Folding intermediates of wild-type and mutants of barnase. I. use of φ-value analysis and m-values to probe the cooperative nature of the folding pre-equilibrium

It is difficult to determine whether transient folding intermediates have a cooperative (or first-order) folding transition without measuring their rates of formation directly. An intermediate I could be formed by a second-order transition from a denatured state D that is progressively changed into I as conditions are changed. We have not been able to monitor the rate of formation of the folding intermediate of barnase directly, but have analysed its reactivity and the equilibrium constant for its formation over a combination of wide ranges of temperature, concentration of denaturant and structural variation. Phase diagrams have been constructed for wild-type and 16 mutant proteins to map out the nature of the energy landscape of the denatured state. The free energy of unfolding of I, Δ G D-I, changes with [urea] according to a highly cooperative transition. Further, m D-I(=δΔ G D-I/δ[urea]) for wild-type and several mutants is relatively insensitive to temperature, as would be expected for an intermediate that is formed cooperatively, rather than one that melts out according to a second-order transition. The φ-values for the formation of I change abruptly through the folding transitions rather than have the smooth changes expected for a second-order transition. There is a subset of mutants for which both m D-I and φ-value analysis indicate that a second intermediate becomes populated close to the melting temperatures of the native proteins. The folding intermediate of barnase is, thus, a relatively discrete and compact entity which is formed cooperatively.