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The Journal of Physical Chemistry, Voi. 83, No. 21, 1979
1. M. Yaacobi and A. Ben-Naim, J . Solution Chem., 2, 425 (1973). A. Ben-Naim and M. Yaacobi, J . Phys. Chem., 78, 170 (1974). W. Y. Wen and J. H. Hung, J . Phys. Chem., 74, 170 (1969). D. B. Wethlaufer, S. K. Malik, L. Stoller, and P. L. Coffin, J . Am. Chem. SOC., 86, 508 (1964). (6) (a) T. C. W. Mak, J. Chem. Phys., 43, 2799 (1965); (b) G. A. Jeffrey and T. C. W. Mak, Science, 149, 178 (1965). (7) D. W. Davidson, Can. J . Chem., 46, 1024 (1968). (8) G. Barone, V. Crescenzi, A. M. Liquori, and F. Quadrifoglio, J . Phys. Chem., 71, 984 (1967). (9) V. Crescenzi, F. Quadrifoglio, and V. Vitagliano, J. Phys. Chem., 71, 2313 (1967). (10) V. Crescenzi, F. Quadrifoglio, and V. Vitagliano, Ric. Sci., 37, 529 11967). (11) F. Quadrifoglio, V. Crescenzi, A. Ceslro, and F. Delben, J. Phys. Chem., 75, 3633 (1971). (12) G. Barone, V. Crescenzi, and V. Vitagliano, J. Phys. Chem., 72, 2588 (1968). (13) L. Cosiantino, V. Crescenzi, and V. Vitagliano, J. Phys. Chem., 72, 149 (1968). (14) F. Franks, M. Pedley, and D. S. Reid, J. Chem. Soc., Faraday Trans. 1 , 72, 359 (1976). (15) J. J. Kozak, W. S. Knight, and W. Kauzmann, J. Chem. Phys., 48, 675 (1968). (2) (3) (4) (5)
K. Gekko and H. Noguchl (16) G. Barone, G. Castronuovo, V. Crescenzi, V. Elia, and E. Rizzo, J. Solution Chem., 7 , 179 (1978). (17) J. J. Savage and R. H. Wood, J. Solution Chem., 5, 733 (1976). (18) R. A. Robinson and R. H. Stokes, J. Phvs. Chem.. 65. 1954 (1961). (19) H. D. Ellerton and P. J. Dunlop, J. Phis. Chem.,.70, 1831 (i966j. (20) H. L. Friedman and C. V. Krishnan, J. Solution Chem., 2, 119 (1973). (21) G. Barone, G. Castronuovo, V. Era, and A. Menna, J. Solution Chem., 8, 157 (1979). (22) A. Ben-Naim, "An Introduction to a Molecular Theory of Water and Aqueous Solutions", Plenum Press, New York, 1974. (23) W. Kauzmann, Adv. Protein Chem., 14, 1 (1959). (24) (a) G. Nemethy and H. A. Sheraga, J. Chem. Phys., 36, 3382 (1962); (b) ibid., 36, 3401 (1962); (c) J. Phys. Chem., 66, 1773 (1962). (25) (a) C. Tanford, Adv. Protein Chem., 23, 121 (1968); (b) ibid., 24, 1 (1970). A.'Ben-Nalm and S. Baer, Trans. Faraday SOC., 60, 1736 (1964). H. S. Frank and M. W. Evans, J. Chem. Phys., 13, 507 (1945). L. W. Winkler, Berichte, 36, 1408 (1901), taken from Landok-Bornstein Tabellen, Vol. 1, 1923, pp 763-764. (29) W. F. Claussen and M. F. Polglase, J. Am. Chem. SOC.,74, 4817 (1952). (30) T. J. Morrison and F. Billet, J. Chem. SOC.,3819 (1952). (31) V. Crescenzi, F. Quadrifoglio, and A. Ceshro, Inf. J. Protein Res., 3, 49 (1971). (32) A. Ben-Naim, J. Wilf, and M. Jaacobi, J. Phys. Chem., 77, 95 (1973).
Compressibility of Globular Proteins in Water at 25 "C Kunihlko Gekko" and Hajlme Noguchl Department of Food Science and Technology, Faculty of Agriculture, Nagoya Universify, Nagoya 464, Japan (Received April 3, 1979) Publication costs assisted by Nagoya University
The adiabatic compressibility, p,, of 14 globular proteins in water was determined at 25 "C by sound velocity measurements with a "sing around pulse method". All proteins studied showed positive compressibilities, suggesting a large internal compressibility for the proteins. To discuss the data obtained from the viewpoint of void and hydration of the proteins, a correlation was examined between p, and some molecular parameters such as the partial specific volume, hydrophobicity,and polarity of the proteins. Further, an attempt was made to estimate separately the contributions of void and hydration to the compressibilityof proteins. These results revealed that a large negative compression of the void by pressure compensates a positive compression due to the hydration of the protein, resulting in a small positive value for p,. Such a large compressibility of the void supports the proposition that the increase in compressibility of the protein by denaturation is due to the high local concentration of nonpolar groups of denatured protein. From the obtained adiabatic compressibility data, the isothermal compressibility of six proteins was estimated by using the thermal expansion coefficient and the heat capacity data for the proteins.
Introduction The denaturation and reaction of proteins under the . high static pressure or ultracentrifugal force have been a matter of concern for many in~estigat0rs.l~ In such works, the compressibility of native proteins in solution has been an indispensable quantity t o analyze, in detail, the obtained results. The protein compressibility in solution has been thus far estimated by following two methods. One is the measurement of the partial specific volume of protein in solution as a function of pressure by the direct densimetric method6 or ultracentrifuge.6 This method gives isothermal compressibility data. Another method uses sound velocity measurements with an ultrasonic interferometer.'~~The compressibility obtained by this technique is adiabatic. An important result in these compressibility studies is that globular proteins have a positive compressibility while the constitutive amino acids have negative ones due to the hydration effect. This result suggests that the compressibility of the protein interior is 0022-365417912083-2706$0 1.OOlO
very large. At present, however, it is difficult to understand the compressibility of proteins on a molecular level because few compressibility data6-8have been reported, probably due to technical difficulties. The partial molar volume of a protein in solution is known to result from three contribution^:^ (1)the constitutive atomic volume, (2) the void volume because of imperfect atomic packing, and (3) the volume change due to solvation. Since the constitutive atomic volume should be approximated as incompressible, compressibility data of globular proteins in water will produce useful information on the internal structure and the hydration structure of protein, which are still obscure. Furthermore, such compressibility data should present important information to the understanding of the mechanisms of pressure-induced denaturation or reaction of proteins. In this paper, we will report the results of adiabatic compressibility measurements of 14 globular proteins, including enzymes, by the recently developed "sing around 0 1979 American Chemical Society
The Journal of Physic81 Chemistty, Vol. 83, No. 21, 1979 2707
Compressibility of Proteins
TABLE I: Characteristic of the Proteins Studied
Pb
HC
protein
source
Co. and lot no.
