Transition-state structure as a unifying basis in protein-folding mechanisms: contact order, chain topology, stability, and the extended nucleus mechanism

Abstract

I attempt to reconcile apparently conflicting factors and mechanisms that have been proposed to determine the rate constant for two-state folding of small proteins, on the basis of general features of the structures of transition states. Phi-Value analysis implies a transition state for folding that resembles an expanded and distorted native structure, which is built around an extended nucleus. The nucleus is composed predominantly of elements of partly or well-formed native secondary structure that are stabilized by local and long-range tertiary interactions. These long-range interactions give rise to connecting loops, frequently containing the native loops that are poorly structured. I derive an equation that relates differences in the contact order of a protein to changes in the length of linking loops, which, in turn, is directly related to the unfavorable free energy of the loops in the transition state. Kinetic data on loop extension mutants of CI2 and alpha-spectrin SH3 domain fit the equation qualitatively. The rate of folding depends primarily on the interactions that directly stabilize the nucleus, especially those in native-like secondary structure and those resulting from the entropy loss from the connecting loops, which vary with contact order. This partitioning of energy accounts for the success of some algorithms that predict folding rates, because they use these principles either explicitly or implicitly. The extended nucleus model thus unifies the observations of rate depending on both stability and topology.

Figure 1

Plot of logk vs. 100 × CO for two-state folding proteins listed in Table 18.1 of ref. and unpublished data from this laboratory.

Figure 2

Cartoon of the extended (specific) nucleus mechanism of the nucleation-condensation mechanism. This is for the extreme case of the connecting loops being unstructured. The filled circles represent native-like elements of secondary structure that interact mainly by native tertiary interactions. The shaded part of the loop illustrates an insertion of length l.

Figure 3

Plots of logk vs. 100 × CO for loop insertion mutants of CI2 and the α-spectrin SH3 domain.

Figure 4

(Lower) Simplified energy diagrams for true two-state folding via nucleation-condensation and apparent two-state kinetics for a framework mechanism that involves the formation of, say, an α-helix, at a higher energy than the denatured state. If both mechanisms involve an extended network of long-range native-like tertiary interactions around the helix, then the free energy of activation, ΔG^‡, responds to changes in structure in a similar manner for both mechanisms, because ΔG^‡ depends just on the difference in energy between similar transition states and the denatured state. (Upper) Two-dimensional representation of the merging of the nucleation-condensation and framework mechanisms. In the framework mechanism, the Φ-values for the formation of the helix are close to 1, because it is relatively stable and can form to an appreciable extent in the absence of tertiary interactions. As the helix becomes less stable, it requires more tertiary interactions to become stable in the transition state, and so the formation of helix is coupled with that of tertiary structure. The Φ-values for formation of the helix can then be appreciably less than 1.