Differences in the folding transition state of ubiquitin indicated by phi and psi analyses

Abstract

We compare the folding transition state (TS) of ubiquitin previously identified by using psi analysis to that determined by using analysis. Both methods attempt to identify interactions and their relative populations at the rate-limiting step for folding. The TS ensemble derived from psi analysis has an extensive native-like chain topology, with a four-stranded beta-sheet network and a portion of the major helix. According to analysis, however, the TS is much smaller and more polarized, with only a local helix/hairpin motif. We find that structured regions can have values far from unity, the canonical value for such sites, because of structural relaxation of the TS. Consequently, these sites may be incorrectly interpreted as contributing little to the structure of the TS. These results stress the need for caution when interpreting and drawing conclusions from analysis alone and highlight the need for more specific tools for examining the structure and energetics of the TS ensemble.

Fig. 1.

Ub TS identified by using ψ and φ analyses. (A) Schematic representation of ψ values. Bi-His sites are shown (circles with italic letters); each site was studied individually. The color intensity represents the value of ψ.(B) The major folding pathway identified by using ψ analysis (14) is best described with a TS ensemble that emerges from a conserved nucleus. This preTS structure, defined by regions where ψ = 1, either spreads in a number of possible directions reflecting TS heterogeneity, illustrated here with three representative structures, or contains distorted regions with binding affinities less than those in the native structure. The postTS structure is the union of all structures with fractional ψ values. (C) The smaller and polarized TS determined by using φ analysis is based on the present mutational data and earlier studies (14). Renderings were created in swiss-pdb viewer (Glaxo Wellcome).

Fig. 2.

Analysis of TS heterogeneity. (A) Application of ψ analysis to a two-route scenario, illustrated with a helical site with native binding affinity that is formed on 9% of the pathways before addition of metal. The absent route contains a TS that cannot bind metal without undergoing a conformational transition. The folding rate for the route with the bi-His site present (k_present, lower pathway) increases from 1 to 100 upon the addition of 2.86 kcal·mol^–1 of metal-ion-binding energy at 20°C. This enhancement increases the flux down the metal-ion-stabilized route (divalent metal ion, M²⁺) relative to all other routes (k_absent), from , to metal-enhanced condition, ρ_M²⁺ = 10/100, where ρ₀ is the ratio of rates in the absence of metal ions for pathways in which the bi-His site is formed to those in which the bi-His site is not formed. The corresponding ψ values increase from ψ₀ = 0.1 to ψ_M²⁺ = 0.9. The binding energy, , required to stabilize a TS and switch a minor route to a major route identifies the barrier height for this route relative to that for all other routes. (B) In the corresponding Brønsted plot, the fraction of TSs with the site present is the ψ value, which is the instantaneous slope at any given [M²⁺]. The equations shown are applicable to this situation. Alternatively, when the metal binding affinity in the TS is less than in the native state, the curvature also can be accounted for with a homogeneous TS ensemble with the ψ value at the origin equating to the fraction of the native binding energy realized in TS. (C) Brønsted plot illustrating that, when there is TS heterogeneity, φ values underestimate the relative importance of an interaction. For a completely native-like interaction that is present in only 50% of the TS ensemble (K_eq = 1), destabilizing mutations of 0.4, 1.3, and 2.7 kcal·mol^–1 reduce K_eq to 0.33, 0.09, and 0.01, respectively. The corresponding φ values will be 0.42, 0.26, and 0.15, although the contribution of the residue to the TS of the wild-type protein is φ (0) = 0.5. Hence, the desirability of having large energetic perturbations to generate accurate φ values (27) can be detrimental to correctly assessing the contribution of a residue to the TS ensemble.

Fig. 3.

Denaturant dependence of folding rates for Ub. Locations of the mutations in the TS^{φ analysis} and the TS^{ψ analysis}, defined by theψ = 1 sites, are shown with Corey–Pauling–Koltun space-filling spheres. All variants contained the F45W substitution to permit folding to be monitored by fluorescence, whereas the H68N mutation was introduced in all but variants I3A and L67A to avoid complications caused by spurious metal-ion interactions in the original ψ analysis study. Experiments were conducted at 20°C, 50 mM Hepes, pH 7.5, and a final protein concentration of 0.2–1 μM. GdmCl, guanidinium chloride.