Urea-induced conformational changes in cold- and heat-denatured states of a protein, Streptomyces subtilisin inhibitor.

Streptomyces subtilisin inhibitor (SSI) is known to exist in at least two distinct denatured states, cold-denatured (D') and heat-denatured (D) under acidic conditions. In the present work, we investigated the manner how increasing urea concentration from 0 to 8 M changes the polypeptide chain conformation of SSI that exists initially in the D' and D states as well as in the native state (N), in terms of the secondary structure, the tertiary structure, and the chain form, based on the results of the experiments using circular dichroism (CD), small-angle X-ray scattering (SAXS) and 1H-NMR spectroscopy. Our results indicate that the urea-induced conformational transitions of SSI under typical conditions of D' (pH 1.8, 3 degrees C) occur at least in two steps. In the urea concentration range of 0-2 M (step 1), a cooperative destruction of the tertiary structure occurs, resulting in a mildly denatured state (DU), which may still contain a little amount of secondary structures. In the concentration range of 2-4 M urea (step 2), the DU state gradually loses its residual secondary structure, and increases the radius of gyration nearly to a maximum value. At 4 M urea, the polypeptide chain is highly disordered with highly mobile side chains. Increasing the urea concentration up to 8 M probably results in the more highly denatured or alternatively the stiffer chain conformations. The conformational transition starting from the N state proceeds essentially the same way as in the above scheme in which D' is replaced with N. The conformational transition starting from the D state lacks step 1 because the D state contains no tertiary structures and is similar to the DU state. The fact that similar conformations are reached at urea concentrations above 2 M from different conformations of D', D, and N indicates that the effect of urea dominates in determining the polypeptide conformation of SSI in the denatured states rather than the pH and temperature.     

Structural details of urea binding to barnase: a molecular dynamics analysis.

BACKGROUND: The molecular mechanism of urea-induced protein unfolding has not been established. It is generally thought that denaturation results from the stabilizing interactions of urea with portions of the protein that are buried in the native state and become exposed upon unfolding of the protein. RESULTS: We have performed molecular dynamics simulations of barnase (a 110 amino acid RNase from Bacillus amyloliquefaciens) with explicit water and urea molecules at 300 K and 360 K. The native conformation was unaffected in the 300 K simulations at neutral and low pH. Two of the three runs at 360 K and low pH showed some denaturation, with partial unfolding of the hydrophobic core 2. The first solvation shell has a much higher density of urea molecules (water/urea ratio ranging from 2.07 to 2.73) than the bulk (water/urea ratio of 4.56). About one half of the first-shell urea molecules are involved in hydrogen bonds with polar or charged groups on the barnase surface, and between 15% and 18% of the first-shell urea molecules participate in multiple hydrogen bonds with barnase. The more stably bound urea molecules tend to be in crevices or pockets on the barnase surface. CONCLUSIONS: The simulation results indicate that an aqueous urea solution solvates the surface of a polypeptide chain more favorably than pure water. Urea molecules interact more favorably with nonpolar groups of the protein than water does, and the presence of urea improves the interactions of water molecules with the hydrophilic groups of the protein. The results suggest that urea denaturation involves effects on both nonpolar and polar groups of proteins.     

Molecular Dynamics/Free Energy Perturbation Studies of the Thermostable V74I Mutant of Ribonuclease HI

Abstract

Recent site-directed mutagenesis and thermodynamic studies have shown that the V74I mutant of Escherichia coli ribonuclease HI (RNase HI) is more stable than the wild type protein [Ishikawa et al., Biochemistry 32, 6171 (1993)]. In order to clarify the stabilization mechanism of this mutant, we calculated the free energy change due to the mutation Val 74→Ile in both the native and denatured states by free energy perturbations based on molecular dynamics (MD) simulations. We carried out inclusive MD simulations for the protein in water; i.e., fully solvated, no artificial constraints applied, and all long-range Coulomb interactions included. We found that the free energy of the mutant increased slightly relative to the wild type, in the native state by 1.60 kcal/mol, and in the denatured state by 2.25 kcal/mol. The unfolding free energy increment of the mutant (0.66 ± 0.19 kcal/mol) was in good agreement with the experimental value (0.6 kcal/mol). The hysteresis error in the free energy calculations, i.e., forward and reverse perturbations, was only ±0.19 kcal/mol. These results show that the V74I mutant is stabilized relative to the wild type by the increased free energy of the denatured state and not by a decrease in the free energy of the native state as had been proposed earlier based on the mutant X-ray structure. It was found that the stabilization was caused by a loss of solvation energy in the mutant denatured state and not by improved packing interactions inside the native protein.     

