Complex Pathways in Folding of Protein G Explored by Simulation and Experiment

The B1 domain of protein G has been a classic model system of folding for decades, the subject of numerous experimental and computational studies. Most of the experimental work has focused on whether the protein folds via an intermediate, but the evidence is mostly limited to relatively slow kinetic observations with a few structural probes. In this work we observe folding on the submillisecond timescale with microfluidic mixers using a variety of probes including tryptophan fluorescence, circular dichroism, and photochemical oxidation. We find that each probe yields different kinetics and compare these observations with a Markov State Model constructed from large-scale molecular dynamics simulations and find a complex network of states that yield different kinetics for different observables. We conclude that there are many folding pathways before the final folding step and that these paths do not have large free energy barriers.     

Direct Observation of Downhill Folding of λ-Repressor in a Microfluidic Mixer

The protein λ_6-85 has been implicated in barrierless folding by observations of kinetic relaxation after nanosecond T-jump. In this work we observed folding of this protein after dilution of a high denaturant in an ultrarapid microfluidic mixer at temperatures far below the thermal midpoint. The observations of total intensity and spectral shift of tryptophan fluorescence yielded distinctly different kinetics and activation energies. These results may be explained as diffusion on a low-barrier, one-dimensional, free-energy surface, with different probes having different sensitivities along the reaction coordinate. Additionally, we observed an extremely fast phase within the mixing time that was not observed by T-jump, suggesting that the ensemble of unfolded states populated at high denaturant is distinct from those accessible at high temperature.     

Protein folding in the landscape perspective: Chevron plots and non-arrhenius kinetics

We use two simple models and the energy landscape perspective to study protein folding kinetics. A major challenge has been to use the landscape perspective to interpret experimental data, which requires ensemble averaging over the microscopic trajectories usually observed in such models. Here, because of the simplicity of the model, this can be achieved. The kinetics of protein folding falls into two classes: multiple-exponential and two-state (single-exponential) kinetics. Experiments show that two-state relaxation times have “chevron plot” dependences on denaturant and non-Arrhenius dependences on temperature. We find that HP and HP+ models can account for these behaviors. The HP model often gives bumpy landscapes with many kinetic traps and multiple-exponental behavior, whereas the HP+ model gives more smooth funnels and two-state behavior. Multiple-exponential kinetics often involves fast collapse into kinetic traps and slower barrier climbing out of the traps. Two-state kinetics often involves entropic barriers where conformational searching limits the folding speed. Transition states and activation barriers need not define a single conformation; they can involve a broad ensemble of the conformations searched on the way to the native state. We find that unfolding is not always a direct reversal of the folding process. Proteins 30:2–33, 1998. © 1998 Wiley-Liss, Inc.     

Folding of Cu, Zn superoxide dismutase and familial amyotrophic lateral sclerosis

Cu, Zn superoxide dismutase (SOD1) has been implicated in the familial form of the neurodegenerative disease amyotrophic lateral sclerosis (ALS). It has been suggested that mutant mediated SOD1 misfolding/aggregation is an integral part of the pathology of ALS. We study the folding thermodynamics and kinetics of SOD1 using a hybrid molecular dynamics approach. We reproduce the experimentally observed SOD1 folding thermodynamics and find that the residues which contribute the most to SOD1 thermal stability are also crucial for apparent two-state folding kinetics. Surprisingly, we find that these residues are located on the surface of the protein and not in the hydrophobic core. Mutations in some of the identified residues are found in patients with the disease. We argue that the identified residues may play an important role in aggregation. To further characterize the folding of SOD1, we study the role of cysteine residues in folding and find that non-native disulfide bond formation may significantly alter SOD1 folding dynamics and aggregation propensity.     

The final stages of folding of the membrane protein bacteriorhodopsin occur by kinetically indistinguishable parallel folding paths that are mediated by pH

