Correlation between relative contact order and folding rates of two-state proteins. (A) The RCO values of the three proteins, ubiquitin, acyl phosphatase, and BdpA, studied using ψ-analysis span the RCO range. (B) Native and TS models of the three proteins.

RNA folding rates and ^redCO. (A) RNA folding is multistate with highly structured intermediates that accumulate prior to the rate-limiting step. A sample calculation of ^RedCO is depicted for a model RNA with five tertiary contacts. ^RedCO is the sum of the length of the shortest paths between each contact. Numbers denote residue length of each unstructured segment. (B) The measured or extrapolated folding rates at 37°C and ∼10 mM Mg²⁺ for 10 RNAs. The black and red lines identify the fast and slow folding classes, respectively.

Proposed Ub folding pathway. Ub's folding pathway is described by a largely sequential pathway with a conserved nucleus. The β-hairpin, the most stable of isolated SecStr, forms first. Other initial structures are less plausible, such as the α-helix (low intrinsic helicity) or the parallel association between the two terminal strands (big loop closure penalty). The sequence proximity and increased hydrophobic burial for helix association suggests that it generally folds prior to the carboxy-terminal strand (upper route preferred). The addition of the fourth β-strand completes the TS, although some “microscopic heterogeneity” may exist involving frayed strands and helices. The two remaining elements, the 3₁₀ helix and fifth strand, add on the way down. Native-state HX suggests that the 3₁₀ helix folds first.

RNA folding pathways. (A) Folding pathway of the S-domain from Bacillus subtilis illustrated with the native crystal structure, I_eq, and two hypothetical late kinetic intermediates. (B) Reaction scheme for the I_eq-to-N macroscopic transition with two kinetic intermediates and three microscopic transitions. (C) Observed relaxation rates plotted as a function of final [Mg²⁺] for folding (●) and unfolding measurements (○) generate a Mg²⁺ chevron. (D) Corresponding free energy surfaces change with [Mg²⁺]. At [Mg²⁺] >> K_Mg (dashed line), folding rates saturate at k _f due to the rapid formation of a folding intermediate, I_1k, followed a Mg²⁺-independent barrier. At low [Mg²⁺ ] << K_Mg (dotted line), unfolding rates saturate at k _u due to the formation of an unfolding intermediate, I_2k. At [Mg²⁺] ∼ K_Mg, the observed rate reflects the relative population of the kinetic intermediate times the rate of going over the Mg²⁺-independent barrier. Although the RLS does not involve an uptake of additional metal ions for the bulk solution, it is sensitive to cation type. These results indicate that the RLS represents a small-scale structural consolidation around one or more prebound metal ions.