φ values in protein-folding kinetics have energetic and structural components

Phi values are experimental measures of how the kinetics of protein folding is changed by single-site mutations. Phi values measure energetic quantities, but they are often interpreted in terms of the structures of the transition-state ensemble. Here, we describe a simple analytical model of the folding kinetics in terms of the formation of protein substructures. The model shows that Phi values have both structural and energetic components. It also provides a natural and general interpretation of "nonclassical" Phi values (i.e., < 0 or > 1). The model reproduces the Phi values for 20 single-residue mutations in the alpha-helix of the protein C12, including several nonclassical Phi values, in good agreement with experiments.