Non-Sequence-Specific Interactions Can Account for the Compaction of Proteins Unfolded under “Native” Conditions

Proteins unfolded by high concentrations of chemical denaturants adopt expanded, largely structure-free ensembles of conformations that are well approximated as random coils. In contrast, globular proteins unfolded under less denaturing conditions (via mutations, or transiently unfolded after a rapid jump to native conditions) and molten globules (arising due to mutations or cosolvents) are often compact. Here we explore the origins of this compaction using a truncated equilibrium-unfolded variant of the 57-residue FynSH3 domain. As monitored by far-UV circular dichroism, NMR spectroscopy, and hydrogen-exchange kinetics, CΔ4 (a 4-residue carboxy-terminal deletion variant of FynSH3) appears to be largely unfolded even in the absence of denaturant. Nevertheless, CΔ4 is quite compact under these conditions, with a hydrodynamic radius only slightly larger than that of the native protein. In order to understand the origins of this molten-globule-like compaction, we have characterized a random sequence polypeptide of identical amino acid composition to CΔ4. Notably, we find that the hydrodynamic radius of this random sequence polypeptide also approaches that of the native protein. Thus, while native-like interactions may contribute to the formation of compact “unfolded” states, it appears that non-sequence-specific monomer-monomer interactions can also account for the dramatic compaction observed for molten globules and the “physiological” unfolded state.     

The unfolded state of NTL9 is compact in the absence of denaturant

Interest in the unfolded state of proteins has grown with the realization that this state can have considerable structure in the absence of denaturants. Natively unfolded proteins, mutations that unfold proteins under native conditions, and changes in pH that induce unfolding are attractive models for the unfolded state in the absence of denaturant. The unfolded state of the N-terminal domain of ribosomal protein L9 (NTL9) was previously shown to contain significant non-native electrostatic interactions [Cho, J. H., Sato, S., and Raleigh, D. P. (2004) J. Mol. Biol. 338, 827-837]. NTL9 has a mixed alpha-beta structure and folds via a two-state mechanism. We have generated a model of the unfolded state of NTL9 in the absence of denaturant by substitution of an alanine for phenylalanine 5 located in the core of this protein. The CD spectrum of the variant, denoted as F5A, exhibits significantly less structure than the wild type; however, the mean residue ellipticity of F5A at 222 nm (-8200 deg cm(2) dmol(-)(1)) is considerably larger than expected for a fully unfolded protein, indicating that residual secondary structure is populated. F5A also has more residual structure than the urea-unfolded wild type. The stability of F5A is estimated to be at least 1 kcal/mol unfavorable, showing that the unfolded state is populated to 84% or more. NMR pulsed-field gradient measurements yield a hydrodynamic radius of 16.1 A for wild-type NTL9 and 20.8 A for the F5A variant in native buffer. The physiologically relevant unfolded state of wild-type NTL9 is likely to be even more compact than F5A since the mutation should reduce the level of hydrophobic clustering in the unfolded state in the absence of denaturant. The hydrodynamic radius of F5A increases to 25.9 A in 8 M urea, and a value of 23.5 A is obtained for the wild type under similar conditions. The results show that the unfolded state of F5A in the absence of denaturant is more compact and contains more structure than the urea-unfolded form.     

Intrinsic structural disorder and sequence features of the cell cycle inhibitor p57Kip2.

The cell cycle inhibitor p57Kip2 induces cell cycle arrest by inhibiting the activity of cyclin-dependent kinases. p57, although active as a cyclin A-CDK2 inhibitor, is largely unfolded or intrinsically disordered as shown by circular dichroism and fluorescence spectra characteristic of an unfolded protein and a hydrodynamic radius consistent with an unfolded structure. In addition, the N-terminal domain of p57 is both functionally independent as a cyclin A-CDK2 inhibitor and unstructured, as demonstrated by circular dichroism and fluorescence spectra indicative of unfolded proteins, a lack of 1H chemical shift dispersion and a hydrodynamic radius consistent with a highly unfolded structure. The amino acid compositions of full-length p57 and the excised QT domain of p57 exhibit significant deviations from the average composition of globular proteins that are consistent with the observed intrinsic disorder. However, the amino acid composition of the CDK inhibition domain of p57 does not exhibit such a striking deviation from the average values observed for proteins, implying that a general low level of hydrophobicity, rather than depletion or enrichment in specific amino acids, contributes to the intrinsic disorder of the excised p57 CDK inhibition domain.     

