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A model is proposed to account for the observation that the denaturation of small proteins apparently occurs in two kinetic phases. It is suggested that only one of these phases--the fast one--is actually an unfolding process. The slow phase is assumed to arise from the cis-trans isomerism of proline residues in the denaturated protein. From model compound data, it is shown that the expected rate for isomerism is in satisfactory agreement with the rates actually observed for protein folding. It is also shown that a simple model of protein unfolding based on the isomerism concept is very successful in accounting for many known experimental characteristics of the kinetics and thermodynamic of protein denaturation. Thus, the model is able to predict that two kinetic phases will be seen in the transition region while none are seen in the base-line regions, that both the fast and slow refolding phases lead to the native protein as the product, that the fast phase becomes the only observable phase for jumps ending far in the denatured base-line region, that most or all small proteins show a limiting low-temperature activation energy of ca. 20,000 cal, and that the relaxtion time for the slow phase seen in cytochrome c denaturation is much shorter than for all other small proteins. By utilizing "double-jump" experiments, it is shown directly that the slow phase is not part of the unfolding process but that it corresponds to a transition among two or more denatured forms which have identical spectroscopic (286.5 nm) properties. Thus, the slow relaxation is "invisible" except in the transition region where it couples to the fast unfolding equilibrium. Finally, since the present model assumes that only one of the major kinetic phases seen in denaturation reactions is concerned with the denaturation process per se, it is in agreement with numerous thermodynamic studies which show consistency with the two-state model for unfolding.

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 10(40) M-1 or higher, while most equilibrium methods fail well below 10(10) 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. 10(5) to 10(20) M-1, while the interaction constant for assembly of aspartate transcarbamoylase was estimated as 10(37) 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.(ABSTRACT TRUNCATED AT 400 WORDS)

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