Origin of Unusual f-values in Protein Folding: Evidence Against Specific Nucleation Sites Ignacio E. Sa ´ nchez and Thomas Kiefhaber* Department of Biophysical Chemistry, Biozentrum der Universita ¨t Basel Klingelberstrasse 70, CH-4056 Basel, Switzerland f f -value analysis is one of the most common methods to characterize the structure of protein folding transition states. It compares the effects of mutations on the folding kinetics with the respective effects on equili- brium stability. The interpretation of the results usually focuses on a few unusual f f -values, which are either particularly high or which are larger than 1 or smaller than 0. These mutations are believed to affect the most important regions for the folding process. A major uncertainty in experi- mental f f -values is introduced by the commonly used analysis of only a single mutant at various positions in a protein (two-point analysis). To test the reliability of two-point f f -values we used reference data from three positions in two different proteins at which multiple mutations have been introduced. The results show that two-point f f -values are highly inaccurate if the difference in stability between two variants is less than 7 kJ/mol, corresponding to a 20-fold difference in equilibrium con- stant. Comparison with reported f f -values for 11 proteins shows that most unusual f f -values are observed in mutants which show changes in protein stability that are too small to allow a reliable analysis. The results argue against specific nucleation sites in protein folding and give a picture of transition states as distorted native states for the major part of a protein or for large substructures. q 2003 Elsevier Ltd. All rights reserved. Keywords: protein folding kinetics; phi-value analysis; rate-equilibrium free energy relationships; transition state *Corresponding author Introduction Rate-equilibrium free energy relationships (REFERs) have been widely used to characterize mechanisms and transition states in chemical and biochemical reactions. 1–8 It was observed that changes in activation free energy (DG 0‡ ) induced by a perturbation like a change in solvent con- ditions or by a structural change in the reactants are linearly related to the corresponding changes in equilibrium free energy (DG 0 ) between reactants and products. 1,6 A proportionality constant, a x ¼ð›DG 0‡ =›xÞ=ð›DG 0 =›xÞ, was defined to quan- tify the energetic sensitivity of the transition state relative to the ground states in response to a per- turbation, ›x: 1 One of the most popular ways to characterize the structure of transition states of protein folding reactions is the introduction of structural changes by site-directed mutagenesis and comparison of the resulting effects on the fold- ing kinetics and on equilibrium stability: 9 – 11 a s ¼ f f ¼ ›DG 0‡ f =›Structure ›DG 0 =›Structure ð1Þ a S is commonly called f f 11 and reports on the ener- getics of all interactions formed by a side-chain with the rest of the protein in the transition state relative to the native state with the unfolded pro- tein serving as the reference state. If the mutated side-chain only forms native-like interactions with the rest of the protein in the transition state, f f should take values between 0 (energetics of inter- actions in the transition state are the same as in the unfolded state) and 1 (energetics of interactions in the transition state are the same as in the native state). Several small single domain proteins have been extensively mutagenized to obtain a picture of the folding transition state at an atomic resolution. The results revealed that most f f -values are low, 0022-2836/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. E-mail address of the corresponding author: t.kiefhaber@unibas.ch Abbreviation used: REFER, rate-equilibrium free energy relationship. doi:10.1016/j.jmb.2003.10.016 J. Mol. Biol. (2003) 334, 1077–1085