Studies of the unfolding of an unstable mutant of staphylococcal nuclease: Evidence for low temperature unfolding and compactness of the high temperature unfolded state

Fluorescence and circular dichroism data as a function of temperature were obtained to characterize the unfolding of nuclease A and two of its less stable mutants. These spectroscopic data were obtained with a modified instrument that enables the nearly simultaneous detection of both fluorescence and CD data on the same sample. A global analysis of these multiple datasets yielded an excellent fit of a model that includes a change in the heat capacity change, ΔC_p, between the unfolded and native states. This analysis gives a ΔC_p of 2.2 kcal/mol/·K for thermal unfolding of the WT protein and 1.3 and 1.8 kcal/mol/K for the two mutants. These ΔC_p values are consistent with significant population of the cold unfolded state at ∼0°C. Independent evidence for the existence of a cold unfolded state is the observation of a separately migrating peak in size exclusion chromatography. The new chromatographic peak is seen near 0°C, has a partition coefficient corresponding to a larger hydrodynamic radius, and shows a red-shifted fluorescence spectrum, as compared to the native protein. Data also indicate that the high-temperature unfolded form of mutant nuclease is relatively compact. Size exclusion chromatography shows the high temperature unfolded form to have a hydrodynamic radius that is larger than that for the native form, but smaller than that for the urea or pH-induced unfolded forms. Addition of chemical denaturants to the high-temperature unfolded form causes a further unfolding of the protein, as indicated by an increase in the apparent hydrodynamic radius and a decrease in the rotational correlation time for Trp140 (as determined by fluorescence anisotropy decay measurements). Proteins 28:227–240, 1997 © 1997 Wiley-Liss Inc.     

Reduced BPTI is collapsed. A pulsed field gradient NMR study of unfolded and partially folded bovine pancreatic trypsin inhibitor.

Pulsed field gradient NMR was used to measure the hydrodynamic behavior of unfolded variants of bovine pancreatic trypsin inhibitor (BPTI). The unfolded BPTI species studied were [R]Abu, at pH 4.5 and pH 2.5, and unfolded [14-38]Abu, at pH 2.5. These were prepared by chemical synthesis. [R]Abu is a model for reduced BPTI; all cysteine residues are replaced by alpha-amino-n-butyric acid (Abu). [14-38]Abu retains cysteines 14 and 38, which form a disulfide bond, while the other cysteine residues are replaced by Abu. In the PFG experiments, the diffusion coefficient is measured as a function of protein concentration, and the value of D degree -the diffusion coefficient extrapolated to infinite dilution-is determined. From D degree, a value of the hydrodynamic radius. Rh, is computed from the Stokes-Einstein relationship. At pH 4.5, [R]Abu has an Rh value significantly less than the value calculated for a random coil, while at pH 2.5 the experimental Rh value is the same as for a random coil. In view of the changes in NMR detected structure of [R]Abu at pH 4.5 versus pH 2.5 (Pan H, Barbar E, Barany G, Woodward C. 1995. Extensive non-random structure in reduced and unfolded bovine pancreatic trypsin inhibitor. Biochemistry 34:13974-13981), the collapse of reduced BPTI at pH 4.5 may be associated with the formation of non-native hydrophobic clusters of pairs of side chains one to three amino acids apart in sequence. The diffusion constant of [14-38]Abu was also measured at pH 4.5, where the protein is partially folded. An increase in hydrodynamic radius of partially folded [14-38]Abu, relative to native BPTI, is similar to the increase in radius of gyration measured for other proteins under "molten globule" conditions.     

