Protein folding and binding in confined spaces and in crowded solutions

Simple theoretical models are presented to illustrate the effects of spatial confinement and macromolecular crowding on the equilibria and rates of protein folding and binding. Confinement is expected to significantly stabilize the folded state, but for crowding only a marginal effect on protein stability is expected. In confinement the unfolded chain is restricted to a cage but in crowding the unfolded chain may explore different interstitial voids. Because confinement and crowding eliminate the more expanded conformations of the unfolded state, folding from the compact unfolded state is expected to speed up. Crowding will shift the binding equilibrium of proteins toward the bound state. The significant slowing down in protein diffusion by crowding, perhaps beneficial for chaperonin action, could result in a decrease in protein binding rates.     

Protein unfolding transitions in an intrinsically unstable annexin domain: molecular dynamics simulation and comparison with nuclear magnetic resonance data

Unfolding transitions of an intrinsically unstable annexin domain and the unfolded state structure have been examined using multiple approximately 10-ns molecular dynamics simulations. Three main basins are observed in the configurational space: native-like state, compact partially unfolded or intermediate compact state, and the unfolded state. In the native-like state fluctuations are observed that are nonproductive for unfolding. During these fluctuations, after an initial loss of approximately 20% of the core residue native contacts, the core of the protein transiently completely refolds to the native state. The transition from the native-like basin to the partially unfolded compact state involves approximately 75% loss of native contacts but little change in the radius of gyration or core hydration properties. The intermediate state adopts for part of the time in one of the trajectories a novel highly compact salt-bridge stabilized structure that can be identified as a conformational trap. The intermediate-to-unfolded state transition is characterized by a large increase in the radius of gyration. After an initial relaxation the unfolded state recovers a native-like topology of the domain. The simulated unfolded state ensemble reproduces in detail experimental nuclear magnetic resonance data and leads to a convincing complete picture of the unfolded domain.     

Effects of confinement in chaperonin assisted protein folding: rate enhancement by decreasing the roughness of the folding energy landscape

Chaperonins, such as the GroE complex of the bacteria Escherichia coli, assist the folding of proteins under non-permissive folding conditions by providing a cavity in which the newly translated or translocated protein can be encapsulated. Whether the chaperonin cage plays a passive role in protecting the protein from aggregation, or an active role in accelerating folding rates, remains a matter of debate. Here, we investigate the role of confinement in chaperonin mediated folding through molecular dynamics simulations. We designed a substrate protein with an alpha/beta sandwich fold, a common structural motif found in GroE substrate proteins and confined it to a spherical hydrophilic cage which mimicked the interior of the GroEL/ES cavity. The thermodynamics and kinetics of folding were studied over a wide range of temperature and cage radii. Confinement was seen to significantly raise the collapse temperature, T(c), as a result of the associated entropy loss of the unfolded state. The folding temperature, T(f), on the other hand, remained unaffected by encapsulation, a consequence of the folding mechanism of this protein that involves an initial collapse to a compact misfolded state prior to rearranging to the native state. Folding rates were observed to be either accelerated or retarded compared to bulk folding rates, depending on the temperature of the simulation. Rate enhancements due to confinement were observed only at temperatures above the temperature T(m), which corresponds to the temperature at which the protein folds fastest. For this protein, T(m) lies above the folding temperature, T(f), implying that encapsulation alone will not lead to a rate enhancement under conditions where the native state is stable (T相似文献   

Polypeptide in the chaperonin cage partly protrudes out and then folds inside or escapes outside

The current mechanistic model of chaperonin-assisted protein folding assumes that the substrate protein in the cage, formed by GroEL central cavity capped with GroES, is isolated from outside and exists as a free polypeptide. However, using ATPase-deficient GroEL mutants that keep GroES bound, we found that, in the rate-limiting intermediate of a chaperonin reaction, the unfolded polypeptide in the cage partly protrudes through a narrow space near the GroEL/GroES interface. Then, the entire polypeptide is released either into the cage or to the outside medium. The former adopts a native structure very rapidly and the latter undergoes spontaneous folding. Partition of the in-cage folding and the escape varies among substrate proteins and is affected by hydrophobic interaction between the polypeptide and GroEL cavity wall. The ATPase-active GroEL with decreased in-cage folding produced less of a native model substrate protein in Escherichia coli cells. Thus, the polypeptide in the critical GroEL-GroES complex is neither free nor completely confined in the cage, but it is interacting with GroEL's apical region, partly protruding to outside.     

