Osmolyte-induced protein folding free energy changes.

Upon addition of protecting osmolyte to an aqueous solution of an intrinsically unstructured protein, spectral observables are often seen to change in a sigmoid fashion as a function of increasing osmolyte concentration. Commonly, such data are analyzed using the linear extrapolation model (LEM), a method that defines a scale from 0%-100% folded species at each osmolyte concentration by means of extending pre- and post-folding baselines into the transition region. Defining the 0%-100% folding scale correctly for each osmolyte is an important part of the analysis, leading to evaluation of the fraction of folded protein existing in the absence of osmolytes. In this study, we used reduced and carboxyamidated RNase T1 (RCAM-T1) as an intrinsically unstructured protein, and determined the thermodynamic stability of RCAM-T1 induced by naturally occurring osmolytes. Because the folded fraction of the protein population determined by experiments of thermal and urea-induced denaturation is nonzero in the absence of osmolytes at 15 degrees C, the commonly used LEM can lead to false values of DeltaG[stackD-->N0] for protein folding due to the arbitrary assumption that the protein is 100% unfolded in the presence of buffer alone. To correct this problem, titration of the protein solution with urea and extrapolating back to zero urea concentration gives the spectral value for 100% denatured protein. With fluorescence as the observable we redefine F/F0 to F/F0extrap = 1.0 and require that the denatured-state baseline have this value as its intercept. By so doing, the 0%-100% scale-corrected DeltaG[D-->N0] values of RCAM-T1 folding in the presence of various osmolytes are then found to be identical, with small error, demonstrating that DeltaG[D-->N0] is independent of the osmolytes used. Such a finding is an important step in validating this quantity derived from the LEM as having the properties expected of an authentic thermodynamic parameter. The rank order of osmolyte efficacies in stabilizing RCAM-T1 is sarcosine > sucrose > sorbitol > proline > betaine > glycerol.

Thermodynamics of denaturant-induced unfolding of a protein that exhibits variable two-state denaturation.

Free energy changes (DeltaG(degrees)(N-->D)) obtained by denaturant-induced unfolding using the linear extrapolation method (LEM) are presumed to reflect the stability differences between native (N) and denatured (D) species in the absence of denaturant. It has been shown that with urea and guanidine hydrochloride (GdnHCl) some proteins exhibit denaturant-independent (DeltaG(degrees)(N-->D)). But with several other proteins urea and GdnHCl give different (DeltaG(degrees)(N-->D)) values for the same protein, meaning that the free energy difference between N and D is not the only contribution to one or both (DeltaG(degrees)(N-->D)) values. Using beta1, a mutant form of the protein G B1 domain, we show that both urea- and GdnHCl-induced denaturations are two-state and reversible but that the denaturants give different values for (DeltaG(degrees)(N-->D)). While spectral observables are sensitive to the shift between N and D states (between states effect), they are not sensitive to denaturant-induced changes that occur within the individual N and D states (within state effect). By contrast, nonspectral observables such as Stokes radius and thermodynamic observables such as proton uptake/release are often sensitive to both "between states" and "within state" effects. These observables, along with spectral measurements, provide descriptions of urea- and GdnHCl-induced denaturation of beta1. Our results suggest that in the predenaturation concentration range GdnHCl changes the free energy of the native ensemble in a nonlinear manner but that urea does not. As with RNase A and beta-lactoglobulin, beta1 exhibits variable two-state behavior with GdnHCl-induced denaturation in that the free energy of the native ensemble in the predenaturation zone changes (varies) with GdnHCl concentration in a nonlinear manner.

Effects of naturally occurring osmolytes on protein stability and solubility: issues important in protein crystallization.

Protein solubility and stability are issues of consideration in attempts to crystallize proteins. These two properties of proteins are also at issue in the cells of organisms that have adapted to water stress conditions that could ordinarily denature or inactivate some proteins. Most organisms that have adapted to environmental stresses have done so by production and accumulation of certain small organic molecules, known as osmolytes, that arose by natural selection and have the ability to stabilize intracellular proteins against the environmental stress. Here, concepts developed to understand the special properties of the naturally occurring osmolytes in effecting protein stability and solubility, and the principles that have come from studies of these compounds have been presented. Along with excluded volume and preferential interaction parameters, identification of the osmophobic effect and the attenuation of this effect by favorable interactions of solute with side-chains appear to contribute to the full set of effects protecting osmolytes have on protein stability and solubility. With these concepts in mind and the fact that urea interacts favorably with the peptide backbone we note that: (1) osmolyte-induced effects on protein stability ranging from denaturation to forcing proteins to fold can be achieved experimentally and the underlying principles understood at near molecular-level detail, and (2) osmolyte-mediated solubility effects ranging from protein precipitation to protein solubilization are predictable based on these principles. These effects are contrasted and compared with effects of 2-methyl-2,4-pentanediol and polyethylene glycol on proteins, and how the principles found for the naturally occurring osmolytes can be applied to these two commonly used protein crystallizing agents.

