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Protein Science (2001), 10:1187-1194.
Copyright © 2001 The Protein Society

Some thermodynamic implications for the thermostability of proteins

Douglas C. Rees1 and Andrew D. Robertson2

1 Howard Hughes Medical Institute and Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
2 Department of Biochemistry, College of Medicine, University of Iowa, Iowa City, Iowa 52242, USA

Reprint requests to: Douglas C. Rees, Howard Hughes Medical Institute and Division of Chemistry and Chemical Engineering, 147-75CH, California Institute of Technology, Pasadena, California 91125, USA; e-mail: dcrees{at}caltech.edu; fax: (626) 744-9524.

(RECEIVED January 16, 2001; FINAL REVISION March 15, 2001; ACCEPTED March 15, 2001)

Article and publication are at www.proteinscience.org/cgi/doi/10.1110/ps.180101.


   Abstract
TOP
 Abstract
Introduction
 Temperature dependence of...
 Conclusions
 References
 
An analysis of the thermodynamics of protein stability reveals a general tendency for proteins that denature at higher temperatures to have greater free energies of maximal stability. To a reasonable approximation, the temperature of maximal stability for the set of globular, water-soluble proteins surveyed by Robertson and Murphy occurs at T* ~283K, independent of the heat denaturation temperature, Tm. This observation indicates, at least for these proteins, that thermostability tends to be achieved through elevation of the stability curve rather than by broadening or through a horizontal shift to higher temperatures. The relationship between the free energy of maximal stability and the temperature of heat denaturation is such that an increase in maximal stability of ~0.008 kJ/mole/residue is, on average, associated with a 1°C increase in Tm. An estimate of the energetic consequences of thermal expansion suggests that these effects may contribute significantly to the destabilization of the native state of proteins with increasing temperature.

Keywords: Protein stability; thermal expansion; protein volumes; stability curve


   Introduction
TOP
 Abstract
 Introduction
Temperature dependence of...
 Conclusions
 References
 
The temperature dependence of the free energy change, {Delta}G(T), for protein unfolding:


(1)

under a given set of conditions (pH, ionic strength, reduction potential, etc.) may be conveniently represented by the stability curve (Becktel and Schellman 1987) as depicted in Figure 1Go. When the heat capacity is temperature independent, the stability curve is determined by the values of three parameters, Tm, {Delta}Hm, and {Delta}Cp through the relationship (Hawley 1971; Privalov and Gill 1988):



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  		Fig. 1. Schematic representation of the stability curve (Becktel and Schellman 1987) illustrating the temperature dependence of the free energy of unfolding, {Delta}G. With this convention, the native state of the protein is favored in the temperature range when {Delta}G > 0. The temperatures of maximal stability, T*, and heat denaturation, Tm, are indicated.

 

(2)

in which Tm is the temperature of heat denaturation with {Delta}G(Tm) = 0; {Delta}Hm is the enthalpy of unfolding at Tm; {Delta}Cp is the heat capacity change on unfolding. The positive {Delta}Cp of protein denaturation likely reflects the exposure to water of hydrophobic groups that were buried in the native state. One consequence of {Delta}Cp > 0 is that the stability curve is indeed a curve (Brandts 1964), and it shows a free energy of maximal stability at a temperature T*. In addition to Tm, there is a second point on the stability curve where {Delta}G is also equal to zero that corresponds to the phenomenon of cold denaturation (Privalov 1990).

The stability curve may be approximated as a quadratic function of the temperature with a free energy of maximal stability occurring at a temperature T* (Zipp and Kauzmann 1973; Stowell and Rees 1995), in which:


(3)

Studies relating the thermodynamics of protein stability to structural features have shown that the enthalpy, entropy, and heat capacity of protein unfolding are, to first approximation, proportional to the size of the protein as described, for example, by the number of residues, N. Using a reference state of 60°C = 333K, Robertson and Murphy (1997) determined the following parameterizations, based largely on data for small globular proteins:



(4)


which reproduced the experimental data with correlation coefficients of 0.86, 0.77, and 0.74, respectively. Because the thermodynamic parameters are all proportional to N, the stability curves of different proteins should scale according to the number of residues.