Dual function of protein confinement in chaperonin-assisted protein folding.

The GroEL/GroES chaperonin system mediates the folding of a range of newly synthesized polypeptides in the bacterial cytosol. Using a rapid biotin-streptavidin-based inhibition of chaperonin function, we show that the cage formed by GroEL and its cofactor GroES can have a dual role in promoting folding. First, enclosure of nonnative protein in the GroEL:GroES complex is essential for folding to proceed unimpaired by aggregation. Second, folding inside the cage can be significantly faster than folding in free solution, independently of ATP-driven cycles of GroES binding and release. This suggests that confinement of unfolded protein in the narrow hydrophilic space of the chaperonin cage smoothes the energy landscape for the folding of some proteins, increasing the flux of folding intermediates toward the native state.     

Shortening a loop can increase protein native state entropy

Protein loops are essential structural elements that influence not only function but also protein stability and folding rates. It was recently reported that shortening a loop in the AcP protein may increase its native state conformational entropy. This effect on the entropy of the folded state can be much larger than the lower entropic penalty of ordering a shorter loop upon folding, and can therefore result in a more pronounced stabilization than predicted by polymer model for loop closure entropy. In this study, which aims at generalizing the effect of loop length shortening on native state dynamics, we use all‐atom molecular dynamics simulations to study how gradual shortening a very long or solvent‐exposed loop region in four different proteins can affect their stability. For two proteins, AcP and Ubc7, we show an increase in native state entropy in addition to the known effect of the loop length on the unfolded state entropy. However, for two permutants of SH3 domain, shortening a loop results only with the expected change in the entropy of the unfolded state, which nicely reproduces the observed experimental stabilization. Here, we show that an increase in the native state entropy following loop shortening is not unique to the AcP protein, yet nor is it a general rule that applies to all proteins following the truncation of any loop. This modification of the loop length on the folded state and on the unfolded state may result with a greater effect on protein stability. Proteins 2015; 83:2137–2146. © 2015 Wiley Periodicals, Inc.     

Prediction of natively unfolded regions in protein chain

We have shown that the ability of a protein to be in globular or in natively unfolded state (under native conditions) may be determined (besides low overall hydrophobicity and a large net charge) by such a property as the average environment density, the average number of residues enclosed at the given distance. A statistical scale of the average number of residues enclosed at the given distance for 20 types of amino acid residues in globular state has been created on the basis of 6626 protein structures. Using this scale for separation of 80 globular and 90 natively unfolded proteins we fail only in 11% of proteins (compared with 17% of errors which are observed if to use hydrophobicity scale). The present scale may be used both for prediction of form (folded or unfolded) of the native state of protein and for prediction of natively unfolded regions in protein chains. The results of comparison of our method of predicting natively unfolded regions with the other known methods show that our method has the highest fraction of correctly predicted natively unfolded regions (that is 87% and 77% if to make averaging over residues and over proteins correspondingly).     

Study of multiple unfolding trajectories and unfolded states of the protein GB1 under the physical property space