The folding of the transmembrane protein bacteriorhodopsin that occurs during the binding of its retinal cofactor is investigated in a membrane-like environment. Changes in the retinal absorption band reveal two transient retinal-protein intermediate states, with apparent absorption maxima at 380 nm and 440 nm, respectively. Studies on a bacteriorhodopsin mutant of Lys216, which cannot bind retinal covalently, add to evidence that retinal is non-covalently bound in these intermediate states. The two retinal-protein intermediates are genuine intermediate states that form in parallel, each with an observed rate constant of 1.1 s-1. Meanwhile no formation of the folded state is detected. Folded bacteriorhodopsin, with all trans retinal covalently bound, forms from both retinal-bound intermediates with the same apparent rate constant of 0.0070 s-1 that is independent of retinal concentration. Retinal isomerisation then occurs with a rate constant of 0.00033 s-1 to give bacteriorhodopsin containing all trans and 13 cis-retinal. These results provide experimental evidence for multiple folding routes for a membrane protein that are pH dependent, with pH conditions determining the apparent folding route. These observed parallel folding paths are kinetically indistinguishable, which contrasts with most other observations of parallel folding pathways where only pathways with different kinetics have been reported. Furthermore, together with previous work, this study shows that bacteriorhodopsin has to populate at least two folding intermediates, during folding in the mixed lipid micelles investigated here, before the final fold is attained.     

Cooperativity and the origins of rapid, single-exponential kinetics in protein folding

The folding of naturally occurring, single-domain proteins is usually well described as a simple, single-exponential process lacking significant trapped states. Here we further explore the hypothesis that the smooth energy landscape this implies, and the rapid kinetics it engenders, arises due to the extraordinary thermodynamic cooperativity of protein folding. Studying Miyazawa-Jernigan lattice polymers, we find that, even under conditions where the folding energy landscape is relatively optimized (designed sequences folding at their temperature of maximum folding rate), the folding of protein-like heteropolymers is accelerated when their thermodynamic cooperativity is enhanced by enhancing the nonadditivity of their energy potentials. At lower temperatures, where kinetic traps presumably play a more significant role in defining folding rates, we observe still greater cooperativity-induced acceleration. Consistent with these observations, we find that the folding kinetics of our computational models more closely approximates single-exponential behavior as their cooperativity approaches optimal levels. These observations suggest that the rapid folding of naturally occurring proteins is, in part, a consequence of their remarkably cooperative folding.     

Mechanism of induced folding: Both folding before binding and binding before folding can be realized in staphylococcal nuclease mutants

A considerable number of functional proteins are unstructured under physiological condition. These "intrinsically disordered" proteins exhibit induced folding when they bind their targets. The induced folding comprises two elementary processes: folding and binding. Two mechanisms are possible for the induced folding: either folding before binding or binding before folding. We found that these two mechanisms can be distinguished by the target-concentration dependence of folding kinetics. We also created two types of mutants of staphylococcal nuclease showing the different inhibitor-concentration dependence of induced folding kinetics. One mutant obeys the scheme of binding before folding, while the other the folding before binding. This is the first experimental evidence demonstrating that both mechanisms are realized for a single protein. Binding before folding is possible, when the protein lacks essential nonlocal interaction to stabilize the native conformation. The results cast light on the protein folding mechanism involved in the intrinsically disordered proteins.     

Role of unfolded state heterogeneity and en-route ruggedness in protein folding kinetics

In order to improve our understanding of the physical bases of protein folding, there is a compelling need for better connections between experimental and computational approaches. This work addresses the role of unfolded state conformational heterogeneity and en-route intermediates, as an aid for planning and interpreting protein folding experiments. The expected kinetics were modeled for different types of energy landscapes, including multiple parallel folding routes, preferential paths dominated by one primary folding route, and distributed paths with a wide spectrum of microscopic folding rate constants. In the presence of one or more preferential routes, conformational exchange among unfolded state populations slows down the observed rates for native protein formation. We find this to be a general phenomenon, taking place even when unfolded conformations interconvert much faster than the "escape" rate constants to folding. Dramatic kinetic deceleration is expected in the presence of an increasing number of folding-incompetent unfolded conformations. This argues for the existence of parallel folding paths involving several folding-competent unfolded conformations, during the early stages of protein folding. Deviations from single-exponential behavior are observed for unfolded conformations exchanging at comparable rates or more slowly than folding events. Analysis of the effect of en-route (on-path) intermediate formation and landscape ruggedness on folding kinetics leads to the following unexpected conclusions: (1) intermediates, which often retard native state formation, may in some cases accelerate folding, and (2) rugged landscapes, usually associated with stretched exponentials, display single-exponential behavior in the presence of late high-friction paths.     