Characterization of goat plasma vitronectin

Vitronectin (VN) was isolated and characterized from goat plasma in native and denatured state. Native VN consisted of 160 and >250 kDa polypeptides, whereas denatured VN showed bands of 81 and >250 kDa on SDS-gel. Storage of 81 kDa polypeptide for 3 days at 4 degrees C resulted in formation of 160 and >250 kDa proteins. Hence high molecular weight forms of VN may be dimer and multimeric forms of 81 kDa monomer. Both native as well as denatured VN showed cell adhesive activity. Cells bound to native VN were round, whereas cells adhered to denatured VN were fully spread, a characteristic also observed with 81 kDa polypeptide. The 81 kDa VN bound to Heparin, whereas the 160 kDa preparation did not bind to Heparin in presence of urea. Absence of EDTA resulted in the degradation of goat VN. Similarly, addition of excess Ca(2+) caused total degradation of VN polypeptides in buffers with EDTA, suggesting metalloprotease activity inthe protein.     

Trifluoroethanol-induced beta --> alpha transition in beta-lactoglobulin: hydration and cosolvent binding studied by 2H, 17O, and 19F magnetic relaxation dispersion

Alcohols, such as 2,2,2-trifluoroethanol (TFE), have been shown to induce a cooperative transition to an open helical structure in many proteins, but the underlying molecular mechanism has not been identified. Here, we employ the technique of magnetic relaxation dispersion (MRD) to study the TFE-induced beta --> alpha transition of beta-lactoglobulin at pH 2.4. Unlike traditional techniques that focus on protein secondary structure, the MRD method directly monitors the solvent, providing quantitative information about preferential solvation and solvent penetration and about the overall size and structural integrity of the protein. In this multinuclear MRD study, we use the (2)H and (17)O resonances to examine hydration and the (19)F resonance to study TFE. The transformation from the native to the helical state via an intermediate state at 300 K is found to be accompanied by a progressive expansion of the protein and loss of specific long-lived hydration sites. The observation of (17)O and (19)F dispersions from the helical state shows that water and TFE penetrate the protein. The MRD data indicate a strong accumulation of TFE at the surface as well as in the interior of the protein. At 277 K, BLG is much less affected by TFE, remaining in the native state at 16% TFE, but adopting a nonnative structure at 30% TFE. This nonnative structure is not penetrated by long-lived water molecules. The implications of these findings for the mechanism of TFE-induced structural transformations are discussed.     

Exploring Early Stages of the Chemical Unfolding of Proteins at the Proteome Scale

After decades of using urea as denaturant, the kinetic role of this molecule in the unfolding process is still undefined: does urea actively induce protein unfolding or passively stabilize the unfolded state? By analyzing a set of 30 proteins (representative of all native folds) through extensive molecular dynamics simulations in denaturant (using a range of force-fields), we derived robust rules for urea unfolding that are valid at the proteome level. Irrespective of the protein fold, presence or absence of disulphide bridges, and secondary structure composition, urea concentrates in the first solvation shell of quasi-native proteins, but with a density lower than that of the fully unfolded state. The presence of urea does not alter the spontaneous vibration pattern of proteins. In fact, it reduces the magnitude of such vibrations, leading to a counterintuitive slow down of the atomic-motions that opposes unfolding. Urea stickiness and slow diffusion is, however, crucial for unfolding. Long residence urea molecules placed around the hydrophobic core are crucial to stabilize partially open structures generated by thermal fluctuations. Our simulations indicate that although urea does not favor the formation of partially open microstates, it is not a mere spectator of unfolding that simply displaces to the right of the folded←→unfolded equilibrium. On the contrary, urea actively favors unfolding: it selects and stabilizes partially unfolded microstates, slowly driving the protein conformational ensemble far from the native one and also from the conformations sampled during thermal unfolding.     

