J. theor. Biol. (1975) 50,245-252

A Discussion of Pressure-Volume Effects in Aqueous Protein solutions AA.SE HVIDT Chemistry Laboratory IZZ, H. C. Orsted Znstitutet, Universitetsparken DK-2100, Copenhagen 0, Denmark

5,

(Received 25 April 1974) Recent investigations of the thermodynamics of protein denaturation, in particular of pressure effects, have questioned the fundamental importance, hitherto assumed, of hydrophobic interactions in the native conformations of proteins. The volume changes observed on protein denaturation are incompatible with the voltmre changes estimated on the basis of volume effects observed in low molecular weight model systems of the aliphatic groups. In the present paper the model systems generally considered are critically discussed. It is concluded, that solutions of low molecular weight alkanes may not be any adequate models of aliphatic groups in proteins. Studies of more appropriate model systems suggest that the volume changes to be expected, when buried aliphatic groups of proteins are exposed to water, are small and 1positive, and mainly due to structural changes of the water. These volume changes are in accordance with the volume changes actually measured of protein denaturation, and the latter volume effects are taken as supporting evidence of the importance of hydrophobic interactions in protein conformations.

1. rntroduction Recent investigations of pressure-volume effects in aqueous protein solutions have implicated critical considerations and discussions of the importance of hydrophobic interactions in protein conformations (Brandts, Oliveira & Westort, 1970; Hawley, 1971; Suzuki & Taniguchi, 1972; Zipp & Kauzmann, 1973). The volume changes observed of thedenaturation of globular proteins are considerably smaller than expected, if the native conformations are stabilized chie%y by hydrophobic interactions-and in some cases of opposite sign. The volume changes following the exposure to water of buried aliphatic groups of protein molecules have tentatively been estimated on the basis of the large, negative volume changes accompanying the transfer of methane or ethane from hexane to aqueous solutions; the changes are suggested to be about -20 cm3 per mole of aliphatic sidechains in the proteins (Kauzmann, 1959), or -0.74 cm3 per mole of water brought into

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contact with the aliphatic groups (Nemethy & Scheraga, 1962). These estimates are incompatible with the volume changes measured of protein denaturation, and the discrepancy has involved that the decisive role, hitherto assumed of hydrophobic interactions for the stability of the native protein conformations, has been seriously questioned (Brandts er al., 1970; Hawley, 1971; Suzuki & Taniguchi, 1972; Zipp & Kauzmann, 1973). It is the aim of the present paper to demonstrate that solutions of methane or ethane may not be representative models of the aliphatic sidechains of protein molecules. Investigations of more appropriate model systems indicate that the volume changes following the exposure to solvent water of buried aliphatic groups of proteins are, most likely, small and positive, in accordance with the volume changes actually observed of protein denaturation. The pressure-volume effects measured of aqueous protein solutions are, therefore, taken as supporting evidence of the fundamental importance of hydrophobic interactions in the conformations of native proteins. 2. Volume Effects in Aqueous Solutions of Low Molecular Weight Substances

Figure 1 illustrates, by available data (Boje & Hvidt, 1971), the deviation from ideality of the volume of binary mixtures of water and various low molecular weight substances. The infinitely dilute aqueous solution is taken as the reference state of the components, and the excess functions depicted are : Au = {v-(wAG +WH,OV;,OHWA (1) and AV

=

{v

-

(XA

v.

+ xH20

hi,,,>/%

(2)

In equation (1) v is the specific volume (the volume per gm) of a mixture with the weight fraction wA of the non-aqueous component A, and uz and v&O are the partial specific volume of A and of water in the reference state. In equation (2) V, V; and VGzoare the corresponding molar volumes, and x, is the mole fraction of A. Au and AV express the deviation from ideal values of the volume of the mixtures, measuredper gm, and per mole of A, respectively. Equations (1) and (2) can be rewritten Au = VA- VA”+ T

(i&o -

Of,,,)

(3)

and AV = VA - Vz + xF

(Vn/o-V;Io).

(4)

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- (b)

0.14

b

0.06

2

$ Q

0.04

I

I

I

I

0.2

0.4

0.6

0.8

XA

FIG. 1. Excess volumes of binary aqueous mixtures at 25°C. wA is the weight fraction and xA is the mole fraction of the non-aqueous compotient. ‘I’he inilnitely diiute aqueous solution is taken as the reference state, and the exce& volumes Av and AY (defined in equations (l)-(4)) are measured per gm, and per mole,, rezwctively, of the non-aqueous component. The data is from BBje & Hvidt (1971). and from references therein, and the substances studied are: . . , . ., urea; -- --, fotiamide; --. --. -, acetone; - . - . - . -, ethanol; -- . -- . --, N-methylacetamide; -, tertiary butanol.

