744
P. MOSER,P. G. SQUIRE,AND C. T. O'KONSKI
Electric Polarization in Proteins-Dielectric
Dispersion and Kerr Effect
Studies of Isoionic Bovine Serum Albumin1
by P. Moser, P. G. Squire, and C. T. O'Konski Department of Chemistry and Hormone Research Laboratory, University of California, Berkeley, California (Received August 30,1966)
Dielectric dispersion and transient birefringence data are reported for the isoionic and defatted monomer of bovine serum albumin as a function of concentration at 25". Dielectric dispersion data are also presented for the monomer at 1" and the dimer at 25". Crystalline albumin was defatted, deionized, and fractionated on a Sephadex column, Various mechanisms of electric polarization are considered and it is shown that the dielectric properties of the protein are due mainly to an orientation polarization process. This suggests that the protons of the isoionic protein are not sufficiently mobile to contribute a large ionic polarization or a fluctuation polarization at the dispersion frequency, and tends to reinstate dielectric dispersion for protein size and shape studies. A dipole moment of 384 D. was computed for the monomer. Interpretation of the dielectric and birefringence relaxation times leads to an axial ratio of 3.0 and a hydration of 0.64 g of HzO/ g of protein for a prolate ellipsoidal model. The dielectric relaxation behavior at 1" shows the effect of strong intermolecular interactions even at the lowest concentrations which could be measured. These interactions are also visible at 25", and are believed responsible in part for earlier interpretations which led to higher axial ratios. In this research, extrapolation to zero concentration was successful at 25". Proton fluctuation phenomena are interpreted kinetically in a manner which permits important intermolecular forces to exist while contributions to the dielectric dispersion may be negligible.
Introduction The usefulness of dielectric dispersion measurements for studying rigid macromolecules in solution was demonstrated by Oncley and his co-workers in an extensive series of investigations of the dielectric properties of protein molecules during the late 1930's and the early 1 9 4 0 ' ~ . ~They showed how information could be obtained about the size and shape of the macromolecule, the permanent dipole moment, and the dipole direction with respect to the ellipsoidal axes. Their interpretations were based on the assumption that the dielectric increments were due solely to the orientation of permanent dipoles, and that the dielectric dispersion corresponded to rotation of the macromolecule as a rigid unit. The ClausiusMosotti-Debye theory, developed for insulating dielectric systems, was used to calculate dipole moments, with the aid of an empirical constant.
Subsequent experimental studies suggested that polyelectrolyte macromolecules may exhibit dielectric dispersions associated with the motion of the counterions in an applied electric fielda3 Studies of the Kerr effect in this laboratory showed that in certain macromolecules the electric field orientation effect was determined primarily by the polarization associated with ionic motion^.^^^ Independent investigations by Eigen and Schwarz, who studied the anisotropy of conductiv(1) This is paper XVIII of the series, "Electric Properties of Macromolecules." Presented at the Ninth Annual Meeting of the Biophysical Society, San Francisco, Calif., Feb 24-26, 1965. (2) (a) J. L. Oncley, Chem. Rev., 30, 433 (1942); (b) J. T. Edsall and J. Wyman, "Biophysical Chemistry," Vol. I, Academic Press, Inc., New York, N. Y . , 1958, Chapter 6. (3) H. M. Dintzis, J. L. Oncley, and R. M. Fuoss, Proc. Natl. Acad. Sci. U.S., 40, 62 (1954). (4) C. T. O'Konski and A. J. Haltner, J . Am. Chem. SOC.,79, 5634 (1957). (5) C. T. O'Konski, J . Phys. Chem., 64, 605 (1960).
ELECTRIC PROPERTIES OF MACROMOLECULES
ity accompanying orientation of polyphosphates in an electric field, confirmed thk6?7 During the same period, several theoretical contributions were made in which alternative explanations for the dielectric properties of proteins were proposed. Among these were the concepts of proton fluctuations and ionic polarization,6”’ both of which presuppose appreciable mobility of charge carriers. These studies reopened the entire question of the interpretation of dielectric dispersion in protein systems. Thus, there is a need for definitive studies in which the various theoretical proposals are considered and evaluated in interpreting the experimental results. The necessity of doing this was illustrated by recent studies on various ion forms of montmorillonite,’O for which it was found that both orientation polarization and ionic polarization processes are important. For the present study we have selected bovine serum albumin (BSA) as a typical example of a crystalline protein which may be obtained in highly purified form by recently developed techniques. It has been studied extensively with a wide variety of physicochemical methods.“ Interpretations of various kinds of measurements led to somewhat discordant conclusions regarding molecular parameters. l 2 A major source of difficulty has been the presence of polymeric forms of BSA in the preparations studied. lleasurements were made of dielectric constant and loss factor of BSA4solutions over the dispersion region as a function of concentration, temperature, and sample preparation. To aid in interpreting the data, sediment ation constants were determined a t low ionic strengths, and a precise molecular weight was obtained for highly purified monomer.l 3 Improved values of molecular size, shape, and hydration were obtained, after it mas established that all data are consistent with a permanent dipole orientation mechanism. The results are discussed in relation to other data in the literature. Experimental Section
Materials. The preparation and characterization of the bovine serum albumin fractions used in this study will be described in detail e1~ewhere.l~These fractions had been (1) defatted by filtration at low pH, (2) fractionated by gel filtration into monomer, dimer, and oligomer fractions, and (3) deionized by being passed through a mixed-bed ion exchange column. Sedimentation velocity and equilibrium measurem e n t ~demonstrated ~~ that the mass homogeneity, especially of the monomer fraction, was exceedingly high. Dielectric Apparatus. A wide-range capacitance-
745
conductance bridge constructed in this laboratory14 was used in making measurements between l o 3 and 5 X lo5 cps. The precision of the capacity readings is .t0.07% and of the conductance readings, *0.5%, Between 5 X lo6 and 3 X lo7 cps a General Radio reactance bridge, Type 1606-A, was used. Measurements of reactance with this instrument had a precision of f0.2% at 5 X lo6 cps and f l % at 3 X lo7 cps, while the resistance measurements had a precision of f1% from 0.5 to 5.0 Rlcps. The errors in resistance measurements increase markedly above this frequency range, but resistance data were not required there because this was beyond the dispersion region. The reactance bridge output was detected by means of a tuned receiver. This provided high sensitivity and harmonic rejection. The cell used in the dielectric measurements consisted of two concentric cylindrical platinum electrodes with sandblasted surfaces. This type of surface has been recommended by Oncley15 in order to reduce electrode polarization effects. The electrodes were rigidly mounted in a glass cell surrounded by a brass water jacket which acted as an electric shield. Water from a thermostat was circulated through the jacket, maintaining thc temperature of the cell within *0.1”. The temperature was recorded following each measurement, and corrections were applied for small temperature fluctuations. Birefringence Apparatus. Birefringence decay measurements were carried out with the use of an apparatus described by Krause and O’Konski.*6 Pulses of 1.6psec duration and of amplitudes up to 5000 v were applied to the BSA solution contained in a strainbirefringence-free, temperature-controlled glass cell. The pulse decay time, to 20% of the pulse height, was 0.02 psec. The platinum electrode assembly, with a separation of 1.98 mm, was similar to that described (6) hl. Eigen and G. Schwarz, J. Colloid Sei.,12, 181 (1957). (7) G. Schwarz, 2. Phusik, 145, 563 (1956). (8) J. G. Kirkwood and J. B. Schumaker, Proc. Xatl. Acad. Sci.