Role of electrostatic interactions for the stability and folding behavior of cold shock protein

The impacts of three charged‐residue‐involved mutations, E46A, R3E, and R3E/L66E, on the thermostability and folding behavior of the cold shock protein from the themophile Bacillus caldolyticus (Bc‐Csp) were investigated by using a modified Gō‐like model, in which the nonspecific electrostatic interactions of charged residues were taken into account. Our simulation results show that the wild‐type Bc‐Csp and its three mutants are all two‐sate folders, which is consistent with the experimental observations. It is found that these three mutations all lead to a decrease of protein thermodynamical stability, and the effect of R3E mutation is the strongest. The lower stability of these three mutants is due to the increase of the enthalpy of the folded state and the entropy of the unfolded state. Using this model, we also studied the folding kinetics and the folding/unfolding pathway of the wild‐type Bc‐Csp as well as its three mutants and then discussed the effects of electrostatic interactions on the folding kinetics. The results indicate that the substitutions at positions 3 and 46 largely decrease the folding kinetics, whereas the mutation of residue 66 only slightly decreases the folding rate. This result agrees well with the experimental observations. It is also found that these mutations have little effects on the folding transition state and the folding pathway, in which the N‐terminal β sheet folds earlier than the C‐terminal region. We also investigated the detailed unfolding pathway and found that it is really the reverse of the folding pathway, providing the validity of our simulation results. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Ultra-fast barrier-limited folding in the peripheral subunit-binding domain family

We have determined the solution structures, equilibrium properties and ultra-fast folding kinetics for three bacterial homologues of the peripheral subunit-binding domain (PSBD) family. The mesophilic homologue, BBL, was less stable than the thermophilic and hyper-thermophilic variants (E3BD and POB, respectively). The broad unfolding transitions of each PSBD, when probed by different techniques, were essentially superimposable, consistent with co-operative denaturation. Temperature-jump and continuous-flow fluorescence methods were used to measure the folding kinetics for E3BD, POB and BBL. E3BD folded fairly rapidly at 298K (folding half-time approximately 25 micros) and BBL and POB folded even faster (folding half-times approximately 3-5 micros). The variations in equilibrium and kinetic behaviour observed for the PSBD family resembles that of the homeodomain family, where the folding pattern changes from apparent two-state transitions to multi-state kinetics as the denatured state becomes more structured. The faster folding of POB may be a consequence of its higher propensity to form helical structure in the region corresponding to the folding nucleus of E3BD. The ultra-fast folding of BBL appears to be a consequence of residual structure in the denatured ensemble, as with engrailed homeodomain. We discuss issues concerning "one-state", downhill folding, and find no evidence for, and strong evidence against, it occurring in these PSBDs. The shorter construct used previously for BBL was destabilized significantly and the stability further perturbed by the introduction of fluorescent probes. Thermal titrations for 11 side-chains scattered around the protein, when probed by (13)C-NMR experiments, could be fit globally to a common co-operative transition.     

Simulation and experiment conspire to reveal cryptic intermediates and a slide from the nucleation-condensation to framework mechanism of folding

There is a change from three-state to two-state kinetics of folding across the homeodomain superfamily of proteins as the mechanism slides from framework to nucleation-condensation. The tendency for framework folding in this family correlates with inherent helical propensity. The cellular myeloblastis protein (c-Myb) falls in the mechanistic transition region. An earlier, preliminary report of protein engineering experiments and molecular dynamics simulations (MD) showed that the folding mechanism for this protein has aspects of both the nucleation-condensation and framework models. In the more in-depth analysis of the MD trajectories presented here, we find that folding may be attributed to both of these mechanisms in different regions of the protein. The folding of the loop, middle helix, and turn is best described by nucleation-condensation, whereas folding of the N and C-terminal helices may be described by the framework model. Experimentally, c-Myb folds by apparent two-state kinetics, but the MD simulations predict that the kinetics hide a high-energy intermediate. We stabilized this hypothetical folding intermediate by deleting a residue (P174) in the loop between its second and third helices, and the mutant intermediate is long-lived in the simulations. Equilibrium and kinetic experiments demonstrate that folding of the DeltaP174 mutant is indeed three-state. The presence and shape of the intermediate observed in the simulations were confirmed by small angle X-ray scattering experiments.     

Recombination of S-peptide with S-protein during folding of ribonuclease S. I. Folding pathways of the slow-folding and fast-folding classes of unfolded S-protein.