Forty nine molecular dynamics simulations of unfolding trajectories of the segment B1 of streptococcal protein G (GB1) provide a direct demonstration of the diversity of unfolding pathway and give a statistically utmost unfolding pathway under the physical property space. Twelve physical properties of the protein were chosen to construct a 12-dimensional property space. Then the 12-dimensional property space was reduced to a 3-dimensional principle component property space. Under the property space, the multiple unfolding trajectories look like "trees", which have some common characters. The "root of the tree" corresponds to the native state, the "bole" homologizes the partially unfolded conformations, and the "crown" is in correspondence to the unfolded state. These unfolding trajectories can be divided into three types. The first one has the characters of straight "bole" and "crown" corresponding to a fast two-state unfolding pathway of GB1. The second one has the character of "the standstill in the middle tree bole", which may correspond to a three-state unfolding pathway. The third one has the character of "the circuitous bole" corresponding to a slow two-state unfolding pathway. The fast two-state unfolding pathway is a statistically utmost unfolding pathway or preferred pathway of GB1, which occupies 53% of 49 unfolding trajectories. In the property space all the unfolding trajectories construct a thermal unfolding pathway ensemble of GB1. The unfolding pathway ensemble resembles a funnel that is gradually emanative from the native state ensemble to the unfolded state ensemble. In the property space, the thermal unfolded state distribution looks like electronic cloud in quantum mechanics. The unfolded states of the independent unfolding simulation trajectories have substantial overlaps, indicating that the thermal unfolded states are confined by the physical property values, and the number of protein unfolded state are much less than that was believed before.     

Abstracts: Albany 2007, The 15th Conversation

Abstract

Forty nine molecular dynamics simulations of unfolding trajectories of the segment B1 of streptococcal protein G (GB1) provide a direct demonstration of the diversity of unfolding pathway and give a statistically utmost unfolding pathway under the physical property space. Twelve physical properties of the protein were chosen to construct a 12-dimensional property space. Then the 12-dimentional property space was reduced to a 3-dimentional principle component property space. Under the property space, the multiple unfolding trajectories look like “trees”, which have some common characters. The “root of the tree” corresponds to the native state, the “bole” homologizes the partially unfolded conformations, and the “crown” is in correspondence to the unfolded state. These unfolding trajectories can be divided into three types. The first one has the characters of straight “bole” and “crown” corresponding to a fast two-state unfolding pathway of GB1. The second one has the character of “the standstill in the middle tree bole”, which may correspond to a three-state unfolding pathway. The third one has the character of “the circuitous bole” corresponding to a slow two-state unfolding pathway. The fast two-state unfolding pathway is a statistically utmost unfolding pathway or preferred pathway of GB1, which occupies 53% of 49 unfolding trajectories. In the property space all the unfolding trajectories construct a thermal unfolding pathway ensemble of GB1. The unfolding pathway ensemble resembles a funnel that is gradually emanative from the native state ensemble to the unfolded state ensemble. In the property space, the thermal unfolded state distribution looks like electronic cloud in quantum mechanics. The unfolded states of the independent unfolding simulation trajectories have substantial overlaps, indicating that the thermal unfolded states are confined by the physical property values, and the number of protein unfolded state are much less than that was believed before.     

Effect of unfolding on the tryptophanyl fluorescence lifetime distribution in apomyoglobin

Proteins exhibit, even in their native state, a large number of conformations differing in small details (substates). The fluorescence lifetime of tryptophanyl residues can reflect the microenvironmental characteristics of these subconformations. We have analyzed the lifetime distribution of the unique indole residue of tuna apomyoglobin (Trp A-12) during the unfolding induced by temperature or guanidine hydrochloride. The results show that the increase of the temperature from 10 to 30 degrees C causes a sharpening of the lifetime distribution. This is mainly due to the higher rate of interconversion among the conformational substates in the native state. A further temperature increase produces partially or fully unfolded states, resulting in a broadening of the tryptophanyl lifetime distribution. The data relative to the guanidine-induced unfolding show a sigmoidal increase of the distribution width, which is due to the transition of the protein structure from the native to the random-coiled state. The broadening of the lifetime distribution indicates that, even in the fully unfolded protein, the lifetime of the tryptophanyl residues is influenced by the protein matrix, which generates very heterogeneous microenvironments.     

pH-induced denaturation of proteins: a single salt bridge contributes 3-5 kcal/mol to the free energy of folding of T4 lysozyme