Charge-charge interactions influence the denatured state ensemble and contribute to protein stability

Several recent studies have shown that it is possible to increase protein stability by improving electrostatic interactions among charged groups on the surface of the folded protein. However, the stability increases are considerably smaller than predicted by a simple Coulomb's law calculation, and in some cases, a charge reversal on the surface leads to a decrease in stability when an increase was predicted. These results suggest that favorable charge-charge interactions are important in determining the denatured state ensemble, and that the free energy of the denatured state may be decreased more than that of the native state by reversing the charge of a side chain. We suggest that when the hydrophobic and hydrogen bonding interactions that stabilize the folded state are disrupted, the unfolded polypeptide chain rearranges to compact conformations with favorable long-range electrostatic interactions. These charge-charge interactions in the denatured state will reduce the net contribution of electrostatic interactions to protein stability and will help determine the denatured state ensemble. To support this idea, we show that the denatured state ensemble of ribonuclease Sa is considerably more compact at pH 7 where favorable charge-charge interactions are possible than at pH 3, where unfavorable electrostatic repulsion among the positive charges causes an expansion of the denatured state ensemble. Further support is provided by studies of the ionic strength dependence of the stability of charge-reversal mutants of ribonuclease Sa. These results may have important implications for the mechanism of protein folding.     

Polyelectrolyte and unfolded protein pore entrance depends on the pore geometry

We determined the ability of Maltose Binding Protein and the polyelectrolyte dextran sulfate to enter into and interact with channels formed by Staphylococcus aureus α-hemolysin. The entry of either macromolecule in the channel pore causes transient, but well-defined decreases in the single-channel ionic current. The protein and polyelectrolyte were more likely to enter the pore mouth at the channel's cap domain than at the stem side. When the cap domain was denatured in the presence of 4 M urea, the probability that either the denatured protein or polyelectrolyte entered the pore from the cap-domain side decreased. For channels in their native conformation, the polyelectrolyte-induced current blockades were characterized by two mean residence times that were independent of the side of entry. For channels with a denaturated cap domain, the mean polyelectrolyte residence times for relatively long-lived blockades decreased, while that for short-lived blockades were unchanged. For denatured protein, we also observed 2 characteristic residence times that were relatively fast. Only the relatively short-lived blockades were observed with native channels. When the α-hemolysin monomers in aqueous solution were incubated in 4 M urea before channel formation, the two characteristic residence times were greater than those for pre-formed pores that were subsequently perturbed by urea. These times might correspond to the interactions between the unfolded protein and the partially unfolded channel.     

Perturbations of the denatured state ensemble: modeling their effects on protein stability and folding kinetics.

By considering the denatured state of a protein as an ensemble of conformations with varying numbers of sequence-specific interactions, the effects on stability, folding kinetics, and aggregation of perturbing these interactions can be predicted from changes in the molecular partition function. From general considerations, the following conclusions are drawn: (1) A perturbation that enhances a native interaction in denatured state conformations always increases the stability of the native state. (2) A perturbation that promotes a non-native interaction in the denatured state always decreases the stability of the native state. (3) A change in the denatured state ensemble can alter the kinetics of aggregation and folding. (4) The loss (or increase) in stability accompanying two mutations, each of which lowers (or raises) the free energy of the denatured state, will be less than the sum of the effects of the single mutations, except in cases where both mutations affect the same set of partially folded conformations. By modeling the denatured state as the ensemble of all non-native conformations of hydrophobic-polar (HP) chains configured on a square lattice, it can be shown that the stabilization obtained from enhancement of native interactions derives in large measure from the avoidance of non-native interactions in the D state. In addition, the kinetic effects of fixing single native contacts in the denatured state or imposing linear gradients in the HH contact probabilities are found, for some sequences, to significantly enhance the efficiency of folding by a simple hydrophobic zippering algorithm. Again, the dominant mechanism appears to be avoidance of non-native interactions. These results suggest stabilization of native interactions and imposition of gradients in the stability of local structure are two plausible mechanisms involving the denatured state that could play a role in the evolution of protein folding and stability.     

Small-angle X-ray scattering of reduced ribonuclease A: effects of solution conditions and comparisons with a computational model of unfolded proteins

