Protein stability as a function of denaturant concentration: the thermal stability of barnase in the presence of urea.

The conventional procedure for analyzing urea denaturation curves assumes that the free energy of unfolding (delta GU-F) is linearly related to [urea] that is, delta GU-F = delta GH2O(U-F)--m[urea], where m is a constant, specific for each protein, and delta GH2O(U-F) is the free energy of unfolding in water. This relationship can be measured directly, however, over only a small concentration range of approximately +/- 0.8 M urea around the midpoint of the unfolding transition. A nagging discrepancy (1.6 kcal mol-1) between delta GH2O(U-F) at 298 K of barnase extrapolated from such an equation and the equivalent value obtained from thermal unfolding measurements has stimulated a re-evaluation of the equation. Differential scanning calorimetric measurements have been made of the thermal unfolding of barnase in the presence of concentrations of urea between 0 and 4.5 M, the midpoint of the unfolding transition at 298 K, to test the denaturation equation over a wide range of [urea]. Values for delta GU-F at 298 K (delta G298U-F) for each concentration of urea were extrapolated from the calorimetrically measured enthalpies and the denaturational heat capacity change (delta Cdp) measured for that concentration of urea. A plot of delta G298U-F against [urea] deviates systematically from linearity and fits better the equation: delta G298U-F = 10.5 +/- 0.08 - ((2.65 +/- 0.05) x [urea]) + ((0.08 +/- 0.01) x [urea]2) kcal mol-1. The curvature in the plot leads to apparent values of m that increase when measurements are made at lower concentrations of urea. This could account for increases in m at low values of pH or in destabilized mutants since the protein denatures at lower concentrations of urea. It has been shown previously that small curvature in the free energy of unfolding versus [urea] leads to negligible errors in measurements of delta delta GU-F, the change in free energy of unfolding on mutation, providing that the curvature is similar for all mutants. The calorimetrically measured enthalpies of unfolding are decreased in the presence of urea while delta Cdp is increased. Both of these observations are consistent with an overall exothermic interaction between urea and protein with a net increase on unfolding.