Kinetics of loop formation and breakage in the denatured state of iso-1-cytochrome c

The earliest events in protein folding involve the formation of simple loops. Observing the rates of loop closure under denaturing conditions can provide direct insight into the relative probability and sequence determinants for formation of loops of different sizes. The persistence of these initial contacts is equally important for efficient folding, so measurement of rates of loop breakage under denaturing conditions is also essential. We have used stopped-flow and continuous-flow methods to measure the rates of histidine-heme loop formation and breakage in the denatured state of iso-1-cytochrome c (in the presence of 3 M guanidine HCl). The data indicate that the mechanism for forming loops is a two-step process, the first step being the deprotonation of the histidine, and the second step being the binding of the histidine to the heme. This mechanism makes it possible to extract both the rate constants of formation, k_f, and breakage, k_b, of loops from the pH dependence of the observed rate constant, k_obs. To determine the dependence of k_f and k_b on loop size, we have carried out kinetic measurements for seven single surface histidine variants of iso-1-cytochrome c. A scaling factor (the dependence of k_f on log[loop size]) of approximately -1.8 is observed for loop formation, similar to that observed in other systems. The magnitude of k_b varies from 30 s^-1 to 300 s^-1, indicating that the stability of different loops varies considerably. The implications of the kinetics of loop formation and breakage in the denatured state for the mechanism of protein folding are discussed.