Direct characterization of the folded, unfolded and urea-denatured states of the C-terminal domain of the ribosomal protein L9

The stability of the isolated C-terminal domain of the ribosomal protein L9 (CTL9) is strongly dependent upon pH. Below pH 4.2, the folded and unfolded states are both populated significantly. Their interconversion is slow on the NMR chemical shift time-scale and separate, well-resolved resonances from each state are observed. This allows the hydrodynamic properties of both states to be studied under identical conditions by using pulse field gradient NMR experiments. Hydrodynamic radii of the folded, unfolded and urea denatured protein molecules at pD 3.8 have been derived. The acid-denatured protein has a significantly smaller hydrodynamic radius, 28.2A, compared to that of the urea-denatured protein, which is 33.6A at pD 3.8. Far-UV CD spectra show that there is more residual secondary structure retained in the acid-denatured ensemble than in the urea-denatured one. ANS binding experiments and analysis of the CD data show that this acid-denatured species is not a molten globule state. Diffusion measurements of CTL9 were conducted over the pD range from 2.1 to 7.0. The hydrodynamic radii of both the folded and the acid-unfolded protein start to increase below pD 4, with the radius of hydration of the acid-unfolded state increasing from 25.1A at pD 4.2 to 33.5A at pD 2.1. The hydrodynamic radius of the urea-denatured protein is much less sensitive to pH. The unfolded protein at pD 2.1, no urea, has almost the same hydrodynamic radius as the urea-denatured protein at pD 3.8. The CD spectra, however, show significant differences in residual secondary structure, and the acid-denatured state contains more structure.     

A compact monomeric intermediate identified by NMR in the denaturation of dimeric triose phosphate isomerase

The denaturation of triose phosphate isomerase (TIM) from Saccharomyces cerevisiae by guanidine hydrochlorids at pH 7.2 has been monitored by NMR spectroscopy in conjunction with optical spectroscopy. In the absence of denaturant, the hydrodynamic radius of 29.6(+/-0.25) A and the substantial chemical shift dispersion evident in the NMR spectrum are consistent with the highly structured dimeric native state of the protein. On the addition of 2. 2 M guanidine hydrochloride the effective hydrodynamic radius increases to 51.4(+/-0.43) A, consistent with that anticipated for the polypeptide chain in a highly unstructured random coil state. In 1.1 M guanidine hydrochloride, however, the effective hydrodynamic radius is 24.0(+/-0.25) A, a value substantially decreased relative to that of the native dimeric state but very close to that anticipated for a monomeric species with native-like compaction (23. 5 A). The lack of chemical shift dispersion indicates, however, that few tertiary interactions persist within this species. Far UV CD and intrinsic fluorescence measurements show that this compact intermediate retains significant secondary structure and that on average the fluorophores are partially excluded from solvent. Such a species could be important in the formation of dimeric TIM from its unfolded state.     

Realistic modeling of the denatured states of proteins allows accurate calculations of the pH dependence of protein stability

Computational techniques based on continuum electrostatics treatments have been successful in predicting and interpreting the pKa values of ionizable amino acids in folded proteins. Despite this progress, efforts to reproduce the pH-dependence of protein stability have met with only limited success: agreement with experimental results has been only qualitative. It has been argued previously that the most likely reason for discrepancies is the presence of residual electrostatic interactions in the unfolded state, which cause pKa values to be shifted from their model compound values. Here we show that by constructing atomistic models of the unfolded state with a simple molecular mechanics protocol that uses the native state as a starting point, much improved reproduction of pH effects on protein stability can be obtained. In contrast, when a fully extended model of the unfolded state is used, no such improvement is obtained, a result that suggests that local interactions with residues nearby in the sequence are not sufficient to properly account for the pKa shifts in the unfolded state. In comparison to model compound values, the pKa values of acidic residues in "native-like" unfolded states are typically found to be shifted downwards by approximately 0.3 pH unit, in good agreement with the average downward shift deduced from experimental measurements. Given its success in the present situation, the protocol employed here for developing simple models of the unfolded state may prove useful in other computer simulation applications.     

