assembly of aspartate transcarbamoylase was estimated as 1037 in molarity units. For most of these systems, the DSC interaction constants compared favorably with other literature estimates, for some it did not for reasons unknown, while for still others this represented the first estimate. Simulations show that for proteins having two binding sites for the same ligand within a single cooperative unit, ligand rearrangement will occur spontaneously during a DSC scan as the transition temperature of the unliganded protein is approached. The tendency is to form more of the unliganded and doubly liganded protein than is present at lower temperatures, which then leads to the absence of a transition for the singly liganded form. Although this tendency will always exist, it may not be expressed in systems where the kinetics for ligand rearrangement are slow relative to the experimental scan rate, in which case the ligand distribution will be frozen in the low-temperature configuration and a transition for the singly liganded form(s) might be seen. For the four systems of this type that were examined, only one (ovotransferrin-Fe3+) appeared to remain in a low-temperature configuration during scanning. © 1990, American Chemical Society. All rights reserved.
