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

Abstract

New experimental data and a quantitative theoretical treatment are given for the kinetics of the thermal folding transition of RNase A at pH 3.0. A 3-species mechanism is used as a starting point for the analysis: U1 (slow) .dblarw. U2 .dblarw. (fast) .dblarw. N, where U1 and U2 are 2 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 of refolding show 2 phases, a fast phase and a slow phase, over a range of temperatures extending above the transition midpoint, Tm. The 3-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 4-species mechanism is complex, it is not difficult to extend the 3-species analysis for the special case found here, in which the fast reaction (I .dblarw. N) is well separated from the other 2 reactions. At temperatures below the transition zone the slow phase of refolding becomes kinetically complex. No attempt was made to extend the analysis to include this effect. The basic test of the 3-state analysis is the prediction as a function of temperature of .alpha.2, the relative amplitude of the fast phase, both for unfolding and refolding. At temperatures above Tm, for which the 3-state analysis must be extended to include the new intermediate I, a corresponding quantity .alpha.2(cor) is predicted and compared with measured values. Data used in the 3-state prediction are values of .tau.2 and .tau.1, the time constants of the fast and slow kinetic phases, plus a single value of .alpha.2 measured when .tau.2 and .tau.1 are well separated. The observed and predicted values of .alpha.2 agree within experimental error. The analysis predicts correctly that, for these experiments, .alpha.2 should have the same value in unfolding as in refolding in the same 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: the drop in .alpha.2 to a minimum near Tm as well as the delayed rise in .alpha.2 above Tm; the vanishing of .alpha.1 above the transition zone; the sharp drop in .tau.1 inside the transition zone followed by a partial leveling off outside this zone; the passage of .tau.2 through a maximum near Tm. Through a comparison of observed and predicted values of .alpha.2, the analysis also rules out the alternative three-species mechanism U1 (slow) .dblarw. N (fast) .dblarw. U2. The temperature dependence of the amplitude for the fast reaction (I .dblarw. N) is discussed: the behavior of I is like that of U2, and I may be an unfolded species populated at equilibrium. If so, I accounts for only 2% of the total unfolded enzyme and would not be detected in refolding experiments below Tm. Possible molecular interpretations of the U1 .dblarw. U2 .dblarw. I .dblarw. N mechanism are discussed briefly.