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T. TAKAHASHI, I. NODA,AND M. NAGASAWA
between benzene-carbon tetrachloride and benzenecyclohexane and they are considerably more ideal than carbon tetrachloride-aniline. Even this last mixture has been considered normal as far as dielectric measurements are concerned. The principal concern is the avoidance of complex formation. This would result in a large negative enthalpy of mixing. The system chloroform-acetone, which shows large negative deviations from Raoult’s law, has a maximum Q p of -2000
J/mol. The small positive values for QP found here indicate a slight tendency for like species to cluster, a circumstance which might lead to small deviations from Debye behavior for the dispersion of the individual species in the mixture provided the clusters persisted over a time comparable to the time required for dielectric relaxation.” This would seem unlikely, however, since the dielectric behavior of the two mixtures with benzene is Debye-like at all concentrations.
Electrophoresis of a Rod-like Polyelectrolyte in Salt Solution by Toru Takahashi, Ichiro Noda, and Mitsurw Nagasawa DewTtment of Synthetic Chemistry, Faculty of Engineering, Nagoya University, Chilcusa-ku, Nagoya, Japan (Recewed September 8 , 1960)
The electrophoretic mobilities of a-helical poly(sodium glutamate) at a degree of neutralization of 0.25 are measured in NaC1 solutions of various ionic strengths, The mobilities obtained compare favorably with the theory of Henry for rigid cylinders at high ionic strengths. However, a disagreement between experimental mobilities and calculated ones is observed at low ionic strengths if the Debye-Huckel approximation is assumed in calculating the electrostatic potential at the surface of the cylinder. The agreement is improved if numerical solutions of the Poisson-Boltzmann equation are used for the comparison.
Introduction Moving boundary electrophoresis in the Tiselius apparatus has long been employed for the characterization of biological molecules, for example, in the determination of the composition of protein mixtures, the electric charge density of a protein molecule, and the number of ions bound on a protein molecule.1b2 I n practice, much useful information of a somewhat qualitative nature has been obtained from electrophoretic patterns. However, concerning the quantitative determination of the electric charge densities of various proteins, agreement between the theory of electrophoresis and experimental data is not very satisfactory. The charge densities calculated from electrophoretic mobilities are often lower than the values determined by other analytical methods. The disagreement is usually attributed to ion binding, but this explanation appears to be too arbitraryS2 One of the reasons for the lack of definite conclusions on the validity of electrophoresis in obtaining the charge density of biological molecules may surely be the complexity of biological systems. However, another reason may be that the assumptions involved in the theories of electrophoretic mobility of a rigid sphere or a rigid cylinder have not yet been fully examined by experiments in well defined systems. The Journal of Physical Chemistry
The purpose of the present paper is to determine the electrophoretic mobility of helical poly(sodium glutamate) in sodium chloride solutions of various concentm tion and to compare the observed mobilities with the values calculated from the theories of Henry3 and Gorin’ for rod-like molecules. The molecular conformation of poly(g1utamic acid) (PGA) at various degrees of neutralization and ionic strengths has been well clarified by the potentiometric titration and other There exists a pH range (corresponding to a range of degree of neutralization) in which the molecule has the conformation of an a-helix and is molecularly dispersed. Moreover, it is unnecessary to take into account specific ion binding if me use a simple salt such as sodium chloride as the added salt, since the (1) H . A. Abramson, L. S. Moyer, and M. H. Gorin, “Electrophoresis of Protein,” Reinhold Publishing Corp., New York, N . Y., 1942. (2) M . Bier, “Electrophoresis,” Academic Press Inc., London, 1959. (3) D. C. Henry, Proc. Roy. Soc., A123,216 (1929). (4) A. Wada, J . Mol. Phys., 3,409 (1960). (5) M. Nagasawa and A. Holtzer, J . Amer. Chem. SOC.,86, 538 (1964). (6) J. Hermans, Jr., ibid., 88,248 (1966); J. Hermans, Jr., J . Phys. Chem., 70, 510 (1966); A. Ciferri, D. Puett, L. Rajagh, and J. Hermans, Jr., Biopolymers, 6,1019 (1968). (7) D. Olander and A. Holtzer, J . Amer. Chem. Soc., 90, 4549 (1968).
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ELECTROPHORESIS OF A ROD-LIKEPOLYELECTROLYTE ionizable groups on PGA are exclusively carboxylic acid groups. Therefore, helical PGA appears to be an appropriate sample to test the theory of Henry and Gorin for rod-like molecules quantitatively.