The existence of hyperthermophilic organisms illustrates dramatically the ability of proteins to maintain a stable tertiary structure to temperatures > 100°C. This phenomenon naturally raises the question as to how thermostability is achieved (see Szilagyi and Zavodszky [2000] for a recent discussion of the structural basis for thermostability). In terms of the stability curve, there are several thermodynamic mechanisms by which the thermostability of proteins could be increased, such as those depicted in Figure 2Go. These possibilities can be considered to arise by a combination of raising the stability curve, shifting the curve to high temperatures, and broadening the curve.



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  		Fig. 2. Stability curves representing different thermodynamic mechanisms for achieving protein hyperthermostability. The thermal stability of a protein can be formally increased relative to the mesophilic homologue (a, thick line) by various combinations of raising the stability curve (b), shifting the stability curve (c), and increasing the breadth of the stability curve (d).

 
The thermodynamics of thermostability can be approached by examining how the stability curve of a protein is coupled to Tm by estimating {Delta}Cp and {Delta}Hm from the parameterizations of Robertson and Murphy (1997). The maximal stability can be derived by substituting these parameters into equation 3:




(5)


This predicted relationship between {Delta}G(T*)/N and Tm is in general agreement with experimentally observed values (Table 1A,BGo), as illustrated in Figure 3Go. Similar trends between maximal stability and Tm are also evident when the stabilities of a single protein under different conditions are measured, as illustrated with wild-type and variant T4 lysozymes studied over a range of pH conditions (Fig. 3Go; Table 1CGo).


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  		Table 1. Summary of thermodynamic parameters for protein stability
 


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  		Fig. 3. Relationship between free energies of maximal stability {Delta}G(T*) and the temperature of heat denaturation Tm for the proteins in Table 1Go. The filled circles, open circles, and Xs designate water-soluble proteins tabulated in Robertson and Murphy (1997) as shown in Table 1AGo, proteins from hyperthermophiles in Table 1BGo, and T4 lysozyme variants in Table 1CGo, respectively. The black curve represents the predicted dependence from equation 5.

 
With this parameterization, the temperature of maximal stability, T*, is predicted to be ~283K, independent of the values of {Delta}G(T*) and Tm:



(6)


Observed values of T* for proteins included in the Robertson and Murphy (1997) survey are generally consistent with this expectation (Fig. 4Go), with average and standard deviations of 285K ± 19K and 280K ± 6K observed for the proteins in Table 1AGo and the T4 lysozyme in Table 1CGo. The few hyperthermophilic proteins included in this survey (Table 1BGo) appear to have systematically higher values for T* (~310K) and values of {Delta}G(T*) somewhat lower than predicted from equation 5 (Fig. 3Go), although the generality of this observation is weakened by the small sample size and neglect of the temperature dependence of {Delta}Cp (Privalov et al. 1989) that will become significant for hyperthermophilic proteins.



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  		Fig. 4. Relationship between the temperature of maximal stability, T*, and the temperature of heat denaturation, Tm, for the proteins in Table 1Go. The different symbols are defined in the legend to Figure 3Go. The expected value for T* from equation 6 is 283K.

 
There are several implications of these observations. The most significant is that proteins denaturing at higher values of Tm tend to have greater maximal stability (Fig. 3Go). Although this seems perhaps obvious, there is no a priori reason to expect that this must be true (see Fig. 2Go). Furthermore, the observation that increased thermostability can be achieved while T* remains approximately constant suggests, as noted by Jaenicke and Böhm (1998), that thermostability is typically achieved by "pulling up" the stability curve (Fig. 2Go, curve b), at least for nonhyperthermophilic proteins. This observation is clearly a generalization, however, and other thermodynamic mechanisms can be used to generate thermostability; for example, Hollien and Marqusee (1999) have described an analysis of two ribonucleases H, in which the more thermostable protein not only has a greater maximal stability, but also has a small {Delta}Cp that generates a broader stability curve and hence contributes to a higher Tm. Another example, noted above, may be provided by the shift toward values of T* > 300K for hyperthermophilic proteins, which suggests that these proteins use somewhat different thermodynamic strategies for increased thermostability (see Szilagyi and Zavodszky 2000).