Osmolyte effects on kinetics of FKBP12 C22A folding coupled with prolyl isomerization.

Unfolding and refolding kinetics of human FKBP12 C22A were monitored by fluorescence emission over a wide range of urea concentration in the presence and absence of protecting osmolytes glycerol, proline, sarcosine and trimethylamine-N-oxide (TMAO). Unfolding is well described by a mono-exponential process, while refolding required a minimum of two exponentials for an adequate fit throughout the urea concentration range considered. The bi-exponential behavior resulted from complex coupling between protein folding, and prolyl isomerization in the denatured state in which the urea-dependent rate constant for folding was greater than, equal to, and less than the rate constants for prolyl isomerization within the urea concentration range of zero to five molar. Amplitudes and the observed folding and unfolding rate constants were fitted to a reversible three-state model composed of two sequential steps involving the native state and a folding-competent denatured species thermodynamically linked to a folding-incompetent denatured species. Excellent agreement between thermodynamic parameters for FKBP12 C22A folding calculated from the kinetic parameters and those obtained directly from equilibrium denaturation assays provides strong support for the applicability of the mechanism, and provides evidence that FKBP12 C22A folding/unfolding is two-state, with prolyl isomer heterogeneity in the denatured ensemble. Despite the chemical diversity of the protecting osmolytes, they all exhibit the same kinetic behavior of increasing the rate constant of folding and decreasing the rate constant for unfolding. Osmolyte effects on folding/unfolding kinetics are readily explained in terms of principles established in understanding osmolyte effects on protein stability. These principles involve the osmophobic effect, which raises the Gibbs energy of the denatured state due to exposure of peptide backbone, thereby increasing the folding rate. This effect also plays a key role in decreasing the unfolding rate when, as is often the case, the activated complex exposes more backbone than is exposed in the native state.

Efficacy of macromolecular crowding in forcing proteins to fold.

The intrinsically unstructured protein, reduced and carboxyamidated RNase T1 (TCAM) was used to determine the degree to which macromolecular crowding agents increase the equilibrium constant for folding. TCAM is not catalytically active in an aqueous assay system alone, but becomes catalytically active on addition of 400 mg/ml dextran 70. The activity observed accounts for approximately 16% of the total available TCAM in solution. We interpret this result to mean that 16% of the TCAM becomes folded protein in the presence of the 400 mg/ml dextran 70, and this translates into an approximately five-fold increase in the equilibrium constant for folding. Sarcosine-induced folding of TCAM was performed in the presence of 0, 100, 200 and 300 mg/ml dextran 70, and apparent deltaG(o)(N-D) values determined from the linear extrapolation method provide an estimated 22% folded TCAM formed in the limit of zero sarcosine concentration and in presence of 400 mg/ml dextran 70. The increase in TCAM folding equilibrium constant using this method of determination is approximately 7.5-fold. Overall, the results indicate that macromolecular crowding agents are only modestly effective in promoting folding of this intrinsically unstructured protein.

The osmophobic effect: natural selection of a thermodynamic force in protein folding.

Intracellular organic osmolytes are present in certain organisms adapted to harsh environments and these osmolytes protect intracellular macromolecules against the denaturing environmental stress. In natural selection of organic osmolytes as protein stabilizers, it appears that the osmolyte property selected for is the unfavorable interaction between the osmolyte and the peptide backbone, a solvophobic thermodynamic force that we call the osmophobic effect. Because the peptide backbone is highly exposed to osmolyte in the denatured state, the osmophobic effect preferentially raises the free energy of the denatured state, shifting the equilibrium in favor of the native state. By focusing the solvophobic force on the denatured state, the native state is left free to function relatively unfettered by the presence of osmolyte. The osmophobic effect is a newly uncovered thermodynamic force in nature that complements the well-recognized hydrophobic interactions, hydrogen bonding, electrostatic and dispersion forces that drive protein folding. In organisms whose survival depends on the intracellular presence of osmolytes that can counteract denaturing stresses, the osmophobic effect is as fundamental to protein folding as these well-recognized forces.