mol wt
ribonuclease A ovomucoid lysozyme or-chymotrypsinogen A trypsin conalbumin ovalbumin bovine serum albumin myoglobin hemoglobin p -lact oglo bulin a,-casein a-lactalbumin pepsin
bovine pancreas (type IIA) chicken egg white egg white bovine pancreas (type 11) bovine pancreas (type 111) chicken egg white (type I) egg (grade V) bovine serum whale skeletal muscle (type 11) human (type IV) bovine milk bovine milk bovine milk (grade 11) hog stomach mucosa (type 111)
Sigma 56C-8020 prepared Seikagaku Kogyo E7101A Sigma 66C-8125 Sigma 3 7 C - 0 4 2 3 - 1 Sigma 7 2 C - 8 0 2 4 Sigma 1 0 5 C - 8 9 2 3 Sigma 1 7 C - 8 1 4 5 Sigma 8 5 0 0 1 3 8 Sigma 65C-8150 Sigma 1 0 6 C 0 8 0 7 2 prepared Sigma 75C-8110 Sigma 1 0 7 C - 8 0 5 0
13 700 28 000 14 300 25 7 0 0 23 000 75 5 0 0 46 000 6 8 000 17 000 6 8 000 1 8 400 23 6 0 0 14300 ( 3 5 500)e
780 830 890 950 (910)c 980 98 0
1000 1040 960 1070 (1050)d 1050 (940y
1.73 1.49 1.18 0.83 (1.19)c 1.30 0.92 1.22 1.09 0.84 0.96 1.27
1.11 ( 0.87)e
parameter of Bige10w.j~ a The total hydrophobicity divided by the number of residues ( c a l / r e s i d ~ e ) . ~ Polarity ~ Calculated from the amino acid composition. e Data for pepsin from bovine. for trypsinogen.
pulse method". By this technique, the sound velocity of the solution can be conveniently measured with an accuracy of f l cm/s,loJ1 compared with the classical ultrasonic interferometer with an accuracy of about f20 cm/s. The obtained compressibility data will be discussed on the molecular level by separately estimating the contributions of void and hydration. Furthermore, the isothermal compressibility of some proteins will be estimated from the adiabatic compressibility data by using the thermal expansion coefficient and the heat capacity data which have been recently clarified. Experimental Section Materials. Egg white lysozyme was purchased from Seikagaku Kogyo, Co., Ltd. Ovomucoid prepared freshly from chicken egg white was kindly supplied by Dr. Kenji Watanabe (Nagoya University). a,-Casein, which was kindly supplied by Dr. Tamotsu Imade (Kagawa University), was prepared from bovine milk according to the procedure described by Tsugo and Yamauchi.12 The other proteins used in this study were obtained from Sigma Chemicals, Inc. The source and the lot number of these proteins are listed with their molecular parameters in Table I. The commercial products were used without further purification. The water soluble proteins were completely deionized by exhaustive dialysis against distilled water at 4 "C and lyophilized after passage through a mix-bed ion-exchange column (Amberlite IR-120 and IRA-400) to obtain isoionic proteins. Since @-lactoglobulin, a-lactalbumin, as-casein,and pepsin were insoluble in pure water, they were lyophilized without passage through the ion-exchange column after exhaustive dialysis against distilled water at 4 "C. For the water soluble proteins, five sample solutions with different concentration were freshly prepared by dissolving them in deionized distilled water before measurements of sound velocity and density. The water insoluble proteins mentioned above were further dried under vacuum at 40 "C in the presence of silica gel for 15-20 h. As fast as possible after the oven cooled to room temperature, a definite amount of phosphate buffer (pH 7.0, ionic strength 0.10) was added to dissolve the proteins. The prepared sample solutions were kept as still as possible in order to avoid mechanical or surface denaturation. Sound Velocity Measurements. The sound velocity in the protein solution was measured by a "sing around pulse method (3 MHz) of high stability and precision developed by Greenspan and Tschiegg,13following the procedure in previous papers.lOJ1 The accuracy of the measurements corresponds to a sensitivity of one part in lo6, i.e., f l cm/s. All measurements were carried out in a concentration
Data
range of less than 1%at 25 f 0.001 "C. The partial specific adiabatic compressibility of solute, p,, is defined,as follows
p, = -(l/oo)(a~o/aP), = (PO/oo) lim (@/Po - V,)/c C-0
(1)
where
v, = (d - c ) / d ,
(2)
o0 = lim (1- V,)/c
(3)
c-0
where @ is the adiabatic compressibility of the solution; Po, the adiabatic compressibility of the solvent; d, the density of the solution; do, the density of the solvent; c, the concentration of solute, grams per milliliter of solution; V,, the apparent volume fraction of solvent in solution; Uo, the partial specific volume of solute. The values of @ and Po can be calculated from the results of measurements on the sound velocity, u, and the density, d, of the solution or solvent, using the following Laplace equation @ = l/du2
(4) Density Measurements. The densities of the solvent and solutions were measured with a precision density meter DMA-02C (Anton Paar, Gratz). The principles of the meter's operation have been demonstrated by Kratky et The density of an unknown liquid, dl, is measured by reference to a known standard density, d2,through the measurement of the time lapse of each solution, TI and
Tz; dl - dz = (1/A)(Tl2 - 2'2)
(5) The instrument constant, A, is determined by a calibration measurement with samples of known density. In this work, NaCl solutions were used for this calibration by using the density data in the "International Critical Tables". This constant, A, did not change within an experimental period. All the measurements were made at 25 f 0.01 "C which was maintained with a Sharp thermoelectric bath (Model TE-1OK). The partial specific volume of protein, uo, was calculated from eq 2 and 3. Protein Concentration Determination. The concentration of the following four proteins in solution was determined by absorbance measurements with the values of extinction coefficient: a-chymotrypsinogen A, 19.7 dL/(g.cm) at 282 nm;15 a,-casein, 10.1 dL/(g.cm) at 280 nm;16 ovomucoid, 4.10 dL/(g.cm) at 278 nm;17 &lactoglobulin, 9.6 dL/(g.cm) at 278 nm1.18 The absorbance measurement was carried out with a Hitachi 356 spectrophotometer after measurements of sound velocity and density. As high protein concentration was used, the
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The Journal of Physical Chemistry, Vol. 83, No. 21, 1979
K. Gekko and H. Noguchi
TABLE 11: Partial Specific Volume and Adiabatic Compressibility of Proteins in Water at 25 C sample no.
