17400
J. Phys. Chem. 1996, 100, 17400-17405
Effect of Surface Tension on the Stability of Heat-Stressed Proteins: A Molecular Thermodynamic Interpretation Federico Cioci Department of Chemical Engineering, UniVersity of Rome “La Sapienza”, Via Eudossiana, 18-I-00184 Roma, Italy ReceiVed: May 14, 1996; In Final Form: July 18, 1996X
The stability behavior of four globular proteins (glucose oxidase, ribonuclease, lysozyme, and carbonic anhydrase) in pure buffer and in the presence of water-miscible hydroxylic additives (alcohols, polyols, and sugars) was analyzed. Attention was focused on the influence of these compounds on the melting temperature of the proteins. For all of the proteins examined, this latter quantity was found to be linearly related to the bulk surface tension of the mixed solvent. To provide a quantitative interpretation to the above observation, a molecular thermodynamic model, based on the additive-induced perturbation of the equilibrium between the folded and the unfolded protein forms, was developed. It is shown that, under some limiting conditions, the Gibbs equilibrium criterion applied to the two-state unfolding process yields a linear dependence of the melting temperature on the bulk surface tension, as observed for the proteins considered. The results obtained appear to indicate that the conformational stability of heat-stressed proteins in water-hydroxylic cosolvent mixtures does not rely on any special property of these substances but rather on their ability to affect the interfacial free energy between the protein and the solvent through perturbations of the surface tension of water. The model proposed can be used for interpretation and correlation of thermal unfolding data and, as a diagnostic tool, to assess whether the surface tension mechanism provides the overwhelming contribution to protein unfolding.
Introduction The elaborate molecular mechanisms causing the transformation of the random-coil polypeptide chain into the compact, highly ordered, structure of proteins are mainly mediated by hydrophobic interactions1 and by nonlocal entropic effects due to steric constraints in the folded state.2 Their contributions to the free energy of stabilization are nearly equal in magnitude,3 but whereas hydrophobic interactions favor the native conformation, nonlocal entropic effects destabilize this state. The interplay of these two major and opposing driving forces manifests itself in the small free energies of stabilization commonly observed:4-6 typical values for globular proteins are in the range 5-15 kcal/mol. Native proteins, therefore, are only marginally stable, and this intrinsic lability makes them easily susceptible to denaturation. Thermal inactivation is one of the most important forms of protein denaturation.7,8 Although there is still considerable uncertainty about the mechanisms by which the polypeptide chain loses its compactness and biological activity, it now seems to be ascertained that the first and, perhaps, the only universal step in thermal inactivation is represented by partial unfolding.9-11 Valuable information about the physical bases of this process can be gained by perturbing the protein environment, for instance by addition of a water-miscible component, and analyzing the resulting changes in stability. The stability behavior of several proteins in the presence of stabilizers (such as polyols, amino acids, and salts) or destabilizers (such as urea and guanidine hydrochloride) has been extensively investigated.12-14 The influence of additives on protein stability can be interpreted largely in terms of preferential interactions of proteins with solvent components.15 In particular, the following rule appears to hold: additives that stabilize the native structure of proteins are preferentially excluded from the X
Abstract published in AdVance ACS Abstracts, September 15, 1996.
