On the precision of experimentally determined protein folding rates and phi-values.

Phi-values, a relatively direct probe of transition-state structure, are an important benchmark in both experimental and theoretical studies of protein folding. Recently, however, significant controversy has emerged regarding the reliability with which phi-values can be determined experimentally: Because phi is a ratio of differences between experimental observables it is extremely sensitive to errors in those observations when the differences are small. Here we address this issue directly by performing blind, replicate measurements in three laboratories. By monitoring within- and between-laboratory variability, we have determined the precision with which folding rates and phi-values are measured using generally accepted laboratory practices and under conditions typical of our laboratories. We find that, unless the change in free energy associated with the probing mutation is quite large, the precision of phi-values is relatively poor when determined using rates extrapolated to the absence of denaturant. In contrast, when we employ rates estimated at nonzero denaturant concentrations or assume that the slopes of the chevron arms (mf and mu) are invariant upon mutation, the precision of our estimates of phi is significantly improved. Nevertheless, the reproducibility we thus obtain still compares poorly with the confidence intervals typically reported in the literature. This discrepancy appears to arise due to differences in how precision is calculated, the dependence of precision on the number of data points employed in defining a chevron, and interlaboratory sources of variability that may have been largely ignored in the prior literature.

Protein folding: defining a "standard" set of experimental conditions and a preliminary kinetic data set of two-state proteins.

Recent years have seen the publication of both empirical and theoretical relationships predicting the rates with which proteins fold. Our ability to test and refine these relationships has been limited, however, by a variety of difficulties associated with the comparison of folding and unfolding rates, thermodynamics, and structure across diverse sets of proteins. These difficulties include the wide, potentially confounding range of experimental conditions and methods employed to date and the difficulty of obtaining correct and complete sequence and structural details for the characterized constructs. The lack of a single approach to data analysis and error estimation, or even of a common set of units and reporting standards, further hinders comparative studies of folding. In an effort to overcome these problems, we define here a "consensus" set of experimental conditions (25 degrees C at pH 7.0, 50 mM buffer), data analysis methods, and data reporting standards that we hope will provide a benchmark for experimental studies. We take the first step in this initiative by describing the folding kinetics of 30 apparently two-state proteins or protein domains under the consensus conditions. The goal of our efforts is to set uniform standards for the experimental community and to initiate an accumulating, self-consistent data set that will aid ongoing efforts to understand the folding process.

Apparent Debye-Huckel electrostatic effects in the folding of a simple, single domain protein.

We have monitored the effects of salts and denaturants on the folding of the simple, two-state protein FynSH3. As predicted by Debye-Huckel limiting law, both the stability and (log) folding rate of FynSH3 increase nearly perfectly linearly (r(2)> 0.99) with the square root of ionic strength upon increasing concentrations of the relatively nonchaotropic salt sodium chloride. The stability of FynSH3 is also linear in square root ionic strength when the relatively nonchaotropic salts sodium bromide, potassium bromide, and potassium chloride are employed. Comparison of the kinetic and equilibrium effects of sodium chloride suggests that the electrostatic interactions formed in the folding transition state are approximately 50% as destabilizing as those formed in the native state, presumably reflecting the more compact nature of the latter. In contrast, the relationship between concentration and folding kinetics is more complex when the highly chaotropic salt guanidine hydrochloride (GuHCl) is employed. At moderate to high GuHCl concentrations the net effect of the linear, presumably chaotrope-induced deceleration and the presumed, square root-dependent ionic strength-induced acceleration is well approximated as linear, thus accounting for the observation of "chevron behavior" (log folding rate linear in denaturant concentration) typically reported for the folding of single domain proteins. At very low GuHCl concentrations, however, significant kinetic rollover is observed. This rollover is reasonably well fitted as a sum of a linear, presumably chaotropic effect and a square root-dependent, presumably electrostatic effect. These results thus not only provide insight into the nature of the folding transition state but also suggest that caution is in order when extrapolating GuHCl-based chevrons to estimate folding rates in the absence of denaturant and in interpreting deviations from chevron linearity as evidence for non-two-state kinetics.

Experimental investigation of the frequency and substitution dependence of negative phi-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 approximately 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.