U.S.9 855 (1952). (9) C. T. O’Konski, J. Chem. Phgs., 23, 1559 (1955). (10) C. T. O’Konski and M. Shirai in “Chemical Physics of Ionic Solutions,” B. E. Conway and R. G. Barradas, Ed., John Wiley and Sons, Inc., New York, N. Y., in press. (11) J. F. Foster in “The Plasma Proteins,” 1’01. 1, Frank W. Putnam, Ed., Academic Press, New York, N. Y., 1960, Chapter 6. (12) R. A. Phelps and F. W. Putnam, ref 11, Chapter 5. (13) P. G. Squire, P. Moser, and C. T. O’Konski, in preparation. (14) C. T. O’Konski, J. Am. Chem. SOC.,73, 5093 (1951); unpublished notes of F. E. Harris, Jr., and C. T. O’Konski (1957); see also P. M. Gross, Jr., and R. M. Fuoss, Reu. Sei.Inatr., 20, 252 (1949). (15) J. L. Oncley, J. Phys. Chem., 44, 1103 (1940). (16) S. Krause and C. T. O’Konski, J. A m . Chem. SOC.,81, 5082 (1959). 38,
Volume 70,Number 3 March 1966
P. MOSER,P. G. SQUIRE,AND C. T. O’KONSKI
746
where C, and C;, are the measured capacities of the cell filled with, respectively, protein solution and an NaCl solution having precisely the same low-frequency conductivity, c is the protein concentration in grams per liter, and Cois the cell constant
An
co = c w - c d EW
I/ -4 0.2ps.
TIME Figure 1. Birefringence signals from deionized BSA solution, 15 g/l., 25”, and propylene carbonate (PC). Sweep speed 0.2 psec/cm.
by Pytkowicz and 0’Konski.l’ The pulse and the transient birefringence were displayed on a Tektronix Type 555 dual trace oscilloscope and photographed on Kodak Tri-X film. A typical signal obtained from a BSA solution of 15 g/l. is shown jn Figure 1. Figure 1 also shows the positive transient birefringence of propylene carbonate, which was used to test the performance of the apparatus. The relaxation time of the propylene carbonate signal was 0.05 psec, which is much longer than the expected molecular relaxation time. It is quite certain that this relaxation time reflects the RC-time constant of the detecting circuit. We therefore took the results of this experiment as a basis for the correction of the BSA relaxation curves. Treatment of Experimental Data. (a) Dielectric Dispersion. A major problem encountered in the measurement of dielectric constants of aqueous solutions is the increment in capacity arising from electrode polarization, an effect which becomes increasingly troublesome at low frequencies and at high conductivities. Several empirical methods have been proposed to correct for electrode polarization. 16,18--21 In general, one can use a cell in which the distance between the electrodes can be varied, or one can make corrections by comparisons with data on a salt solution of the same conductivity. We tried both methods in a preliminary study of the dielectric constant of glycine over the accessible frequency range and found that, in the range of low salt concentrations used and with the cells at our disposal, better precision was obtained by the second method. In applying this correction, the real part of the specific dielectric increment, Ae’lc, was calculated at a given frequency according to the equation
CP - c.3 A ~ ’ / c= cco T h e Journal of Physical Chemistry
where C, is the measured capacity of the cell filled with water, c d is the distributed capacity of the cell and connections (19 pf in this case), and e, is the dielectric constant of water at the temperature of the measurement . We have observed that the electrode polarization depends not only upon the conductivity of the solution, but also upon the nature of the polymer solute. This dependence upon the solute was noticeable, however, only at frequencies below the dispersion region of BSA, and could therefore be disregarded in this study. At frequencies above 5 X lo5 cps the series inductance of the cell (0.0506 phenry) became important and the necessary corrections were applied. At 20 to 30 R4cps the inductive reactance approached the value of the capacitative reactance of the cell and the correction introduced substantial errors. The specific dielectric loss, Ar“/c, is given by the relation
A€’’/C = 1.80
x
10‘2(Kp,f-
(3) where K p , f and K ~ , O are the specific conductivities of the protein solution in ohm-’ cm-’ at a frequency f and below the dispersion region, respectively. The value of K ~ , Owas around 5 X ohm-’ cm-l in most measurements. A small but significant dielectric loss was measured when the cell was empty, requiring a correction at higher frequencies. The correction was made on the assumption that the loss could be treated as a conductance in parallel with the cell. The dielectric behavior in the dispersion region was analyzed with the use of Debye’P equations Kp,O)/Cf
~
(17) R.M. Pytkowicz and C. T. O’Konski, Biochim. Biophys. Acta, 36, 466 (1959). (18) W.Kuhn, P. Moser, and H. Majer, Helv. Chin?. Acta, 44, 770 (1961). (19) J. L. Oncley, J . Am. Chem. Soc., 60, 1115 c1938). (20) H.P. Schwan, Z.Naturforsch., 6 b , 121 (1951). (21) S. Takashima, Biopolymers, 1, 171 (1963). (22) P. Debye, “Polar Molecules,” Reinhold Publishing Gorp., New York, N. Y., 1929,Chapter V.