The low-pH unfolded state of the C-terminal domain of the ribosomal protein L9 contains significant secondary structure in the absence of denaturant but is no more compact than the low-pH urea unfolded state

There is considerable interest in the properties of the unfolded states of proteins, particularly unfolded states which can be populated in the absence of high concentrations of denaturants. Interest in the unfolded state ensemble reflects the fact that it is the starting point for protein folding as well as the reference state for protein stability studies and can be the starting state for pathological aggregation. The unfolded state of the C-terminal domain (residues 58-149) of the ribosomal protein L9 (CTL9) can be populated in the absence of denaturant at low pH. CTL9 is a 92-residue globular alpha, beta protein. The low-pH unfolded state contains more secondary structure than the low-pH urea unfolded state, but it is not a molten globule. Backbone ( (1)H, (13)C, and (15)N) NMR assignments as well as side chain (13)C beta and (1)H beta assignments and (15)N R 2 values were obtained for the pH 2.0 unfolded form of CTL9 and for the urea unfolded state at pH 2.5. Analysis of the deviations of the chemical shifts from random coil values indicates that residues that comprise the two helices in the native state show a clear preference for adopting helical phi and psi angles in the pH 2.0 unfolded state. There is a less pronounced but nevertheless clear tendency for residues 107-124 to preferentially populate helical phi and psi values in the unfolded state. The urea unfolded state has no detectable tendency to populate any type of secondary structure even though it is as compact as the pH 2.0 unfolded state. Comparison of the two unfolded forms of CTL9 provides direct experimental evidence that states which differ significantly in their secondary structure can have identical hydrodynamic properties. This in turn demonstrates that global parameters such as R h or R g are very poor indicators of "random coil" behavior.     

Protein unfolded states populated at high and ambient pressure are similarly compact

The relationship between the dimensions of pressure-unfolded states of proteins compared with those at ambient pressure is controversial; resolving this issue is related directly to the mechanisms of pressure denaturation. Moreover, a significant pressure dependence of the compactness of unfolded states would complicate the interpretation of folding parameters from pressure perturbation and make comparison to those obtained using alternative perturbation approaches difficult. Here, we determined the compactness of the pressure-unfolded state of a small, cooperatively folding model protein, CTL9-I98A, as a function of temperature. This protein undergoes both thermal unfolding and cold denaturation, and the temperature dependence of the compactness at atmospheric pressure is known. High-pressure small angle x-ray scattering studies, yielding the radius of gyration and high-pressure diffusion ordered spectroscopy NMR experiments, yielding the hydrodynamic radius were carried out as a function of temperature at 250 MPa, a pressure at which the protein is unfolded. The radius of gyration values obtained at any given temperature at 250 MPa were similar to those reported previously at ambient pressure, and the trends with temperature are similar as well, although the pressure-unfolded state appears to undergo more pronounced expansion at high temperature than the unfolded state at atmospheric pressure. At 250 MPa, the compaction of the unfolded chain was maximal between 25 and 30°C, and the chain expanded upon both cooling and heating. These results reveal that the pressure-unfolded state of this protein is very similar to that observed at ambient pressure, demonstrating that pressure perturbation represents a powerful approach for observing the unfolded states of proteins under otherwise near-native conditions.     

Interactions of lysozyme in guanidinium chloride solutions from static and dynamic light-scattering measurements

The interactions of partially unfolded proteins provide insight into protein folding and protein aggregation. In this work, we studied partially unfolded hen egg lysozyme interactions in solutions containing up to 7 M guanidinium chloride (GdnHCl). The osmotic second virial coefficient (B(22)) of lysozyme was measured using static light scattering in GdnHCl aqueous solutions at 20 degrees C and pH 4.5. B(22) is positive in all solutions, indicating repulsive protein-protein interactions. At low GdnHCl concentrations, B(22) decreases with rising ionic strength: in the absence of GdnHCl, B(22) is 1.1 x 10(-3) mLmol/g(2), decreasing to 3.0 x 10(-5) mLmol/g(2) in the presence of 1 M GdnHCl. Lysozyme unfolds in solutions at GdnHCl concentrations higher than 3 M. Under such conditions, B(22) increases with ionic strength, reaching 8.0 x 10(-4) mLmol/g(2) at 6.5 M GdnHCl. Protein-protein hydrodynamic interactions were evaluated from concentration-dependent diffusivity measurements, obtained from dynamic light scattering. At moderate GdnHCl concentrations, lysozyme interparticle interactions are least repulsive and hydrodynamic interactions are least attractive. The lysozyme hydrodynamic radius was calculated from infinite-dilution diffusivity and did not change significantly during protein unfolding. Our results contribute toward better understanding of protein interactions of partially unfolded states in the presence of a denaturant; they may be helpful for the design of protein refolding processes that avoid protein aggregation.     