-
protein
Vc,' mL/g
uo, mL/g
ribonuclease A 0.711 0.704 i- 0.001 ovomucoid 0.696 i 0.003 lysozyme 0.717 0.712 i 0.001 trypsin 0.719 0.717 * 0.002 a-chymotrypsinogen A 0.734 0.733 * 0.001 conalbumin 0.731 0.728 i 0.001 ovalbumin 0.737 0.746 i 0.003 bovine serum albumin 0.736 0.735 * 0.001 myoglobin 0.747 0.742 i 0.001 hemoglobin 0.745 0.754 i 0.002 p-lactoglobulinc 0.746 0.751 i 0.002 &,-caseinc 0.725 0.732 k 0.002 a-lactalbuminc 0.723 0.736 i 0.002 pepsinC 0.743 * 0,001 oxyhemoglobind hemocyanind horse serum albumind a Constitutive volume estimated by Cohn and Edsall's method.24 7.0, ionic strength 0.10). Jacobson's data a t 20 "C.' 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
protein solutions were diluted to some extent with the solvent. This dilution was done gravimetrically on a balance and the dilution factor obtained was converted to volumetric values from the density data of the solvent and solution by assuming the additivity of their volumes. The concentration of other proteins was determined by the dry weight method and it was confirmed to be in good agreement with the concentration estimated by absorption measurement which used literature values of the extinction coefficients.
duldc, m.mL/g.s
limc-to ( p / p , - V,)/c
291.0 268.7 257.1 371.6 302.0 272.6 234.1 222.4 254.9 245.0 276.2 270.0 250.1 251.9
0.017, i 0.001 0.052, i 0.006 0.074, i 0.002 0.014, i 0.002 0.066, * 0.003 0.079, i 0.003 0.153 i 0.007 (0.16)b 0.173 i 0.002 0.149 i 0.005 0.183 i 0.008 0.144 ?: 0.007 0.094, i 0.007 0.138 i 0.005 0.145 * 0.004
Miyahara's data at 20 "C.'
cm2/dyn 1.12 i 0.06 3.38 f 0.43 4.67 i 0.11 0.92 2 0.15 4.05 i 0.19 4.89 * 0.22 9.18 * 0.45 10.5 * 0.17 8.98 -t 0.32 10.9 i 0.45 8.45 i 0.44 5.68 i 0.42 8.27 i 0.32 8.60 i 0.24 9.8 10.6 9.1
In phosphate buffer (pH
0 20
-3
0.10
\
I aLo
\
Results and Discussion The apparent partial specific volume of most proteins was independent of the protein concentration, while some proteins showed a good linear function of the protein concentration with a slight slope. In general, it has been accepted that this constancy of the apparent specific volume is due to the delicate balancing of two counteracting e f f e c t ~the , ~ ~hydrophobic effect and the electrostrictional effect (or charge effect); the former causes lowering of the specific volume and the latter elevates it with increasing concentration. These two effects would be well balanced for globular proteins since both the hydrophobic residues and the ionized groups are distributed on the surface of the molecule. The partial specific volume, DO, was determined as the extrapolated value of the apparent specific volume to zero protein concentration by the least-squares method and the results were presented with their experimental uncertainty in Table 11. The values of Do for most proteins may be regarded as identical with, or very close to, the literature values, considering the experimental uncertainty and the different experimental conditions, such as solvent and temperature. For all proteins studied, the sound velocity of the solutions increased in proportion to the protein concentration in the concentration range studied. The concentration dependence of the sound velocity, duldc, was calculated by the least-squares method and the results are listed in the fifth column of Table 11. The values of du/dc for most proteins were found to fall in the range 220-300 mmL/g-s while the value was exceptionally high for trypsin. It is interesting to note that these values of du/dc are not much different from those for neutral or ionic polysaccharides.lO,ll There were linear relationships between (@/PoVo)/c and c for all the proteins as shown in Figure 1where the results for some proteins are omitted to avoid com-
a Y
0
-0.10
0
4
8
c
12
x io3 ( g / m l )
Figure 1. Typical plots of (PIPo - V J c against protein concentration, c . The numbers attached to the lines are the same as the sample numbers corresponding to the respective proteins in Table 11.
plication of the figure. The values of lime+, (/3//3, - V,)/c obtained by an extraporation procedure are listed in the sixth column of Table 11. The values of P, calculated with eq 1 are listed in the last column of the same table. In an earlier work, Jacobson7 measured the adiabatic compressibility of oxyhemoglobin, hemocyanin, and horse serum albumin in salt-free aqueous solution by using an ultrasonic interferometer. The same method was applied to measure the adiabatic compressibility of ovalbumin in salt-free water by Miyahara.8 The results obtained by them are also presented in Table 11. On account of the limited compressibility data for proteins, no discussion has been made about the correlation between the compressibility and the characteristic properties of individual protein. In this work, it has been found that all globular proteins examined show positive p,, depending on the characteristic properties of individual protein. For example, ribonuclease A, one of the most hydrophilic proteins, has a very small p, in comparison with other hydrophobic proteins. The adiabatic compressibility of any amino acid constituting a protein has been known to be negative due to its hydration Therefore, we cannot easily deduce the adiabatic compressibility of a protein from the compressibility data of its constituent
The Journal
Compressibility of Proteins
amino acids although the partial specific volume can be calculated with good accuracy from the sum of the constitutive atomic or groups volume^.^^-^^ Thus, the compressibility of a protein is dependent to a high degree on the internal compressibility of the molecule which results from the existence of a void in the molecule. According to Kauzmann's a n a l y ~ i sthe , ~ partial molar volume of a protein in solution results from three contributions: (1)the constitutive volume (V,) estimated as a sum of constitutive atomic or groups volumes, (2) the void volume (Vvoid)in the molecule because of the imperfect atomic packing, and (3) the volume change due to the structural change of water or solvation (AVsOl) Do = V,
+ Vvoid + AV,,,
12
of Physical
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I Z 4 t
L
I
0
4
0
1 0 70
(6)
Chemistry, Vol. 83,No. 27, 7979 2709
0 72
0 74
0 76
V o (mI/g)