Continuing with this analysis, it is possible to estimate how much Tm will increase with an increase in {Delta}G(T*) by differentiating equation 5 to give:


(7)

This has the value of ~0.0090 kJ/(mole residue K) at 340K, whereas a linear fit to the experimental curve gives a slope of 0.0082 kJ/(mole residue K). Consequently, a ~0.008 kJ/(mole residue) increase in maximal stability corresponds, on average, to an increase in Tm of ~1°C. Three recent examples illustrate that this relationship can capture the behavior of real protein systems:

  1. In an analysis of ribonuclease H thermostabilities (Hollien and Marqusee 1999), it was found that {Delta}G(T* = 293K) = 53.1 kJ/mole and Tm = 359K for the more thermostable protein, and {Delta}G(T* = 297K) = 31.4 kJ/mole and Tm = 339K for the less thermostable protein. The change in maximal stability associated with these changes in Tm may be calculated (taking 160 as the average number of residues in each protein) to be:


(8)

  1. The thermostabilities of a series of packing mutants of staphylococcal nuclease have been characterized (Chen et al. 2000); the data are described by an approximately linear relationship between the {Delta}G for unfolding at 293K and Tm (Fig. 5Go). The value of {Delta}G(293) should approximate the maximal stability for these variants, because the measurement temperature is close to the generic value for T* (283K). Dividing the slope of this line by the number of residues, N = 149, gives:



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  		Fig. 5. Relationship between Tm and {Delta}G for unfolding of staphylococcal nuclease variants at 293K (Chen et al. 2000). A linear fit to these points has a slope of 1.01 kJ/(mole K) and a correlation coefficient of 0.96.

 

(9)

  1. Following the introduction of the R3E mutation into the 66 residue Bacillus caldolyticus cold shock protein (Pace 2000; Perl et al. 2000), decreases were observed in Tm and {Delta}G(T*) of 17.8°C and 7.1 kJ/mole, respectively. For this case, the derivative may be estimated:


(10)

In these examples, the relationships between changes in maximal stability and Tm, on a per residue basis, are all close to the value 0.008 kJ/(mole residue K) derived above, illustrating that this general analysis of thermostability provides a useful framework for characterizing the relationship between protein stability and melting temperature.


   Temperature dependence of protein structure
TOP
 Abstract
 Introduction
 Temperature dependence of...
Conclusions
 References
 
A tacit assumption in addressing the structural origins of protein stability is that the native structure is independent of temperature, so that interactions such as hydrogen bonds, salt bridges, buried surface area, and others can be enumerated independently of the conditions of the structure determination. Even without consideration of such factors as the possibility of large-scale conformational changes and the influence of crystallization conditions on the structure, the assumption of structural invariance cannot be strictly accurate. Like most materials, proteins expand with increasing temperature. The coefficient of thermal expansion, {alpha} = ((1/V) (dV/dT))P, has been estimated from thermodynamic measurements and structural studies, and is found to be ~10-4 K-1 for many proteins (Frauenfelder et al. 1987; Tilton et al. 1992; Young et al. 1994). This implies, for example, that the volumes of proteins will contract several percent between room temperature and the ~100K typically used for cryocrystallographic data collection.

As indicated by the preceding considerations, this increase in volume with increasing temperature is not energetically benign, but is associated with changes in the thermodynamic parameters of both the N and D states. One example of this is the volume dependence of the internal energy, given by the quantity, (dE/dV)T, which is also known as the internal pressure (Barton 1971). Values of (dE/dV)T may be obtained from the coefficients of thermal expansion ({alpha}) and compressibility ß = (-(1/V) (dV/dP))T, via the thermodynamic relationships:





(11)



