Orientation effects on the electrophoretic mobility of rod-shaped

1592. Anal. Cham. 1990, 62, 1592-1596. Orientation Effects on the Electrophoretic Mobility of. Rod-Shaped Molecules in Free Solution. Paul D. Grossman...
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Anal. Chem. 1990, 62, 1592-1596

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Orientation Effects on the Electrophoretic Mobility of Rod-Shaped Molecules in Free Solution Paul D. Grossman and David S. Soane*

Department of Chemical Engineering, University of California at Berkeley, Berkeley, California 94720

The effect of molecular orientation on the electrophoretic mobility of rod-shaped polylons as measured by free solutlon capillary electrophoresis Is studled by uslng the tobacco mosaic vlrus (TMV) as a model solute. Thls orientatlonal dependence of molecular moblllty Is measured by observing the Influence of electrical field strength (up to 400 V/cm) on the electrophoretic moMUty of TMV. The electrophoretic mobllity of TMV Increases with lncreaslng field strength. Thls Increase can be quantitatively correlated with the decrease in the translatlonal frlctional coefflclent ( t ) due to the lncreaslng allgment of TMV with the electrk field. A model is developed relatlng the decrease in f to the alignment of TMV wlth the electric field through its polarirablllty and aspect ratio. To conflrm the observed orientational affects on mobility, control experiments were performed with 0.364 pm dlameter Latex spheres. Due to their spherlcal symmetry, no orlentatlonal effects would be expected. Indeed, no Increase in mobility was observed for these spherlcal particles. Calcuiatlons are presented to demonstrate that the Increase In mobility is unlikely to be caused by either the Wlen effect or any temperature variation resulting from Joule heatlng of the electrophoresls buffer.

INTRODUCTION The orientation of rod-shaped charged polyelectrolytes under the influence of an electric field has been measured by a number of techniques including electrical birefringence (1-61, electrical conductivity (7,8), and transient electric dichroism (9).

In this study, we establish directly the effect of molecular orientation on the electrophoretic mobility of a macroion in free solution by using the technique of capillary electrophoresis. Furthermore, these changes in the electrophoretic mobility are related to the translational friction coefficient of the polyion as a function of molecular orientation. Previously, it was not possible to study electrophoretic mobilities in free solution under strong electric field strengths because of the dispersive effects of Joule heating. With the advent of capillary electrophoresis, this is no longer a limitation (10, 11). The primary aim of this work is therefore to show that molecular orientation can play a significant role in determining the electrophoretic mobility of rod-shaped polyions in free solution and identifying an additional process parameter which can be exploited to affect the selectivity of electrophoretic separations in free solution.

THEORY Electrophoretic Mobility. Electrophoresis involves the motion of charged particles in solution under the influence of an electric field. When a charged particle is placed in an electric field, E , it experiences a force, Felec,which is proportional to its net charge, q , and the electrical field strength, E

* Author

In addition to the electrical force, once the particle has begun to move with a finite velocity, u, it experiences a drag force in the direction opposite to its direction of motion. This drag force, Fdrag, is proportional to the particle velocity Fdrag

= f*u

(2)

where the proportionality constant f is called the translational friction coefficient. For example, in the case of a spherical particle undergoing creeping flow (i.e. Reynolds number less than O.l), f is given by Stokes law as f = 6nqr (3) where 7 is the viscosity of the surrounding medium and r is the apparent hydrodynamic radius of the particle. Thus, the equation describing the translational motion of a particle under the influence of an electric field is F,, = m(du/dt) = q E - f v . (4) where m is the mass of the particle. When the particle reaches its steady-state velocity, u,,, the electrical force is exactly counterbalanced by the drag force. It can be easily shown with eq 4 that for a particle of molecular dimensions, the steadystate velocity is reached almost instantaneously, on the order of lo-'* s (12). The resulting steady-state velocity can be related to the charge and frictional properties of the particle by the simple relationship us,

= qE/f

(5)

Furthermore, the electrophoretic mobility, p , of a particle is defined as the steady-state velocity per unit field strength, or, from eq 5 P = q/f

(6)

As is clear from eq 6, differences in the electrophoretic mobility of molecules can arise as a result of differences in frictional properties, i.e. size or shape, or as a result of differences in the net charge on the molecule. It is these differences in the properties of molecules that form the basis for all electrophoretic separations. Translational Friction Coefficient. It is clear from eq 3 that the translational frictional coefficient for a sphere is only a function of the particle radius in creeping flow. However, for a rod-shaped particle the situation is not so simple. For a rod-shaped particle, the friction coefficient is also a function of its aspect ratio and orientation with respect to the direction of motion. The functional form of this relationship for a rigid-rod-shaped particle is given by (13) f = p(K1-l sin2 0

+ K3-l cos2

where In (24) + 0.5

to whom correspondence should be addressed. 0003-2700/90/0382-1592$02.50/00 1990 American Chemical Society