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Experimental Section Sample. Poly(D-sodium glutamate) used in this study was kindly supplied by Ajinomoto Co., Ltd. The molecular weight of the sample was determined from the intrinsic viscosity in 0.1 M sodium chloride solution using an intrinsic viscosity-molecular weight relationships and found to be 75,000. The sodium form of the sample was purified by repeated precipitation from aqueous solutions with a 1 : 3 mixture of methyl alcohol and acetone, and then freeze-dried from an aqueous solution. The sodium form of the sample thus purified was converted into the acidic form by passing its aqueous solution through a mixed-bed ion-exchange resin column of Amberlite IRA 400 and IR 120. The polymer concentration was determined by the potentiometric titration in the presence of 0.02 M NaC1. For the measurement of electrophoretic mobility, aqueous solutions of the acidic form were brought to desired degrees of neutralization and desired concentrations of sodium chloride by adding calculated amounts of 0.1 M sodium hydroxide and concentrated sodium chloride solutions successively. The sample solutions used for electrophoresis were dialyzed against NaCl solutions used as solvent until Donnan equilibrium was reached. The polymer concentrations (C,) used in this work were between 0.15 and 0.02 g/dl, while the concentrations of NaCl solution used as solvent(C,) were between 0.2 and 0.0035 M . It was reported that partially neutralized PGA molecules associate with each other at high ionic strengths even if the pH is as high as 5.0n9 I n all measurements of electrophoresis reported here, however, only a single peak was observed on the schlieren patterns even at the highest polymer concentration, i.e., C, = 0.15 g/dl, and moreover, the sedimentation pattern of a sample of 0.25 degree of neutralization taken with a Beckman Spinco Model E ultracentrifuge did not show double peaks in 0.2 M and 0.0035 M NaCl solutions. Determination of Helix Region. To determine the helix region of PGA, the potentiometric titration of the acidic sample was carried out in sodium chloride solutions of 0.0035, 0.02, and 0.2 M . Plots of pH log (1 - a)/. vs. a are shown in Figure 1, where a is the degree of neutralization. The concentration of hydrogen ion was calculated from pH values by assuming that the activity coefficient of hydrogen ion is not affected by the presence of PGA.'O The titration curves of poly(D-glutamic acid) are entirely the same as those of poly(L-glutamic acid) as reported previ~usly.~Thus, the helix of PGA is stable throughout all ionic strengths used here, if a = 0.25 is selected. To confirm it, measurement of the optical rotatory dispersion of the par-
+
a. Figure 1. Examples of potentiometric titration curves: (I) 0.0035 M NaCl; 0.0216 iV PGA; (11) 0.02 M NaC1, 0.0226 A; PGA; (111)0.2 M NaCl, 0.0086 N PGA. A, B,and C regions denote aggregated, helix, and transition regions of PGA, respectively.6
tially neutralized PGA at a = 0.25 was carried out in 0.0035 M and 0.2 M NaCl by using a spectropolarimeter manufactured by Japan Spectroscopic Co., Ltd., Model ORD/UV-5. The slopes obtained from the Moffitt plot" were found to be -635 at 0.0035 M and -612 at 0.2 n/l of NaCl solutions. Thus, it is certain that the helix content is 100% at a = 0.25 within the limit of experimental error. Electrophoresis, Electrophoresis was carried out by using a Beckman Spinco Model H electrophoresis apparatus with a schlieren optical system at 25 f 0.01" and displacements of schlieren peaks on photographic plates were measured by a Shimadzu microcomparator. The limiting electrophoretic mobility was obtained by extrapolating the apparent mobilities to zero polymer concentration in the same way as reported previously. l2118
Results A typical example of a plot of the apparent electrophoretic mobilities of helical PGA (a = 0.25) vs. poly(8) R. B. Hawkins, Jr., Dissertation, Washington University, 1967. (9) T . M . Schuster, Biopolymers, 3, 681 (1965). (10) C. Tanford, "Electrochemistry in Biology and Medicine," T. Shedlovsky, Ed., John Wiley & Sons, Inc., New York, N . Y., 1955. (11) W. Moffitt, J. Chem. Phys., 25,467 (1956). (12) M . Iiagasawa, A. Soda, and I. Kagawa, J . PoZym. Sci., 31, 439 (1958). (13) I. Noda, M. Nagasawa, and M . Ota, J . Amer. Chem. Soc., 86, 5075 (1964). Volume 74, Number 6 March 19,1.970
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T. TAKAHASHI, I. NODA,AND M. NAGASAWA
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Figure 4. Comparison between the observed and the calculated mobilities: 1, observed; 2, calculated with use ofothe DebyeHiickel approximation, b = 7.5 d, a - b = 1.88 A assumed; 3, calculated from numerical solutions of the PoissonBoltzmann equation wit+t use of the Debye-Huckel approximation, b = 7.5 A, a - b = 1.28 A, assumed.