S0022-3654(96)01458-X CCC: $12.00
protein domain.16-20 The exclusion of an additive or its tendency to accumulate in the surface layer can be conveniently expressed through a characteristic preferential interaction parameter.21,22 This quantity can be related to the change in the chemical potential of the protein induced by additions of that component. Because of the direct correlation between preferential exclusion and structure stabilization, evaluation of the preferential interaction parameter allows for a qualitative estimation of the ability of an additive to stabilize proteins. A physical explanation for the stabilizing action exerted by preferentially excluded additives can be found in the fact that unfolded proteins have much greater surface area exposed to solvent than do native proteins.23 Protein unfolding is therefore accompanied by a more or less pronounced increase in the zone of exclusion. Since this situation is thermodynamically unfavorable, media containing additives capable of being preferentially excluded from the protein-solvent surface of contact would cause a displacement of the unfolding equilibrium toward the native state, leading to protein stabilization. For most stabilizers preferential exclusion seems to be dependent on increases in the surface tension of water caused by the additive.5,13,23,24 The dependence of protein stability on surface tension is in qualitative agreement with the Gibbs adsorption isotherm,25 according to which substances increasing the surface tension of water exhibit a negative excess in the surface layer, that is, are preferentially excluded from the protein interface. The Gibbs adsorption isotherm can be used to evaluate the contribution of the surface tension increment due to the additive to the change in the chemical potential of the protein, but no information can be derived on the extent to which this contribution affects the value of physically meaningful properties. Further complications arise when considering the unusual behavior of some additives that seem to contradict the above evidence. This is the case, for instance, of urea,26 which increases the surface tension of water but favors unfolding, or © 1996 American Chemical Society
Stability of Heat-Stressed Proteins glycerol16,17 and betaine,18 which lower the surface tension of water but stabilize proteins. The central role played by surface tension in a number of solvent effects involving proteins or smaller molecules is also emphasized by the solvophobic theory developed by Sinanogˇlu.27-29 In this theory, the free energy for creating a cavity enveloping the solubilized molecule is expressed in terms of the so-called microthermodynamic surface tension. This quantity accounts for curvature differences between molecular and macroscopic surfaces. Microthermodynamic surface tension is assumed to be proportional to the macroscopic value by a factor depending on the class of solvent (polar, nonpolar) and on the size of the cavity relative to the average radius of the solvent molecule. Although the solvophobic theory has been applied satisfactorily in a variety of fields ranging from quantum chemistry30 to drug-biomolecule complexation,31 its extension to heatinduced protein unfolding is not straightforward. In particular, it appears questionable to assess whether the protein-solvent interface should be treated as microscopic or macroscopic. Moreover, the temperature dependence of the microthermodynamic surface tension, which is not known a priori, should be carefully assumed prior to analysis of thermal effects on protein stability. Finally, the free energy of cavity formation arguments cannot be applied to additives whose influence on protein stability is not consistent with the surface tension effect. Despite the difficulties that may be encountered when interpreting the stability behavior of proteins in mixed solvents, it seems quite apparent that interfacial phenomena should play a major role. From a quantitative point of view, however, attempts to analyze their influence on protein unfolding have been largely unsuccessful. This limitation reveals itself in the lack of rigorous relationships between macroscopic quantities reflecting the structural state of the protein, on the one hand, and the physical properties of the solvent, on the other. In this contribution we show that the thermal behavior of a protein in media containing hydroxylic additives can be fairly well described by a linear relation between the melting temperature of the protein and the bulk surface tension of the mixed solvent. This result was obtained by analyzing the heat-induced unfolding behavior of four different proteins (glucose oxidase, ribonuclease, lysozyme, and carbonic anhydrase) in pure buffer and in the presence of a variety of additives. To provide a theoretical framework to the above finding, a molecular thermodynamic model was developed which is based on the additive-induced perturbation of the equilibrium between the folded and the unfolded protein forms. It is shown that under some limiting conditions the analytical relationships derived from the Gibbs equilibrium criterion yield a linear dependence of the melting temperature on the surface tension of the medium, as observed for the proteins investigated. Protein Unfolding in Aqueous Systems Containing Hydroxylic Additives The stability behavior of heat-stressed proteins in mixed solvents was investigated by analyzing the results of thermal unfolding experiments performed in pure buffer or in the presence of hydroxylic additives. The melting temperature, namely, the temperature at which the mole fractions of the folded and unfolded protein are equal, was used as an index of protein stability. Surface tensions of systems containing xylitol, erythritol, and sugars (glucose, fructose, maltose, sucrose, and sorbitol) were measured at 20 ( 0.1 °C using a calibrated Traube stalagmom-
J. Phys. Chem., Vol. 100, No. 43, 1996 17401
Figure 1. Melting temperature (Tm) of Aspergillus niger glucose oxidase Vs surface tension (γmix) at pH 5.5. Additives include ethanediol, 1,2-propanediol, and glycerol. The experimental Tm data were taken from ref 24. The arrow indicates the melting temperature of the protein in pure buffer.
