Molecular basis of cooperativity in protein folding IV. Core: A general cooperative folding model

The cooperative nature of the protein folding process is independent of the characteristic fold and the specific secondary structure attributes of a globular protein. A general folding/unfolding model should, therefore, be based upon structural features that transcend the peculiarities of α-helices, β-sheets, and other structural motifs found in proteins. The studies presented in this paper suggest that a single structural characteristic common to all globular proteins is essential for cooperative folding. The formation of a partly folded state from the native state results in the exposure to solvent of two distinct regions: (1) the portions of the protein that are unfolded; and (2) the “complementary surfaces,” located in the regions of the protein that remain folded. The cooperative character of the folding/unfolding transition is determined largely by the energetics of exposing complementary surface regions to the solvent. By definition, complementary regions are present only in partly folded states; they are absent from the native and unfolded states. An unfavorable free energy lowers the probability of partly folded states and increases the cooperativity of the transition. In this paper we present a mathematical formulation of this behavior and develop a general cooperative folding/unfolding model, termed the “complementary region” (CORE) model. This model successfully reproduces the main properties of folding/unfolding transitions without limiting the number of partly folded states accessible to the protein, thereby permitting a systematic examination of the structural and solvent conditions under which intermediates become populated. It is shown that the CORE model predicts two-state folding/unfolding behavior, even though the two-state character is not assumed in the model. © 1993 Wiley-Liss, Inc.     

The folding of an enzyme. III. Structure of the transition state for unfolding of barnase analysed by a protein engineering procedure.

The structure of the first significant transition state on the unfolding pathway of barnase has been analysed in detail by protein engineering methods. Over 50 mutations placed strategically over the whole protein have been used as probes to report on the local structure in the transition state. Several different probes for many regions of the protein give consistent results as do multiple probes at the same site. The overall consistency of phi values indicates that the mutations have not produced changes in the protein that significantly alter the transition state for unfolding. A fine-structure analysis of interactions has also been conducted by removing different parts of the same side-chains. Many of the results of simple mutations fall nicely into the two clear-cut cases of phi = 1 or 0, indicating that the local noncovalent bonds are either fully broken or fully made in the transition state. Much of the structure of barnase in the transition state for unfolding is very similar to that in the folded protein. Both major alpha-helices fray at the N terminus. The last two turns in helix1 are certainly intact, as is the C terminus of helix2. The general picture of the beta-sheet is that the three central beta-strands are completely intact while the two edge beta-strands are mainly present but certainly weakened. The first five residues of the protein unwind but the C terminus remains folded. Three of the five loops are unfolded. The edges of the main hydrophobic core (core1) are significantly weakened, however, and their breaking appears partly rate determining. The centre of the small hydrophobic core3 remains intact. Core2 is completely disrupted. The first events in unfolding are thus: the unfolding of several loops, the unwinding of the helices from the N termini, and the weakening and disruption of the hydrophobic cores. The values of phi are found to be substantially the same under conditions that favour folding as under conditions that are highly denaturing, and so the structure of the unfolding transition state is substantially the same in water as in the presence of denaturant. The structure of the final kinetically significant transition state for refolding is identical to that for unfolding. The final events in refolding are, accordingly, the consolidation of the hydrophobic cores, the closing of many loops and the capping of the N termini of the helices.     

Microscopic reversibility of protein folding in molecular dynamics simulations of the engrailed homeodomain

The principle of microscopic reversibility states that at equilibrium the number of molecules entering a state by a given path must equal those exiting the state via the same path under identical conditions or, in structural terms, that the conformations along the two pathways are the same. There has been some indirect evidence indicating that protein folding is such a process, but there have been few conclusive findings. In this study, we performed molecular dynamics simulations of an ultrafast unfolding and folding protein at its melting temperature to observe, on an atom-by-atom basis, the pathways the protein followed as it unfolded and folded within a continuous trajectory. In a total of 0.67 micros of simulation in water, we found six transient denaturing events near the melting temperature (323 and 330 K) and an additional refolding event following a previously identified unfolding event at a high temperature (373 K). In each case, unfolding and refolding transition state ensembles were identified, and they agreed well with experiment on the basis of a comparison of S and Phi values. On the basis of several structural properties, these 13 transition state ensembles agreed very well with each other and with four previously identified transition states from high-temperature denaturing simulations. Thus, not only were the unfolding and refolding transition states part of the same ensemble, but in five of the seven cases, the pathway the protein took as it unfolded was nearly identical to the subsequent refolding pathway. These events provide compelling evidence that protein folding is a microscopically reversible process. In the other two cases, the folding and unfolding transition states were remarkably similar to each other but the paths deviated.     