Flgure 2. Relationship between the adiabatic compressibility, 0 , and Here, vvoid involves not only the incompressible void the partial specific volume, Vo, of proteins. The numbers attached to formed by the closest packing of atoms but also the plots are the same as the sample numbers corresponding to the compressible void or space generated by the random close respective proteins in Table 11. packing of them. It is known that packing density of small molecules is near 0.70 for closest packing in crystals of I I organic corn pound^,^^^^ 0.64 for random close p a ~ k i n g , ~ ~ , ~12~ ~ ? ~ ~ has and 0.60 for loose random p a ~ k i n g . ~BernaP4 proposed that simple liquids correspond in structure to a randomly closed-packed array of hard spheres. In the native globular protein, the bulky hydrophobic groups must be packed together with little or no solvent penetration into voids. The density of the hydrophobic regions in the interior of the carboxypeptidase molecule has been estimated to be 0.93 g/mL on the basis of the observed X-ray structure.35 This density lies between the density -8 -4 0 4 8 12 16 of solid benzene, 1.10 g/mL at 0 "C, and that of liquid ( V"- V, x 10' (rnl/g) benzene, 0.88 g/mL. On the other hand, the compressibility of liquid hydrocarbons is much larger than that of Flgure 3. Relationship between the adiabatic compressibility, p , and water. Thus, it is likely that there is a considerable amount the sum of void and hydration volume, (9' - V J , of proteins. The of compressible volume in the interior of the protein. The numbers attached to the plots are the same as the sample numbers corresponding to the respective proteins in Table 11. The error bars term Vvoid should contribute positively, and AVsolshould attached to plots were calculated from the error involved in Vo. negatively, to Do. Both terms have been known to tend to cancel almost completely, which makes it possible to of the individual proteins. However, it would be observable calculate the partial specific volume of a protein to a good that a protein with a larger Do tends to have a larger p,, approximation as the sum of constitutive atomic or groups being expected from the positive contribution of the void volume^.^^-^^ and the negative contribution of hydration to Do. A noDifferentiation of eq 6 with pressure, P, at isoentropic ticeable point is that the 6, values of a protein with Do larger (adiabatic) condition yields the following equation for 6,: than 0.735 are, within (9.5 f 1.5) X cm2/dyn, inp, = -(l/b0)(aDo/aP), = dependent of its partial specific volume. However, these proteins with large DO do not necessarily have a large -(l/fio)(dVc/aP + d v v o i d / a P + aAV,,l/aP), (7) molecular weight (see Table I), that is, no correlation was Since the constitutive volume, V,, may be substantially observed between the molecular weight of protein and its regarded as the sum of the van der Waals volume of the 6,. Thus, the intuition that a protein with a large molecular constitutive atoms, one may assume, as a first approxiweight may contain a large amount of void and have a large mation, that the first term on the right-hand side of eq 7 6, does not necessarily hold true. is equal to zero. Thus, the observed adiabatic compresSecond, the correlation of p, with (Vvoid 4- AV,,,) was sibility of the protein would be mainly determined by both examined. The calculation of (vvoid + AVd), which is equal the contributions of voids and hydration, then to (DO - V,), must be done with care since it is a very small positive or negative value due to almost complete canceling of the void and hydration effects. The value of V, can be Therefore, a larger value of p, can be expected for a protein estimated from the amino acid composition of a protein with many voids or less hydration as the first term on the by using the Cohn and Edsall method.24 However, it right-hand side contributes positively and the second term should be noted that this method does not give an accurate negatively to p,. The observed positive values for P, suggest V, for proteins containing a constitutive metal ion or that the internal compressibility of proteins takes a very carbohydrate. Then, in the present discussion, the values large positive value so that the void effect overcomes the of (vvoid + AV,,,) were calculated for some typical globular hydration effect. proteins which would give a relatively correct V,. The Let us examine this more quantitatively by analyzing values of V , used in this calculation are shown in the third the compressibility data in terms of some molecular or column of Table 11. The values of (Oo - V,) are plotted conformational parameters of protein molecules. First, the against P, in Figure 3. Taking into consideration the correlation of p, with the partial specific volume of protein uncertainty in (Oo - V,) and the different compressibilities was examined. As shown in Figure 2, the correlation seems of void and hydrated water for individual protein, we find to be fair probably due to the difference in the V, term that the correlation is rather surprising; (3, seems to in-
2710
The Journal of Physical Chemistry, Vol. 83, No. 21, 1979
IC
0
8
K. Gekko and H. Noguchi
1
IO 8
0
0
5
0 0
0 I
4
0
I
0
0 8 00
1000
900
He
I100
01
02
03
log p
&,
(cal/residue)
&,
Flgure 4. Relationship between the adiabatic compressibility, and of proteins. The numbers attached to plots the hydrophobicity, /-I$, are the same as the sample numbers corresponding to the respective proteins in Table 11.
crease in proportion to the increase in (DO - V,) or (Vvoid + AV,,,), with exceptions of bovine serum albumin and myoglobin. The void should be formed in the interior of the globular protein molecule in which most hydrophobic amino acid residues are packed. Therefore, it would be probable that the voids are formed mainly by imperfect packing of such hydrophobic groups and the void volume is a function of the hydrophobicity of the protein. Of course, the void volume in the interior of the protein may be varied with the content of the ordered structure such as helix, 0 structure, and S-S linkage in the molecule. Although it would be difficult to estimate the contributions of these structures to V,, so much compressible void volume does not seem to be generated in such parts since the packing density of such ordered structure parts would be close to that of crystals. In fact, there seemed to be no correlation between p, and the helix or structure content of the proteins. Then, in order to ascertain the hypothesis that the hydrophobicity is a dominant factor to generate the void, the correlation between p, and the hydrophobicity of the proteins was examined. The hydrophobicity of a protein has been estimated as the average hydrophobic energy of the side chains of the ~ ~ t ~the ~ constitutive amino acids, H4 ( c a l / r e s i d ~ e ) , and calculated H4 values for many proteins have been collected in ref 38. The values of H4 for the proteins used in this study are listed in Table I and they are plotted as a function of p, in Figure 4. It is generally acceptable that the more hydrophobic a protein is the more it is compressible. This suggests that the increase in hydrophobicity would cause more void and less hydration. Although H4 is a convenient measure of the hydrophobicity of a protein, a volumetric parameter would be desirable in order to evaluate the contribution of hydrophobicity to the packing density of a protein. In this sense, a polarity , ~ ~ as a volume parameter, P, proposed by B i g e l ~ wdefined ratio of polar amino acids to nonpolar amino acids, may be a proper measure since it involves both contributions of polarity and hydrophobicity of a protein P = CNiPViP/&NjnV," (9) I
0
J
where N and V are the number and volume of amino acid residues signified with subscript, respectively, and superscript p and n refered to polar and nonpolar amino acids, respectively. Most polar amino acids in a protein molecule would have to be localized on the surface of the molecule to cause much hydration. On the other hand,
Figure 5. Relationship between the adiabatic compressibility, and Bigelow's polarity parameter, P , of proteins. The numbers attached to plots are the same as the sample numbers corresponding to the respective proteins in Table 11.