The disulfide-reduced form of bovine ribonuclease A, with the Cys thiols irreversibly blocked, was characterized by small-angle x-ray scattering. To help resolve the conflicting results and interpretations from previous studies of this model unfolded protein, we measured scattering profiles using a range of solution conditions and compared them with the profiles predicted by a computational model for a random-coil polypeptide. Analysis of the simulated and experimental profiles reveals that scattering intensities at intermediate angles, corresponding to interatomic distances in the range of 5-20 Å, are particularly sensitive to changes in solvation and can be used to assess the internal scaling behavior of the polypeptide chain, expressed as a mass fractal dimension, D_m. This region of the scattering curve is also much less sensitive to experimental artifacts than is the very small angle regime (the Guinier region) that has been more typically used to characterize unfolded proteins. The experimental small-angle x-ray scattering profiles closely matched those predicted by the computational model assuming relatively small solvation energies. The scaling behavior of the polypeptide approaches that of a well-solvated polymer under conditions where it has a large net charge and at high urea concentrations. At lower urea concentrations and neutral pH, the behavior of the chain approaches that expected for θ-conditions, where the effects of slightly unfavorable interactions with solvent balance those of excluded volume, leading to scaling behavior comparable to that of an idealized random walk chain. Though detectable, the shift toward more compact conformations at lower urea concentrations does not correspond to a transition to a globule state and is associated with little or no reduction in conformational entropy. This type of collapse, therefore, is unlikely to greatly reduce the conformational search for the native state.     

Conformational stability of ribonuclease T1. I. Thermal denaturation and effects of salts.

The thermal transition of RNase T1 was studied by two different methods; tryptophan residue fluorescence and circular dichroism. The fluorescence measurements provide information about the environment of the indole group and CD measurements on the gross conformation of the polypeptide chain. Both measurements at pH 5 gave the same transition temperature of 56 degrees C and the same thermodynamic quantities, delta Htr (= 120 kcal/mol) and delta Str (= 360 eu/mol), for the transition from the native state to the thermally denatured state, indicating simultaneous melting of the whole molecule including the hydrophobic region where the tryptophan residue is buried. Stabilization by salts was observed in the pH range from 2 to 10, since the presence of 0.5 m NaCL caused an increase of about 5 degrees C to 10 degrees C in the transition temperature, depending on the pH. The fluorescence measurements on the RNase T1 complexed with 2'-GMP showed a transition with delta Htr =167 kcal/mol and delta Str =497 eu/mol at a transition temperature about 6 degrees C higher than that for the free enzyme. The large value of delta Htr for RNase T1 indicates the highly cooperative nature of the thermal transition; this value is much higher than those of other globular proteins. Analysis of the CD spectrum of thermally denatured RNase T1 suggests that the denatured state is not completely random but retains some ordered structures.     

Effects of urea and guanidine · HCl on the folding and unfolding of pancreatic trypsin inhibitor

Concentrated solutions of urea and of guanidine · HCl produced a random spectrum of single-disulphide forms of the polypeptide chain of the pancreatic trypsin inhibitor. Guanidine · HCl also unfolded completely, with accompanying interchange of disulphide bonds, the two-disulphide form of this protein in the native-like conformation; urea produced an equilibrium mixture in which one-quarter of the molecules had the native-like conformation and disulphide bonds. The unfolded forms of the protein in the denaturants were very flexible polypeptide chains. The observations suggest that urea and guanidine · HCl are denaturants because they produce essentially equally favourable solvation of all portions of a polypeptide.The energetics of the conformational transitions involved in folding and unfolding of the inhibitor were determined in urea and compared with those observed in its absence. The denaturant lowers the stability of the native, folded inhibitor relative to that of the reduced, unfolded state by 6.5 kilocalories per mole; the greatest part of this apparent free-energy difference was expressed at the two-disulphide stage of folding. The results are consistent with other indications that most of the favourable interactions stabilizing the native conformation of this protein are not encountered until the final stage of folding, when all may occur simultaneously.The unfolded one- and two-disulphide species produced in guanidine · HCl were trapped, and their rearrangement to the normal intermediates followed after removal of the denaturant. The random single-disulphide species, with one exception, reverted very rapidly to the non-random spectrum of intermediates normally observed during folding; this confirms that these species are normally rapidly interconverted and that normal refolding of the reduced protein is not dependent kinetically upon residual stable conformation in the reduced protein. The unfolded two-disulphide species refolded to the native-like conformation more slowly, but appeared to pass through the same intermediates normally observed during refolding from the fully reduced state.     