Physical characteristics of 16 S rRNA under reconstitution conditions

The hydrodynamic shape and conformation of the 16 S ribosomal RNA in reconstitution buffer at both 4 degrees C and 37 degrees C were determined and compared with the corresponding properties of the 30 S ribosomal subunit at 4 degrees C in order to understand the role of the RNA molecule in the assembly of the 30 S subunit. At 4 degrees C, the 16 S rRNA has a sedimentation coefficient s020,w of 21.0 S, a diffusion coefficient D020,w of 1.72 X 10(-7) cm2/s, a frictional coefficient f/fmin of 2.37, and a hydrodynamic radius of 125 A. At 37 degrees C, the 16 S rRNA has a sedimentation coefficient s020,w of 18.4 S, a diffusion coefficient D020,w of 1.39 X 10(-7) cm2/s, a frictional coefficient f/fmin of 2.91, and a hydrodynamic radius of 153 A. At 4 degrees C, the 30 S subunit has a sedimentation coefficient s020,w of 31.8 S, a diffusion coefficient D020,w of 1.97 X 10(-7) cm2/s, a frictional coefficient f/fmin of 1.77, and a hydrodynamic radius of 109 A. These results suggested that the free RNA in solution at 4 degrees C is less folded than the RNA in the ribosomal subunit. At 37 degrees C, the free 16 S rRNA is unfolded when compared to the structure of the same RNA at 4 degrees C. This implies that the folding step accompanying the RI to RI transformation in the assembly process needs the presence of both the RNA and core proteins.     

Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.     

Solvent-induced collapse of alpha-synuclein and acid-denatured cytochrome c

The effects of solution conditions on protein collapse were studied by measuring the hydrodynamic radii of two unfolded proteins, alpha-synuclein and acid-denatured ferricytochrome c, in dilute solution and in 1 M glucose. The radius of alpha-synuclein in dilute solution is less than that predicted for a highly denatured state, and adding 1 M glucose causes further collapse. Circular dichroic data show that alpha-synuclein lacks organized structure in both dilute solution and 1 M glucose. On the other hand, the radius of acid-denatured cytochrome c in dilute solution is consistent with that of a highly denatured state, and 1 M glucose induces collapse to the size and structure of native cytochrome c. Taken together, these data show that alpha-synuclein, a natively unfolded protein, is collapsed even in dilute solution, but lacks structure.     

Folding of bovine growth hormone is consistent with the molten globule hypothesis

Previous results from equilibrium and kinetic studies of the folding of bovine growth hormone (bGH) have demonstrated that bGH does not follow a simple two-step folding mechanism. These results are summarized and interpreted according to the "molten globule" model. The molten globule state of bGH is characterized as a folding intermediate which is largely alpha-helical, retains a compact hydrodynamic radius, has packing of the aromatic side chains that is similar to the unfolded state, and possesses a solvent-exposed hydrophobic surface along helix 106-127 that readily leads to association.     

Hydrodynamic radii of native and denatured proteins measured by pulse field gradient NMR techniques

Pulse field gradient NMR methods have been used to determine the effective hydrodynamic radii of a range of native and nonnative protein conformations. From these experimental data, empirical relationships between the measured hydrodynamic radius (R(h)) and the number of residues in the polypeptide chain (N) have been established; for native folded proteins R(h) = 4.75N (0.29)A and for highly denatured states R(h) = 2.21N (0.57)A. Predictions from these equations agree well with experimental data from dynamic light scattering and small-angle X-ray or neutron scattering studies reported in the literature for proteins ranging in size from 58 to 760 amino acid residues. The predicted values of the hydrodynamic radii provide a framework that can be used to analyze the conformational properties of a range of nonnative states of proteins. Several examples are given here to illustrate this approach including data for partially structured molten globule states and for proteins that are unfolded but biologically active under physiological conditions. These reveal evidence for significant coupling between local and global features of the conformational ensembles adopted in such states. In particular, the effective dimensions of the polypeptide chain are found to depend significantly on the level of persistence of regions of secondary structure or features such as hydrophobic clusters within a conformational ensemble.     