747
ELECTRIC PROPERTIES OF MACROMOLECULES
( A € ~ / c - AE,/C)WT~
time, r,, at low BSA concentrations, it was necessary to correct for the birefringence of the solvent. It 1 (wrJ2 was assumed that the total birefringence was a sum in which hto,fc and h , / c are the specific dielectric of contributions due to solvent and solute and that the increments at frequencies below and above the diswater birefringence would decay with the same persion region, respectively, w is the angular frequency instrumental time constant as found for propylene 2n;f, and r , is the dielectric relaxation time. The effects carbonate, 0.05 psec. The relaxation times were of concentration dependence were eliminated by found from a plot of log 6 os. time.24 It was seen by ext,rapolating the dispersion curves to infinite dilusolving the differential equations for an exponentially tion. This was done by plotting the logarithm of the decaying signal in an RC circuit that the finite time frequency for chosen values of the relative increment, constant of the detecting circuit mentioned earlier, (A€' - Acm)/(Aeo - A€,), us. the concentrati~n.~~affected only the beginning of the decay curves. Apart I n general, dispersion curves extrapolated to infinite from this initial period, the slopes of the log 6 us. time dilution could not be represented by a one-term curves did not change, and r , could be determined in Debye equation, but could be closely approximated the usual manner." At the lowest concentration the by an equation with two or three relaxation times relaxation time was found independently by computer analysis and it agreed well with the one determined from the graph. The relaxation time determined from birefringence decay, r,, is relatedz6-* to the rotary The A t are the components of the relative increment diffusion coefficient, Ob, by having a relaxation time ret. Values of A t and ret = '/ern (9) were obtained with the aid of a digital computer by least-squares fitting of the experimental data. and to the longer dielectric relaxation time, rel,by The dipole moment p of the protein molecule may be 7, = red3 (10) estimated from the following equation due to O n ~ l e y ' ~ A€"/C =
+
(5)
Results (7)
p
= 0.4034;
WC
Here, N is Avogadro's number, IC is Boltzmann's constant, M is the molecular weight of the protein, Aet/c is the total dielectric increment at unit concentration (grams/liter), A.et/c = AQ/C - Ae,/c, T is the absolute temperature, b is an empirical parameter given as b = 5.8 by Oncley from the known dipole moment of glycine, and p is in Debye units. Equation 7 is based on the original Debye equation for nonpolar solvents, but has been extended empirically to amino acids in polar solvents where it has been found to give reasonable results. (b) Birefringence Decay. The optical retardation, 6, was calculated essentially as described by O'Konski and Haltnerz4 and Krause and O'Konski.16 Tracings of the enlarged photographs of the transients were used to find 6 as a function of time. Before and after each experiment the vertical axis of the screen of the oscilloscope was calibrated in terms of r, the angle of rotation of the analyzer from the crossed position. The retardation was obtained by a combination of eq 1 and 2 in ref 24 and eq 1 of ref 16. I n the calculation of the birefringence relaxation
The specific dielectric increment and loss were measured throughout the frequency range lo3 to 3 X lo7 cps at various concentrations of the purified BSA monomer at 25 and lo,and of the purified dimer at 25". In Figure 2a the specific dielectric increment of the BSA monomer at 25" is shown as a function of the frequency at three concentrations. In Figure 2b similar data at 1" are reported. Included in Figures 2a and 2b are the specific dielectric loss data at 44 g/l. The results of measurements of the dielectric loss at lower concentrations showed so much scatter due to the low value of the loss factor that they were not included. Similar results on the BSA dimer at 25" are given in Figure 3. Due to the smallness of the specific dielectric increments, the measurements had to be carried out at fairly high concentrations. It was thus necessary to extrapolate the data to infinite dilution because of the effect of interactions on the dielectric increments and on the broadness of the dispersion curves. In (23) H.M.Dint&, Ph.D. Thesis, Harvard University, 1952. (24) C. T. O'Konski and A. J. Haltner, J. Am. Chem. Soc., 7 8 , 3604 (1956). (25) C.T.O'Konski and B. H. Zimm, Science, 111, 113 (1950). (26) H.Benoit, Ann. Phys., 6 , 561 (1951). (27)I. Tinoco, J. Am. Chem. Soc., 77, 3476 (1955).
Volume 70,Number 3 March 1966
748
P. h'fOSER, P. G. SQUIRE,
I
I
AND
c. T. O'KONSKI
I
A
1 I
I
I
I
I
-O.I
t-
-0.2 lo3
to5
IO
I o7
io6
FREOUENCY (CRS.)
Figure 3. Dielectric dispersion curves of deionized bovine serum albumin dimer at 25" for three different concentrations: 35 g/l., 0;24 g/l., 0 ; and 12 g/l., V and A (two independent measurements). The specific dielectric loss, Ae"/c, is shown for the concentration 35 g/l., x.
-02
I
I
I
I
o
0.2 5
Figure 4 the low frequency (static) specific dielectric increments of the BSA monomers and dimer are plotted as a function of concentration. It may be seen that the concentration dependence is substantial in the case of the monomer, at lo, while the BSA dimer shows no detectable concentration dependence in the narrow range studied. Data on a monomer fraction, obtained from a BSA preparation which had not been defatted, gave a normalized dispersion curve agreeing with that expected for the defatted material at the same concentration. However, this sample had a lower low frequency specific dielectric increment, 0.136 at 27.5 g/l., than the value of 0.189 of the defatted material. The dispersion data were extrapolated to infinite dilution in two different ways. The first method, used with the monomer, consisted of an analysis of each dispersion curve at 25 and 1' in terms of the twoterm Debye expressions, using the raw experimental data and finding the parameters A,, r,, by computer analysis. Results are recorded in Table I. The 7 values were extrapolated to zero concentration by The Journal of Physical Chemistry
OJ5
DIMER
t
0.I 00
20
40
60
80
100
CONCENTRATION (g./k?.l
Figure 4. Concentration dependence of the low-frequency specific dielectric increment for bovine serum albumin monomer at 25", 0;monomer at lo, 0 ; dimer at 2 5 O , A.
linear regression.28 In the second method, the dispersion data were extrapolated to infinite dilution by plotting the logarithm of the frequency for chosen values of the relative dielectric increment, ( A d Aem)/(Ae, - Ae,), against the c~ncentration.~~ Results of a computer fit to a two-term Debye equation are given, under c = 0, in Table I. The dispersion of the relative dielectric increments for all three samples extrapolated to infinite dilution (28) D. 8. Villars, "Statistical Design and Analysis of Experiments for Development Research," W. C. Brown Co., Dubuque, Iowa, 1951.
ELECTRIC PROPERTIES OF MACROMOLECULES
Table I:
749
Dielectric Dispersion of Bovine Serum Albumin Monomer and Dimer Conon,
Vila,
Sample
Temp
g/l.
