A quantitative treatment of the kinetics of the folding transition of ribonuclease A

New experimental data and a quantitative theoretical treatment are given for the kinetics of the thermal folding transition of ribonuclease A at pH 3.0. A three-species mechanism is used as a starting point for the analysis: U1 (slow) in equilibrium U2(fast) in equilibrium N, where U1 and U2 are two forms of the unfolded enzyme with markedly different rates of refolding and N is the native enzyme. This mechanism is based on certain facts established in previous studies of refolding. The kinetics of unfolding and refolding show two phases a fast phase and a slow phase, over a range of temperatures extending above the transition midpoint, Tm. The three-species mechanism can be used in this range. At higher temperatures a new much faster kinetic phase is also observed corresponding to the transient formation of a new intermediate (I). Although the general solution for a four-species mechanism is complex it is not difficult to extend the three-species analysis for the special case found here, in which the fast reaction (I in equilibrium N) is well separated from the other two reactions. At temperatures below the transition zone the slow phase of refolding becomes kinetically complex. No attempt has been made to extend the analysis to include this effect. The basic test of the three-state analysis is the prediction as a function of temperature of alpha2, the relative amplitude of the fast phase, both for unfolding and refolding. At temperatures above Tm for which the three-state analysis must be extended to include the new intermediate I, a crresponding quanitity alpha2(cor) is predicted and compared with measured values. Data used in the three-state prediction are values of tau2 and tau1, the time constants of the fast and slow kinetic phases, plus a single value of alpha2 measured when tau2 and tau1 are well separated. The observed and predicted values of alpha2 agree within experimental error. The analysis predicts correctly that, for these experiments, alpha2 should have the same value in unfolding as in refolding in the final conditions. The analysis also predicts satisfactorily the equilibrium transition curve from kinetic data alone. Four striking properties of the kinetics are explained or correlated by the analysis: (a) the drop in alpha2 to a minimum near Tm as well as the delayed rise in alpha2 above Tm;(b) the vanishing of alpha1 above the transition zone; (c) the sharp drop in tau1 inside the transition zone followed by a partial leveling off outside this zone; and (d) the passage of tau2 through a maximum near Tm. Through a comparison of observed and predicted values of alpha2, the analysis also rules out the alternative three-species mechanism U1 (slow) in equilibrium N (fast) in equilibrium U2. Finally, the temperature dependence of the amplitude for the fast reaction (I in equilibrium N) is discussed; the behavior of I is like that of U2 and I may be an unfolded species populated at equilibrium...