The refolding kinetics of ribonuclease S have been measured by tyrosine absorbance, by tyrosine fluorescence emission, and by rapid binding of the specific inhibitor 2′CMP ² to folded RNAase S. The S-protein is first unfolded at pH 1.7 and then either mixed with S-peptide as refolding is initiated by a stopped-flow pH jump to pH 6.8, or the same results are obtained if S-protein and S-peptide are present together before refolding is initiated. The refolding kinetics of RNAase S have been measured as a function of temperature (10 to 40 °C) and of protein concentration (10 to 120 μm). The results are compared to the folding kinetics of S-protein alone and to earlier studies of RNAase A. A thermal folding transition of S-protein has been found below 30 °C at pH 1.7; its effects on the refolding kinetics are described in the following paper (Labhardt &; Baldwin, 1979).In this paper we characterize the refolding kinetics of unfolded S-protein, as it is found above 30 °C at pH 1.7, together with the kinetics of combination between S-peptide and S-protein during folding at pH 6.8. Two classes of unfolded S-protein molecules are found, fast-folding and slow-folding molecules, in a 20: 80 ratio. This is the same result as that found earlier for RNAase A; it is expected if the slow-folding molecules are produced by the slow cis-trans isomerization of proline residues after unfolding, since S-protein contains all four proline residues of RNAase A.The refolding kinetics of the fast-folding molecules show clearly that combination between S-peptide and S-protein occurs before folding of S-protein is complete. If combination occurred only after complete folding, then the kinetics of formation of RNAase S should be rather slow (5 s and 100 s at 30 °C) and nearly independent of protein concentration, as shown by separate measurements of the folding kinetics of S-protein, and of the combination between S-peptide and folded S-protein. The observed folding kinetics are faster than predicted by this model and also the folding rate increases strongly with protein concentration (apparent 1.6 order kinetics). The fact that RNAase S is formed more rapidly than S-protein alone is sufficient by itself to show that combination with S-peptide precedes complete folding of S-protein. Computer simulation of a simple, parallel-pathway scheme is able to reproduce the folding kinetics of the fast-folding molecules. All three probes give the same folding kinetics.These results exclude the model for protein folding in which the rate-limiting step is an initial diffusion of the polypeptide chain into a restricted range of three-dimensional configurations (“nueleation”) followed by rapid folding (“propagation”). If this model were valid, one would expect comparable rates of folding for RNAase A and for S-protein and one would also expect to find no populated folding intermediates, so that combination between S-peptide and S-protein should occur after folding is complete. Instead, RNAase A folds 60 times more rapidly than S-protein and also combination with S-peptide occurs before folding of S-protein is complete. The results demonstrate that the folding rate of S-protein increases after the formation, or stabilization, of an intermediate which results from combination with S-peptide. They support a sequential model for protein folding in which the rates of successive steps in folding depend on the stabilities of preceding intermediates.The refolding kinetics of the slow-folding molecules are complex. Two results demonstrate the presence of folding intermediates: (1) the three probes show different kinetic progress curves, and (2) the folding kinetics are concentration-dependent, in contrast to the results expected if complete folding of S-protein precedes combination with S-peptide. A faster phase of the slow-refolding reaction is detected both by tyrosine absorbance and fluorescence emission but not by 2′CMP binding, indicating that native RNAase S is not formed in this phase. Comparison of the kinetic progress curves measured by different probes is made with the use of the kinetic ratio test, which is defined here.     

Solvation effects and driving forces for protein thermodynamic and kinetic cooperativity: how adequate is native-centric topological modeling?

What energetic and solvation effects underlie the remarkable two-state thermodynamics and folding/unfolding kinetics of small single-domain proteins? To address this question, we investigate the folding and unfolding of a hierarchy of continuum Langevin dynamics models of chymotrypsin inhibitor 2. We find that residue-based additive Gō-like contact energies, although native-centric, are by themselves insufficient for protein-like calorimetric two-state cooperativity. Further native biases by local conformational preferences are necessary for protein-like thermodynamics. Kinetically, however, even models with both contact and local native-centric energies do not produce simple two-state chevron plots. Thus a model protein's thermodynamic cooperativity is not sufficient for simple two-state kinetics. The models tested appear to have increasing internal friction with increasing native stability, leading to chevron rollovers that typify kinetics that are commonly referred to as non-two-state. The free energy profiles of these models are found to be sensitive to the choice of native contacts and the presumed spatial ranges of the contact interactions. Motivated by explicit-water considerations, we explore recent treatments of solvent granularity that incorporate desolvation free energy barriers into effective implicit-solvent intraprotein interactions. This additional feature reduces both folding and unfolding rates vis-à-vis that of the corresponding models without desolvation barriers, but the kinetics remain non-two-state. Taken together, our observations suggest that interaction mechanisms more intricate than simple Gō-like constructs and pairwise additive solvation-like contributions are needed to rationalize some of the most basic generic protein properties. Therefore, as experimental constraints on protein chain models, requiring a consistent account of protein-like thermodynamic and kinetic cooperativity can be more stringent and productive for some applications than simply requiring a model heteropolymer to fold to a target structure.     