most hydrophobic amino acids would have to be buried in the interior of the molecule to cause the void by their imperfect packing. Therefore, an increase in the parameter P would give rise to decrease in 6, through the above two contributions. This idea can be confirmed by a clear correlation between 8, and P as shown in Figure 5, with the exception of bovine serum albumin, a-chymotrypsinogen, and trypsin; the p, values of the proteins examined can be expressed as a function of P by the following the most probable curve with an uncertainty of f1.5 X cm2/dyn p, = (-30 log P + 8.0) X cm2/dyn (10) The reason for the exceptional deviation for three proteins is not clear. The large p, of bovine serum albumin may be due to the fact that this protein binds significantly less water than it should as judged by its polar residue content.40 Although the above equation is empirical, it may be useful for estimating the approximate p, values of unknown globular proteins when their P values or their amino acid composition are known. Adopting the hypothesis that the compressibility of a protein is due to both effects of void and hydration of protein, what values does each contribution to p, take? This question has remained unsolved because the exact amount and the compressibility of the hydrated water of a protein were not clear. Jacobson7 ignored the effect of hydration and ascribed the obtained p, to the internal compressibility only. Strictly speaking, however, this treatment is oversimplified because the hydration effect must be an important factor in the partial specific volume of a protein in water. The amount of hydration of proteins has been estimated by several methods, being reviewed recently by Kuntz and K a ~ z m a n n .On ~ ~ the molecular level, this hydration phase should be formed cooperatively by three contributions, electrostriction, hydrogen bonded hydration around polar groups and peptide groups, and hydrophobic hydration around nonpolar atoms. It is certainly probable that some fraction of the surface of a globular protein in aqueous solution is hydrophobic in the sense that the surface is occupied by atoms which cannot form hydrogen bonds, as demonstrated by cytochrome c and lysozyme by Bull and Bree~e.~O In order to analyze separately the contribution of void and hydration to p,, it is necessary to determine AV,,, since estimation of Vvoid is impossible a t present. It has been known that there is a contraction of 5 4 % of the protein volume when anhydrous proteins are dissolved in water.42This contraction, however, should not be equivalent to AV,,, because a part of the volume change may be due to filling of some of the
The Journal of Physical Chemistry, Vol. 83,
Compressibility of Proteins
voids in the anhydrous protein with water, and due to improved space filling by the protein when water is presentagp4lTherefore, in this work, a new attempt was made to estimate AV,, by considering each volume change of the three modes of hydration. If e milliliters of free water is bound electrostrictively to the ionic groups on 1 g of protein and the volume reduces e’ milliliters, the volume change due to the electrostriction is expressed as (e’ - e ) . In the same way, volume changes due to hydrogen bonded hydration and hydrophobic hydration are (b’- b ) and (h’- h ) ,respectively, where h and b represent the volumes of free water which are changed to h’ and b’milliliters by hydrophobic hydration and hydrogen bonded hydration, respectively. Thus, the volume change of solvation, AVwl,can be written as follows:” AV,,, = ( e ’ - e ) (b’- b) (h’- h) (11) At present, it is difficult to estimate the terms of (b’ - b) and (h’- h ) ,while the estimation of electrostriction, (e’ - e ) , may be possible as follows. It has been proposed that each pair of charged groups would cause a contraction of about 20 mL when it is dissolved in water by examining the difference in partial molar volume between dipolar ions and their isomeric uncharged m ~ l e c u l e . ~By ~ ~this ~ ’ assumption, the volume change due to the electrostriction of some proteins has been estimated to be on the order of 2-370 of the molar volume of the protein^.^^^^^ This classical method may provide more probable volume change near the isoelectric point of the protein while it is usually close to the isoionic point. On the other hand, the amount of electrostriction of a protein may be also derived as the sum of the hydration of each ionic amino acid constituting the protein. Recently, K u n t ~has ~ ~proposed that the hydration number of negatively charged amino acids are 6,7, and 7 mol of water per mole of amino acid for Asp-, Glu-, and Tyr-, respectively, and the corresponding values of the positively charged ones are 3, 4, and 4 for Arg+, His+, and Lys’, respectively. Thus, it may be assumed that the hydration of anionic and cationic groups is at most 7 and 4 mol of water per mole of amino acid residue, respectively. This assumption would not be incompatible with the result of Bull and Breese40 that about 6 mol of water, on the average, are complexed with each ionic amino acid residue. Therefore, the amount of electrostriction can be estimated by the above two ways if the number of charges per protein molecule is known by the pH titration method. Thus, the obtained number or weight of electrostricted water can be converted to the corresponding volume change by using the molar contraction of water by electrostriction which has been estimated by several investigators to be -2.0 ~ -3.0 mL/m01.~~If the m L / m 0 1 , ~-2.7 ~ m L / m 0 1 , ~and amount of electrostriction can be estimated, the sum of remaining two modes of hydration may be estimated by using the total hydration data for the protein. Differentiation of eq 11with respect to pressure yields the following re1ation:ll (aAV8,1/aP), = P,(h + b + e ) - (hph + b’ob + eye) (12) where P h , P h , P,, and 0, represent the adiabatic cornpressibilities of the water of hydrophobic hydration, hydrogen bonded hydration, electrostriction, and free water, respectively. I t has been known that Ob is close to the cmz/dyn,10g47and that compressibility of ice, 18 X electrostricted water has a very small compressibility, nearly zero. On the other hand, Conway and VerralP have proposed that the compressibility of water of hydrophobic
+
+
No. 21, 1979 2711
hydration is between that of ice and free water. In earlier work^,^^^^^ we have evaluated a probable value of Ph to be 35-40 X cm2/dyn. Thus, at present, we have available data for the compressibility of water of hydration. With these values in mind, we have attempted to estimate AVs01 and to separate the contributions of void and solvation to p,. The example calculation for bovine serum albumin is demonstrated below. Adopting 0.40 g per gram of bovine serum albumin as the total amount of hydration43 h b e = 0.40 g/g = 0.40 mL/g (13)
+ +
The number of pairs of charged groups can be found to be 96 per molecular weight of 65000 from hydrogen ion titration data.50 Then, the volume change due to electrostriction is e ’ - e = 96 X (-20)/65000 = -0.030 mL/g (14) Assuming a value of -2.7 mL/mol as the molar volume change of water by electrostriction, the value of e can be derived by using the value of ( e ’ - e ) e = (-0.030) X 18/(-2.7) = 0.197 mL/g
Therefore, from eq 13 and 15 h + b = 0.40 - 0.197 = 0.203 mL/g
(15)51 (16)