Denatured proteins and early folding intermediates simulated in a reduced conformational space

Conformations of globular proteins in the denatured state were studied using a high-resolution lattice model of proteins and Monte Carlo dynamics. The model assumes a united-atom and high-coordination lattice representation of the polypeptide conformational space. The force field of the model mimics the short-range protein-like conformational stiffness, hydrophobic interactions of the side chains and the main-chain hydrogen bonds. Two types of approximations for the short-range interactions were compared: simple statistical potentials and knowledge-based protein-specific potentials derived from the sequence-structure compatibility of short fragments of protein chains. Model proteins in the denatured state are relatively compact, although the majority of the sampled conformations are globally different from the native fold. At the same time short protein fragments are mostly native-like. Thus, the denatured state of the model proteins has several features of the molten globule state observed experimentally. Statistical potentials induce native-like conformational propensities in the denatured state, especially for the fragments located in the core of folded proteins. Knowledge-based protein-specific potentials increase only slightly the level of similarity to the native conformations, in spite of their qualitatively higher specificity in the native structures. For a few cases, where fairly accurate experimental data exist, the simulation results are in semiquantitative agreement with the physical picture revealed by the experiments. This shows that the model studied in this work could be used efficiently in computational studies of protein dynamics in the denatured state, and consequently for studies of protein folding pathways, i.e. not only for the modeling of folded structures, as it was shown in previous studies. The results of the present studies also provide a new insight into the explanation of the Levinthal's paradox.     

Heat capacity and conformation of proteins in the denatured state

Heat capacity, intrinsic viscosity and ellipticity of a number of globular proteins (pancreatic ribonuclease A, staphylococcal nuclease, hen egg-white lysozyme, myoglobin and cytochrome c) and a fibrillar protein (collagen) in various states (native, denatured, with and without disulfide crosslinks or a heme) have been studied experimentally over a broad range of temperatures. It is shown that the partial heat capacity of denatured protein significantly exceeds the heat capacity of native protein, especially in the case of globular proteins, and is close to the value calculated for an extended polypeptide chain from the known heat capacities of individual amino acid residues. The significant residual structure that appears at room temperature in the denatured states of some globular proteins (e.g. myoglobin and lysozyme) at neutral pH results in a slight decrease of the heat capacity, probably due to partial screening of the protein non-polar groups from water. The heat capacity of the unfolded state increases asymptotically, approaching a constant value at about 100 degrees C. The temperature dependence of the heat capacity of the native state, which can be determined over a much shorter range of temperature than that of the denatured state and, correspondingly, is less certain, appears to be linear up to 80 degrees C. Therefore, the denaturational heat capacity increment seems to be temperature-dependent and is likely to decrease to zero at about 140 degrees C.     

Electrostatic interactions in the denatured state and in the transition state for protein folding: effects of denatured state interactions on the analysis of transition state structure

The development of electrostatic interactions during the folding of the N-terminal domain of the ribosomal protein L9 (NTL9) is investigated by pH-dependent rate equilibrium free energy relationships. We show that Asp8, among six acidic residues, is involved in non-native, electrostatic interactions with K12 in the transition state for folding as well as in the denatured state. The perturbed native state pK(a) of D8 (pK(a) = 3.0) appears to be maintained through non-native interactions in both the transition state and the denatured state. Mutational effects on the stability of the transition state for protein (un)folding are often analyzed in respect to change in ground states. Thus, the interpretation of transition state analysis critically depends on an understanding of mutational effects on both the native and denatured state. Increasing evidence for structurally biased denatured states under physiological conditions raises concerns about possible denatured state effects on folding studies. We show that the structural interpretation of transition state analysis can be altered dramatically by denatured state effects.     

Thermodynamic stability of ribonuclease A in alkylurea solutions and preferential solvation changes accompanying its thermal denaturation: a calorimetric and spectroscopic study

The effect of methylurea, N,N'-dimethylurea, ethylurea, and butylurea as well as guanidine hydrochloride (GuHCl), urea and pH on the thermal stability, structural properties, and preferential solvation changes accompanying the thermal unfolding of ribonuclease A (RNase A) has been investigated by differential scanning calorimetry (DSC), UV, and circular dichroism (CD) spectroscopy. The results show that the thermal stability of RNase A decreases with increasing concentration of denaturants and the size of the hydrophobic group substituted on the urea molecule. From CD measurements in the near- and far-UV range, it has been observed that the tertiary structure of RNase A melts at about 3 degrees C lower temperature than its secondary structure, which means that the hierarchy in structural building blocks exists for RNase A even at conditions at which according to DSC and UV measurements the RNase A unfolding can be interpreted in terms of a two-state approximation. The far-UV CD spectra also show that the final denatured states of RNase A at high temperatures in the presence of different denaturants including 4.5 M GuHCl are similar to each other but different from the one obtained in 4.5 M GuHCl at 25 degrees C. The concentration dependence of the preferential solvation change delta r23, expressed as the number of cosolvent molecules entering or leaving the solvation shell of the protein upon denaturation and calculated from DSC data, shows the same relative denaturation efficiency of alkylureas as other methods.     