The energetics of a salt bridge formed between the side chains of aspartic acid 70 (Asp70) and histidine 31 (His31) of T4 lysozyme have been examined by nuclear magnetic resonance techniques. The pKa values of the residues in the native state are perturbed from their values in the unfolded protein such that His31 has a pKa value of 9.1 in the native state and 6.8 in the unfolded state at 10 degrees C in moderate salt. Similarly, the aspartate pKa is shifted to a value of about 0.5 in the native state from its value of 3.5-4.0 in the unfolded state. These shifts in pKa show that the salt bridge is stabilized 3-5 kcal/mol. This implies that the salt bridge stabilizes the native state by 3-5 kcal/mol as compared to the unfolded state. This is reflected in the thermodynamic stability of mutants of the protein in which Asp70, His31, or both are replaced by asparagine. These observations and consideration of the thermodynamic coupling of protonation state to folding of proteins suggest a mechanism of acid denaturation in which the unfolded state is progressively stabilized by protonation of its acid residues as pH is lowered below pH 4. The unfolded state is stabilized only if acidic groups in the folded state have lower pKa values than in the unfolded state. When the pH is sufficiently low, the acid groups of both the native and unfolded states are fully protonated, and the apparent unfolding equilibrium constant becomes pH independent. Similar arguments apply to base-induced unfolding.(ABSTRACT TRUNCATED AT 250 WORDS)     

Folding simulations of Trp‐cage mini protein in explicit solvent using biasing potential replica‐exchange molecular dynamics simulations

Replica exchange molecular dynamics (RexMD) simulations are frequently used for studying structure formation and dynamics of peptides and proteins. A significant drawback of standard temperature RexMD is, however, the rapid increase of the replica number with increasing system size to cover a desired temperature range. A recently developed Hamiltonian RexMD method has been used to study folding of the Trp‐cage protein. It employs a biasing potential that lowers the backbone dihedral barriers and promotes peptide backbone transitions along the replica coordinate. In two independent applications of the biasing potential RexMD method including explicit solvent and starting from a completely unfolded structure the formation of near‐native conformations was observed after 30–40 ns simulation time. The conformation representing the most populated cluster at the final simulation stage had a backbone root mean square deviation of ～1.3 Å from the experimental structure. This was achieved with a very modest number of five replicas making it well suited for peptide and protein folding and refinement studies including explicit solvent. In contrast, during five independent continuous 70 ns molecular dynamics simulations formation of collapsed states but no near native structure formation was observed. The simulations predict a largely collapsed state with a significant helical propensity for the helical domain of the Trp‐cage protein already in the unfolded state. Hydrogen bonded bridging water molecules were identified that could play an active role by stabilizing the arrangement of the helical domain with respect to the rest of the chain already in intermediate states of the protein. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Characterization of molten globule state of cytochrome c at alkaline, native and acidic pH induced by butanol and SDS

In our earlier communications, we had studied the acid induced unfolding of stem bromelain, glucose oxidase and fetuin [Eur. J. Biochem. 269 (2002) 47; Biochem. Biophys. Res. Comm. 303 (2003) 685; Biochim. Biophys. Acta 1649 (2003) 164] and effect of salts and alcohols on the acid unfolded state of alpha-chymotrypsinogen and stem bromelain [Biochim. Biophy. Acta 1481 (2000) 229; Arch. Biochem. Biophys. 413 (2) (2003) 199]. Here, we report the presence of molten globule like equilibrium intermediate state under alkaline, native and acid conditions in the presence of SDS and butanol. A systematic investigation of sodium dodecyl sulphate and butanol induced conformational alterations in alkaline (U(1)) and acidic (U(2)) unfolded states of horse heart ferricytochrome c was examined by circular dichroism (CD), tryptophan fluorescence and 1-anilino-8-napthalene sulfonate (ANS) binding. The cytochrome c (cyt c) at pH 9 and 2 shows the loss of approximately 61% and 65% helical secondary structure. Addition of increasing concentrations of butanol (0-7.2 M) and sodium dodecyl sulphate (0-5 mM) led to an increase in ellipticity value at 208 and 222 nm, which is the characteristic of formation of alpha-helical structure. Cyt c is a heme protein in which the tryptophan fluorescence is quenched in the native state by resonance energy transfer to the heme group attached to cystines at positions 14 and 17. At alkaline and acidic pH protein shows enhancement in tryptophan fluorescence and quenched ANS fluorescence. Addition of increasing concentration of butanol and SDS to alkaline or acid unfolded state leads to decrease in tryptophan and increase in ANS fluorescence with a blue shift in lambda(max), respectively. In the presence of 7.2 M butanol and 5 mM SDS two different intermediate states I(1) and I(2) were obtained at alkaline and acidic pH, respectively. States I(1) and I(2) have native like secondary structure with disordered side chains (loss of tertiary structure) as predicted from tryptophan fluorescence and high ANS binding. These results altogether imply that the butanol and SDS induced intermediate states at alkaline and acid pH lies between the unfolded and native state. At pH 6, in the presence of 7.2 M butanol or 5 mM SDS leads to the loss of CD bands at 208 and 222 nm with the appearance of trough at 228 nm also with increase in tryptophan and ANS fluorescence in contrast to native protein. This partially unfolded intermediate state obtained represents the folding pathway from native to unfolded structure. To summarize; the 7.2 M butanol and 5 mM SDS stabilizes the intermediate state (I(1) and I(2)) obtained at low and alkaline pH. While the same destabilizes the native structure of protein at pH 6, suggesting a difference in the mechanism of conformational stability.     

