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The molecular origin of the nonideal behavior for concentrated binary solutions of biochemical compounds is examined. The difference between activities expressed in the molar and molal conventions can be large. Considering the range from dilute to concentrated, we show that molar activity coefficients can be represented by simple but rigorous equations involving between one and three parameters only. We derive a universal relationship interconverting the scales of molarity and molality without requiring the density of the solution. The equations are developed from first principles using a statistical thermodynamic theory of molar activity coefficients. It is shown how to express activity coefficients in different concentration scales, and the advantages and disadvantages of using certain scales are discussed and compared with the experimental data. Several classes of biochemically relevant compounds, many of which are naturally occurring osmolytes, are discussed: six saccharides (glucose, xylose, maltose, mannose, raffinose, and sucrose), four polyols (glycerol, mannitol, erythritol, and sorbitol), five amino acids (glycine, alanine, sarcosine, glycine betaine, and proline), and urea. Of the 16 solutes, 10 could be described in terms of a single parameter that is due to pure first-order effects (packing, hydration, or space limitation). The remaining six exhibit significant second-order effects (solute-solute interactions) and require two additional parameters, one typically identified with the volume occupied per solute molecule in the pure solute (crystal or liquid) and the other with a self-association constant. The activity coefficients of the osmolytes roughly display the rank order found with respect to their ability to stabilize proteins. These findings are discussed in terms of the physical principles that give rise to the activity coefficients.

It is shown how the leading terms of a semi grand canonical partition function (GCPF) can be used to develop analytic expressions relating activity to concentrations in two-component systems. The simple analytic expressions for activity coefficients can be fitted to activity coefficient versus concentration data for a wide range of aqueous solute systems. Only one or two parameters are required to accurately describe the activity coefficients of nonelectrolyte and electrolyte aqueous solute systems over their entire range of solubility. These forms derive from low-order number expressions of the GCPF that take into account the effective solvent interactions with the solute and between solute molecules for a variable amount of solvent. The GCPF leading terms and fitting parameters define apparent solute−solute oligomerization and solute packing phenomena that increase with solute concentration. Advantages using this grand canonical approach versus previous approaches are discussed.

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

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

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

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

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

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

Trimethylamine N-oxide (TMAO) is a solute concentrated in the urea-rich cells of elasmobranchs and coelacanth to offset the damaging effects of urea on intracellular protein structure and function. On the basis of transfer free energy measurements, favorable interaction of TMAO with amino acid side chains promote protein denaturation. This effect is more than offset by highly unfavorable TMAO-peptide backbone interactions that not only oppose denaturation but also provide stabilization against denaturation by urea. By combining transfer free energies of side chains and backbone with surface area exposure in the native and unfolded states of ribonuclease T1, the transfer free energies of native and unfolded protein from water to 1 M TMAO are estimated as 1.7 and 5.9 kcal/mol, respectively. These estimates agree favorably with the respective values of 1.2 and 5.4 kcal/mol determined experimentally by Lin and Timasheff [(1994) Biochemistry 33, 12695-12701]. The unfavorable transfer free energies of native and unfolded protein from water to TMAO provides a molecular level rationale for preferential hydration of proteins by osmolytes. Promotion of denaturation by urea is found to be offset by TMAO in a manner that is roughly additive of the combined effects of both solutes. The favorable interaction of urea with the backbone provides the dominant driving force for protein unfolding by this denaturant, and the unfavorable interaction of TMAO with backbone is the dominant force opposing urea denaturation. In solutions that contain significant organic solute concentration, the ascendance of the role of the peptide backbone over that of side chains can explain many observed effects in protein denaturation and stability induced by a variety of stabilizing and destabilizing organic solutes.

