The roles of stability and contact order in determining protein folding rates

nature structural biology • volume 8 number 1 • january 2001 21 The mechanism by which a protein folds, like any reaction, is determined by the underlying free energy surface 1. A large separation in energy between the native state and the structurally dissimilar states (an 'energy gap') has been shown to be a thermodynamic and kinetic requirement for folding in both analytical theories 2,3 and simulations of lattice models 4,5. The ability of a sequence to fold rapidly correlates strongly with measures of the stability of its native (ground) state (such as the Z-score or the gap between the ground and first excited compact states). The relationship between the kinetics and the thermodynamics arises from the fact that the transition state involves a subset of the native interactions 1,6. Thus, lowering the (free) energy of the native state also tends to stabilize the transition state. This behavior is consistent with the Hammond effect (the movement of a transition state along a reaction coordinate away from a reactant, intermediate or product state that is stabilized), which has been observed experimentally to hold for certain proteins 7. It was surprising, therefore, that the folding rate constants (k f) of small two-state proteins were found to be essentially independent of the stabilities of their native states (as measured by the free energy of unfolding, ∆G) 8,9. Instead, k f depends strongly on the 'topology' of the native state, in particular, the contact order (the average residue separation of atomic contacts , c) 8–13. For the 33 proteins considered in the present study (listed in the caption to Fig. 1), the Pearson linear correlation coefficient (r) between log k f and c is r c,log k f =-0.73, and that between log k f and ∆G is r ∆G,log k f = 0.29 (normalizing c and ∆G by the sequence lenght, N, as is often done, yields slightly stronger correlations: r c/N,log k f =-0.79 and r ∆G/N,log k f = 0.37). Increasing the fraction of contacts that are short range in the native state (and by assumption, in the transition state) can accelerate folding in two (related) ways if the activation energy is not rate limiting 14 : it facilitates locating the transition state by a diffusive search 15–17 and it lowers the entropic barrier to folding 6. Nevertheless, in addition to the theoretical and simulation results mentioned above, the absence of …