The volume chimge per mole of water by hydrogen bonded hydration is known to be about -1 mL/mol of wateragOn the other hand., the volume change of water accompanying hydrophobic hydration is not clearly known. However, recent s t u d i e ~ lhave ‘ ~ ~revealed ~ ~ ~ ~ that the volume change is on the order of -1 to -2 mL per mole of methylene group while it has bean believed for a long time to be about -20 mL per mole of hydrocarbon. This result suggests that only a few water molecules would be hydrated around the methylene group, and the volume change of water due to hydrophobic hydration would be, at most, on the order of -1 mL per mole of water. Thus, assuming that both volume changes of water due to hydrogen bonded hydration and hydrophobic hydration are -1 mL per mole of water (h’- h ) + (b’- b) = 0.203 X (-1)/18 = -0.011 mL/g (17) From eq 16 and 17 h’ b’ = 0.192 mL/g (18)
+
Therefore, from eq 14 and 17, we can estimate the value of the total volume change due to hydration, AV,,, is -0.041 mL/g. However, it is impossible to estimate separately the terms of (h’- h) and (b’- b). Accordingly, the analysis of the pressure effect on the partial specific volume of a protein will be possible at only two limiting situations as follows: (a) the volume of hydrated water expressed by eq 18 is composed of hydrogen bonded hydration only (h = h’= 0, b’= 0.192 mL/g) and (b) the volume is produced by hydrophobic hydration only (b’= b = 0, h’= 0.192 mL/g). In the case of situation (a), using 0, = 45 X lo-’’ cm2/dyn,P b = 18 X cm2/dyn, and p, = 0, we obtain (aAV,,,/aP), = P,(h + b + e ) - (h’& + b’Pb + e’&,) = P,(h + b + e ) - b p b = 14.5 x mL.cm2/g.dyn (19) From eq 8 (aV,,id/aP), = -Dop, - (aAV,,i/aP), = -22.2 x 10-l2 mL-cm2/g.dyn (20)
2712
The Journal of Physical Chemistry, Vol. 83, No. 21, 1979
K. Gekko and H. Noguchi
TABLE 111: Estimated Contributions of Void and Hydration to the Compressibility of Proteins in Water at 25 Ca
x protein
hydration,b -(e' - e ) , g/ g mL/g
lysozyme
0.34
a-chymotrypsinogen A oval bumin
0.34
bovine serum albumin myoglobin P-lactoglobulin a,-casein
0.33 0.40 0.42 0.55d 0.55d
0.015 (0,028) 0.011 (0.019) 0.018c (0.046) 0.030 (0.045) (0.0471 0.023 0.023'
aP),
no. of pairs of charged groups/105 g of protein
3.33
74e
2.97
56f
6.85
9 18
7.72
148h
6.66 6.35 4.16
llY
loLzmL.cmz/g*dyn
-aVSo1, mL/g
Vvoid, mL/g
-(a Vvoid/
0.0 28 (0.036) 0.026 (0.031) 0.030 (0.048) 0.04 1 (0.051) (0.053) 0.045 0.045
0.023 (0.031) 0.025 (0.030) 0.039 (0.057) 0.042 (0.050) (0.048) 0.050 0.052
12-17 (13-16) 11-17 (10-15) 17-21 (21) 18-22 (22-24) (22-23) 9-17 7-15
(aa Vso,/
W,
9-14 (10-13) 8-14 (7-12) 10-14 (14) 10-14 (14-16) (15-16) 3-11 3-11
-(avo/
113i
a The numbers in parentheses are estimated by assuming 7 mol of hydrated water per negative charge and 4 mol of water per positive charge (see text). From hydration data by NMR.43 Reference 24. d, Hydration determined by Reference 50. Reference 68. Reference 69. calorimeter.% e Reference 65. f Reference 66. g Reference 67. lZ Reference 42. J
For situation (b), an assumption of Ph = 40 X cm2/ dyn yields (aAV,,,/aP), = P,(h + b + e ) - h'Ph = 10.3 X mL.cm2/g.dyn (21) and (aV,,id/aP),
= -18.0 x
mL.cm2/g.dyn
(22)
Since both hydrogen bonded hydration and hydrophobic hydration exist in practice on the surface of a protein molecule, the real compression of void and hydration water would exist between the two limiting situations. Therefore, the probable value of (aVvoid/aP),may be estimated to be mL-cm2/g.dyn and that of -18.0 X lo-'' to -22.2 X to 14.5 X mL.cm2/ (aAV,,,/aP), to be 10.3 X gndyn. By usage of the electrostriction estimated as the sum of the hydration of each ionic amino acid, which is shown in References and Notes section,51 the value of to 16 X (aAV,,l/aP), was found to be 14 X mL.cm2/g.dyn, then the value of (aV,,id/~P), was -22 X to -24 X mL.cm2/g-dyn. The same procedures were applied to other six proteins and the calculated values of (aVvoid/aP)s and (aAV,,l/aP), are listed with the values of (e' - e ) , AVsol,and Vvoidin Table 111, where the values of Vvoidwere calculated from eq 6 by using the values of oo, V,, and AVml. It is seen that the value of AV,, amounts to 3.543% of the partial specific volume of proteins, more than half of which seems to be ascribed to electrostriction. This result suggests that the contributions of hydrogen bonded hydration and hydrophobic hydration to AV,,, cannot be neglected in the compressibility study of protein in water. It should be noted that the values of AV,,, obtained are slightly less than the volume contraction of 5-8% of the protein produced when anhydrous protein is dissolved in water. The positive value of (aAV,,,/aP), indicates that the amount of hydration decreases with increasing pressure, while the void is compressed under pressure as (dVvoid/aP), takes on negative value. The apparent adiabatic compressibility of voids, defined as (-l/Vvoid)(aVv,id/aP),, can be found to be in the order of few hundred X lo-'' cm2/ cm2/dyn for bovine serum aldyn, e.g., 430-530 X bumin. This value is much larger than that of water, 45 X cm2/dyn. Therefore, it may be concluded quantitatively that both the void and the hydration effects are canceled at an absolute compression of the order of 10 X mL.cm2/g.dyn, resulting in small negative values of (abo/aP), or small positive p, of globular proteins. At
present, however, it seemed difficult to compare the compression values calculated for different proteins because of some assumed values for parameters in the calculations. The adiabatic compressibility, p,, is related to the isothermal compressibility, &, by the following equation
& = PT (cu/ c p )
(23)
where C, is the specific heat at constant volume and C, is the isobaric specific heat. This equation can be rewritten as follow by using the thermal expansion coefficient, a, and the density, d:
P, = & - d'T/dC,
(24)
a = (l/oO)(aoO/aQp
(25)
Here, the density, d, may be regarded as (l/iio) for the infinitely dilute solution of protein. Therefore, we can estimate the value of ,ZITfrom eq 23 when C, and C, are known, or from eq 24 when a and C, are known even if C, is unknown. At present, data on C, of proteins in solution are very scarce while the values of C have been elucidated by the recent calorimetric studies.15GMOn the other hand, the values of a can be estimated from the temperature dependence of the partial specific volume of the protein.59 Since there is no datum on the partial specific volume of protein at 0 "C and 1 atm, we have evaluated a by regarding the condition of 25 "C and 1atm as a standard state. Thus calculated values of a and & are shown for six proteins in Table IV. If the standard state is set at 0 "C and 1 atm, a would become slightly larger (about 1.5%) because the value of bo for these proteins may be expected to be smaller by about 0.010 mL/g at 0 "C than at 25 "C from the temperature dependence of bo. This difference will result in an increase of about 2.2% in a2T/dC,, which will not exceed the experimental error in the determination of C The & obtained is found to be larger by 3-4 X cmP'/dyn than p,, independent of the protein. Estimation of PT for some proteins has been attempted by measuring the partial specific volume in aqueous solution as a function of pressure up to 400 atm, but no significant change in the specific volume of protein was observeda5 From these data, however, Brandts et al.' deduced that the compressibility of ribonuclease would be less than 5 x IO4 atm-l at pH 9.1 and 20 "C. This value cm2/dyn (= 5.55 is close to our result at 25 "C, 5.48 X
The Journal of Physical Chemisrry, Vol. 83, No. 21, 1979 2713
Compressibility of Proteins
TABLE IV: Isothermal Commessibilitv of Proteins in Water at 25 " C q = i / d ) , 104(a33/aT),= io4&,& protein mL/g mL/g.deg l/deg ribonuclease A a-chymotrypsinogen A lysozyme @-lactoglobulin ovalbumin bovine serum albumin a From ref 59. Reference 57.
