  Phi-values are experimental measures of how the kinetics of protein folding
is changed by single-site mutations. Phi-values measure energetic quantities,
but 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. In addition, it
provides a natural and general interpretation of "nonclassical" Phi-values
(i.e., less than zero, or greater than one). The model reproduces the
Phi-values for 20 single-residue mutations in the alpha-helix of the protein
CI2, including several nonclassical Phi-values, in good agreement with
experiments.