eter. Measurements were made in bidistilled and degassed water. The observed accuracy was within (0.05 mN m-1. Surface tensions of mixtures containing liquid additives were estimated from the properties of pure components by the following relationship32 1/4
γmix
N
zjγj1/4
j)1
Fj
) Fmix∑
(1)
where γ, F, and z are the surface tension, molar density, and mole fraction, respectively. The density of the mixed solvent, Fmix, was calculated as
/
Fmix ) 1
N
zj
∑ j)1 F
(2) j
The properties of the different buffers were assumed equal to those of water, and the temperature dependence of γ was expressed by the Guggenheim equation25
γ ) γ0
(
Tc - T Tc - T0
)
(3)
where γ0 is the surface tension of the pure component at the temperature T0, Tc is the critical temperature of the same component, and is an empiric constant depending on the particular class of compounds considered. We assumed ) 0.73 for water and ) 1.22 for all other substances.25 In the case of solid additives Tc was set equal to the critical temperature of water (Tc ) 647.3 K). Figure 1 displays the trend of the melting temperature of Aspergillus niger glucose oxidase (Tm) as a function of the surface tension of the protein solution at that temperature. Data were taken from a work of Cioci et al.,24 who used UV difference spectroscopy to follow protein unfolding. The additives examined include ethanediol, 1,2-propanediol, and glycerol. These compounds were added to the protein solution individually or as binary or ternary mixtures. As results from the picture, the experimental melting temperatures are linearly related to the bulk surface tension of the solvent and decrease with γmix. It seems interesting to note that all of the above additives exerted a detrimental action on the thermal stability of glucose oxidase, i.e., caused a reduction of the melting temperature. Also in the presence of stabilizers, however, an analogous dependence of Tm on γmix was observed. Points reported in Figure 2 represent data selected from those published by Gerlsma,33 who analyzed the unfolding behavior of bovine pancreatic ribonuclease by UV difference spectros-
17402 J. Phys. Chem., Vol. 100, No. 43, 1996
Figure 2. Melting temperature (Tm) of bovine pancreatic ribonuclease Vs surface tension (γmix) at pH 5.5. Additives include ethanol, 1-propanol, ethanediol, 1,2-propanediol, 1,4-butanediol, glycerol, erythritol, and sorbitol. The experimental Tm data were taken from ref 33. The arrow indicates the melting temperature of the protein in pure buffer.
Cioci
Figure 4. Melting temperature (Tm) of bovine erythrocyte carbonic anhydrase Vs surface tension (γmix) at pH 7. Additives include ethanol, 1-propanol, ethanediol, 1,2-propanediol, xylitol, glucose, fructose, maltose, and sucrose. The experimental Tm data were taken from refs 35 and 36. The arrow indicates the melting temperature of the protein in pure buffer.
Figure 5. Hypothetical path for calculating the Gibbs free energy change associated with the unfolding process. Figure 3. Melting temperature (Tm) of chicken egg white lysozyme Vs surface tension (γmix) at pH 4. Additives include methanol, ethanediol, erythritol, xylitol, and sorbitol. The experimental Tm data were taken from ref 34. The arrow indicates the melting temperature of the protein in pure buffer.