Tryptophan-tryptophan energy migration as a tool to follow apoflavodoxin folding

Submolecular details of Azotobacter vinelandii apoflavodoxin (apoFD) (un)folding are revealed by time-resolved fluorescence anisotropy using wild-type protein and variants lacking one or two of apoFD's three tryptophans. ApoFD equilibrium (un)folding by guanidine hydrochloride follows a three-state model: native ↔ unfolded ↔ intermediate. In native protein, W128 is a sink for Förster resonance energy transfer (FRET). Consequently, unidirectional FRET with a 50-ps transfer correlation time occurs from W167 to W128. FRET from W74 to W167 is much slower (6.9 ns). In the intermediate, W128 and W167 have native-like geometry because the 50-ps transfer time is observed. However, non-native structure exists between W74 and W167 because instead of 6.9 ns the transfer correlation time is 2.0 ns. In unfolded apoFD this 2.0-ns transfer correlation time is also detected. This decrease in transfer correlation time is a result of W74 and W167 becoming solvent accessible and randomly oriented toward one another. Apparently W74 and W167 are near-natively separated in the folding intermediate and in unfolded apoFD. Both tryptophans may actually be slightly closer in space than in the native state, even though apoFD's radius increases substantially upon unfolding. In unfolded apoFD the 50-ps transfer time observed for native and intermediate folding states becomes 200 ps as W128 and W167 are marginally further separated than in the native state. Apparently, apoFD's unfolded state is not a featureless statistical coil but contains well-defined substructures. The approach presented is a powerful tool to study protein folding.     

Reversible deactivation of beta-lactamase by quinacillin. Extent of the conformational change in the isolated transitory complex.

Conditions have been established where the deactivation of the beta-lactamase from Staphylococcus aureus PC1 by the penicillin substrate, quinacillin, is close to complete but fully reversible. The temperature-dependence of the rate of re-activation indicated a half-life of about 170 min for the deactivated state at 0 degrees C. Measurement of the relative viscosity of mixtures of enzyme and quinacillin at 8.4 degrees C ruled out any significant difference in shape or solvation between the deactivated and the normal enzyme. C.d. measurements of the deactivated protein, separated from excess quinacillin, showed that the quinacillin side-chain chromophore was bound in an asymmetric environment. The ellipticity associated with the bound quinacillin chromophore decreased with the same first-order rate constant as that for reappearance of enzyme activity. These findings support the accumulation of a deactivated state that contains bound quinacillin or a derivative. Quinacillin caused a 3-fold increase in the rate of 3H exchange-out (at a rate that was low compared with that for the substantially unfolded or expanded protein). However, there was rapid exchange-out of about 50 3H atoms on addition of 1 M-urea to the deactivated enzyme, whereas the same concentration had no effect on the exchange-out of 3H from native enzyme. The interpretation that quinacillin increases the susceptibility of the native state to unfolding in the presence of urea is supported by the demonstration that SO4(2)- ions decreased the rate and extent of deactivation but had no effect on the rate of re-activation, as predicted from the observation that SO4(2)- ions, in competition with urea, stabilize the native state relative to the partially unfolded state H [Mitchinson & Pain (1985) J. Mol. Biol. 184, 331-342].     