Am/c
Atm/c
Att/c
Monomer
25 '
95 44 12 12 0
0.160 0.195 0.206 0.190 0.202
-0.061 -0.062 -0.062 -0.062 -0.062 (-0.083)
0.22 0.26 0.27 0.25 0.26
1"
95 44 12 12 0
0.228 0.271 0.284 0.321
-0.078 -0.069 -0.070 -0.070 -0.070 (-0.095)
0.31 0.34 0.35 0.39
25 O
35 24 12 0
0.270 0.270 0.270 0.270
-0.042 -0.042 -0.042 -0.042
Ai
+et,
w o
0.131 0.140 0.077 0.067 0.074
A2
1.23 0.98 0.31 0.26 0.22
0.59 0.43 0.63 0.68
0.74
0.07
0.14
3.09 1.66 3.73 1.89 2.49
0.63 0.44 0.25 0.27
0.24 0.29 0.40 0.32 0.37
0.37 0.56 0.75 0.73
1.59
0.33
0.28
0.67
Mcps
0.41 0.57 0.37 0.32
Remarks
a a
1.09
b d
0.93
a a
b C
0 Dimer
Pseo
C
0 Monomer
Tfl,
0.31 0.31 0.31 0.31
0.38
d
e 0.41
a Two independent measurements were made on the same sample a t the same concentration. Extrapolations to infinite dilution Theoretical values of the high-frequency decrement were calcuof the above Aeo/c and Tet values were made by linear regression. The parameters] A t , Ttt, were fitted to a dispersion curve extrapolated to infinite dilution as outlined in lated from eq 6.14 of ref 5. the text. e See ref 5.
according to the second method is shown in Figure 5. I n all three cases the experimental curves are broader than a single-term dispersion curve (dashed curve), suggesting more than one relaxation time. The deviations for the rnonomer at 25" from the theoretical curve for a single relaxation time are rather small. Nevertheless, the discrepancies were judged to be outside of experimental error. The dispersion curves for the monomer a t 25 and 1" thus were both fitted with two relaxation times. Three relaxation times were used for the dimer, which had a much broader dispersion region. The values A t and rtf determined in this manner are recorded in Table I. Birefringence decay measurements were carried out at six different concentrations on solutions of monomer prepared in exactly the same way as the ones used for the dielectric experiments. Figure 6 shows the birefringence relaxation times, rn, determined from corrected log 8 us. time plots, not presented here, as a function of the concentration a t 25". Below 30 g/L, straight log 6 vs. time curves were obtained, indicating single relaxation times. At 30 g/l., however, the plot of log 6 us. time was curved due to concentration-dependent interaction, and a single rn could not be defined. The points in Figure 6 lie reasonably well on a straight line so that the relaxation time a t infinite dilution could be found by linear regression. The
FREOUENCY (C.PS.1
Figure 5. Relative dielectric increments for deionized BSA a t infinite dilution vs. frequency. The points are values extrapolated to zero concentration as explained in the text for monomer a t 25", 0;monomer a t lo,A ; dimer a t 25", 0 . The solid curves represent computer analyses of these points in terms of Debye dispersions with two relaxation times for the monomer and three for the dimer. The dashed curve represents a single Debye relaxation time.
value thus determined is rn,c-o= 0.076 psec, and the corresponding rotational diffusion constant is 9, = I / ~ T , = 2.18 X lo+ sec-' (see Table 11). The specific Kerr constant extrapolated to zero concentration was found to be 17.0 X 10-9 in cgs units. This is higher Volume 70, Number 8 March 1966
P. MOSER,P. G.SQUIRE, AND C. T. O'KONSKI
750
0 -
b
b
m
0
0
0
7 9
Y
than the value reported earlier, 13 unfractionated samples.
*
3
9 0
to
4
* m
0
0
0 0
?
0
c?
"?
%Ib 3
8I
5 0
99 0 0
I /
3
8I
5 % CJ 9 rl 00
a
9
%r
6"
$0 U
€2"
9
4
0 0
99 m 3 e4
.3
$
f
2 X
for
Discussion
i "
;iN.
30
Figure 6. Concentration dependence of the birefringence relaxation time for BSA monomer a t 2 5 O , 0. Data found in a previous investigation16 on BSA containing a n unspecified amount of oligomer are shown by X , and one value, reported by P. Ingram and H. G. Jerrard, Nature 196, 57 (1962), and corrected to 25O, is shown by A.
c?
rig
10 20 CONCENTRATION ( g./R.l
9 02
0
0
0
1. Mechanism of Dielectric Dispersion in Proteins. Various models are available for interpretation of these dielectric dispersion data. They might be explained in terms of orientation of permanent dipoles, or by the motion of mobile charges associated with the macromolecule; in the general case both processes may contribute. One may assume the macromolecule is rigid, or one may include the possibility of flexibility. Because BSA is a crystallizable globular protein, and because it has considerable helical c ~ n t e n t , a~ rather ~ * ~ compact and ordered structure is indicated at the isoionic point, pH 5.15, at which the present studies were made. There are numerous physicochemical studies on BSA in aqueous solutions, and the available data support the proposal that it is rigid, except in acid solutions, where subunit motion has been suggested. Foster" argues from various l6tS1
s
.2
a
.. W
The Journal of Physical Chemistry
(29) E. Shechter and E. R. Blout, Proc. Natl. A d . Sci. U.S.,51, 695 (1964). (30) J. T.Yang, Tetrahedron, 13, 143 (1961). (31) W.F. Harrington, P. Johnson, and R. H. Ottewill, Biochem. J., 6 2 , 669 (1956).