Study of the compact denatured state of a protein by molecular dynamics simulation]

The native state can be considered as a unique conformation of the protein molecule with the lowest free energy of residue contacts. In this case, all other conformations correspond to the denatured state. The degree of their compactness varies significantly. Under folding conditions, the compact denatured state rather than the random coil is in equilibrium with native protein. The balance between the main forces of protein folding, the solvophobic interactions and conformational entropy, suggests that some properties of the compact denatured state are close to those of native protein, whereas other properties are close to those of the random coil. To investigate the molecular structure of the compact denatured state, the method of molecular dynamics simulation seems to be very useful.     

Preferential interactions of urea with lysozyme and their linkage to protein denaturation

The interactions involved in the denaturation of lysozyme in the presence of urea were examined by thermal transition studies and measurements of preferential interactions of urea with the protein at pH 7.0, where it remains native up to 9.3 M urea, and at pH 2.0, where it undergoes a transition between 2.5 and 5.0 M urea. The destabilization of lysozyme by urea was found to follow the linear dependence on urea molar concentration, M(u), DeltaG(u)(o)=DeltaG(w)(o)-2.1 M(u), over the combined data, where DeltaG(u)(o) and DeltaG(w)(o) are the standard free energy changes of the N right harpoon over left harpoon D reaction in urea and water, respectively. Combination with the measured preferential binding gave the result that the increment of preferential binding, deltaGamma(23)=Gamma(23)(D)-Gamma(23)(N), is also linear in M(u). A temperature dependence study of preferential interactions permitted the evaluation of the transfer enthalpy, DeltaHmacr;(2,tr)(o), and entropy, DeltaSmacr;(2,tr)(o) of lysozyme from water into urea in both the native and denatured states. These values were found to be consistent with the enthalpy and entropy of formation of inter urea hydrogen bonds (Schellman, 1955; Kauzmann, 1959), with estimated values of DeltaHmacr;(2,tr)(o)=ca. -2.5 kcal mol(-1) and DeltaSmacr;(2,tr)(o)=ca. -7.0 e.u. per site. Analysis of the results led to the conclusion that the stabilization of the denatured form was predominantly by preferential binding to newly exposed peptide groups. Combination with the knowledge that stabilizing osmolytes act by preferential exclusion from peptide groups (Liu and Bolen, 1995) has led to the general conclusion that both the stabilization and destabilization of proteins by co-solvents are controlled predominantly by preferential interactions with peptide groups newly exposed on denaturation.     

Mechanism of the stabilization of ribonuclease A by sorbitol: preferential hydration is greater for the denatured then for the native protein.

The effect of interactions of sorbitol with ribonuclease A (RNase A) and the resulting stabilization of structure was examined in parallel thermal unfolding and preferential binding studies with the application of multicomponent thermodynamic theory. The protein was stabilized by sorbitol both at pH 2.0 and pH 5.5 as the transition temperature, Tm, was increased. The enthalpy of the thermal denaturation had a small dependence on sorbitol concentration, which was reflected in the values of the standard free energy change of denaturation, delta delta G(o) = delta G(o) (sorbitol) - delta G(o)(water). Measurements of preferential interactions at 48 degrees C at pH 5.5, where protein is native, and pH 2.0 where it is denatured, showed that sorbitol is preferentially excluded from the denatured protein up to 40%, but becomes preferentially bound to native protein above 20% sorbitol. The chemical potential change on transferring the denatured RNase A from water to sorbitol solution is larger than that for the native protein, delta mu(2D) > delta mu(2N), which is consistent with the effect of sorbitol on the free energy change of denaturation. The conformity of these results to the thermodynamic expression of the effect of a co-solvent on denaturation, delta G(o)(W) + delta mu(D)(2)delta G(o)(S) + delta mu(2D), indicates that the stabilization of the protein by sorbitol can be fully accounted for by weak thermodynamic interactions at the protein surface that involve water reversible co-solvent exchange at thermodynamically non-neutral sites. The protein structure stabilizing action of sorbitol is driven by stronger exclusion from the unfolded protein than from the native structure.