copy. The additives used comprise alcohols (ethanol, 1-propanol) and polyols (ethanediol, 1,2-propanediol, 1,4-butanediol, glycerol, erythritol, sorbitol). Some of these components stabilized ribonuclease, whereas some others resulted in a sharp destabilization of the protein. Figure 3 shows thermal stability data relative to hen egg white lysozyme. Experimental melting temperatures were obtained by Gekko,34 who made use of differential scanning calorimetry to study protein unfolding. The systems considered consisted in aqueous mixtures of methanol or polyhydric compounds (ethanediol, erythritol, xylitol, and sorbitol). Finally, Figure 4 illustrates the stability behavior of bovine erythrocyte carbonic anhydrase in pure buffer and in media containing ethanol, 1-propanol, ethanediol, 1,2-propanediol, xylitol, glucose, fructose, maltose, and sucrose. The experimental melting temperatures were determined by Cioci35 and by Cioci et al.36 using UV difference spectroscopy. The results obtained for the four proteins clearly indicate that changes in stability resulting from addition of hydroxylic compounds can, as a first approximation, be described by a linear relationship between Tm and γmix. For each protein, moreover, the same relationship appears to describe equally well the thermal behavior of the macromolecule in stabilizing as well as destabilizing media. Molecular Thermodynamic Model A large number of experimental investigations support the possibility to describe the unfolding equilibrium of singledomain proteins by the two-state model:37-41 F a U, according
to which the protein exists in one out of two states only, the native folded state (F) and the polymorphous unfolded state (U). The equilibrium criterion (dGT,P ) 0) applied to this process yields
µF ) µU
(4)
where µ is the chemical potential of the protein. For the sake of simplicity, the solvent was regarded as a single component (pseudocomponent), either in the case of pure buffer or in the presence of additives. The Gibbs free energy of the system consisting of the protein and the solvent can then be written as 3
G ) ∑ nigi0 + ∆G
(5)
i)1
where ni are the moles of component i, gi0 is the molar free energy of the same component in its reference state, and subscripts 1, 2, and 3 denote the folded protein, the unfolded protein, and the mixed solvent, respectively. The reference state is defined as follows: temperature T; pressure P; pure solid (ordered or amorphous) in the conformation assumed in water, for components 1 and 2; pure liquid, for component 3. The Gibbs free energy change relative to this reference state can be evaluated by the thermodynamic cycle schematically shown in Figure 5. Accordingly, we can write
∆G ) ∆GI + ∆GII + ∆GIII
(6)
The first step is represented by the structural transformations needed for the two protein forms to assume the conformations they exhibit in the mixture. We have
Stability of Heat-Stressed Proteins
J. Phys. Chem., Vol. 100, No. 43, 1996 17403
2
∆GI ) ∑ ni∆giconf
(7)
TABLE 1: Least-Squares Analysis of Heat-Induced Unfolding Experiments According to Eq 20a
i)1
The second step corresponds to the ideal mixing with the solvent. It leads to a free energy change equal to 3
∆GII ) RT∑ ni ln xi
(8)
σ* ψ* ∆γ pH (K mN-1 m) (mN m-1) (mN m-1)
protein glucose oxidase ribonuclease lysozyme carbonic anhydrase
5.5 5.5 4.0 7.0
0.57 0.68 1.02 1.19
521.5 427.1 280.7 217.3
43.6-65.9 45.2-69.2 44.1-67.1 52.1-68.8
r 0.98 0.93 0.96 0.97
a σ* and ψ* are the parameters defined by eq 19, ∆γ is the range of surface tension values, and r is the correlation coefficient.