Test for cooperativity in the early kinetic intermediate in lysozyme folding

During the folding of many proteins, collapsed globular states are formed prior to the native structure. The role of these states for the folding process has been widely discussed. Comparison with properties of synthetic homo and heteropolymers had suggested that the initial collapse represented a shift of the ensemble of unfolded conformations to more compact states without major energy barriers. We investigated the folding/unfolding transition of a collapsed state, which transiently populates early in lysozyme folding. This state forms within the dead-time of stopped-flow mixing and it has been shown to be significantly more compact and globular than the denaturant-induced unfolded state. We used the GdmCl-dependence of the dead-time signal change to characterize the unfolding transition of the burst phase intermediate. Fluorescence and far-UV CD give identical unfolding curves, arguing for a cooperative two-state folding/unfolding transition between unfolded and collapsed lysozyme. These results show that collapse leads to a distinct state in the folding process, which is separated from the ensemble of unfolded molecules by a significant energy barrier. NMR, fluorescence and small angle X-ray scattering data further show that some local interactions in unfolded lysozyme exist at denaturant concentrations above the coil-collapse transition. These interactions might play a crucial role in the kinetic partitioning between fast and slow folding pathways.     

The hydrodynamic and conformational properties of denatured proteins in dilute solutions

Published data on the characterization of unfolded proteins in dilute solutions in aqueous guanidine hydrochloride are analyzed to show that the data are not fit by either the random flight or wormlike chain models for linear chains. The analysis includes data on the intrinsic viscosity, root‐mean‐square radius of gyration, from small‐angle X‐ray scattering, and hydrodynamic radius, from the translational diffusion coefficient. It is concluded that residual structure consistent with that deduced from nuclear magnetic resonance on these solutions can explain the dilute solution results in a consistent manner through the presence of ring structures, which otherwise have an essentially flexible coil conformation. The ring structures could be in a state of continual flux and rearrangement. Calculation of the radius of gyration for the random‐flight model gives a similar reduction of this measure for chains joined at their endpoints, or those containing loop with two dangling ends, each one‐fourth the total length of the chain. This relative insensitivity to the details of the ring structure is taken to support the behavior observed across a range of proteins.     

Velocity-dependent mechanical unfolding of bacteriorhodopsin is governed by a dynamic interaction network

Bacteriorhodopsin is a model system for membrane proteins. This seven transmembrane helical protein is embedded within a membrane structure called purple membrane. Its structural stability against mechanical stress was recently investigated by atomic force microscopy experiments, in which single proteins were extracted from the purple membrane. Here, we study this process by all-atom molecular dynamics simulations, in which single bacteriorhodopsin molecules were extracted and unfolded from an atomistic purple membrane model. In our simulations, key features from the experiments like force profiles and location of key residues that resist mechanical unfolding were reproduced. These key residues were seen to be stabilized by a dynamic network of intramolecular interactions. Further, the unfolding pathway was found to be velocity-dependent. Simulations in which the mechanical stress was released during unfolding revealed relaxation motions that allowed characterization of the nonequilibrium processes during fast extraction.     

Is the hydrophobic effect stabilizing or destabilizing in proteins? The contribution of disulphide bonds to protein stability

It has been recently concluded that the hydrophobic effect, hitherto regarded as a major driving force in the folding of proteins, destabilizes the folded state relative to the unfolded state. We summarize the properties of the hydrophobic effect obtained from solvent transfer experiments and show that the recent conclusion is an artifact of crosslinking in the unfolded state, caused by disulphide bonds, metals or cofactors. We show that, for the proteins in the data set, crosslinks surprisingly destabilize folded structures entropically, but stabilize them enthalpically to a greater extent. We also calculate non-polar surface areas of these unfolded proteins. These surface areas are decreased by crosslinks. The unfolded state of proteins lacking constraints, such as myoglobin, is well approximated by a mixture of residues containing alpha-helical and beta-sheet dihedral angles. Surface areas of unfolded proteins cannot be obtained by summing the surface areas of individual residues, since this ignores any unavoidable side-chain-side-chain interactions.