ψ-Constrained Simulations of Protein Folding Transition States: Implications for Calculating ϕ

ψ-analysis has been used to identify interresidue contacts in the transition state ensemble (TSE) of ubiquitin and other proteins. The magnitude of ψ depends on the degree to which an inserted bihistidine (biHis) metal ion binding site is formed in the TSE. A ψ equal to zero or one indicates that the biHis site is absent or fully native-like, respectively, while a fractional ψ implies that in the TSE, the biHis site recovers only part of the binding-induced stabilization of the native state. All-atom Langevin dynamics simulations of the TSE are performed with restrictions imposed only on the distances between the pairs of residues with experimentally determined ψ of unity. When a site with a fractional ψ lies adjacent to a site with ψ = 1, the fractional ψ generally signifies that the “fractional site” has a distorted geometry in the TSE. When a fractional site is distal to the sites with ψ = 1, however, the histidines sample configurations in which the site is absent. The simulations indicate that the ψ = 1 sites by themselves can be used to generate a well-defined TSE having near-native topology. ϕ values calculated from the TS simulations exhibit mixed agreement with the experimental values. The origin and implication of the disparities are discussed.