Conserved and nonconserved features of the folding pathway of hisactophilin, a beta-trefoil protein

Based on previous studies of interleukin-1beta (IL-1beta) and both acidic and basic fibroblast growth factors (FGFs), it has been suggested that the folding of beta-trefoil proteins is intrinsically slow and may occur via the formation of essential intermediates. Using optical and NMR-detected quenched-flow hydrogen/deuterium exchange methods, we have measured the folding kinetics of hisactophilin, another beta-trefoil protein that has < 10% sequence identity and unrelated function to IL-1beta and FGFs. We find that hisactophilin can fold rapidly and with apparently two-state kinetics, except under the most stabilizing conditions investigated where there is evidence for formation of a folding intermediate. The hisactophilin intermediate has significant structural similarities to the IL-1beta intermediate that has been observed experimentally and predicted theoretically using a simple, topology-based folding model; however, it appears to be different from the folding intermediate observed experimentally for acidic FGF. For hisactophilin and acidic FGF, intermediates are much less prominent during folding than for IL-1beta. Considering the structures of the different beta-trefoil proteins, it appears that differences in nonconserved loops and hydrophobic interactions may play an important role in differential stabilization of the intermediates for these proteins.     

Temperature-dependent folding pathways of Pin1 WW domain: an all-atom molecular dynamics simulation of a Gō model

We study the folding thermodynamics and kinetics of the Pin1 WW domain, a three-stranded beta-sheet protein, by using all-atom (except nonpolar hydrogens) discontinuous molecular dynamics simulations at various temperatures with a Gō model. The protein exhibits a two-state folding kinetics near the folding transition temperature. A good agreement between our simulations and the experimental measurements by the Gruebele group has been found, and the simulation sheds new insights into the structure of transition state, which is hard to be straightforwardly captured in experiments. The simulation also reveals that the folding pathways at approximately the transition temperature and at low temperatures are much different, and an intermediate state at a low temperature is predicted. The transition state of this small beta-protein at its folding transition temperature has a well-established hairpin 1 made of beta1 and beta2 strands while its low-temperature kinetic intermediate has a formed hairpin 2 composed of beta2 and beta3 strands. Theoretical results are compared with other simulation results as well as available experimental data. This study confirms that specific side-chain packing in an all-atom Gō model can yield a reasonable prediction of specific folding kinetics for a given protein. Different folding behaviors at different temperatures are interpreted in terms of the interplay of entropy and enthalpy in folding process.     

Structural transitions of confined model proteins: molecular dynamics simulation and experimental validation

Proteins fold in a confined space not only in vivo, i.e., folding assisted by molecular chaperons and chaperonins in a crowded cellular medium, but also in vitro as in production of recombinant proteins. Despite extensive work on protein folding in bulk, little is known about how and to what extent the thermodynamics and kinetics of protein folding are altered by confinement. In this work, we use a Gō-like off-lattice model to investigate the folding and stability of an all beta-sheet protein in spherical cages of different sizes and surface hydrophobicity. We find whereas extreme confinement inhibits correct folding, a hydrophilic cage stabilizes the protein due to restriction of the unfolded configurations. In a hydrophobic cage, however, strong attraction from the cage surface destabilizes the confined protein because of competition between self-aggregation and adsorption of hydrophobic residues. We show that the kinetics of protein collapse and folding is strongly correlated with both the cage size and the surface hydrophobicity. It is demonstrated that a cage of moderate size and hydrophobicity optimizes both the folding yield and kinetics of structural transitions. To support the simulation results, we have also investigated the refolding of hen-egg lysozyme in the presence of cetyltrimethylammoniumbromide (CTAB) surfactants that provide an effective confinement of the proteins by micellization. The influence of the surfactant hydrophobicity on the structural and biological activity of the protein is determined with circular dichroism spectrum, fluorescence emission spectrum, and biological activity assay. It is shown that, as predicted by coarse-grained simulations, CTAB micelles facilitate the collapse of denatured lysozyme, whereas the addition of beta-cyclodextrin-grafted-PNIPAAm, a weakly hydrophobic stripper, dissociates CTAB micelles and promotes the conformational rearrangement and thereby gives an improved recovery of lysozyme activity.     