ELECTRIC PROPERTIES OF MACROMOLECULES
lines of evidence, including titration and denaturation studies, that the protein is tightly folded in aqueous solutions above pH 4. Therefore, we adopt a rigid model for interpretations of the present results. I n the deionized samples employed here, the only mobile charges which might possibly contribute to dielectric polarization would be protons. We may estimate the critical dispersion frequencies for relaxation of ionic polarization from equations given by one of the present authors5 if we know the size and shape of the macromolecule, the number of carriers on its surface, and the mobility of the carriers. It will be assumed that the protons are distributed uniformly over the surface of the macromolecule. Carboxyl and histidine groups are the only groups with pK close enough to the isoionic point to contribute to fluctuation From the known chemical composition,32the number of carboxyl sites available for protons is 100. Titration studies give 96 for the number of carboxyl groups ionized a t the isoionic point.33 This leaves four bound carboxyl protons. Assuming a prolate ellipsoid of revolution of axial ratio 3, with semiaxes a = 69 A, 6 = 23 A, reported in this research, we calculate a mean density of carboxyl protons of 2.4 X 10l2 protons cmV2. Assuming a proton mobility of 3.62 X loT3em2v-l sec-', the value of protons in aqueous solution, one may calculate from eq 2.2 of ref 5 a value of surface conductivity, = 1.4 X loT9 ohm-', which is of the order of previously reported values. This should be an upper limit because the actual mobility on the surface of the protein would be expected to be less due to binding. Inseiting this value into the equations5 for the longitudinal and transverse relaxation times of the prolate ellipsoid of revolution, we obtain the following estimates for the dielectric relaxation times and critical frequencies: r, = 4.8 X sec; rb = 1.0 X sec; v,, = 3.3 X 10' cps; Vcb = 1.6 X lo8 cps. It is seen that these frequencies are well above the dispersion region which was observed experimentally. If the mobility of the protons on the surface were lower than the value used here, the dispersion would shift to lower frequency, perhaps into the range observed. Such a shift would require that the mobility be reduced by a factor of about 100. This decrease in mobility would be consistent with the recent observation that the dielectric dispersion frequency for the hydrogen form of a polyelectrolyte is considerably lower than that for the sodium form.l0 If NaC1 were added, one would expect that the chloride would be bound, and that the sodium counterions would shift the dispersion frequencies to higher values. I n an experiment not mentioned in the Results section
751
above, it was found that addition of 1/3 mole of S a c 1 per mole of protein shifted the critical frequency only slightly, and to lower rather than to higher values. This suggests that ionic processes are not very important. Similar results were obtained by Taka~hima3~ in a study of the effect of ions on the dielectric dispersion of ovalbumin solutions. Furthermore, the dispersion frequency observed here shifted to a lower value a t lower temperature (1") roughly as expected for a dipole orientation process. (Extrapolation of the data at 1" to infinite dilution was unsatisfactory. Experiments at 40" resulted in extensive denaturation.) Most importantly, the dielectric relaxation times obtained from the analysis of the dielectric dispersion curves extrapolated to zero concentration agree with the values expected on the basis of other studies of size and shape of the BSA molecule, as discussed under Relaxation Times below. I n view of the above considerations, we conclude that the dielectric increments and dispersion in isoionic BSA solutions arise from a dipole orientation process. Some contribution from the proton fluctuation mechanism may exist, but it must be relatively small. This means that permanent dipoles are mainly responsible for the dielectric increments. Attempts to identify an electric polarization contribution from the proton fluctuation mechanism have been made previously. For example, Haltner and one of the present authors4 measured the Kerr constant of tobacco mosaic virus solutions as a function of pH through the pK region of the amino acids present, and were not able to see a contribution from this process. More recently, Lumry and Y u advanced ~ ~ ~ kinetic arguments against protonic contributions. Scheider also discussed the kinetics of the process,36abut finally concluded that "more needs to be known about the protein-water surface before proton migration can be either discussed or satisfactorily analyzed." Takashima's data36bare not inconsistent with the presence of some contributions from proton fluctuations; he concluded, however, that the Kirkwood-Shumaker theory was not adequate to explain the results. 2. Relaxation Times. We shall adopt the usual model of an ellipsoid of revolution to describe the properties of the BSA monomer. As pointed out by EdsalLn the two dielectric relaxation times of an (32) P. F. Spahr and J. T. Edsall, J. Biol. Chem., 239,850 (1964) (33) C. Tanford, S. A. Swanson, and W. S. Shore, J . Am. Chem. SOC.,7 7 , 6414 (1955). (34) S. Takashima, J . Polymer Sci., 11, 2791 (1963). (35)R. Lumry and R. H. Yue, J . Phys. Chem., 69, 1162 (1965). (36) (a) W. Scheider, Bwphys. J., 5 , 617 (1965); (b) S. Takashima, J . Phys. Chem., 69, 2281 (1965).
Vo'olume70,Number 3 March 1966
P. RJOSER, P. G. SQUIRE,
752
oblate ellipsoid cannot differ by more than lo%, so this shape is ruled out by the dielectric and birefringence relaxation data (Table 11) ; hence, we assume that the ellipsoid is prolate. We may attribute the longer dielectric relaxation time, rei, and the birefringence relaxation time, T,, to the rotation of the semimajor a axis about the short ( b = c) axes.% The corresponding rotary diffusion constant is 6, = l / 2 r e 1 = 1 / 6 ~ , . 3 9 The short dielectric relaxation time, rC2,corresponds to the rotation of the b = c axes about the a and b axes, with 6, = 1/re2. Perrin@ rotary diffusion constants 0, has given the equations of T , ~ / T O = O 1 / 6 , and r , 2 / r 0 = 260/(6, 6,) where 6 0 and TO are, respectively, the rotary diffusion constant and relaxation time of an equivalent sphere having the same volume as the ellipsoid, and are given by
+
+
60
=
‘/*TO
=
kT/8~~b~qo
c. T. O’KONSKI
calculated with these relaxation times and the A I is shown as a solid curve in Figure 5 and it can be seen that it deviates only slightly and rvithin the limits of experimental error from the experimental curve, The rms deviation for 20 points was 0.011, the estimated experimental rms uncertainty was 0.02. I n comparison, the rnis deviation of the closest possible fit of the extrapolated curve with two relaxation times (Table I) was 0.0074, also for 20 points. This shows that the constrained fitting with one predetermined parameter increases the deviat,ion only slightly, but leads to a much more reliable value for the axial ratio. The best value, then, from this evaluation of the dielectric and birefringence relaxation times is p = 3.0, which gives a hydration of 0.64 g of H20/g of protein.