i)1
Finally, the last step is given by the introduction of nonideality in the mixture so obtained. This can be accomplished by accounting for the various interactions between the protein and the surrounding medium (dispersion forces, dipole-dipole interactions, hydrogen bonding, hydrophobic interactions, etc.). These interactions are responsible for the work required to separate the protein surface from that of the medium, and their contribution to the free energy change can be calculated as
x2/x1. At the melting temperature (Tm) this quantity is equal to one. Moreover, since ∆g* can be expressed as ∆h* - T∆s*, eq 14 can also be written as
Tm )
∆a ∆h* ∆(γRa) γ + + ∆s* 3 ∆s* ∆s*
(18)
Finally, if the following quantities are defined 2
∆GIII ) ∑ niγi,3ai
(9)
σ* )
i)1
where γi,3 is the interfacial free energy between the protein and the solvent and ai is the molar surface area of the protein. The term γi,3 can be related to the interfacial free energies of pure components by the Dupre´ equation,42 to give
γi,3 ) γ3 + γi - ∆gi,3adh (i ) 1, 2)
(10)
where γi is the surface tension of component i and ∆gi,3adh is the free energy of adhesion between the protein and the surrounding medium per unit protein surface area. Since there is no way to evaluate the quantities γi and ∆gi,3adh separately, it may be convenient to lump them into a residual term, γi,R, so as to obtain
γi,3 ) γ3 + γi,R (i ) 1, 2)
(11)
where γi,R ) γi - ∆gi,3adh. Substitution of eqs 6-11 into eq 5 yields 3
2
3
i)1
i)1
i)1
G ) ∑nigi0 + ∑ni∆giconf + RT∑ni ln xi + 2
ni(γ3 + γi,R)ai ∑ i)1
(12)
The above equation allows us to evaluate the chemical potential of component i, defined as
µi )
( ) ∂G ∂ni
(13) P,T,nj*i
By equating µ1 and µ2, we get
∆g* + γ3∆a + ∆(γRa) + RT ln Kx ) 0
(14)
∆g* ) (g20 + ∆g2conf) - (g10 + ∆g1conf)
(15)
∆a ) a2 - a1
(16)
∆(γRa) ) γ2,Ra2 - γ1,Ra1
(17)
where
Kx is the equilibrium constant for protein unfolding, equal to
∆h* + ∆(γRa) ∆a ; ψ* ) ∆s* ∆a
(19)
eq 18 reduces to
Tm ) σ*γ3 + σ*ψ*
(20)
This equation indicates that if σ* and ψ* can be assumed constant, i.e., temperature- and additive-independent, the transition temperature varies linearly with the surface tension of the mixed solvent. Of course, σ* and ψ* are apparent quantities, whose physical meaning is difficult to grasp. Plots relative to the thermal behavior of the proteins examined (Figures 1-4), however, support the assumed independence of σ* and ψ* on temperature and on the additive nature, demonstrating the ability of eq 20 to describe the cosolvent effects on the conformational stability of the four proteins. These parameters were estimated by a least-square procedure, obtaining the values listed in Table 1. Discussion The results emerging from the present investigation provide additional evidence that the ability of several hydroxylic additives to stabilize or destabilize proteins can be related to the extent to which they perturb the surface tension of water. Explanation of these results is to be found in the close relation of surface tension to the interfacial free energy between the protein and the surrounding medium, which should be considered the primary factor governing protein unfolding. In particular, the following considerations can be made. Since the protein-solvent surface of contact increases during unfolding, it seems apparent that additives increasing the interfacial free energy between the protein and the solvent should make the transition toward the unfolded form less thermodynamically favorable than in water. When added to the protein solution, these components would tend to migrate away from the macromolecule, leaving behind a layer enriched in water and causing an increase of the melting temperature of the protein. Conversely, additives decreasing the interfacial free energy between the protein and the solvent should make the native protein less stable than in water. These components would tend to accumulate in the surface layer and cause a reduction of the melting temperature of the protein. Since additives stabilizing the proteins examined were found to increase the surface tension of water, whereas destabilizers decreased this quantity, we must assume that on addition of these components the interfacial free energy between the protein and the surrounding medium varies
17404 J. Phys. Chem., Vol. 100, No. 43, 1996
Cioci
TABLE 2: Effect of Glycerol on Lysozyme Stability at pH 4a glycerol concn (% w/w) Tmexp (°C)b γmix (mN m-1)c Tmcalc (°C) ∆Tm (°C) 0 10 20 30 40 50
74.8 75.9 76.6 77.8 79.3 81.7
64.1 61.9 61.9 60.7 59.5 58.1
77.2 76.3 75.4 74.5 73.5 72.5
-2.4 -0.4 1.2 3.3 5.8 9.2
a T exp is the experimental melting temperature, γmix is the surface m tension of the mixed solvent at the temperature Tmexp, Tmcalc is the melting temperature calculated by eq 20, and ∆Tm is the difference between experimental and calculated melting temperatures. b Experimental data taken from ref 34. c Estimated by eq 1.
