Interpretation of Protein Folding ψ Values

The structural characterization of transition states is essential for understanding the mechanism of protein folding. Analyzing the effect of mutations on protein stability and folding kinetics in ϕ-value analysis is commonly used to gain information about the presence of side-chain interactions in transition states. Recently, specific binding of ligands to engineered binding sites was applied to monitor the formation of local structures in transition states (ψ analysis). A surprising result from ψ analysis was the presence of parallel folding pathways in all reported studies and a major discrepancy between ϕ and ψ values measured in the same protein. Here, we show that ψ values cannot be analyzed in the same way as other rate-equilibrium free energy relationships due to the involvement of bimolecular reactions that may have different dissociation constants for the native, unfolded and transition state. As a consequence, ψ values reflect the relative binding energy (κ) of the transition state only for the extreme values of κ=0 or κ=1. In all other cases, non-linear rate-equilibrium free-energy relationships (Leffler plots) are observed. This apparently indicates the presence of parallel folding pathways even if folding occurs over a single homogeneous transition state. Consequently, the results from Leffler plots do not yield information about the structural properties of the transition state. This explains the lack of agreement between results from ψ analysis and other methods used to characterize protein folding transition states. We further show that the same considerations apply for the analysis of the effect of pH on protein folding.