The conformation of the glucocorticoid receptor af1/tau1 domain induced by osmolyte binds co-regulatory proteins.

The activation domains of many transcription factors appear to exist naturally in an unfolded or only partially folded state. This seems to be the case for AF1/tau1, the major transactivation domain of the human glucocorticoid receptor. We show here that in buffers containing the natural osmolyte trimethylamine N-oxide (TMAO), recombinant AF1 folds into more a compact structure, as evidenced by altered fluorescence emission, circular dichroism spectra, and ultracentrifugal analysis. This conformational transition is cooperative, a characteristic of proteins folding to natural structures. The structure resulting from incubation in TMAO causes the peptide to resist proteolysis by trypsin, chymotrypsin, endoproteinase Arg-C and endoproteinase Gluc-C. Ultracentrifugation studies indicate that AF1/tau1 exists as a monomer in aqueous solution and that the presence of TMAO does not lead to oligomerization or aggregation. It has been suggested that recombinant AF1 binds both the ubiquitous coactivator CBP and the TATA box-binding protein, TBP. Interactions with both of these are greatly enhanced in the presence of TMAO. Co-immunoadsorption experiments indicate that in TMAO each of these and the coactivator SRC-1 are found complexed with AF1. These data indicate that TMAO induces a conformation in AF1/tau1 that is important for its interaction with certain co-regulatory proteins.

Effects of guanidine hydrochloride on the proton inventory of proteins: implications on interpretations of protein stability.

The DeltaG degrees (N)(-)(D) value obtained from extrapolation to zero denaturant concentration by the linear extrapolation method (LEM) is commonly interpreted to represent the Gibbs energy difference between native (N) and denatured (D) ensembles at the limit of zero denaturant concentration. For DeltaG degrees (N)(-)(D) to be interpreted solely in terms of N and D, as is common practice, it must be shown to be independent of denaturant concentration. Because DeltaG degrees (N)(-)(D) is often observed to be dependent on the nature of the denaturant, it is necessary to determine the circumstances under which DeltaG degrees (N)(-)(D) can be interpreted as a property solely of the protein. Here, we use proton inventory, a thermodynamic property of both the native and denatured ensembles, to monitor the thermodynamic character of denaturant-dependent aspects of N and D ensembles and the N right arrow over left arrow D transition. Use of a thermodynamic rather than a spectral parameter to monitor denaturation provides insight into the manner in which denaturant affects the meaning of DeltaG degrees (N)(-)(D) and the nature of the N right arrow over left arrow D transition. Three classes of proteins are defined in terms of the thermodynamic behaviors of their N right arrow over left arrow D transition and N and D ensembles. With guanidine hydrochloride as a denaturant, the classification of protein denaturations by these procedures determines when the LEM gives readily interpretable DeltaG degrees (N)(-)(D) values with this denaturant and when it does not.

Structural thermodynamics of a random coil protein in guanidine hydrochloride.

An important problem in protein folding is to understand the relationship between the structure of a denatured ensemble and its thermodynamics. Using 0 - 6M GdnHCl at fixed pH, we evaluated dimensional changes of an extensively denatured ensemble along with a thermodynamic parameter (Deltaupsilon) that monitors the proton inventory of the ensemble. Reduced and carboxyamidated ribonuclease A (RCAM) is a member of a class of disulfide-free RNase A molecules believed to be random coils (extensively denatured) in aqueous solution. Because GdnHCl interacts more favorably with the protein than water does, this denaturant is observed to increase the Stokes radius of the random coil, with the greatest Stokes radius change occurring in the 0 - 1.5M GdnHCl range. Measurement of the degree of protonation (proton inventory) of the ensemble as a function of GdnHCl at the fixed pH shows that the thermodynamic character of the ensemble also changes markedly in the 0 - 1.5M GdnHCl range, but with little or no change beyond 1.5M GdnHCl. To obtain denaturant-independent DeltaG degrees (N-D) values, the linear extrapolation method (LEM) requires the thermodynamic character of the native and denatured ensembles to be invariant in the transition zone. The results reported here indicate that proteins with a transition midpoint in the 0 - 1.5M GdnHCl range will not give denaturant-concentration independent DeltaG degrees (N-D) values. Such LEM-derived DeltaG degrees (N-D) quantities are a property of the protein and the denaturant, a condition that considerably limits their value in understanding structural energetics.