(11)
where k is the Boltzmann constant and qo is the viscosity of the solvent. The axial ratio, p = u/b, can be obtained easily from r , 1 / r e 2 using a nomogram given by Wynian and Ingalls. * l The dielectric relaxation times obtained by the two methods of extrapolation to infinite dilution as described in the Results section have been shown in Table I. The obvious reason for the scatter of relaxation times of the monomer is related to the close approximation of the dispersion curve to a single-term Debye curve. This means that, with slightly different experimental results, substantial variations of the parameters A,, ret are possible. Therefore, conclusions about the shape of molecules cannot be drawn from the analysis of dielectric dispersion curves alone. I n order to eliminate the ambiguity of these interpretations, the dielectric dispersion results may be combined with results from other methods. The birefringence decay gives, as mentioned earlier, the rotary diffusion constants of the long axis around the short axes according to eq 9. Therefore, this rotary diffusion constant, which is unambigu~usly~~ determined with reasonable accuracy, mas used in combination with the dielectric dispersion curve in the following way. The parameter rt1 in the two-term Debye equation was set equal to 37, and other parameters AI, Az, and rt2 were determined with the computer so as to give minimum rms deviation from the experimental data extrapolated to zero concentration. The values of the parameters found in this way are shown in Table 111, together with the axial ratio and the dimensions of the BSA calculated on the basis of these relaxation times, using the Wyman-Ingalls plot to determine p , eq 11, and Perrin’s equations. The dispersion curve The Journal of Physical Chemistry
AND
Table 111: Summary of Properties of Bovine Serum Albumin IIonomer at Infinite Dilution“ Temperature PH Relaxation times: 7 6 1 = 37, 7f2
25
5.15 0 . 2 3 psec 0.11 psec
Rotary diffusion constants: ob
+ Ob)/2 Harmonic mean of relaxation (0,
times, 7 h Dipole moment Axial ratio, p = a/b Semimajor axis, u Semiminor axis, b Hydrated volume, v h Hydration (g of HlO/g of protein)
2.18 X 106 sec-1 4 . 4 8 X 106sec-1 0.15 psec 384 D.
3.0 69 A 23 A 153,000 A3
0.64
All values are obtained from dielectric and birefringence data of this research.
It was established in this research that it is important to extrapolate all data to infinite dilution. An example of the effect of concentration is the birefringence data shown in Figure 6. The birefringence relaxation time found in this research, r, = 0.076 psec, is to be (37) J. T. Edsall in “The Proteins,” Vol. I, H. Neurath and K. Bailey, Ed., Part B, Academic Press, New York, N. Y., 1953. (38) J. L. Oncley in “Proteins, Amino -4cids and Peptides,” E. J. Cohn and J. T. Edsall, Ed., Reinhold Publishing Corp., New York, N. Y., 1943, p 543. (39) J. T.Edsall, ref 36,p 506. (40) F. Perrin, J . Phys. Radium, 5, 497 (1934). (41) J. Wyman, Jr., and E. N. Ingalls, J . Biol. C5em., 147, 297 (1943).
(42) Unambiguously, because it is clear that birefringence is related to molecular reorientation, whereas the dielectric relaxation may involve ionic relaxation processes.
ELECTRIC PROPERTIES OF MACROMOLECULES
753
compared to the one determined in an earlier study in value reported by Harrington, et al.,310.124 psec a t this laboratory16 where a value of T, = 0.20 psec was pH 7.3. All three values agree within the experifound. About one-half of the discrepancy is due to mental errors of the measurements. the fact that the relaxation times had not been exThe good agreement between the harmonic means trapolated to infinite dilution but were measured a t from fluorescence depolarization, and from a combinaabout 1% in the earlier study. The remainder may tion of dielectric and birefringence relaxation substanbe due to the fact that the sample used in the earlier tiates that the polarization is due to permanent dipole investigation had not been fractionated and probably orientation and that the macromolecule rotates as a contained as much as 20 to 30% oligomers.ll Further, complete unit. the faster oscjlloscope used in this research provided As is expected, the dimer dielectric dispersion, better accuracy for short relaxation times. extrapolated to zero concentration, occurs a t lower The dispersion curve obtained by Oncley' for horse frequencies than that of the monomer. In addition, serum albumin was broader than the one we have obthe dispersion curve is broader, requiring a series of tained for BSA monomer. As a consequence, the three relaxation times for a satisfactory fit (rms deviacalculated axial ratio for the horse serum albumin is tion of 0.0063). The numerical results are shown in greater than that for BSA. In view of the persistent Table IV. Extrapolation to infinite dilution was made presence of polymeric products in serum albumin by only one method because of the very wide disperpreparations, it seems likely that this broadening may sion range and small concentration dependence. Three have been due in part to heterogeneity. This leaves relaxation times were necessary to reduce the standard unanswered the question of whether the axial ratio of deviation to a reasonable value in a computer fit. the equine monomer is actually greater than that of the This yielded the parameters AI = 0.22, .rei = 3.33 bovine. psec, A2 = 0.63, 7,2 = 0.353 psec, A B = 0.151, 7,s = When the dielectric data of the monomer at 1" were 0.067 psec. For HSA, DintzisZ3 obt,ained Al = 0.25, analyzed, it was found that the dispersions a t comrel = 2.0 psec, A 2 = 0.6, re2 = 0.5 psec, A s = 0.15, parable concentrations were wider than at 25", indi7,s = 0.16 psec. The longest of the three dimer relaxacating stronger intermolecular interactions. Due to tion times, 3.33 psec, cannot be explained by simple the relatively low dielectric increment of bovine dimerization. It would correspond to a particle serum albumin, measurements could not be carried length of approximately 430 A which is much longer out on solutions with concentrations of less than 10 than a particle formed by end to end aggregation of two monomer molecules (Table 111). g/l. DintzisZ3was able to measure human mercaptalbumin (HNA) at 0" down to lower concentrations, about 3 g/l., because it has a threefold higher dielectric Table IV : Dielectric Dispersion of increment than BSA. I t was seen there that at relaBovine Serum Albumin Dimer tive increments >0.6 the log f vs. c plots were no longer straight at low concentrations, indicating strong interTemp, Concn, Aam/c, Adc, actions affecting mostly the long relaxation times. O C g/l. l./g 1. / g Mcps Because extrapolations of our data to infinite