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It is seen from equations (l)-(4) that the functions Au and AV register the volume changes observed, when water is gradually isolated from an infinitely dilute aqueous solution, containing a unit amount of A. By this process the specific volume of the isolated water remains constant (and equal to the u&~); the volume changes are due to the variation with concentration of the excess volume of the solution. The transfer of water from an aqueous solution to pure water, expressed in molar quantities, is illustrated in Fig. 2. Au and AV measure the variation with concentration of the so-called “apparent volume” of the non-aqueous component A. We refrain from using the term the “apparent volume” of A, because the volume effects observed are, as explained in the following, ascribed partly to changes of the water.

Total volume:

V

Total volume:

V’

v’-v=A[A~(Q-Au~~)] FIG. 2. The volume change accompanying the transfer of water from an aqueous mixture to pure water, expressed by the excess function AV, defined in equation (2). xA and xi are mole fractions of the non-aqueous component before and after removal of the water, and AV(x,) and AV(x;) are the corresponding values of the excess function.

It appears from Fig. 1 that the excess volumes measured per unit amount of the non-aqueous component, vary considerably, and unsymmetrically with the composition of the binary mixtures. For all mixtures studied of water with low molecular weight substances containing aliphatic groups (alcohols, ethers, ketones and amides), a minimum is observed in the waterrich concentration range, and this minimum is absent in mixtures of water with urea or formamide (Bsje & Hvidt, 1971). A minimum indicates that two volume effects are present in the solutions. The decrease in the excess volume with increasing concentration of A, apparently typical of non-polar groups, is in accordance with the existence around the aliphatic groups of icelike water structures, characterized by a larger specific volume than that of pure water (Frank & Evans, 1945). The data supports the suggestion made by Kauzmann (1959) that the number of water molecules co-operating in these structures may be one or two dozen per aliphatic groups, and possibly even more (Bsje 8z Hvidt, 1971). In infinitely dilute aqueous solu-

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tions the conditions for the formation of Frank-Evans water structures are optimal, and the decrease in the excess volume, observed in the waterrich concentration range, may be explained by the rupture of these structures with increasing concentration of non-polar groups. The increase in the excess functions with increasing concentration of A is related to the high value of the spec& volume of organic liquids, as compared to water. The organic liquids have a rather open structure, and the volume changes observed can be ascribed, primarily, to the ability of the small water molecules to fill in some void space between the larger organic molecules. 3. Low Mokcular

Weight Snbstmces as Models of Proteins

If the conformation of dissolved protein molecules can be described as an equilibrium between two conformations N e D, with the equilibrium constant K = [D]/[N], the effect of changes in pressure on the conformation can be expressed as RTdlnK=-Av” d.lJ

.

(5)

AV” is the change in molar standard volume of the N G D transition. It should be noted that AV” in equation (5) is the change in the voIume of the solution containing one mole of the protein, not the change in the partial volume of the solute. For this reason, the excess functions, defined in equations (l)-(4), are suitable in attempts to estimate AV” on the basis of measurements on low molecular weight model systems. A dilute aqueous protein solution may tentatively be considered as consisting of two “phases”; one is the pure bulk water, the other comprehends the protein molecules and their solvation spheres. [By the solvation sphere of a protein molecule is meant the part of the solvent, which is directly influenced by the presence of the protein molecules (Tanford, 1961).] Conformational transitions of the proteins may involve that some water is transferred between the two phases. By the unfolding of the native conformations, the N + D transition, water is presumably transferred from the bulk phase to the solvation spheres. Provided adequate models of the constituent groups of the protein molecules are available, this unfolding is represented by the reverse of the process, illustrated in Fig. 2, and the accompanying volume changes may, in principle, be estimated on the basis of measurements of AV for solutions of the model compounds. Some of the general problems involved in attempts to predict’ volume effects in macromolecular solutions, on the basis of the behaviour of low

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molecular weight model systems, immediately appear from the data in Fig. 1. The local concentrations in the solvation sphere of a macromolecule never approach zero, but are otherwise difficult to estimate, and quantitative estimates of AY” [equation (5)], on the basis of measurements on model systems, seem first of all to be hampered by the pronounced concentration dependence of the excess volumes, demonstrated in Fig. 1. Furthermore, some fundamental deficiencies of the model systems shall be considered (Brandts et al., 1970; Klapper, 1971; Boje & Hvidt, 1971, 1972). The volume of the constituent groups of macromolecules, in particular of the nonpolar groups, is much smaller than the partial volume in solutions of corresponding low molecular weight compounds (Beje & Hvidt, 1971). The groups of a macromolecule are linked up by the polymeric chain (the backbone), so that the distances between them are shorter than the nearest neighbour distances in organic liquids. The specific volume of hexane, for example, is 1a52 cm3 gm- ‘, and the partial specific volume of methane in this solvent is 3.75 cm3 gm-’ (Masterton, 1954). These values are so much larger than the specific volume of proteins, typically 0.70-0.75 cm3 gm-’ (Tanford, 1961), that solutions of methane in hexane are to be rejected as models of proteins. Klapper (1971) has pointed out, that the interior of a protein resembles, in fact, a solid more than a liquid. The compressibility of a protein is so much smaller than that of liquids that volume changes of a protein solution, due to variations in pressure, are presumably mainly changes in the volume of the solvent. The above-mentioned arguments seem to exclude the possibility of predicting, quantitatively, the volume changes following conformational transitions in protein solutions on the basis of volume effects in low molecular weight model systems. Important conclusions about the sign and the approximate size of the volume effects to be expected, when buried aliphatic groups of proteins are exposed to water, may, however, be drawn from the data in Fig. 1 together with more extensive studies of volume effects in aqueous solutions (Boje & Hvidt, 1971, 1972). The increase of Au, or AV [equations (l)-(4)], observed with increasing concentration of the non-aqueous component, and dominating in the larger part of the concentration ranges studied, is a consequence of the open structure of the organic substances studied, and this effect is presumably absent in the closely packed protein molecules. The decrease in excess volume with increasing concentration of substances containing aliphatic groups-or with decreasing water concentration-is tentatively ascribed to structural changes of water. This effect has also been observed in solutions of acetyl-alanine-methylamide and of synthetic polymers (Boje & Hvidt, 1971, 1972), and exists, most likely, in protein solutions as well. It suggests that the transfer of aliphatic groups