The unfolding enthalpy of the pH 4 molten globule of apomyoglobin measured by isothermal titration calorimetry.

The unfolding enthalpy of the pH 4 molten globule from sperm whale apomyoglobin has been measured by isothermal titration calorimetry, using titration to acid pH. The unfolding enthalpy is close to zero at 20 degrees C, in contrast both to the positive values expected for peptide helices and the negative values reported for holomyoglobin and native apomyoglobin. At 20 degrees C, the hydrophobic interaction should make only a small contribution to the unfolding enthalpy according to the liquid hydrocarbon model. Our result indicates that some factor present in the unfolding enthalpies of native proteins makes the unfolding enthalpy of the pH 4 molten globule less positive than expected from data for peptide helices.

The peculiar nature of the guanidine hydrochloride-induced two-state denaturation of staphylococcal nuclease: a calorimetric study.

This work determines the ratio of DeltaH(vH) /DeltaH(cal) for staphylococcal nuclease (SN) denaturation in guanidine hydrochloride (GdnHCl) to test whether GdnHCl-induced denaturation is two-state. Heats of mixing of SN as a function of [GdnHCl] were determined at pH 7.0 and 25 degrees C. The resulting plot of DeltaH(mix) vs [GdnHCl] exhibits a sigmoid shaped curve with linear pre- and post-denaturational base lines. Extending the pre- and post-denaturational lines to zero [GdnHCl] gives a calorimetric DeltaH (DeltaH(cal)) of 24.1 +/- 1.0 kcal/mol, for SN denaturation in the limit of zero GdnHCl concentration. Guanidine hydrochloride-induced denaturation Gibbs energy changes in the limit of zero denaturant concentration (DeltaG degrees (N)(-)(D)) at pH 7. 0 were determined for SN from fluorescence measurements at fixed temperatures over the range from 15 to 35 degrees C. Analysis of the resulting temperature-dependent DeltaG degrees (N)(-)(D) data defines a van't Hoff denaturation enthalpy change (DeltaH(vH)) of 26. 4 +/- 2.8 kcal/mol. The model-dependent van't Hoff DeltaH(vH) divided by the model-independent DeltaH(cal) gives a ratio of 1.1 +/- 0.1 for DeltaH(vH)/DeltaH(cal), a result that rules out the presence of thermodynamically important intermediate states in the GdnHCl-induced denaturation of SN. The likelihood that GdnHCl-induced SN denaturation involves a special type of two-state denaturation, known as a variable two-state process, is discussed in terms of the thermodynamic implications of the process.

Interdomain signaling in a two-domain fragment of the human glucocorticoid receptor.

Studies of individual domains or subdomains of the proteins making up the nuclear receptor family have stressed their modular nature. Nevertheless, these receptors function as complete proteins. Studies of specific mutations suggest that in the holoreceptors, intramolecular domain-domain interactions are important for complete function, but there is little knowledge concerning these interactions. The important transcriptional transactivation function in the N-terminal part of the glucocorticoid receptor (GR) appears to have little inherent structure. To study its interactions with the DNA binding domain (DBD) of the GR, we have expressed the complete sequence from the N-terminal through the DBD of the human GR. Circular dichroism analyses of this highly purified, multidomain protein show that it has a considerable helical content. We hypothesized that binding of its DBD to the cognate glucocorticoid response element would confer additional structure upon the N-terminal domain. Circular dichroism and fluorescence emission studies suggest that additional helicity as well as tertiary structure occur in the two-domain protein upon DNA binding. In sum, our data suggest that interdomain interactions consequent to DNA binding imparts structure to the portion of the GR that contains a major transactivation domain.

The paradox between m values and deltaCp's for denaturation of ribonuclease T1 with disulfide bonds intact and broken.

