Extrapolation to water of kinetic and equilibrium data for the unfolding of barnase in urea solutions

Assumptions about the dependence of protein unfolding on the concentration of urea have been examined by an extensive survey of the equilibrium unfolding of barnase and many of its mutants measured by urea denaturation and differential scanning calorimetry. The free energy of equilibrium unfolding and the activation energy for the kinetics of unfolding of proteins are generally assumed to change linearly with [urea]. A slight downward curvature is detected, however, in plots of highly precise measurements of logku versus [urea] (where ku is the observed rate constant for the unfolding of barnase). The data fit the equation logku = logkuH2O* + mku*.[urea] - 0.014[urea]2, where mku* is a variable which depends on the mutation. The constant 0.014 was measured directly on four destabilized mutants and wild-type, and was also determined from a global analysis of data from > 60 mutants of barnase. Any equivalent deviations from linearity in the equilibrium unfolding are small and in the same region, as determined from measurements on 166 mutants. The free energy of unfolding of barnase, delta GU-F, appears significantly larger by 1.6 kcal mol-1 when measured by calorimetry than when determined by urea denaturation. However, the changes in delta GU-F on mutation, delta delta GU-F, determined by calorimetry and by urea denaturation are identical. We show analytically how, in general, the curvature in plots of activation or equilibrium energies against [denaturant] should not affect the changes of these values on mutation provided measurements are made over the same concentration ranges of denaturant and the curvature is independent of mutation.