Some recommendations for the practitioner to improve the precision of experimentally determined protein folding rates and phi values

The mechanism by which proteins fold from an initially random conformation into a functional, native structure remains a major unsolved question in molecular biology. Of particular interest to the protein folding community is the structure that the protein adopts in the folding transition state (the highest free energy state on the pathway from unfolded to folded), as that state forms the barrier that defines the folding pathway. Unfortunately, however, unlike those of the initial, unfolded state and the final, folded state of the protein, the structure in the transition state cannot be directly assessed via experiment. Instead, experimentalists infer the structure of the transition state, often by estimating changes in its free energy by measuring the effects of amino acid substitutions on folding and unfolding rates (Phi-value analysis). In this article we show how to obtain more efficient estimates of these important quantities via improved experimental designs, and how to avoid common pitfalls in the analysis of kinetic data during the extraction of these parameters.     

Molecular basis of co-operativity in protein folding.

The folding/unfolding transition of proteins is a highly co-operative process characterized by the presence of very few or no thermodynamically stable partially folded intermediate states. The purpose of this paper is to present a thermodynamic formalism aimed at describing quantitatively the co-operative folding behavior of proteins. In order to account for this behavior, a hierarchical algorithm aimed at evaluating the folding/unfolding partition function has been developed. This formalism defines the partition function in terms of multiple levels of interacting co-operative folding units. A co-operative folding unit is defined as a protein structural element that exhibits two-state folding/unfolding behavior. At the most fundamental level are those structural elements that behave co-operatively as a result of purely local interactions. Higher-order co-operative folding units are formed through interactions between different structural elements. The hierarchical formalism utilizes the crystallographic structure of the protein as a template to generate partially folded conformations defined in terms of co-operative folding units. The Gibbs free energy of those states and their corresponding statistical weights are then computed using experimental energetic parameters determined calorimetrically. This formalism has been applied to the case of myoglobin. It is shown that the hierarchical partition function correctly predicts the presence, energetics and co-operativity of the heat and cold denaturation transitions. The major contribution to the co-operative folding behavior arises from the solvent exposure of non-polar residues located in regions complementary to those that have undergone unfolding. This entropically uncompensated and energetically unfavorable solvent exposure characterizes all partially folded states but not the unfolded state, thus minimizing the population of partially folded intermediates throughout the folding/unfolding transition.     

Kinetic analysis of folding and unfolding the 56 amino acid IgG-binding domain of streptococcal protein G.

The 56 amino acid B domain of protein G (GB) is a stable globular folding unit with no disulfide cross-links. The physical properties of GB offer extraordinary flexibility for evaluating the energetics of the folding reaction. The protein is monomeric and very soluble in both folded and unfolded forms. The folding reaction has been previously examined by differential scanning calorimetry (Alexander et al., 1992) and found to exhibit two-state unfolding behavior over a wide pH range with an unfolding transition near 90 degrees C (GB1) at neutral pH. Here, the kinetics of folding and unfolding two naturally occurring versions of GB have been measured using stopped-flow mixing methods and analyzed according to transition-state theory. GB contains no prolines, and the kinetics of folding and unfolding can be fit to a single, first-order rate constant over the temperature range of 5-35 degrees C. The major thermodynamic changes going from the unfolded state to the transition state are (1) a large decrease in heat capacity (delta Cp), indicating that the transition state is compact and solvent inaccessible relative to the unfolded state; (2) a large loss of entropy; and (3) a small increase in enthalpy. The most surprising feature of the folding of GB compared to that of previously studied proteins is that its folding approximates a rapid diffusion controlled process with little increase in enthalpy going from the unfolded to the transition state.     