dilution 0.31 25 35 -0.042 were not quantitatively justified, we do not draw any 24 -0.042 0.31 conclusions from the relaxation times about the shape 12 -0.042 0.31 0 -0.042 0.31 0.41 of the molecule at 1". It is interesting to note that the Stokes radii of BSA calculated by L o n g s ~ o r t h ~ ~ from his own diffusion data at 1 and 25" (37.55 and 3. Dielectric Increments. The dipole moment is 36.84 A, respectively) agreed rather well, though perthe resultant of the group moments of individual haps not within experimental error. This suggests amino acid residues, the moments of the charged that the shape and hydration are very nearly identical groups about the hydrodynamic center of the macroat the two temperatures in the buffer used by Longsmolecule, and a polarization contribution from the worth (acetate, pH 4.6, ionic strength 0.16). solvent. The fact that the dipole moment of BSA is 'The harmonic mean of the best monomer relaxation as small as 384 D. implies a low degree of asymmetry times obtained by the constrained fitting described of the charge distribution. above, Th = 0.15 psec, is in excellent agreement with the relaxation time found by S t e i r ~ e rfrom ~ ~ measurements of the fluorescence depolarization, T = 0.155 (43) L. F. Longsworth, J. Phys. Chem., 58, 770 (1954). psec at pH 5.22, and in fairly good agreement with the (44) R. G. Steiner, Arch. Biochem. Biophys., 46, 291 (1953). ~
~~
~~
Y1/21
Volume 70, Number 3 March 1966
P. MOSER,P. G. SQUIRE,AND C. T. O'KONSKI
754
The angle between the dipole moment and the long axis of the molecule, 4, can be estimated from an equation given by, Oncley2& tan 4 =
Fb/pa = m i
(12)
Taking the values A1 = 0.4 and A2 = 0.6 for the monomer a t 25' from Table 111, we obtain a dipole angle of 50". This calculation is based on the assumption of a spherical cavity for the dipole in Debye's theory. Since any angle less than 54" will tend to produce positive birefringen~e~~ when the optical anisotropy factor is positive, this angle is consistent with the observation of positive birefringence. Assuming that the optical anisotropy of the molecule is due primarily to its shape rather than to a high intrinsic anisotropy, the observed positive birefringence is consistent with permanent dipole orientation. The value of the dipole moment of the dimer, 636 D., is 1.66 times the dipole moment of the monomer. A comparable relation, p d i m e r = 1.53pm,, has been found by DintziP for human mercaptalbumin. We may, following the arguments given by Dintzis, assume that in the dimer the monomer dipole moments form a mean angle a = 68" (cos 4 2 = pdImer/2pmonomer) with each other to give the resulting dimer dipole moment. From these data It is not possible to decide whether the two monomer dipole moments are in a fixed position relative to each other to give this angle or whether it represents a mean angle as a result of rotation of the monomers around the linking bond. Furthermore, the angles estimated in this way are of uncertain accuracy because the local field depends upon the shape of the macromolec~le.~ The high frequency dielectric decrement, Ae,, can be calculated from an equation which takes into account the shape-dependent depolarization factor A , of ellipsoids5
where 6; is the volume fraction of the solute (7.34 X low4for a 1 g/l. solution), E~ is the dielectric constant of the solute along t h e j axis, E, = 6b = eC = 4.5, and is the dielectric constant of the solvent. The high frequency dielectric decrements calculated by means of this equation have been entered into Table I to facilitate comparison with the values obtained from the experiments. I n this calculation an axial ratio of 3 was assumed at 25" with the corresponding values A, = 0.1085 and Ab = 0.445.5 It should be pointed out that the result depends very little upon the axial ratio. By reference to Table I, it may be seen that the theoretical values of the high frequency specific dielectric The Journal of Physical Chemistry
decrement are about 0.02 lower than the experimental values. It seems possible that this small difference may be due to polarization of the proton distribution which, as pointed out above, might have a critical frequency much higher than that of the main dispersion. T a k a ~ h i m ahas ~ ~ observed dielectric dispersion in BSA in the frequency region from about 3 kcps to 2 Mcps. He reported a small specific dielectric increment (0.089 1./g) and stated he was not able to determine the critical frequency accurately, indicating that it lay between 300 and 500 kcps. He calculated a dipole moment of 220 D., a value one-half of ours and stated that "it may be reasonable to conclude that the electric polarization of BSA is due to a permanent dipole . . . . '' Takashima's lower value of dielectric increment may have been due to the fact that he did not defat his samples. We pointed out above that defatting increased the dielectric increment and Dintzis showed that the addition of oleic acid to defatted material decreased the dielectric increment. 2 3 4. Proton Fluctuations and Intermolecular Forces. It is interesting to explore the possible connections between the mechanism of dielectric dispersion in proteins and the processes producing intermolecular forces. Kirkwood and Sh~maker,~' in an article immediately following their paper on dielectric dispersion and proton fluctuations, introduced the concept of intermolecular forces arising from proton fluctuations. One physical basis for attractive forces would be the reorientation of a macromolecular electric dipole by the field of another, that is, correlation of dipole orientations. In view of the conclusion that dipole fluctuations are not responsible for the dispersion, the question arises as to whether proton fluctuations might still be important in producing intermolecular forces. The studies of Timasheff, Dintxis, Kirkwood, and Coleman48 clearly suggest they are. They found that the reciprocal turbidity of isoionic solutions of BSA, bovine serum mercaptablumin, and human serum mercaptalbumin all varied as the one-half power of the concentration, indicating thermodynamic deviations in accord with Kirkwood and Shumaker's prediction for a proton fluctuation mechanism. Permanent dipole kinteractions would be expected to produce a linear dependence on the concentration, and therefore appeared unimportant. How can this be reconciled with the present (45) C.T.O'Konski and K. Bergmann, t o be published. (46) S. Takashima, Biochem. Biophys. Acta, 79, 531 (1964) (47) J. G. Kirkwood and J. B. Shumaker, Proc. .VatZ. Acad. Sci., U . S., 38, 863 (1952). (48) S. N. Timasheff, H. AM. Dintzis, J. G. Kirkwood, and B. D. Coleman, J . Am. Chcm. SOC.,79, 782 (1957).
