Experimental investigation of the frequency and substitution dependence of negative φ-values in two-state proteins

Negative phi-values, which arise, for example, when a mutation stabilizes the folding transition state while destabilizing the native state, have been the focus of significant theoretical interest. Here we survey the experimental folding kinetics literature to ascertain the frequency with which negative phi-values occur in two-state proteins and describe the detailed experimental characterization of a negative phi-value previously reported to be among the most statistically significant. We find that, while almost 9% of more than 500 reported phi-values (from a set of 16, well-characterized two-state proteins) fall below zero, many of these do not represent statistically significant observations. For example, only 6% of the phi-values for which estimates of precision are available fall even one reported "error bar" below zero, and only 4% are simultaneously negative, significant at this level and associated with free energy changes at or above 2.5 kJ/mol (below which phi-value analysis is widely considered unreliable). Moreover, given the asymmetric distribution of phi-values around zero and given that reported error bars may significantly underestimate true confidence intervals, the actual number of negative phi-values may be much smaller still. We have also performed detailed characterization of one of the most statistically significant negative phi-values reported in the literature to date, the V55F mutant of FynSH3. We find that substitution of the wild-type valine to other hydrophobic residues often increases folding rates without significantly altering folding free energy. This in turn leads to poorly defined phi-values, some of which are formally negative but only one or two of which fall statistically significantly below zero. In contrast, substitution to polar residues significantly destabilizes both the transition and native states, generally producing small but statistically significant positive phi-values of similar to 0.1. Thus, unlike other previously characterized phi-values, the negative phi-value associated with position 55 of the FynSH3 domain appears to be strongly dependent on the substitution employed to measure it, suggesting that subtlety will be required in order to develop a theoretical model of such behavior.