Urea-induced denaturations of RNase T1 and reduced and carboxyamidated RNase T1 (RTCAM) as a function of temperature were analyzed using the linear extrapolation method, and denaturation m values, deltaCp, deltaH, deltaS, and deltaG quantities were determined. Because both deltaCp and m values are believed to reflect the protein surface area newly exposed on denaturation, the prediction is that the ratio of m values for RNase T1 and RTCAM should equal the deltaCp ratio for the two proteins. This is not the case, for it is found that the m value of RTCAM is 1.5 times that of RNase T1, while the denaturation deltaCp's for the two proteins are identical. The paradox of why the two parameters, m and deltaCp, are not equivalent in their behavior is of importance in the interpretations of their respective molecular-level meanings. It is found that the measured denaturation deltaCp's are consistent with deltaCp's calculated on the basis of empirical relationships between the change in surface area on denaturation (deltaASA), and that the measured m value of RNase T1 agrees with m calculated from empirical data relating m to deltaASA. However, the measured m of RTCAM is so much out of line with its calculated m as to call into question the validity of always equating m with surface area newly exposed on denaturation.

Trimethylamine N-oxide-induced cooperative folding of an intrinsically unfolded transcription-activating fragment of human glucocorticoid receptor.

A number of biologically important proteins or protein domains identified recently are fully or partially unstructured (unfolded). Methods that allow studies of the propensity of such proteins to fold naturally are valuable. The traditional biophysical approaches using alcohols to drive alpha-helix formation raise serious questions of the relevance of alcohol-induced structure to the biologically important conformations. Recently we illustrated the extraordinary capability of the naturally occurring solute, trimethylamine N-oxide (TMAO), to force two unfolded proteins to fold to native-like species with significant functional activity. In the present work we apply this technique to recombinant human glucocorticoid receptor fragments consisting of residues 1-500 and residues 77-262. CD and fluorescence spectroscopy showed that both were largely disordered in aqueous solution. TMAO induced a condensed structure in the large fragment, indicated by the substantial enhancement in intrinsic fluorescence and blue shift of fluorescent maxima. CD spectroscopy demonstrated that the TMAO-induced structure is different from the alpha-helix-rich conformation driven by trifluoroethanol (TFE). In contrast to TFE, the conformational transition of the 1-500 fragment induced by TMAO is cooperative, a condition characteristic of proteins with unique structures.

Osmolyte-driven contraction of a random coil protein.

The Stokes radius characteristics of reduced and carboxamidated ribonuclease A (RCAM RNase) were determined for transfer of this "random coil" protein from water to 1 M concentrations of the naturally occurring protecting osmolytes trimethylamine N-oxide, sarcosine, sucrose, and proline and the nonprotecting osmolyte urea. The denatured ensemble of RCAM RNase expands in urea and contracts in protecting osmolytes to extents proportional to the transfer Gibbs energy of the protein from water to osmolyte. This proportionality suggests that the sum of the transfer Gibbs energies of individual parts of the protein is responsible for the dimensional changes in the denatured ensemble. The dominant term in the transfer Gibbs energy of RCAM RNase from water to protecting osmolytes is the unfavorable interaction of the osmolyte with the peptide backbone, whereas the favorable interaction of urea with the backbone dominates in RCAM RNase transfer to urea. The side chains collectively favor transfer to the osmolytes, with some protecting osmolytes solubilizing hydrophobic side chains as well as urea does, a result suggesting there is nothing special about the ability of urea to solubilize hydrophobic groups. Protecting osmolytes stabilize proteins by raising the chemical potential of the denatured ensemble, and the uniform thermodynamic force acting on the peptide backbone causes the collateral effect of contracting the denatured ensemble. The contraction decreases the conformational entropy of the denatured state while increasing the density of hydrophobic groups, two effects that also contribute to the ability of protecting osmolytes to force proteins to fold.

Time-dependent effects of trimethylamine-N-oxide/urea on lactate dehydrogenase activity: an unexplored dimension of the adaptation paradigm.