Figure 2. An example of the concentration dependence of observed migrating velocities. Upper, ascending boundary; lower, descending boundary. NaCl concentration, 0.0035 M ; temperature, 25'.
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Figure 3. Dependence of electrophoretic mobility U on the degree of neutralization a. PGA concentration, 0.05 g/dl; NaCl concentration, 0.02 M ; temperature, 25'. A, B, C, and D regions denote aggregated, helix, transition, and coil regions of PGA, respectively.
mer concentration is shown in Figure 2. The polymer concentration dependence of the apparent electrophoretic mobility is qualitatively similar to that reported for linear flexible polyelectrolytes.12*'a It is clear that both graphs of descending and ascending boundaries give the same intercept at C, = 0, which is the limiting electrophoretic mobility U . Moreover, it may be conoluded12*la that the value of U may be approximately determined by taking the average value between the ascending and descending velocities at a polymer concentration if the ionic strength is high enough. The relationship between the mobility of PGA, U , and the degree of neutralization, a, was determined by this approximate method, as shown in Figure 3. The concentrations of polymer and sodium chloride used were 0.05 g/dl and 0.02 M , respectively. The curve of U us. a is similar to the potentiometric titration curves. Xhe Journal of Physical Chemistry
From this figure it is clear that the helix region of PGA (region B) can be distinguished from its transition and coil regions (C and D). The deviation observed in the region A of lower degree of neutralization ( a < 0.2) is probably due to the aggregation preceding precipitation of the sample. In fact, the peak of the electrophoretic schlieren pattern was split into double peaks at a = 0.1. The limiting eleotrophoretic mobilities of the helical PGA with a = 0.25 at various ionic strengths were determined by the extrapolation method shown in Figure 2. The plot of these limiting mobilities, U , thus determined us. square root of added NaC1 concentrais shown in Figure 4, where the limits of tion, error in observed values are also indicated. From the figure it is clear that the mobility increases with decreasing ionic strength.
dc,
Discussion Although the helix content of partially neutralized PGA (a = 0.25) is almost 100% as calculated from the measurement of optical rotatory dispersion as described in the experimental part, we cannot expect the helical molecule of PGA to be a perfectly rigid rod-like molecule in solution. However, since the broken rod of PGA molecule is undoubtedly free draining for solvent, it may be reasonable to assume that its electrophoretic mobility must be determined by the electrostatic potential around the rod-like helix. Furthermore, we may assume that the rod-like molecules are randomly oriented in the solution so that the observed mobility may be given by the simple average over all possible orientation. That is
u=
2/3u1
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(1)
where U , and U ,1 are the mobilities of the infinite cylinder oriented perpendicular and parallel to the applied electric field. This assumption is justified by the fact
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ELECTROPHORESIS OF A ROD-LIKE POLYELECTROLYTE that the observed mobility is independent of the electric field strength under the present experimental conditions. The electrophoretic mobility of an infinite cylinder oriented perpendicularly to the applied electric field was calculated by Henry3to be
if the helix is an insulating cylinder. Here, $ ( 1 ) and $a are the electrostatic potential around the cylinder given as a function of the distance from the center of cylinder, T , and the value of $ ( 1 ) at the surface of the cylinder(r = b) relative to the electrostatic potential at infinity, respectively, a is the radius within which salt ions are excluded, D , is the dielectric constant, and 7 is the viscosity of solvent. The mobility parallel to the applied field, Uli, has also been given by Henry3 and Gorin,l namely
(3) The electrostatic potential around a cylinder, $cr) , can be calculated from the following Poisson-Boltzmann equation
where C, is the molar concentration of added 1:l electrolyte and N A is Avogadro's number. If the well known Debye-Huckel approximation, e+/kT