Energetics of protein structure and folding

The available experimental date on the kinetics of unfolding and refolding of small proteins are reviewed. Excluding slow transitions in the unfolded protein due to cis–trans isomerization of peptide bonds, the rate-limiting transition state in both unfolding and refolding is concluded to be a high-energy distortion of the fully folded state. Partially folded intermediates are undoubtedly important for folding, but their formation is normally not rate limiting. A simple model is used to illustrate some of the aspects of protein-folding energetics.     

The folding pathway of barnase: the rate-limiting transition state and a hidden intermediate under native conditions

The nature of the rate-limiting transition state at zero denaturant (TS(1)) and whether there are hidden intermediates are the two major unsolved problems in defining the folding pathway of barnase. In earlier studies, it was shown that TS(1) has small phi values throughout the structure of the protein, suggesting that the transition state has either a defined partially folded secondary structure with all side chains significantly exposed or numerous different partially unfolded structures with similar stability. To distinguish the two possibilities, we studied the effect of Gly mutations on the folding rate of barnase to investigate the secondary structure formation in the transition state. Two mutations in the same region of a beta-strand decreased the folding rate by 20- and 50-fold, respectively, suggesting that the secondary structures in this region are dominantly formed in the rate-limiting transition state. We also performed native-state hydrogen exchange experiments on barnase at pD 5.0 and 25 degrees C and identified a partially unfolded state. The structure of the intermediate was investigated using protein engineering and NMR. The results suggest that the intermediate has an omega loop unfolded. This intermediate is more folded than the rate-limiting transition state previously characterized at high denaturant concentrations (TS(2)). Therefore, it exists after TS(2) in folding. Consistent with this conclusion, the intermediate folds with the same rate and denaturant dependence as the wild-type protein, but unfolds faster with less dependence on the denaturant concentration. These and other results in the literature suggest that barnase folds through partially unfolded intermediates that exist after the rate-limiting step. Such folding behavior is similar to those of cytochrome c and Rd-apocyt b(562). Together, we suggest that other small apparently two-state proteins may also fold through hidden intermediates.     

Equilibrium and kinetics of the thermal unfolding of alpha-lactalbumin. The relation to its folding mechanism.

The thermal unfolding of alpha-lactalbumin has been studied by equilibrium measurements of aromatic difference spectra, and by kinetic measurements of the Joule heating temperature-jump. The unfolding at neutral pH is a reversible two-state transition. The equilibrium transition curves are analyzed by the nonlinear squares method, which gives correct values of thermodynamic parameters based on the data in a wide range of temperature. The results are discussed in relation to the previous studies on the unfolding by guanidine hydrochloride or by acid. The thermally unfolded state, a partially unfolded species, is shown to be thermodynamically similar to but not identical with the acid state. The folding pathway deduced from the kinetic results is essentially consistent with the folding model of alpha-lactalbumin proposed previously. Large decreases in entropy and in heat capacity during the reversed activation suggest the packing of the folded segments by hydrophobic interactions, while the forward activation shows a marked temperature dependence, probably caused by the disruption of specific long-range interactions.     

Predicting the equilibrium protein folding pathway: Structure-based analysis of staphylococcal nuclease

The equilibrium folding pathway of staphylococcal nucleas (SNase) has been approximated using a statistical thermodynamic formalism that utilizes the high-resolution structure of the native state as a template to generate a large ensemble of partially folded states. Close to 400,000 different states ranging from the native to the completely unfolded states were included in the analysis. The probability of each state was estimated using an empirical structural parametrization of the folding energetics. It is shown that this formalism predicts accurately the stability of the protein, the cooperativity of the folding/unfolding transition observed by differential scanning calorimetry (DSC) or urea denaturation and the thermodynamic parameters for unfolding. More importantly, this formalism provides a quantitative account of the experimental hydrogen exchange protection factors measured under native conditions for SNase. These results suggest that the computer-generated distribution of states approximates well the ensemble of conformations existing in solution. Furthermore, this formalism represents the first model capable of quantitatively predicting within a unified framework the probability distribution of states seen under native conditions and its change upon unfolding. © 1997 Wiley-Liss, Inc.     