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from the interior of protein molecules to aqueous surroundings is a process accompanied by small, but positive volume changes, and these changes are, mainly, volume changes of the solvent. 4. Evidence of the Importance of Hydrophobic Interactions in Protein Conformations The contributions to AV” [equation (5)] from various types of interactions in protein conformations have been discussed by Brandts et al. (1970); they are a11 assumed’to be negative. Klapper (1971) has, however, pointed out that small, positive changes in the volume of the protein are to be expected, when protein molecules unfold, and this effect, together with the solvent effect, described in the present paper, may counterbalance the other negative volume effects, and thus explain, why the volume changes, actually measured of protein denaturation, are close to zero, and in some cases even positive. The solvent effect supports the assumption that the exposure to water of aliphatic groups is an essential feature of the denaturation of proteins, or that hydrophobic interactions are of fundamental importance in the native conformations. Recent studies of the effect of temperature on protein conformations further elucidate the role of hydrophobic interactions. It is well known that raising the temperature of a protein solution above a characteristic value leads to denaturation of the protein. This means that the change in standard entropy AS” of the N G$ D transition is positive, in accordance with the larger flexibility of the unfolded protein, as compared to the native conformation. There is, however, recent experimental evidence (Brandts et al., 1969; Hawley, 1971; Zipp & Kauzmann, 1973) that some denaturation occurs also on cooling a protein solution. In a range of pressures, there exists a temperature of maximum stability of the native conformation; below this temperature the entropy change of denaturation is negative. There is hardly any doubt that native protein conformations are characterized by a nearly minimal degree of flexibility. It is, therefore, unlikely that the explanation of negative entropy changes on denaturation shall be sought in the conformational changes of the protein molecules; such entropy changes may, however, be ascribed to structural changes of the solvent. Frank-Evans water structures are characterized by a low entropy content (Frank & Evans, 1945; Kauzmann, 1959), and the formation of these structures, when aliphatic groups are exposed to water, may be the reason of negative entropy changes on denaturation. The “solubility” of aliphatic groups in water is higher the lower the temperature is, and the denaturation of proteins on cooling may be a transition of the protein molecules to con-

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formations with a flexibility not much larger than the flexibility of the native conformations, but with a higher degree of exposure to the solvent of the aliphatic groups. For this type of denaturation, the changes in the thermodynamic properties of water, introduced by aliphatic groups, play a decisive role. REFERENCES BRANDTS, J. F., OLIVEIRA, R. J. & WESTORT, C. (1970). Biochemistry, N. Y. 9, 1038. I&m, L. 8c HVIDT, A. (1971). J. them. Thermodynamics 3, 663. BPIJE, L. & HVIDT, A. (1972). Biopolymers 11, 2357. FRANK, H. S. & EVANS, M. J. (1945). J. them. Phys. 13, 507. HAWLEY, S. A. (1971). Biochemistry, N. Y. 10,2436. KAUZMANN, W. (1959). Adv. Protein Chem. 14, 1. KLAPPER, M. H..(1971). Biochim. biophys. A& 229, 557. MASTERTON. W. L. (1954). J. them. Phvs. 22. 1830. NJ!METHY, d. & SCI&RA~A, H. A. (1982). J. ihys. Chem. 66, 1773. SUZUKI, K. & TANIGUCHI, Y. (1972). Symp. Sot. exp. Biof. 26,103. TANFORD, C. (1961). Physical Chemistry of Macromoiecales, chap. 4, 6. New York: Wiley & Sons, Inc. ZIPP, A. & KAUZMANN,

W. (1973). Biochemistry, N. Y. 12,4217.

John

A discussion of pressure-volume effects in aqueous protein solutions.

J. theor. Biol. (1975) 50,245-252 A Discussion of Pressure-Volume Effects in Aqueous Protein solutions AA.SE HVIDT Chemistry Laboratory IZZ, H. C. Or...
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