0.704 0.733 0.712 0.751 0.746 0.735
4.64 3.5d 3.03 3.75 3.50 3.65
Standard state is taken as 25 " C and 1 atm. Reference 54. Reference 58.
x lo4 atm-l) since the hydration should decrease and the void may expand at higher temperature. From the values of ,ElTin Table IV, it is expected that the partial specific volume of these proteins is smaller by 0.2-0.6% at 400 atm than at 1 atm if (aoo/aP)T does not depend on the pressure in this pressure region. This difference at both pressures corresponds to 0.0015 and 0.0043 mL/g in the partial specific volumes for ribonuclease and bovine serum albumin, respectively. The assumption of (aoO/aP)? = 0 has been considered to be reasonable in ultracentrifugation a n a l y ~ i s . Certainly, ~ the change of 0.6% in the partial specific volume leads to at most a 2% deviation in the molecular weight determination. This deviation may not exceed the other experimental errors involved in the molecular weight determination by this technique. However, when ultracentrifugation is applied to estimate the volume change for association or an interacting reaction system of protein, some caution must be taken on interpreting the volume changes obtained since such changes may be often as small as the pressure-induced change in the partial specific volume of the native protein i t ~ e l f . ~ Recently, Scharp et aL7have determined the isothermal compressibility of ovalbumin to be 27 X cm2/dyn by using the analytical ultracentrifuge method. This value is about two times greater than that in this work. This discrepancy may be due to the fact that PT obtained by them includes not only the compressibility of the solvated protein, but also the dependence of preferential hydration on pressure. The pressure-induced denaturation of protein has been recently analyzed in detail.lm3 The most important conclusion in these studies is that the partial molal isothermal compressibility of denatured protein is larger than that of cm2/dyn for ribothe native one by about 1.5 X cm2/dyn for chymotrypsinogen;2 nuclease1 and 1.57 X the latter value was calculated by assuming that the partial specific volume of native chymotrypsinogen is identical with that of the denatured protein because the difference between them is only 0.00056 mL/g. This difference in P T between both native and denatured states would exist also under our experimental condition since the result for ribonuclease is known not to depend significantly on the pH and temperature.l If this is the case, from the PT values of the native proteins in this work, we can estimate PT for the denatured protein to be 7.0 X and 8.5 X cm2/dyn for ribonuclease and chymotrypsinogen, respectively. If in the denaturation process, the hydrophobic groups buried in the interior of the protein are exposed to the solvent accompanying the decrease in void and the increase in hydrophobic or hydrogen bonded hydration, the value of p, or & should be smaller in the denatured state than in the native one. However, the experimental results are completely opposite to this expectation. It has been pointed out that the simple hydrophobic model for the denaturation reaction, expected from the small model compounds, is not adequate and some factors must be taken into consideration to explain the denaturation
c, cal/g.deg
6.59 4.77 4.26 4.99 4.69 4.97 Reference 56.
0.5OC 0.41e 0.30f 0.4d 0.396g 0.32h
1 0 ' y a 2 T l d C P ) , lo'*&, cmZ/dyn cm2/dyn
4.36 2.90 3.06 3.34 2.95 4.04
5.48 6.95 4.67 11.8 12.1 14.6
Assumed value. e Reference 15.
behavior of protein under pre~sure.',~For these factors, a possible explanation is that if the local concentration of nonpolar groups is quite high in a randomly coiled protein, then the volume change for the rupture of hydrophobic bonds could be positive in proteins,6°!61while the hydrophobic contribution to the volume change accompanying protein denaturation has been estimated on the basis of the assumption that the exposed nonpolar groups upon denaturation are essentially at infinite dilution. This explanation is in agreement with the experimental result that the volume change for the transfer of water from the pure state to dilute solution in organic solvents are positive.62 I t is probable that, on protein denaturation, the filling feature of its nonpolar groups or their packing density is changed to increase the compressible void volume. However, such an increase in the void volume would be overcome by the volume decrease due to the increased hydration, resulting in a decrease in the partial specific volume of the protein in the denatured state. The adiabatic compressibility of water newly hydrated around the exposed polar groups and nonpolar groups would be and 40 X cm2/dyn, respectively, at most 18 X as discussed above for native proteins. The electrostriction of the protein would not significantly be affected by denaturation since most ionic groups are already exposed to the solvent in their native state. On the other hand, as discussed above, the apparent compressibility of voids cm2/dyn, amounts up to the order of few hundred X e.g., 550 X cm2/dyn for chymotrypsinogen. Therefore, it is possible that even small increases in the void volume on protein denaturation contribute to make the term (aVVoid/aP)more negative in the denatured state than at native one, which could overcome the increase in (aAV,,/aP) due to the increased hydration which gives rise to an increase in the compressibility of denatured proteins. At present, we do not have any substantial evidence to support the fact that there exists such a high local concentration of nonpolar groups in which a few water molecules penetrate. However, according to the estimation by P0hl,6~ the number of additional nonpolar amino acids exposed to the solvent in the denatured state amounts to only 3-8 of total 49 nonpolar groups per mole of ribonuclease and to 15-40 of total 112 nonpolar groups per mole of chymotrypsinogen. Aune et al.64showed that the unfolding process of lysozyme in water is incomplete. These data are not incompatible with above high local concentration model of nonpolar groups proposed by B$je and Hvidt.60,61Further studies on the compressibility of denatured protein should lead to a progressive understanding of the conformation of denatured proteins. References and Nptes (1) J. F. Brandts, R. J. Ollveira, and C. Westort, Biochemistry, 0,
1038-1047 (1970). (2) S. A. Hawley, Biochemistry, 10, 2436-2442 (1971). (3) A. Zipp and W. Kauzmann, Biochemistry, 12, 4217-4227 (1973). (4) W. F. Harrlngton and G. Kegeles, Methods Enzymol., 27, 306-345 ( 1973).