in the same direction as the bulk surface tension of the solvent. The molecular thermodynamic model presented here can be helpful in providing a rationale for the above observations. In view of eqs 10 and 20, a linear dependence of Tm on γ3 would imply the independence of the term γi,R on the particular additive considered. Since γi,R is expressed as the difference between γi and ∆gi,3adh, this condition signifies that also the free energy of adhesion is solvent-independent. In other words, the influence of the additive appears to be primarily consequent on perturbations of the properties of the solvent induced by the additive, rather than on direct interactions (attractive or repulsive) with the protein, which can be considered basically inert. It seems worth noting that under these conditions the free energy of cavity formation should provide the main driving force for protein stabilization. Consequently, the additive-induced perturbations of stability can be directly related to the contribution of the additive to the free energy required to create a cavity enveloping the macromolecule. When mechanisms other than surface tension are involved, the above-mentioned considerations may fail, in that the residual free energy term can no longer be considered additive independent. In these cases the value of the free energy of cavity formation in the mixed solvent does not provide any information about the influence of the additive on protein stability. Moreover, anomalies could appear on the Tm-γmix plot due to the combined effect of the bulk surface tension and the free energy of adhesion terms on the interfacial free energy between the protein and the solvent. If we focus attention on glycerol, we note that this component slightly decreases the surface tension of water. However, while according to the surface tension effect, glycerol destabilized glucose oxidase, this same additive was found to stabilize ribonuclease and lysozyme. The sensitivity of lysozyme stability to glycerol can be appreciated from the results summarized in Table 2, which shows that at the highest glycerol concentration (50 wt %) the melting temperature of the protein is raised by about 7 °C. The foregoing considerations clearly demonstrate that (1) changes in the interfacial free energy do not always parallel the observed changes in surface tension and (2) the stabilizing or destabilizing action exerted by a particular additive may depend on the protein nature. A physical explanation for these points should account for the different phenomena taking place in the presence of glycerol. This additive, in fact, is known to be preferentially excluded from the protein domain by the solvophobic effect,16 namely, the enhancement of solvent ordering due to the stabilization of networks of structured water. Furthermore, it also exhibits an affinity for the polar regions of proteins.13,16 Thus, the following mechanisms operating simultaneously should be considered: accumulation in the surface layer due to the surface tension effect, migration into the bulk solvent due to the solvophobic effect, and binding to the polar
groups present on the protein surface. Of course, each of the above mechanisms should in principle be considered as capable of perturbing the conformational stability of the macromolecule. In the case of glucose oxidase, the observed reduction in stability upon addition of glycerol appears to suggest that the surface tension mechanism prevails on the others. Alternatively, it can be postulated that, under the experimental conditions adopted, exclusion induced by the solvophobic effect and binding at specific sites of the protein compensate each other. In either case, the residual free energy terms in the presence and in the absence of the additive should be essentially the same. By contrast, since additions of glycerol to ribonuclease and lysozyme increased the stability of the proteins, it can be inferred that in these instances preferential hydration due to the solvophobic effect prevails on glycerol enrichment in the surface layer due to the surface tension decrement and/or affinity for polar regions. Undere these conditions the