Exploring the relationship between funneled energy landscapes and two-state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.     

Exploring the Minimally Frustrated Energy Landscape of Unfolded ACBP

The unfolded state of globular proteins is not well described by a simple statistical coil due to residual structural features, such as secondary structure or transiently formed long-range contacts. The principle of minimal frustration predicts that the unfolded ensemble is biased toward productive regions in the conformational space determined by the native structure. Transient long-range contacts, both native-like and non-native-like, have previously been shown to be present in the unfolded state of the four-helix-bundle protein acyl co-enzyme binding protein (ACBP) as seen from both perturbations in nuclear magnetic resonance (NMR) chemical shifts and structural ensembles generated from NMR paramagnetic relaxation data. To study the nature of the contacts in detail, we used paramagnetic NMR relaxation enhancements, in combination with single-point mutations, to obtain distance constraints for the acid-unfolded ensemble of ACBP. We show that, even in the acid-unfolded state, long-range contacts are specific in nature and single-point mutations affect the free-energy landscape of the unfolded protein. Using this approach, we were able to map out concerted, interconnected, and productive long-range contacts. The correlation between the native-state stability and compactness of the denatured state provides further evidence for native-like contact formation in the denatured state. Overall, these results imply that, even in the earliest stages of folding, ACBP dynamics are governed by native-like contacts on a minimally frustrated energy landscape.     

Protein folding in confined and crowded environments

Confinement and crowding are two major factors that can potentially impact protein folding in cellular environments. Theories based on considerations of excluded volumes predict disparate effects on protein folding stability for confinement and crowding: confinement can stabilize proteins by over 10k_BT but crowding has a very modest effect on stability. On the other hand, confinement and crowding are both predicted to favor conformations of the unfolded state which are compact, and consequently may increase the folding rate. These predictions are largely borne out by experimental studies of protein folding under confined and crowded conditions in the test tube. Protein folding in cellular environments is further complicated by interactions with surrounding surfaces and other factors. Concerted theoretical modeling and test-tube and in vivo experiments promise to elucidate the complexity of protein folding in cellular environments.     

Misfolding dynamics of human prion protein

We report the results of longest to date simulation on misfolding of monomeric human prion protein (HuPrP). By comparing our simulation of a partially unfolded protein to the simulation of the native protein, we observe that the native protein as well as native regions in the partially unfolded protein remain in the native state, and the unfolded regions fold back with increased extended (sheet and PP-II) conformations. The misfolded regions show increased basin hopping from non-helical basins while the amino acids locked in the helical conformation tend to stay locked in that conformation. Our results also validate the hypothesis that denaturation of helices and formation of a partially unfolded intermediate is required for misfolding as the native protein stayed in native conformation for the entire simulation. Finally, we also observe that there is no correlation between misfolding and the chemical identity of amino acids, as both hydrophobic and hydrophilic amino acids showed equal probability of sampling extensively from non-native conformations.     

The cold denatured state is compact but expands at low temperatures: hydrodynamic properties of the cold denatured state of the C-terminal domain of L9

A point mutation of a small globular protein, the C-terminal domain of L9 destabilizes the protein and leads to observable cold-denaturation at temperatures above zero. The cold denatured state is in slow exchange with the native state on the NMR time scale, and this allows the hydrodynamic properties of the cold unfolded state and the native state to be measured under identical conditions using pulsed-field gradient NMR diffusion measurements. This provides the first experimental measurement of the hydrodynamic properties of a cold unfolded protein and its folded form under identical conditions. Hydrodynamic radii of the cold-induced unfolded states were measured for a set of temperatures ranging from 2 °C to 25 °C at pD 6.6 in the absence of denaturant. The cold unfolded state is compact compared to the urea or acid unfolded state and a trend of increasing radii of hydration is observed as the temperature is lowered. These observations are confirmed by experiments on the same protein at pD 8.0, where it is more stable, in the presence of a modest concentration of urea. The expansion of the cold-denatured state at lower temperatures is consistent with the temperature dependence of hydrophobic interactions.