An integrated kinetic analysis of intermediates and transition states in protein folding reactions.

Relaxation rates for folding and unfolding of two proteins have been measured over a range of denaturant concentrations to examine the reaction pathways leading to the late transition state. The proteins were chosen for their marked differences in both kinetic and structural properties. Results for the N-terminal domain of phosophoglycerate kinase (N-PGK), from Bacillus stearothermophilus, reveal the existence of a single intermediate (pathway = U-I-F), and obey the general relationship: kobs = k(U-I) + k(I-U)/[1 + 1/KU/I]. Hen egg white lysozyme folds through two intermediates (pathway = U-I-I.-F) and the relaxation kinetics for formation and decay of the fully folded state are described by: kobs = k(F-I.)+KI.-F)/[1+ 1/KI./I+ 1/(KI/U.KI./I)]. Rate constants apply to the first step in unfolding and the last step in folding, respectively, these being rate-limiting in the stated directions. Equilibrium constants describe the stability of transient intermediates, as indicated by the subscripts. Rate constants alter with denaturant according to the generalized equation k = kw.exp((mg-mt).D), where kw is the rate constant in water, mg and mt are parameters describing the relative solvent exposures of the ground and transition state conformations respectively, and D is the calculated denaturant activity. The same principle applies to equilibrium constants for rapid steps, i.e. for a process A = B; KA/B = KA/B(w).exp((mB-mA).D). The combined application of these relationships allows measurement of the relative free energy and degree of solvation or compactness of intermediates and transition states in folding pathways from a single set of kinetic data. In the case of lysozyme, the fast but measurable rates of interconversion of intermediate states (I and I.) have been examined by use of a sequential mixing technique, so providing additional information on a transition state which is not rate-limiting in the overall pathway. The analysis of rate profiles for folding and unfolding of these proteins yields parameters which are in precise agreement with those derived from equilibrium data.