residual free energy term should increase so as to exceed the decreased surface tension and make the interfacial free energy between the protein and the solvent higher than in pure buffer. Similar arguments could be applied to some non-hydroxylic additives such as urea, which increases the surface tension of water but favors unfolding,26 or betaine, which lowers the surface tension of water but stabilizes proteins.18 In this respect, eq 10 provides a quantitative representation of the competition between the nonspecific surface tension effect and all other mechanisms that may contribute to protein stability. To conclude, as long as the residual free energy term can be considered additive independent, the melting temperature of the protein should vary linearly with the bulk surface tension of the medium. Departures from linearity point out for the presence of different mechanisms acting simultaneously and perturbing to a more or less significative extent the interfacial free energy between the protein and the solvent. Conclusion The experimental evidence provided by this study demonstrates that the stability behavior of heat-stressed proteins in the presence of either stabilizing or destabilizing hydroxylic additives can be fairly well described by a linear relation between the melting temperature of the protein and the bulk surface tension of the solvent. This result suggests that the influence of the additives considered on protein stability does not rely on any special property of these substances, but rather on their ability to perturb the surface tension of water. Although derived under some simplifying assumptions, such as the two-state mechanism for the unfolding process, the molecular thermodynamic model developed allows for a quantitative interpretation of the above observations. In addition, indications are provided that the extent to which an additive affects the conformational stability of a protein is a reflection of its combined influence on the bulk surface tension and the free energy of adhesion between the macromolecule and the surrounding medium. Qualitative information about the relative weights of the two effects can be gained from analysis of the Tm-γmix plot, which can be used to diagnose whether the surface tension mechanism provides the overwhelming contribution to preferential exclusion and hence to protein stabilization. Melting temperature and surface tension are easily measurable quantities, and this supports the possibility to use the model proposed for interpretation and correlation of thermal unfolding data or for developing rational strategies of stabilization against heat-induced unfolding. Undoubtedly, if we were able to express the free energy of adhesion as a function of the additive concentration, a general relationship would be drawn between
Stability of Heat-Stressed Proteins the melting temperature of the protein and the properties of the medium. A deeper understanding of the role of interfacial phenomena in protein unfolding seems therefore to be an essential prerequisite for a more thorough quantitative description of solvent-mediated protein stabilization. List of Symbols a ) molar surface area (m2 mol-1) G ) Gibbs free energy (J) g ) molar Gibbs free energy (J mol-1) h ) molar enthalpy (J mol-1) Kx ) unfolding equilibrium constant n ) number of moles N ) number of components P ) pressure (N m-2) R ) gas constant (8.314 J mol-1 K-1) s ) molar entropy (J mol-1 K-1) T ) temperature (K) T0 ) reference temperature (K) Tc ) critical temperature (K) Tm ) melting temperature (K) x ) mole fraction z ) mole fraction Greek Symbols γ ) interfacial free energy or surface tension (N m-1) ) parameter defined in eq 3 µ ) chemical potential (J mol-1) F ) liquid density (kg m-3) σ* ) parameter defined in eq 19 (K N-1 m) ψ* ) parameter defined in eq 19 (N m-1) Subscripts F ) folded protein i ) ith species mix ) mixture property U ) unfolded protein Superscripts adh ) adhesion conf ) conformational property 0 ) reference state References and Notes (1) Privalov, P. L. In Protein Structure and Protein Engineering; Winnacker, E. L., Huber, R., Eds.; Springer-Verlag: Berlin, 1988; p 6.