Co-operative interactions during protein folding.

The theory for measuring co-operativity between interactions in proteins by protein engineering experiments is developed by introducing a procedure for analysing increasing orders of synergy in a protein with increasing numbers of residues. The (pairwise) interaction energy (delta 2Gint) between two side-chains may be measured experimentally by a double-mutant cycle consisting of the wild-type protein, the two single mutants and the double mutant. This procedure may be extended to three residues to give a value for delta 3Gint for a triple-mutant cube, and to higher orders using multi-dimensional mutant space. We now show that delta 3Gint is the excess energy of adding all three chains compared with the sum of all the pairwise values of delta 2Gint for each of the constituent double-mutant cycles and the sum of all the single addition energies. This physical interpretation extends to higher orders of mutation. delta nGint (i.e. the interaction energy for n residues), thus, reveals the layers of synergy in interactions as a protein is built up. This procedure is applied to measuring changes in synergy during the refolding of barnase for the triad of salt-linked residues Asp8, Asp12 and Arg110, which are mutated to alanine residues. The value of delta 3Gint in the folded structure is 0.77(+/- 0.06) kcal mol-1 (i.e. the triad is 0.77 kcal mol-1 more stable than expected from the sum of the individual pairwise interactions and single contributions). The value of delta 3Gint is still significant in the transition state for unfolding (0.60(+/- 0.07) kcal mol-1) and in the folding intermediate (0.60(+/- 0.13 kcal mol-1)). These results show that synergistic interactions exist in barnase, in its transition state for unfolding and in a refolding intermediate. A direct measurement of the change of co-operativity between the folded state and the transition state for unfolding shows a decrease of 0.17(+/- 0.04) kcal mol-1, suggesting that the initial stages of protein unfolding may be accompanied by some loosening of structure in parts that still interact. The similar extent of co-operativity in the transition state for unfolding and the intermediate in refolding suggests that the intermediate is homogeneous, at least in the region of the salt-linked triad, as heterogeneity would lower the co-operativity.     

Pressure-jump studies of the folding/unfolding of trp repressor.

The dimeric protein, trp apo-repressor of Escherichia coli has been subjected to high hydrostatic pressure under a variety of conditions, and the effects have been monitored by fluorescence spectroscopic and infra-red absorption techniques. Under conditions of micromolar protein concentration and low, non-denaturing concentrations of guanidinium hydrochloride (GuHCl), tryptophan and 8-anilino-1-naphthalene sulfonate (ANS) fluorescence detected high pressure profiles demonstrate that pressures below 3 kbar result in dissociation of the dimer to a monomeric species that presents no hydrophobic binding sites for ANS. The FTIR-detected high pressure profile obtained under significantly different solution conditions (30 mM trp repressor in absence of denaturant) exhibits a much smaller pressure dependence than the fluorescence detected profiles. The pressure-denatured form obtained under the FTIR conditions retains about 50 % alpha-helical structure. From this we conclude that the secondary structure present in the high pressure state achieved under the conditions of the fluorescence experiments is at least as disrupted as that achieved under FTIR conditions. Fluorescence-detected pressure-jump relaxation studies in the presence of non-denaturing concentrations of GuHCl reveal a positive activation volume for the association/folding reaction and a negative activation volume for dissociation/unfolding reaction, implicating dehydration as the rate-limiting step for association/folding and hydration as the rate-limiting step for unfolding. The GuHCl concentration dependence of the kinetic parameters place the transition state at least half-way along the reaction coordinate between the unfolded and folded states. The temperature dependence of the pressure-jump fluorescence-detected dissociation/unfolding reaction in the presence of non-denaturing GuHCl suggests that the curvature in the temperature dependence of the stability arises from non-Arrhenius behavior of the folding rate constant, consistent with a large decrease in heat capacity upon formation of the transition state from the unfolded state. The decrease in the equilibrium volume change for folding with increasing temperature (due to differences in thermal expansivity of the folded and unfolded states) arises from a decrease in the absolute value for the activation volume for unfolding, thus indicating that the thermal expansivity of the transition state is similar to that of the unfolded state.     