Osmolytes are small organic solutes accumulated intracellularly by many organisms as they adapt to environmental stresses. Compatible osmolytes, a functional class of osmolytes, increase protein stability while having little or no effect on protein function. To investigate the interrelationships between protein stability, function, and internal dynamics, a hydrogen exchange (HX) quench method was established and used to study the effects of sucrose (a typical compatible osmolyte) on the structural fluctuations of ribonuclease A. It was found that the HX rates of the amide protons with intermediate rates are not affected by 1 M sucrose, but the slow-exchanging amide protons exchange even slower in 1 M sucrose. The protection factors of the slow-exchanging protons fall into a comparatively narrow range while those of the intermediate-exchanging protons vary widely. In agreement with the two-process model [Woodward, C.K., & Hilton, B. D. (1980) Biophys. J. 32, 561-575], we conclude that for those slow-exchanging amide protons, the exchange occurs mainly from the compact unfolded state ensemble of the protein. The internal dynamics leading to slow exchange involve exposure of large protein surface areas, similar to that which occurs upon the unfolding of protein. Because sucrose opposes such an increase in protein surface area exposure, both the slow HX rates and the protein stability are affected by sucrose. For those amide protons with fast and intermediate HX rates, the exchange occurs mainly from the native state ensemble of the protein. The internal dynamics involved in the exchange are localized without much surface area change, and functionally important structural fluctuations are likely to occur within this dynamic range.(ABSTRACT TRUNCATED AT 250 WORDS)

Transfer free energy measurements of amino acids from water to the osmolytes, sucrose and sarcosine, were made as a function of osmolyte concentration. From these data, transfer free energies of the amino acid side chains were obtained, and the transfer free energy of the peptide backbone was determined from solubility measurements of diketopiperazine (DKP). Using static accessible surface evaluations of the native and unfolded states of ribonuclease A, solvent exposed side chain and peptide backbone areas were multiplied by their transfer free energies and summed in order to evaluate the transfer free energy of the native and unfolded states of the protein from water to the osmolyte solutions. The results reproduced the main features of the free energy profile determined for denaturation of proteins in the presence of osmolytes. The side chains were found collectively to favor exposure to the osmolyte in comparison to exposure in water, and in this sense the side chains favor protein unfolding. The major factor which opposes and overrides the side chain preference for denaturation and results in the stabilization of proteins observed in osmolytes is the highly unfavorable exposure of polypeptide backbone on unfolding. Except for urea and guanidine hydrochloride solutions, it is shown that all organic solvents (e.g., dioxane, ethanol, ethylene glycol) and solutes (osmolytes) for which transfer free energy measurements have been determined exhibit unfavorable transfer free energy of the peptide backbone.(ABSTRACT TRUNCATED AT 250 WORDS)

A thermodynamic cycle is used to explore a host of assumptions, conditions, and criteria which must be met for evaluation of authentic unfolding free energy changes. The thermodynamic cycle involves measurement of the unfolding free energy change (delta GzeroN-U) for RNase A at a reference pH, along with determination of the titration free energy changes for the native and unfolded species over an extended pH range. From these free energy changes, delta GzeroN-U at any pH in the range can be predicted and compared with delta GzeroN-U determined by use of the linear extrapolation method (LEM). Good agreement is found between predicted and determined free energy changes covering a broad range of protein stability changes (5 kcal/mol), pH (pH from 3 to 8.5), and lengths of linear extrapolation (C1/2 values from 2.4 to 7.7 M urea). The agreement between predicted and LEM-determined delta GzeroN-U values demonstrates (1) that delta GzeroN-U determined by the LEM is a function of state; i.e., it has the properties of additivity and independence of pathway required of an authentic free energy quantity; (2) the ability to obtain delta GzeroN-U values which are in agreement with the free energy change predicted by the cycle is independent of the length of linear extrapolation; and (3) the two-state assumption holds over an extensive pH range. The fact that the pH titration curve of unfolded RNase A in 6 M GdnHCl could be used in accurately predicting urea-induced delta GzeroN-U values shows that the unfolded ensemble in 6 M GdnHCl is thermodynamically identical to urea-unfolded RNase A as far as the pH dependence of protein stability is concerned. Urea-induced and GdnHCl-induced RNase A delta GzeroN-U values at pH 3 were found not to agree with one another, but this appears to be due to the inability to control the salt effect of GdnHCl on the native state of RNase A. These results provide strong evidence that the LEM applied to urea-induced unfolding of RNase A results in reliable free energy changes that meet a number of essential criteria for authentic thermodynamic quantities. The titration method is important in its own right in providing a means for evaluating the pH dependence of two-state protein unfolding free energy changes which does not require analysis of denaturant-induced unfolding transitions.

