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 concentra tion of urea have been examined by an extensive survey of the equilibr ium unfolding of barnase and many of its mutants measured by urea dena turation and differential scanning calorimetry. The free energy of equ ilibrium unfolding and the activation energy for the kinetics of unfol ding of proteins are generally assumed to change linearly with [urea]. A slight downward curvature is detected, however, in plots of highly precise measurements of logk(u) versus [urea] (where k(u) is the obser ved rate constant for the unfolding of barnase). The data fit the equa tion logk(u) = logk(u)(H2O) + m(ku)* [urea] - 0.014[urea]2, where m(k u) is a variable which depends on the mutation. The constant 0.014 wa s measured directly on four destabilized mutants and wildtype, and was also determined from a global analysis of data from >60 mutants of ba rnase. Any equivalent deviations from linearity in the equilibrium unf olding are small and in the same region, as determined from measuremen ts on 166 mutants. The free energy of unfolding of barnase, Delta G(U- F), appears significantly larger by 1.6 kcal mol(-1) when measured by calorimetry than when determined by urea denaturation. However, the ch anges in Delta G(U-F) on mutation, Delta Delta G(U-F), determined by c alorimetry and by urea denaturation are identical. We show analyticall y 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 concen tration ranges of denaturant and the curvature is independent of mutat ion.