Energetic coupling between native-state prolyl isomerization and conformational protein folding

In folded proteins, prolyl peptide bonds are usually thought to be either trans or cis because only one of the isomers can be accommodated in the native folded protein. For the N-terminal domain of the gene-3 protein of the filamentous phage fd (N2 domain), Pro161 resides at the tip of a beta hairpin and was found to be cis in the crystal structure of this protein. Here we show that Pro161 exists in both the cis and the trans conformations in the folded form of the N2 domain. We investigated how conformational folding and prolyl isomerization are coupled in the unfolding and refolding of N2 domain. A combination of single-mixing and double-mixing unfolding and refolding experiments showed that, in unfolded N2 domain, 7% of the molecules contain a cis-Pro161 and 93% of the molecules contain a trans-Pro161. During refolding, the fraction of molecules with a cis-Pro161 increases to 85%. This implies that 10.3 kJ mol(-1) of the folding free energy was used to drive this 75-fold change in the Pro161 cis/trans equilibrium constant during folding. The stabilities of the forms with the cis and the trans isomers of Pro161 and their folding kinetics could be determined separately because their conformational folding is much faster than the prolyl isomerization reactions in the native and the unfolded proteins. The energetic coupling between conformational folding and Pro161 isomerization is already fully established in the transition state of folding, and the two isomeric forms are thus truly native forms. The folding kinetics are well described by a four-species box model, in which the N2 molecules with either isomer of Pro161 can fold to the native state and in which cis/trans isomerization occurs in both the unfolded and the folded proteins.     

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.     

A thermodynamic and kinetic analysis of the folding pathway of an SH3 domain entropically stabilised by a redesigned hydrophobic core

The folding thermodynamics and kinetics of the alpha-spectrin SH3 domain with a redesigned hydrophobic core have been studied. The introduction of five replacements, A11V, V23L, M25V, V44I and V58L, resulted in an increase of 16% in the overall volume of the side-chains forming the hydrophobic core but caused no remarkable changes to the positions of the backbone atoms. Judging by the scanning calorimetry data, the increased stability of the folded structure of the new SH3-variant is caused by entropic factors, since the changes in heat capacity and enthalpy upon the unfolding of the wild-type and mutant proteins were identical at 298 K. It appears that the design process resulted in an increase in burying both the hydrophobic and hydrophilic surfaces, which resulted in a compensatory effect upon the changes in heat capacity and enthalpy. Kinetic analysis shows that both the folding and unfolding rate constants are higher for the new variant, suggesting that its transition state becomes more stable compared to the folded and unfolded states. The phi(double dagger-U) values found for a number of side-chains are slightly lower than those of the wild-type protein, indicating that although the transition state ensemble (TSE) did not change overall, it has moved towards a more denatured conformation, in accordance with Hammond's postulate. Thus, the acceleration of the folding-unfolding reactions is caused mainly by an improvement in the specific and/or non-specific hydrophobic interactions within the TSE rather than by changes in the contact order. Experimental evidence showing that the TSE changes globally according to its hydrophobic content suggests that hydrophobicity may modulate the kinetic behaviour and also the folding pathway of a protein.     

Stability and folding properties of a model beta-sheet protein, Escherichia coli CspA.

Although beta-sheets represent a sizable fraction of the secondary structure found in proteins, the forces guiding the formation of beta-sheets are still not well understood. Here we examine the folding of a small, all beta-sheet protein, the E. coli major cold shock protein CspA, using both equilibrium and kinetic methods. The equilibrium denaturation of CspA is reversible and displays a single transition between folded and unfolded states. The kinetic traces of the unfolding and refolding of CspA studied by stopped-flow fluorescence spectroscopy are monoexponential and thus also consistent with a two-state model. In the absence of denaturant, CspA refolds very fast with a time constant of 5 ms. The unfolding of CspA is also rapid, and at urea concentrations above the denaturation midpoint, the rate of unfolding is largely independent of urea concentration. This suggests that the transition state ensemble more closely resembles the native state in terms of solvent accessibility than the denatured state. Based on the model of a compact transition state and on an unusual structural feature of CspA, a solvent-exposed cluster of aromatic side chains, we propose a novel folding mechanism for CspA. We have also investigated the possible complications that may arise from attaching polyhistidine affinity tags to the carboxy and amino termini of CspA.     

