Psi-constrained simulations of protein folding transition states: implications for calculating

Psi-analysis has been used to identify interresidue contacts in the transition state ensemble (TSE) of ubiquitin and other proteins. The magnitude of psi depends on the degree to which an inserted bihistidine (biHis) metal ion binding site is formed in the TSE. A psi equal to zero or one indicates that the biHis site is absent or fully native-like, respectively, while a fractional psi 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 psi of unity. When a site with a fractional psi lies adjacent to a site with psi = 1, the fractional psi generally signifies that the "fractional site" has a distorted geometry in the TSE. When a fractional site is distal to the sites with psi = 1, however, the histidines sample configurations in which the site is absent. The simulations indicate that the psi = 1 sites by themselves can be used to generate a well-defined TSE having near-native topology. values calculated from the TS simulations exhibit mixed agreement with the experimental values. The origin and implication of the disparities are discussed.