ELECTRIC PROPERTIES OF MACROMOLECULES
research? We considered the possibility that fluctuating dipoles with lifetimes greater than the time required to reorient a BSA molecule might be responsible for intermolecular forces, but would appear essentially as permanent dipoles on the time scale appropriate to molecular reorientation. We reject this explanation for the following reason. The magnitude of the mean attractive force between molecules depends upon the degree to which correlations occur between the dipoles of neighboring molecules. This correlation might occur by rotations of the macromolecules or by proton redistribution, but the mechanism which is more rapid would predominate. This, on the above assumption, would be dipole reorientation. We may estimate the order of the relaxation time which will permit effective correlations from the Einstein equation or translational diffusion, &? = 2Dt, where D is the translational diffusion constant of BSA (6.97 X em2sec-l at 25" in HzO). Inserting a root-mean-square distance of 100 A, which appears to us a reasonable estimate of the range of interaction, we find t = 0.7 X sec. This is of the order of the observed molecular reorientation time. Thus, dipole fluctuations appreciably slower than the dielectric relaxation time could not permit effective dipole correlations at distances comparable to the nearest distance of approach of two protein molecules, whereas the dielectric dispersion (molecular reorientation) process is sufficiently fast to allow correlations of the translationally diffusing molecules. H o ~ fthen, , can proton fluctuations result in attractive forces? The charge and multipole fluctuation theory presented by Kirkwood and Shumaker" con), represents the interaction tains a term W L 1 ( R which potential of fluctuating charges and fluctuating multipoles of two interacting molecules. Fluctuating dipoles are apparently ruled out by the present research. Fluctuating multipoles are expected to be of shorter range and therefore even less important than fluctuating dipoles. On the other hand, the fluctuations of the net charge, which we may refer to as fluctuating monopoles, will produce a long-range attractive force, which Kirkwood and Shumaker showed would yield divergent expressions for the thermodynamic functions, except for the existence of Debye-Huckel screening. Now we argue that this type of interaction should be very important even if the fluctuations are slow, for then molecules charged oppositely may diffuse into close proximity before the forces become repulsive, and this will produce deviations of thermodynamic activity as observed in the light scattering studies. The new concept in this discussion is that the rate of
755
the proton fluctuations serves as a deciding factor in the selection of the mechanisms which are important in the two related but significantly different processes of molecular polarization and intermolecular attraction. Thus, the conclusions of this research and the observations of Timasheff, et al., can be reconciled on the basis that the attractive forces arise from the existence of a distribution of the net charge of the protein molecules, with dipole and higher multipole contributions being ~ n i m p o r t a n t . ~ ~ -In~ lgeneral, we observe that fluctuating net charges, leading to the thermodynamic interaction potential W(ll) (R)do not necessarily yield a measurable dipole moment and, vice versa, that a permanent dipole moment does not necessarily give a measurable thermodynamic interaction if attractive forces of longer range predominate. 5. Comparison of Various Albumins. It is frequently considered that serum albumins obtained from various mammalian species are very similar.52 Striking differences in the dielectric properties are apparent, however. In Table 11, we see that the dipole moment of bovine serum albumin, 384 D., is in good agreement with the value 380 D. found by Oncley for equine serum albumin but both values are much smaller than the value 700 D. found by Dinteis for human serum albumin (HSA). It is interesting that both the "spontaneous" dimer of bovine serum albumin and the mercaptalbumin dimer of human serum albumin have dipole moments approximately 50% greater than those of the corresponding monomers. Notable differences in the relaxation times r1 and r2 are also evident as well as marked differences in the amplitude factors A1 and A2, but it would be difficult to judge the significance of their differences since the values assigned to these parameters are highly sensitive to traces of oligomer in the sample. Only in this work was the sample demonstrated to be essentially monodisperse. The HSA monomer has a considerably higher dielectric increment than either BSA monomer or dimer. Therefore, in spite of some uncertainties in A t and rCt values arising from presence of oligomer, HSA monomer has a larger dipole moment than BSA monomer. Acknowledgments. This research was supported (49) Here we refer to monopole interactions arising from net charge fluctuations. We expect additional contributions of a similar nature from microheterogeneity which was shown by Colvin, et a1.,60 to be a general property of proteins and by Foster, et a2.,61 to be an important property of bovine serum albumin in particular. (50)J. R. Colvin, D. B. Smith, and W. H. Cook, Chem. Rev., 54, 687 (1954). (51) M. Sogami and G. F. Foster, J . Biol. Chem., 238, PC2245 (1963);G.F. Foster, M.Sogami, H. A. Petersen, and W. G. Leonard, Jr., ibid., 240, 2495 (1965); H. A. Petersen and G. F. Foster, ibid., 240, 2503,3858 (1965). (52) J. F. Foster in ref 11, p 182.
Volume 70, Number 8 March 1966
756
M. H. LIETZKE AND R. W. STOUGHTON
in part by Grants-in-Aid from the Petroleum Research Fund, Grant No. PRF 581-A5, administered by the American Chemical Society, and from the U. S.
Public Health Service, Research Grant GM 12082-01, from the National Institute of General Medical Sciences.
Electromotive Force Studies in Aqueous Solutions at Elevated Temperatures.
VII.
The Thermodynamic Properties of HCl-BaC1, Mixtures’
by M. H. Lietzke and R. W. Stoughton Chemistry Division, Oak Ridge Nationel Laboratory, Oak Ridge, Tennessee (Received September 1 , 1966)
The activity coefficient of HC1 in HC1-BaC12 mixtures has been studied at 175”. At constant temperature and ionic strength the logarithm of the activity coefficient of HC1 in the mixtures varies linearly witah the ionic strength fraction of BaC12, in conformity with Harned’s rule. The activity coefficient of BaClz in the mixtures was calculated by using the parameters describing this variation and those for the variation of the activity coefficient of BaC12 wit’h ionic strength in pure BaClz solutions.
The thermodynamic properties of HBr-KBr mixtures2 and of HCl-NaC1 mixtures3 have been described in previous papers in this series. In the present work emf measurements of the cell
I
I
Pt-H2 ( p ) HCl(m2), BaClz(m3)AgC1-Ag have been combined with values of the osmotic coefficient of BaC124,5to compute the thermodynamic properties of both HC1 and BaC12 in HC1-BaC12 mixtures.
Experimental Section The high-temperature, high-pressure experimental apparatus and the preparation of electrodes and solutions were the same as described Since this apparatus was built for moderate accuracy over a wide temperature range rather than for maximum accuracy a t low temperatures, the accuracy in the latter range is not as great as that claimed by other investigatorsa8 The emf measurements were carried out in the temperature range 25175” in solutions of total ionic strength 0.5 and 1.0 in which the ratio of HCl The Journal of Physical Chemistry
to BaC12was varied. The emf values taken a t the same temperature were reproducible to cu. h0.5 mv. No drift of emf with time was observed.
Results and Discussion I n treating the results, the hydrogen pressure was calculated by subtracting the vapor pressure of the solution from the observed total pressure, while the (1) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) M. H.Lietske and R. W. Stoughton, J . Phys. Chem., 67, 2573 (1963). (3) M.H. Lietzke, H. B. Hupf, and R. W. Stoughton, ibid., 69, 2395 (1965). (4) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Academic Press, Inc., New York, N. Y., 1955,p 471. (5) C. S. Patterson, L. 0. Gilpatrick, and B. A. Soldano, J . Chem. SOC.,2730 (1960). (6) R. 9. Greeley, W. T. Smith, Jr., R. W. Stoughton. and M. H. Lietske, J . Phys. Chem., 64, 652 (1960). (7) M. B. Towns, R. S. Greeley, and M. H. Lietzke, ibid., 64, 1861 (1960). (8) H.5. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1958,p 456.