A procedure is developed for assessing covalent and noncovalent aspects of the acylation of alpha-chymotrypsin (alpha-Ct) by the substrate trifluoroethyl furoate (S) to form furoyl-chymotrypsin (F-Ct) and trifluoroethanol (P1). The free energy change (-4.31 kcal/mol) for the acylation at pH 7, alpha-Ct+S F-Ct+P1, contains contributions from covalent bond changes as well as noncovalent changes. The noncovalent changes are considered to be manifested in the structures of alpha-Ct and F-Ct, and a noncovalent free energy difference between alpha-Ct and F-Ct has been evaluated from the difference in unfolding free energy changes for these proteins. The unfolding free energy changes demonstrate that F-Ct is 1.6 kcal/mol less stable than alpha-Ct at pH7. Thus, despite an overall favorable free energy change for acyl-enzyme formation (-4.31 kcal/mol), covalent linkage of the furoyl moiety to the active site is thermodynamically destabilizing to the enzyme. The consequence of this unfavorable effect of the furoyl moiety on the noncovalent free energy is that "binding" of the covalently linked furoyl moiety cannot be the driving force for acylation. The source of free energy driving acylation is the covalent bond-breaking and bond-making involved in transesterification of the furoyl group to the enzyme. Since the (noncovalent) Michaelis complex between alpha-Ct and substrate is significantly more stable (thermodynamically) than F-Ct, a substantial amount of noncovalent free energy must be given up on forming F-Ct. The destabilization residing in F-Ct is consistent with the possibility that energy transduction occurs when the Michaelis complex is converted to F-Ct and that destabilization is relieved on reaching the next activated complex.

Organisms and cellular systems which have adapted to stresses such as high temperature, desiccation, and urea-concentrating environments have responded by concentrating particular organic solutes known as osmolytes. These osmolytes are believed to confer protection to enzyme and other macromolecular systems against such denaturing stresses. Differential scanning calorimetric (DSC) experiments were performed on ribonuclease A and hen egg white lysozyme in the presence of varying concentrations of the osmolytes glycine, sarcosine, N,N-dimethylglycine, and betaine. Solutions containing up to several molar concentrations of these solutes were found to result in considerable increases in the thermal unfolding transition temperature (Tm) for these proteins. DSC scans of ribonuclease A in the presence of up to 8.2 M sarcosine resulted in reversible two-state unfolding transitions with Tm increases of up to 22 degrees C and unfolding enthalpy changes which were independent of Tm. On the basis of the thermodynamic parameters observed, 8.2 M sarcosine results in a stabilization free energy increase of 7.2 kcal/mol for ribonuclease A at 65 degrees C. This translates into more than a 45,000-fold increase in stability of the native form of ribonuclease A over that in the absence of sarcosine at this temperature. Catalytic activity measurements in the presence of 4 M sarcosine give kcat and Km values that are largely unchanged from those in the absence of sarcosine. DSC of lysozyme unfolding in the presence of these osmolytes also results in Tm increases of up to 23 degrees C; however, significant irreversibly occurs with this protein.(ABSTRACT TRUNCATED AT 250 WORDS)

