Determination of the transition state ensemble for the folding of ubiquitin from a combination of Phi and Psi analyses

Protein engineering techniques have emerged as powerful tools for characterizing transition states (TSs) for protein folding. Recently, the Ψ analysis, in which double-histidine mutations create the possibility of reversible crosslinking in the native state, has been proposed as an additional approach to the well-established Φ analysis. We present here a combination of these two procedures for defining the structure of the TS of ubiquitin, a small α/β protein that has been used extensively as a model system for both experimental and computational studies of the protein-folding process. We performed a series of molecular dynamics simulations in which Φ and Ψ values were used as ensemble-averaged structural restraints to determine an ensemble of structures representing the TS of ubiquitin. Although the available Ψ values for ubiquitin did not, by themselves, generate well-defined TS ensembles, the inclusion of the restricted set of zero or unity values, but not fractional ones, provided useful complementary information to the Φ analysis. Our results show that the TS of ubiquitin is formed by a relatively narrow ensemble of structures exhibiting an overall native-like topology in which the N-terminal and C-terminal regions are in close proximity.