Given that enzymes in urea-rich cells are believed to be just as sensitive to urea effects as enzymes in non-urea-rich cells, it is argued that time-dependent inactivation of enzymes by urea could become a factor of overriding importance in the biology of urea-rich cells. Time-independent parameters (e.g. Tm, k(cat), and Km) involving protein stability and enzyme function have generally been the focus of inquiries into the efficacy of naturally occurring osmolytes like trimethylamine-N-oxide (TMAO), to offset the deleterious effects of urea on the intracellular proteins in the urea-rich cells of elasmobranchs. However, using urea concentrations found in urea-rich cells of elasmobranches, we have found time-dependent effects on lactate dehydrogenase activity which indicate that TMAO plays the important biological role of slowing urea-induced dissociation of multimeric intracellular proteins. TMAO greatly diminishes the rate of lactate dehydrogenase dissociation and affords significant protection of the enzyme against urea-induced time-dependent inactivation. The effects of TMAO on enzyme inactivation by urea adds a temporal dimension that is an important part of the biology of the adaptation paradigm.

Trimethylamine-N-oxide counteracts urea effects on rabbit muscle lactate dehydrogenase function: a test of the counteraction hypothesis.

Trimethylamine-N-oxide (TMAO) in the cells of sharks and rays is believed to counteract the deleterious effects of the high intracellular concentrations of urea in these animals. It has been hypothesized that TMAO has the generic ability to counteract the effects of urea on protein structure and function, regardless of whether that protein actually evolved in the presence of these two solutes. Rabbit muscle lactate dehydrogenase (LDH) did not evolve in the presence of either solute, and it is used here to test the validity of the counteraction hypothesis. With pyruvate as substrate, results show that its Km and the combined Km of pyruvate and NADH are increased by urea, decreased by TMAO, and in 1:1 and 2:1 mixtures of urea:TMAO the Km values are essentially equivalent to the Km values obtained in the absence of the two solutes. In contrast, values of k(cat) and the Km for NADH as a substrate are unperturbed by urea, TMAO, or urea:TMAO mixtures. All of these effects are consistent with TMAO counteraction of the effects of urea on LDH kinetic parameters, supporting the premise that counteraction is a property of the solvent system and is independent of the evolutionary history of the protein.

Forcing thermodynamically unfolded proteins to fold.

A growing number of biologically important proteins have been identified as fully unfolded or partially disordered. Thus, an intriguing question is whether such proteins can be forced to fold by adding solutes found in the cells of some organisms. Nature has not ignored the powerful effect that the solution can have on protein stability and has developed the strategy of using specific solutes (called organic osmolytes) to maintain the structure and function cellular proteins in organisms exposed to denaturing environmental stresses (Yancey, P. H., Clark, M. E., Hand, S. C., Bowlus, R. D., and Somero, G. N. (1982) Science 217, 1214-1222). Here, we illustrate the extraordinary capability of one such osmolyte, trimethylamine N-oxide (TMAO), to force two thermodynamically unfolded proteins to fold to native-like species having significant functional activity. In one of these examples, TMAO is shown to increase the population of native state relative to the denatured ensemble by nearly five orders of magnitude. The ability of TMAO to force thermodynamically unstable proteins to fold presents an opportunity for structure determination and functional studies of an important emerging class of proteins that have little or no structure without the presence of TMAO.

Monitoring the sizes of denatured ensembles of staphylococcal nuclease proteins: implications regarding m values, intermediates, and thermodynamics.

Fluorescence and size-exclusion chromatography (SEC) are used to monitor urea denaturation of wild-type staphylococcal nuclease (SN) as well as the m+ and m- mutants A69T and V66W, respectively. It is found that the SEC partition coefficient, 1/Kd, is directly proportional to the Stokes radii of proteins. From the Stokes radii, the denatured ensembles of the three proteins are found to be highly compact in the limit of low urea concentration and expand significantly with increasing urea concentration. The m values from fluorescence-detected denaturation of the SN proteins are generally considered to reflect the relative sizes of denatured ensembles. However, the rank order of m values of the SN proteins studied do not correspond to the rank order of denatured ensemble sizes detected by 1/Kd, suggesting that m values reflect more than just surface area increases on denaturation. SEC provides two complementary ways to demonstrate the existence of intermediates in urea denaturation and illustrates that V66W undergoes a three-state transition. Fluorescence-detected urea denaturations of A69T and wt SN do not correspond with 1/Kd-detected denaturation profiles, a result that would ordinarily mean that the transitions are non-two-state. However, this interpretation fails to recognize the rapidly changing size and thermodynamic character of the denatured ensembles of these proteins both within and outside of the transition zone. The implications of the changing sizes and thermodynamic character of the denatured ensembles for SN proteins are manifold, requiring a reconsideration of the thermodynamics of proteins whose denatured ensembles behave as those of SN proteins.