Guanidine hydrochloride (GdnHCl) and thermally induced unfolding measurements on the oxidized form of Escherichia coli thioredoxin at pH 7 were combined for the purpose of assessing the functional dependence of unfolding free energy changes on denaturant concentration over an extended GdnHCl concentration range. Conventional analysis of GdnHCl unfolding exhibits a linear plot of unfolding delta G vs [GdnHCl] in the transition zone. In order to extend unfolding delta G measurements outside of that narrow concentration range, thermal unfolding measurements were performed using differential scanning calorimetry (DSC) in the presence of low to moderate concentrations of GdnHCl. The unfolding delta G values from the DSC measurements were corrected to 25 degrees C using the Gibbs-Helmholtz equation and mapped onto the delta G vs [GdnHCl] plot. The dependence of unfolding delta G on [GdnHCl] was found to be linear over the full denaturant concentration range, provided that the chloride ion concentration was kept at a threshold of greater than or equal to 1.5 M. In the DSC experiments performed in the presence of GdnHCl, chloride concentrations were maintained at 1.5 M by addition of appropriate amounts of NaCl. The linear extrapolation method (LEM) gives an unfolding free energy change in the absence of denaturant (delta G degrees N-U) in excellent agreement with the delta G determined by DSC measurement in 1.5 M NaCl. The various methods give a consensus unfolding delta G value of 8.0 kcal/mol at 25 degrees C in the absence of denaturant.(ABSTRACT TRUNCATED AT 250 WORDS)

The enthalpy change (delta H) accompanying the alpha-helix to random coil transition in water has been determined calorimetrically for a 50-residue peptide of defined sequence that contains primarily alanine. The enthalpy of helix formation is one of the basic parameters needed to predict thermal unfolding curves for peptide helices and it provides a starting point for analysis of the peptide hydrogen bond. The experimental uncertainty in delta H reflects the fact that the transition curve is too broad to measure in its entirety, which precludes fitting the baselines directly. A lower limit for delta H of unfolding, 0.9 kcal/mol per residue, is given by assuming that the change in heat capacity (delta Cp) is zero, and allowing the baseline to intersect the transition curve at the lowest measured Cp value. Use of the van't Hoff equation plus least-squares fitting to determine a more probable baseline gives delta H = 1.3 kcal/mol per residue. Earlier studies of poly(L-lysine) and poly(L-glutamate) have given 1.1 kcal/mol per residue. Those investigations, along with our present result, suggest that the side chain has little effect on delta H. The possibility that the peptide hydrogen bond shows a correspondingly large delta H, and the implications for protein stability, are discussed.

Protein solvation is the key determinant for isothermal, concentration-dependent effects on protein equilibria, such as folding. The required solvation information can be extracted from experimental thermodynamic data using Kirkwood-Buff theory. Here we derive and discuss general properties of proteins and osmolytes that are pertinent to their biochemical behavior. We find that hydration depends very little on osmolyte concentration and type. Strong dependencies on both osmolyte concentration and type are found for osmolyte self-solvation and protein–osmolyte solvation changes upon unfolding. However, solvation in osmolyte solutions does not involve complex concentration dependencies as found in organic molecules that are not used as osmolytes in nature. It is argued that the simple solvation behavior of naturally occurring osmolytes is a prerequisite for their usefulness in osmotic regulation in vivo.

Mixtures of organic osmolytes occur in cells of many organisms, raising the question of whether their actions on protein stability are independent or synergistic. To investigate this question it is desirable to develop a system that permits evaluation of the effect of one osmolyte on the efficacy of another to either force-fold or denature a protein. A means of evaluating the efficacy of an osmolyte is provided by its m-value, an experimental quantity that measures the ability of the osmolyte to force a protein to unfold or fold. An experimental system is presented that enables evaluations of the m-values of osmolytes in the presence and absence of a second osmolyte. The experimental system involves use of a marginally stable protein in 10 mM buffer (pH 7, 200 mM salt, and 34 degrees C) that is at the midpoint of its native to denatured transition. These conditions enable determination of m-values for protecting and denaturing osmolytes in the presence and absence of a second osmolyte, permitting assessment of the extent to which the two osmolytes affect each other's efficacy. The two osmolytes investigated in this work are the denaturing osmolyte, urea, and the protecting osmolyte, sarcosine. Results show unequivocally that neither osmolyte alters the efficacy of the other in forcing the protein to fold or unfold-the osmolytes act independently on the protein despite their combined concentrations being in the multi-molar range. These osmolytes avoid altering one another's efficacy at these high concentrations because the number of osmolyte interaction sites on the protein is large and the binding constants are quite small. Consequently, the site occupancies are low enough in number that the two osmolytes neither compete nor cooperate in interacting with the protein.