Equilibrium collapse and the kinetic 'foldability' of proteins.

An important element of protein folding theory has been the identification of equilibrium parameters that might uniquely distinguish rapidly folding polypeptide sequences from those that fold slowly. One such parameter, termed sigma, is a dimensionless, equilibrium measure of the coincidence of chain compaction and folding that is predicted to be an important determinant of relative folding kinetics. To test this prediction and improve our understanding of the putative relationship between nonspecific compaction of the unfolded state and protein folding kinetics, we have used small-angle X-ray scattering and circular dichroism spectroscopy to measure the sigma of five well-characterized proteins. Consistent with theoretical predictions, we find that near-perfect coincidence of the unfolded state contraction and folding (sigma approximately 0) is associated with the rapid kinetics of these naturally occurring proteins. We do not, however, observe any significant correlation between sigma and either the relative folding rates of these proteins or the presence or absence of well-populated kinetic intermediates. Thus, while sigma approximately 0 may be a necessary condition to ensure rapid folding, differences in sigma do not account for the wide range of rates and mechanisms with which naturally occurring proteins fold.     

Parallel protein-unfolding pathways revealed and mapped

Theoretical studies of protein folding suggest that multiple folding pathways should exist, but there is little experimental evidence to support this. Here we demonstrate changes in the flux between different transition states on parallel folding pathways, resulting in unprecedented upward curvature in the denaturant-dependent unfolding kinetics of a beta-sandwich protein. As denaturant concentration increases, the highly compact transition state of one pathway becomes destabilized and the dominant flux of protein molecules shifts toward another pathway with a less structured transition state. Furthermore, point mutations alter the relative accessibility of the pathways, allowing the structure of two transition states on separate, direct folding pathways to be mapped by systematic Phi-value analysis. It has been suggested that pathways with diffuse rather than localized transition states are evolutionarily selected to prevent misfolding, and indeed we find that the transition state favored at high concentrations of denaturant is more polarized than the physiologically relevant one.     

Structural parameters affecting the kinetics of RNA hairpin formation

There is little experimental knowledge on the sequence dependent rate of hairpin formation in RNA. We have therefore designed RNA sequences that can fold into either of two mutually exclusive hairpins and have determined the ratio of folding of the two conformations, using structure probing. This folding ratio reflects their respective folding rates. Changing one of the two loop sequences from a purine- to a pyrimidine-rich loop did increase its folding rate, which corresponds well with similar observations in DNA hairpins. However, neither changing one of the loops from a regular non-GNRA tetra-loop into a stable GNRA tetra-loop, nor increasing the loop size from 4 to 6 nt did affect the folding rate. The folding kinetics of these RNAs have also been simulated with the program ‘Kinfold’. These simulations were in agreement with the experimental results if the additional stabilization energies for stable tetra-loops were not taken into account. Despite the high stability of the stable tetra-loops, they apparently do not affect folding kinetics of these RNA hairpins. These results show that it is possible to experimentally determine relative folding rates of hairpins and to use these data to improve the computer-assisted simulation of the folding kinetics of stem–loop structures.     

Methods for the accurate estimation of confidence intervals on protein folding phi-values

Phi-values provide an important benchmark for the comparison of experimental protein folding studies to computer simulations and theories of the folding process. Despite the growing importance of phi measurements, however, formulas to quantify the precision with which phi is measured have seen little significant discussion. Moreover, a commonly employed method for the determination of standard errors on phi estimates assumes that estimates of the changes in free energy of the transition and folded states are independent. Here we demonstrate that this assumption is usually incorrect and that this typically leads to the underestimation of phi precision. We derive an analytical expression for the precision of phi estimates (assuming linear chevron behavior) that explicitly takes this dependence into account. We also describe an alternative method that implicitly corrects for the effect. By simulating experimental chevron data, we show that both methods accurately estimate phi confidence intervals. We also explore the effects of the commonly employed techniques of calculating phi from kinetics estimated at non-zero denaturant concentrations and via the assumption of parallel chevron arms. We find that these approaches can produce significantly different estimates for phi (again, even for truly linear chevron behavior), indicating that they are not equivalent, interchangeable measures of transition state structure. Lastly, we describe a Web-based implementation of the above algorithms for general use by the protein folding community.