Transition states and the meaning of Phi-values in protein folding kinetics.

What is the mechanism of two-state protein folding? The rate-limiting step is typically explored through a Phi-value, which is the mutation-induced change in the transition state free energy divided by the change in the equilibrium free energy of folding. Phi-values ranging from 0 to 1 have been interpreted as meaning the transition state is denatured-like (0), native-like (1) or in-between. But there is no classical interpretation for the experimental Phi-values that are negative or >1. Using a rigorous method to identity transition states via an exact lattice model, we find that nonclassical Phi-values can arise from parallel microscopic flow processes, such as those in funnel-shaped energy landscapes. Phi < 0 results when a mutation destabilizes a slow flow channel, causing a backflow into a faster flow channel. Phi > 1 implies the reverse: a backflow from a fast channel into a slow one. Using a 'landscape mapping' method, we find that Phi correlates with the acceleration/deceleration of folding induced by mutations, rather than with the degree of nativeness of the transition state.