We have used trimethylamine N-oxide (TMAO), a protecting osmolyte, to dissect the complex thermodynamic linkages involved in the interaction between the chemokine interleukin-8 (IL-8) and the N-domain of its receptor CXCR1. Our results show that TMAO induces folding in the CXCR1 receptor N-domain and that the N-domain upon folding binds ligand with higher affinity. This represents, to our knowledge, the smallest domain that has been shown to be folded in osmolyte. Using the phase diagram method to analyze this thermodynamic relationship graphically, we also observe that TMAO favors ligand dimerization and that the dimeric ligand binds the receptor domain with lower affinity. We have thus been able to dissect coupling among three distinct processes, receptor domain folding, ligand dimerization, and ligand-receptor domain binding in this chemokine-receptor system. We also observe that the affinity of the related chemokine, melanoma growth stimulatory activity (MGSA), increases concurrent with N-domain folding similar to IL-8 but shows more profound differences on ligand dimerization. These studies establish a novel and innovative use of osmolytes to dissect linkages among different processes and exploit the phase diagram as a tool to graphically represent and dissect complex thermodynamic relationships in biological systems. On the basis of our observations and earlier work, we discuss the relevance of ligand dimerization in chemokine regulation.

An understanding of the impact of the crowded conditions in the cytoplasm on its biomolecules is of clear importance to biochemical, medical, and pharmaceutical science. Our previous work on the use of small biochemical compounds to crowd protein solutions indicates that a quantitative description of their nonideal behavior is possible and straightforward. Here, we show the structural origin of the nonideal solution behavior. We discuss the consequences of these findings regarding protein folding stability and solvation in crowded solutions through a structural analysis of the m-value or the change in free-energy difference of a macromolecule in solution with respect to the concentration of a third component.

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

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

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

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

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

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

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

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

The k(cat) and K(m) kinetic parameters of the labile enzyme rabbit muscle lactic dehydrogenase were determined as a function of the concentration of proline, a solute (osmolyte) accumulated in the cells of many organisms to protect them against environmental stresses. Proline is believed to protect against the stress(es) without altering the functional activity of cellular macromolecules, a property defining it as a "compatible osmolyte." In the range of 0–2 M proline, K(cat) and K(m) values for both substrates are essentially unchanged, but between 2 M and 4 M proline, k(cat) decreases by a factor of 3 to 4, whereas K(m) values are only modestly changed, if at all. These results are consistent with the proposal that compatible osmolytes do not affect functional activity, that the property of compatibility expressed by such osmolytes is generic without regard to the evolutionary history of the protein, and that the organic osmolyte concentration range over which compatibility is exhibited is extensive. In short, the results are in full accord with the principal hypothesis of "compatible osmolytes" in detail and scope.

The thermal stability of opsin and rhodopsin in disk membranes of bovine retinal rod cell outer segments has been examined by differential scanning calorimetry (DSC). Consistent data is obtained when all parameters of the membrane preparation are carefully reproduced. Calorimetric parameters for opsin and rhodopsin vary as a function of scan rate, membrane concentration and pH. Binding of retinal imparts a stabilization to the protein structure indicated by a temperature of thermal denaturation (Tm) of 71.4oC for rhodopsin as compared to 55.3°C for opsin. Similarly, the ΔHcal for rhodopsin (167 kcal/mole) is 43 kcal/mole higher than that for opsin (124 kcal/mole). By contrast, a much smaller effect is obtained in samples subjected to limited proteolysis indicating that the membrane-embedded portion of the protein lends quantitatively more stability to the protein than does its cytoplasmic surface. DSC confirms that the pH of maximal stability of both opsin and rhodopsin is 6.1. DSC can be used successfully to examine stability of rhodopsin in detergent solution. In membrane suspensions, membrane-membrane interactions are indicated by a dependence of ΔHcal on the membrane concentration. Intermolecular interactions within the disk membrane are indicated by a dependence of opsin’s ΔHcal on the extent of bleaching of the membrane suspension.