2714
The Journal of Physical Chemistry, Vol. 83, No. 21, 1979 P. F. Fahey, D. W. Kupke, and J. W. Beams, Proc. Natl. Acad. Sci. U.S.A. 63, 548-555 (1969). D. S. Scharp, N. Fujita, K. Kinzie, and J. B. Ifft, Biopolymers, 17, 817-836 (1978). B. Jacobson, Ark. Kemi, 2, 177-210 (1950). Y. Miyahara, Bull. Chem. SOC.Jpn., 29, 741-742 (1956). W. Kauzmann, Adv. Protein Chem., 14, 1-63 (1959). K. Gekko and H. Noguchi, Biopolymers, 10, 1513-1524 (1971). K. Gekko and H. Noguchi, Macromolecules, 7, 224-229 (1974). T. Tsugo and K. Yamauchi, Bull. Agric. Chem. Soc. Jpn., 24, 96-100 (1960). M. G. &eenspan and C. E. Tschiegg, Rev. Sci. Instrum., 28,897-901 (1956). 0. Kratky, H. Leopold, and H. Stabinger, Methods Enzymol., 27, 98-1 10 (1973). W. M. Jackson and J. F. Brandts, Biochemistry, 9, 2294-2301 (1970). T. T. Herskovits, J. Biol. Chem., 240, 628-638 (1965). J. G. Davis, C. J. Mapes, and J. W. Donovan, Bhhemktry, 10,39-42 (1971). R. Townend, R. J. Winterbotton, and S. N.Timasheff, J . Am. Chem. SOC., 82, 3161-3168 (1960). W. Y. Wen and S. Saito, J . Phys. Chem., 68, 2639-2644 (1964). F. J. Millero, A. L. Surdo, and C. Shin, J. Phys. Chem., 82, 784-792 (1978). A. A. Yayanos, J. Phys. Chem., 76, 1783-1791 (1972). Y. Miyahara, Bull. Chem. SOC.Jpn., 26, 390-393 (1953). S. Goto and T. Isemura, Bull. Chem. SOC.Jpn., 37, 1697-1701 (1964). E. J. Cohn and J. T. Edsall, "Proteins, Amino Acids and Peptides", Reinhold, New York, 1943, pp 370-381. T. L. McMeekin and K. Marshall, Science, 116, 142-143 (1952). J. T. Edsall, "Protelns, Amino Acids and Peptides", Reinhold, New York, 1943, pp 155-165. J. T. Edsall, "The Proteins", H. Neurath and K. Bailey, Ed., Vol. 1, Academic Press, New York, 1953, Chapter 7. A. A. Zamiyatnin, "Progress in Biophysics and Molecular Biology", J. A. V. Butler and D. Noble, Ed., Vol. 24, Pergamon Press, New York, 1972, pp 109-123. E. J. King, J . Phys. Chem., 73, 1220-1232 (1969). A. I.Kitaigorodskii, "Organic Chemical Crystallography", Consultants Bureau, New York, 1961. J. D. Bernal and J. L. Finney, Discuss. Faraday Soc., 43, 62-69 (1967). G. D. Scott, Nature (London), 168, 908-909 (1960). J. D.Bernal and J. Mason, Nafure(London), 186, 910-911 (1960). J. D. Bernal, Nature (London), 165, 68-70 (1960). 1. D. Kuntz, J. Am. Chem. Soc., 94, 8568-8572 (1972). C. Tanford, J. Am. Chem. Soc., 84, 4240-4247 (1962). Y. Nozaki and C. Tanford, J . Biol. Chem., 248, 2211-2217 (1971). C. C. Bigelow and M. Channon, "Handbook of Biochemistry and Molecular Biology, Proteins", Vol. I, G. D. Fasman, Ed., CRC Press, Cleveland, 1976, p 209. C. C. Bigelow, J . Theor. Biol., 16, 187-211 (1967). H. 8. Bull and K. Breese, Arch. Biochem. Biophys., 128, 488-496 (1968). I. D. Kuntz and W. Kauzmann, Adv. Protein Chem., 28, 239-345 (1974).
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+ 4 X 96) X
18/65000 = 0.30 g/g
since there are 96 positive charges and 100 negative charges per 65 000 g of bovine serum albumin.50 Therefore, the volume change due to electrostriction is e ' - e = 0.30 X (-2.7)/18
= -0.045 mL/g
e = 0.30/1 = 0.30 mL/g (52) K. Suzuki, Y. Taniguchi, and T. Watanabe, J . Phys. Chem., 77, 1918-1922 (1973). (53) M. Friedman and H. A. Scheraga, J. Phys. Chem., 69, 3795-3800 (1965). (54) H. B. Bull and K. Breese, Arch. Biochem. Biophys., 126, 497-502 (1968). (55) P. L. Privalov, N. N. Khechinashvili, and B. P. Atanasov, Biopolymers, 10, 1865-1890 (1971). (56) P. L. Privalov, FEBS Lett., 40, suppl. s140-153 (1974). (57) N. N. Khechinashvili, P. L. Privalov, and E. I.Tiktopulos, FEBS Left., 30, 57-60 (1973). (58) P. L. Privalov and D. R. Monaselidze, Bloflzlka, 6, 420-425 (1963). (59) "Handbook of Biochemistry and Molecular Biology, Proteins", Vol. 111, G. D. Fasman, Ed., CRC Press, Cleveland, 1976, p 595. (60) L. Btje and A. Hvidt, Biopolymers, 11, 2357-2364 (1972). (61) L. Bqe and A. Hvidt, J . Chem. Thermodyn., 3, 663-673 (1971). (62) W. Masterton and H. Seller, J. phys. Chem., 72,4257-4262 (1968). (63) F. M. Pohl, FEBS Lett., 3, 60-64 (1969). (64) K. Aune, A. Sakhuddin, M. Zarlengo, and C. Tanford, J. Bid. Chem., 242, 4486-4489 (1967). (65) C. Tanford and M. L. Wagner, J. Am. Chem. Soc., 76,3331-3336 (1954). (66) C. Tanford, Adv. Protein Chem., 17, 69-165 (1962). (67) R. K. Cannan, A. Kibrick, and A. H. Palmer, Ann. N . Y . Acad. Sci., 41, 243-266 (1941). (68) Y. Nozaki, L. Bunviele, and C. Tanford, J . Am. Chem. Soc., 81, 5523-5529 (1959). (69) W. G. Gordon, W. F. Semmett, R. S. Cable, and M. Morris, J . Am. Chem. Soc., 71, 3293-3297 (1949).
Representation of Vapor-Pressure Datat D. W. Scott and A. G. Osborn" BartlesviNe Energy Research Center, Department of Energy, Barflesville, Oklahoma 74003 (Received May 8, 1978) Publication costs assisted by the U.S. Department of Energy
Two equations are proposed for representing vapor-pressure data, one for the entire liquid range and the other for a limited temperature range. Their use is illustrated with selected sets of experimental vapor-pressure data. Each of these equations is shown to have definite advantages over some alternative equations used heretofore. Their use in detecting inconsistent data is emphasized. Original vapor-pressure data are reported for liquid benzene and solid hexafluorobenzene. Introduction Many equations have been proposed for representing vapor-pressure data. Partington,' in 1951, listed 56 such +ContributionNo. 231 from the thermodynamics research laboratory at the Bartlesville Energy Research Center.
equations sequentially and continued with about two dozen more forms of particular equations. Additional equations Proposed in the ensuing quarter of a century have swelled the ranks still further. However, no one equation, or small selection Of equations, has found Universal acceptance among investigators concerned with representing vapor-
This article not subject to US. Copyright. Published 1979 by the American Chemical Society