Pathway and stability of protein folding.

We describe an experimental approach to the problem of protein folding and stability which measures interaction energies and maps structures of intermediates and transition states during the folding pathway. The strategy is based on two steps. First, protein engineering is used to remove interactions that stabilize defined positions in barnase, the RNAse from Bacillus amyloliquefaciens. The consequent changes in stability are measured from the changes in free energy of unfolding of the protein. Second, each mutation is used as a probe of the structure around the wild-type side chain during the folding process. Kinetic measurements are made on the folding and unfolding of wild-type and mutant proteins. The kinetic and thermodynamic data are combined and analysed to show the role of individual side chains in the stabilization of the folded, transition and intermediate states of the protein. The protein engineering experiments are corroborated by nuclear magnetic resonance studies of hydrogen exchange during the folding process. Folding is a multiphasic process in which alpha-helices and beta-sheet are formed relatively early. Formation of the hydrophobic core by docking helix and sheet is (partly) rate determining. The final steps involve the forming of loops and the capping of the N-termini of helices.     

Simulation and experiment at high temperatures: ultrafast folding of a thermophilic protein by nucleation-condensation

We used Phi-value analysis to characterise the transition state for folding of a thermophilic protein at the relatively high temperature of 325 K. PhiF values for the folding of the three-helix bundle, peripheral subunit binding domain from Bacillus stearothermophilus (E3BD) were determined by temperature-jump experiments in the absence of chemical denaturants. E3BD folded in microseconds through a highly diffuse transition state. Excellent agreement was observed between experiment and the results from eight (independent) molecular dynamics simulations of unfolding at 373 K. We used a combination of heteronuclear NMR experiments and molecular dynamics simulations to characterise the denatured ensemble, and found that it contained very little persistent, residual structure. However, those regions that adopt helical structure in the native state were found by simulation to be poised for helix formation in the denatured state. These regions also had significant structure in the transition state for folding. The overall folding pathway appears to be nucleation-condensation.     

Progressive stabilization of intermediate and transition states in protein folding reactions by introducing surface hydrophobic residues

It can be argued from the principle of solvent exclusion that the introduction of hydrophobic residues onto the surface of a protein will not destabilize the folded state because the nonpolar side chain will be at least as exposed in the unfolded state as it is when the protein chain is folded. A comparison of the folding pathway of wild type and 11 site-directed mutants of CD2.d1 shows this to be true. In fact, owing to partial burial of nonpolar groups as folding proceeds, we find that the rapidly formed intermediate state and, to a greater extent, the transition state are generally stabilized by hydrophobic surface mutations. This effect is slightly moderated in the folded state presumably by the perturbation of van der Waals' contacts and/or local electrostatic interactions that have a greater influence in this fully compact structure. The fact that in all but one case we find that stabilization of the rapidly collapsed intermediate is accompanied by a faster acquisition of the folded state refutes the argument that I states are generally "off pathway" conformations or ensembles that lead to the inhibition of otherwise more rapid folding trajectories.     

Reversible denaturation of the gene V protein of bacteriophage f1

The guanidine hydrochloride (GuHCl)-induced denaturation of the gene V protein of bacteriophage f1 has been studied, using the chemical reactivity of a cysteine residue that is buried in the folded protein and the circular dichroism (CD) at 211 and 229 nm as measures of the fraction of polypeptide chains in the folded form. It is found that this dimeric protein unfolds in a single cooperative transition from a folded dimer to two unfolded monomers. A folded, monomeric form of the gene V protein was not detected at equilibrium. The kinetics of unfolding of the gene V protein in 3 M GuHCl and the refolding in 2 M GuHCl are also consistent with a transition between a folded dimer and two unfolded monomers. The GuHCl concentration dependence of the rates of folding and unfolding suggests that the transition state for folding is near the folded conformation.