Hydrolysis of omicron-hydroxy-alpha-toluenesulfonic acid sultone (sultone II) is mediated by alpha-chymotrypsin. Sultone II is a highly strained cyclic ester substrate that forms a covalent intermediate with the enzyme and is therefore expected to release ring-strain energy upon formation of the sulfonyl enzyme species. It is found that the equilibrium constant for forming the covalent intermediate from the Michaelis complex is quite modest (K2 = 16.4), suggesting that perhaps the strain energy is not released in the ring-cleavage event. The implied retention of chemical (strain) energy by the sulfonyl enzyme species raises the question of the means by which the enzyme avoids expression of strain energy and the implications of this effect in the catalytic sequence. High-pressure liquid chromatography (HPLC) rate data demonstrate facile reversion of sulfonyl enzyme to the Michaelis complex, and that reversion is preferred over hydrolysis of the covalent intermediate. pH-independent rate and equilibrium constants are derived for the alpha-chymotrypsin-mediated hydrolysis of sultone II, and pKa values for groups on the enzyme are reported that are consistent with literature values obtained from analysis of nonspecific substrate hydrolysis by the enzyme.

The linear extrapolation method was used to evaluate the unfolding free energy changes (delta G degrees N-U) for phenylmethanesulfonyl chymotrypsin (PMS-Ct) at pH 6.0. The nonlinear least-squares fits of difference spectral data using urea and guanidinium chloride as denaturants gave identical values for delta G degrees N-U and delta epsilon degrees U, the latter being extinction coefficient differences between native and unfolded forms of the protein in the limit of zero concentration of denaturant. The independence of these parameters from the nature of solvent suggests strongly that they are characteristic properties of the protein alone. The delta G degrees N-U data at pH 6.0 and 4.0, which differ by more than 100-fold in stability of the protein, were incorporated into a thermodynamic cycle involving free energy changes for titration of native and unfolded PMS-Ct from pH 4.0 to 6.0. The purpose of the cycle was to test whether delta G degrees N-U obtained by use of the linear extrapolation method exhibits the characteristics required of a thermodynamic function of state. Within error, the thermodynamic cycle was found to accommodate the delta G degrees N-U quantities obtained at pH 4.0 and 6.0 for PMS-Ct.

(1970). The Compulsive Gambler and Spouse in Group Psychotherapy. International Journal of Group Psychotherapy: Vol. 20, No. 1, pp. 77-90.

Characteristics and properties of the unfolding free energy change, delta G degrees N-U, as determined by the linear extrapolation method are assessed for the unfolding of phenylmethanesulfonyl chymotrypsin (PMS-Ct). Difference spectral measurements at 293 nm were used to define PMS-Ct unfolding brought about with guanidinium chloride, urea, and 1,3-dimethylurea. All three denaturants were shown to give identical extinction coefficient differences (delta epsilon N-U) between native and unfolded forms of the protein in the limit of zero concentration of denaturant. The independence of delta epsilon N-U on denaturant supports the linear extension of pre- and postdenaturational base lines into the transition zone, allowing evaluation of unfolding equilibrium constants based on the two-state assumption. An expression, based on the linear extrapolation method, was used to provide estimates of delta G degrees N-U for the three denaturants using nonlinear least-squares fitting of the primary data, delta epsilon versus [denaturant]. The three delta G degrees N-U values were identical, within error, suggesting that the free energy change is a property of the protein system and independent of denaturant. It is suggested that the error in delta G degrees N-U determined from use of the linear extrapolation method is significantly larger than commonly reported in the literature.

A set of experiments that permit evaluation and estimation of rate and equilibrium constants involving an intermediate in the α-chymotrypsin mediated hydrolysis of o-hydroxy-α-toluenesulfonic acid ...