J. Phys. Chem., Vol. 100, No. 43, 1996 17405 (2) Dill, K. A.; Alonso, D. O. V. In Protein Structure and Protein Engineering; Winnacker, E. L., Huber, R., Eds.; Springer-Verlag: Berlin, 1988; p 51. (3) Dill, K. A. Biochemistry 1990, 29, 7133. (4) Pace, C. N. CRC Crit. ReV. Biochem. 1975, 3, 1. (5) Privalov, P. L. AdV. Protein Chem. 1979, 33, 167. (6) Privalov, P. L.; Gill, S. J. AdV. Protein Chem. 1988, 39, 191. (7) Lapanje, S. Physicochemical Aspects of Protein Denaturation; Wiley: New York, 1978. (8) Klibanov, A. M.; Ahern, T. J. In Protein Engineering; Oxender, D. L., Fox, C. F., Eds.; Alan R. Liss: New York, 1987. (9) Kauzmann, W. AdV. Protein Chem. 1959, 14, 1. (10) Zale, S. E.; Klibanov, A. M. Biotechnol. Bioeng. 1983, 25, 2221. (11) Pace, C. N. Trends Biochem. Sci. 1990, 15, 14. (12) Klibanov, A. M. AdV. App. Microbiol. 1983, 29, 1. (13) Timasheff, S. N.; Arakawa, T. In Protein Structure: a Practical Approach; Creighton, T. E., Ed.; IRL Press: Oxford, 1989; p 331. (14) Tomazic, S. J. In Biocatalysts for Industry; Dordick, J. S., Ed.; Plenum Press: New York, 1991; p 241. (15) Schellman, J. A. Biopolymers 1987, 26, 549. (16) Gekko, K.; Timasheff, S. N. Biochemistry 1981, 20, 4667. (17) Gekko, K.; Timasheff, S. N. Biochemistry 1981, 20, 4677. (18) Arakawa, T.; Timasheff, S. N. Arch. Biochem. Biophys. 1983, 244, 169. (19) Arakawa, T.; Timasheff, S. N. Biophys. J. 1985, 47, 411. (20) Lee, L. L. Y.; Lee, J. C. Biochemistry 1987, 26, 7813. (21) Cohen, G.; Eisenberg, H. Biopolymers 1968, 6, 1077. (22) Timasheff, S. N. Biochemistry 1992, 31, 9857. (23) Creighton, T. E. Proteins: Structures and Molecular Properties; W. H. Freeman: New York, 1993; p 287. (24) Cioci, F.; Lavecchia, R.; Marrelli, L. Biocatalysis 1994, 10, 137. (25) Adamson, A. W. Physical Chemistry of Surfaces; Wiley & Sons: New York, 1982. (26) Prakash, V.; Loucheux, C.; Scheufele, S.; Gorbunoff, M. J.; Timasheff, S. N. Arch. Biochem. Biophys. 1981, 210, 455. (27) Sinanogˇlu, O. In Molecular Associations in Biology; Pullman, B., Ed.; Academic Press: New York, 1968; p 487. (28) Sinanogˇlu, O. Int. J. Quantum Chem. 1980, 18, 381. (29) Sinanogˇlu, O. J. Chem. Phys. 1981, 75, 463. (30) Birnstock, F.; Hofmann, H. J.; Ko¨hler, H. J. Theor. Chim. Acta 1976, 42, 311. (31) Sinanogˇlu, O.; Fernandez, A. Biophys. Chem. 1985, 21, 157. (32) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids; McGraw Hill: New York, 1977. (33) Gerlsma, S. Y. J. Biol. Chem. 1968, 243, 957. (34) Gekko, K. J. Biochem. 1982, 91, 1197. (35) Cioci, F. Enzyme Microb. Technol. 1995, 17, 592. (36) Cioci, F.; Lavecchia, R.; Marrelli, L. Fluid Phase Equilib. 1996, 116, 118. (37) Tanford, C. AdV. Protein Chem. 1968, 23, 121. (38) Tanford, C. AdV. Protein Chem. 1970, 24, 1. (39) Pfeil, W.; Privalov, P. L. In Biochemical Thermodynamics; Jones, M. N., Ed.; Elsevier: Amsterdam, 1979; p 75. (40) Cioci, F.; Lavecchia, R. Biochem. Mol. Biol. Int. 1994, 34, 705. (41) Cioci, F. Catal. Lett. 1995, 35, 395. (42) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1985; p 215.
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