Because T{alpha}/ß tends to be much larger than the external pressure P (1 atm), the latter can be generally neglected. For lysozyme, {alpha} ~ 1 x 10-4 K-1 (Young et al. 1994; Kurinov and Harrison 1995) and ß ~ 5 x 10-6 atm-1 (Kundrot and Richards 1987) = 0.08 Å3/(kJ/mole), so that the internal pressure equals ~0.4 kJ/mole/Å3 (= ~6000 atm) at 298K. As a comparison, the volume-dependent term for cavity mutants engineered into T4 lysozyme is ~0.1 kJ/mole/Å3 (Eriksson et al. 1992), whereas the intensity of strain associated with small-to-large mutations introduced into the core of T4 lysozyme has been reported in the range of 0.1–0.8 kJ/mole/Å3 (Liu et al. 2000). The observation that (dE/dV)T > 0 means that the internal energy increases as the volume increases, and is equivalent to the positive correlation between energy and volume fluctuations noted by Cooper (1984).

The increase in energy, {Delta}E, associated with the expansion of a protein over a temperature range, {Delta}T, may be estimated as:


(12)

For a protein with N residues, an average residue molecular weight of 110, and a density of 1.35 gm/cm3 (see Quillin and Matthews 2000), V may be approximated as 135 N Å3, so that an increase in energy associated with a given temperature increase becomes:



(13)

This effect is comparable to the average decrease in {Delta}G(T)/N with temperature between T* and Tm: (1/N) {Delta}G(T*)/(Tm-T*) = 0.0049 kJ/(mole residue K) for Tm = 340K (from equation 5), which indicates that these destabilizing effects because of volume expansion are indeed energetically significant. For reference, these volume expansion effects should also be significant relative to the activation volumes measured for protein unfolding (33 Å3 for staphylococcal nuclease [Vidugiris et al. 1995]), with increases of 40 to 120 Å3 accompanying temperature increases of 20°C to 60°C for a protein of ~150 residues and {alpha} ~ 10-4 K-1.

It is possible that the effects of volume changes on the energy of the native state could be offset by comparable effects on the denatured state. A direct analysis of this phenomenon appears problematic, however, because both {alpha} and ß for the protein-solvent system change on denaturation in a protein-dependent fashion (Brandts et al. 1970; Hawley 1971; Zipp and Kauzmann 1973; Gavish et al. 1983; Prehoda et al. 1998; Panick et al. 1999) that has been difficult to generalize in terms of the relative consequences on (dE/dV)T.


   Conclusions
TOP
 Abstract
 Introduction
 Temperature dependence of...
 Conclusions
References
 
The general behavior of the stability curves for the proteins observed in this study suggests that, on average, increases in Tm are associated with increases in the free energy of maximal stability {Delta}G(T*). Furthermore, the temperature of maximal stability for these proteins tends to be roughly constant at ~283K. These effects may be summarized in the form of a generic stability curve that gives the dependence of {Delta}G(T) on Tm and N:


(14)

As a useful rule of thumb, increases in {Delta}G(T*) of ~0.008 kJ/(mole residue) are associated with an average increase in Tm of 1° C.

The expansion of proteins with increasing temperature is associated with a destabilizing increase in energy. Estimates of this effect suggest that the destabilization energy increases by about 0.005 kJ/(mole residue) per 1°C, roughly comparable to decreases in {Delta}G with increasing T above T*. A similar effect has been described by Palma and Curmi (1999) who noticed a correlation between thermal expansion of protein surface area and stability in computational studies. Protein expansion could contribute not only to the thermodynamics of protein stability, but also to the kinetics of this process, because the introduction of defects should permit conformational rearrangements required for unfolding (Vidugiris et al. 1995), much as the volume of solids increases near their melting temperature (Frenkel 1946; Bondi 1968). The combination of thermodynamic measurements and structural studies at different temperatures should help further illuminate the relationships between protein stability and volume, which would be particularly informative for proteins that function under more exotic conditions, such as hyperthermostable proteins and membrane proteins.


   Acknowledgments
 
This work was supported in part by National Institutes of General Medical Sciences grants GM45162 to D.C.R. and GM46869 to A.D.R. The publication costs of this article were defrayed in part by payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 USC section 1734 solely to indicate this fact.


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 Conclusions
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