The energetics and cooperativity of protein folding: a simple experimental analysis based upon the solvation of internal residues

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Abstract
The reversible unfolding of two dissimilar proteins, phosphoglycerate kinase from Bacillus stearothermophilus (PGK) and Staphylococcus aureus nuclease (SAN), was induced with two denaturants, urea and guanidinium chloride (GuHCl). For each protein, structural transitions were monitored by intrinsic fluorescence intensity changes arising from a unique tryptophan residue. In the case of SAN the single, native tryptophan residue was used, whereas for PGK two versions, one with a tryptophan at position 315 and one at 379, were constructed genetically. The resultant folding curves were analyzed by considering the change in the solvation free energy of internal amino acid residues as the denaturant concentration was varied. We derive the following simple relationship: -RT ln K = delta Gw + n delta Gs,m[D]/Kden. + [D]) where K is the equilibrium constant describing the distribution of folded and unfolded forms at a given denaturant concentration [D], delta Gw is the free energy change for the transition in the absence of denaturant, and n is the number of internal side chains becoming exposed. delta Gs,m and Kden. are constants derived empirically from the solvation energies of model compounds and represent the behavior of an average internal side chain between 0 and 6 M GuHCl and 0 and 8 M urea. For proteins of known structure these values can easily be derived, and for others, average values in guanidinium chloride (delta Gs,m = 0.775 kcal/mol and Kden. = 5.4 M) or urea (delta Gs,m = 1.198 kcal/mol and Kden. = 25.25 M) can be used in the analysis. Results show that the parameters n and delta Gw are independent of the denaturant used for all 12 transitions studied. This supports the hypothesis that the unfolding activity of urea and GuHCl can be accounted for by their effect on the solvation energy of amino acid side chains which are buried in the folded but exposed in the unfolded protein. This simple analytical treatment allows the "cooperativity" of protein folding to be interpreted in terms of the number of side chains becoming exposed to the solvent in a given step and allows accurate estimation of the free energy irrespective of the denaturant concentration needed to induce the transition.