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ANALYTICAL CHEMISTRY, VOL. 62, NO. 15, AUGUST 1, 1990

and R, L, and 4 are the radius, length, and aspect ratio of the cylindrical particle, respectively, and 0 is the angle of orientation with respect to the direction of motion. As one might expect, the translational friction coefficient assumes a maximum value when the rod is oriented perpendicular to the direction of motion, i.e. when 8 = 90, and approaches a minimum value when the rod is totally aligned with the direction of motion, i.e. when 8 = 0. Thus, as the TMV particle becomes more aligned with its direction of motion, we would expect its electrophoretic mobility to increase due to the reduced translational friction coefficient. Note that this functional relationship only holds for low Reynolds number (Re) situations; i.e. when Re < 1.0. However, this constraint is certainly satisfied for all the circumstances encountered in this study where the maximum calculated value of Re in any of our experiments is approximately 1 x Molecular Orientation. The mechanism responsible for the orientation of TMV under the influence of an electric field has been clearly established by O’Konski and co-workers both experimentally and theoretically (3-5). It was found that the orientation of TMV is not due to a permanent dipole moment but rather the result of an induced moment caused by the polarization of the counterion atmosphere immediately adjacent to the TMV particle. Thus the tendency of TMV to orient in an electric field can be expressed in terms of an electrical polarizability, cy1 - a2, where the subscripts 1 and 2 refer to axial and transverse properties respectively. The relationship between polarizability and the degree of orientation has also been established ( 5 ) . For low electrical field strengths, i.e. fields well below saturation, or y (to be defined below) on the order of 1

CP = 27/15

(10)

where y is given by the relationship (“1

Y=

- az)E2 2kT

(11)

and @ is the order parameter, defined as (14) = 0.5 [3(COs2e ) - 11

(12)

Equation 12 is commonly used to describe the average degree of orientation of a particle. In eq 12, 8 is the angle between the long axis of the particle and the electric field, and the brackets indicate an ensemble averaged value. In these experments, 8 is also the angle between the direction of translational motion and the axis of TMV. Thus, if @ = 1, the particle is completely aligned with the field, and if CP = 0, the particle is randomly oriented with respect to the electrical field. From eq 10-12 an expression can be developed that relates the average orientation angle (8) to the electrical polarizability of the molecule and the electrical field strength ( 8 ) = arccos

(

2(al - a2)E2

15k:

+

’)

(13)

where k is the Boltzmann constant and T is the absolute temperature. In addition to the orientation caused by the electric field, the possibility of orientation due to hydrodynamic forces needs to be considered. Under certain conditions it is known that a cylinder which undergoes translational motion will tend to orient itself perpendicularly to the direction of motion. However, this tendency to orient is only significant a t relatively high Reynolds numbers and is negligible compared to the electric field effect a t the Reynolds numbers encountered in these studies (13).

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Time (min)

Figure 1. Example electropherogram of the TMV virus. The peak at 1.97 min is a neutral internal standard (mesityl oxide) used to measure electroosmotic flow (75). Conditions were as follows: field, 273 V/cm; current, 0.1 1 FLA; buffer, 2 mM potassium borate; capillary length, 66 cm (50 cm to detector); temperature, 30.0 f 0.1 OC.

MATERIALS AND METHODS The capillary electrophoresis system used in this work closely resembles that described elsewhere (10, 11). A straight length of polyimide-coated fused silica capillary (Polymicro Technologies, Inc., Phoenix, AZ), 66 cm (50 cm to the detector) long with a 50 wm internal diameter and a 375 pm outside diameter, connects the anodic reservoir with the electrically grounded cathodic reservoir. A high-voltage power supply capable of producing up to 30000 V (Gamma High Voltage Research, Inc., Ormand Beach, FL) was used to drive the electrophoreticprocess. Current through the capillary was measured over a 1-kQresistor in the retum circuit of the power supply using a digital multimeter (Hewlett-Packard, Model 3465B, Palo Alto, CA). On-column UV detection at 200 nm was carried out with a modified variable wavelength detector (Applied Biosystems, Model 783, Foster City, CA). The electrophoresis system was enclosed in an insulated compartment having safety interlocks in order to prevent electric shock. Data were collected with an integrator (Hewlett-Packard,Model 339OA, Palo Alto, CA). Samples were introduced into the capillary by applying a vacuum of 5 in. Hg to the cathodic electrode reservoir for between 2 and 3 s while the anodic end of the capillary was immersed in the sample solution. After the sample slug was introduced into the capillary, the anodic end of the capillary was then placed back into the electrophoresis buffer along with the anodic electrode, and the electrophoretic voltage was then applied. The temperature of the air surrounding the capillary was maintained at 30.0 “C 0.1 for all experiments. An example electropherogram is shown in Figure 1. Due to the negative charge on its surface, the TMV molecule migrates toward the anodic electrode during electrophoresis. However, the overwhelming electroosmotic flow drives the net direction of migration toward the cathodic electrode. This is why the negatively charged TMV elutes at a later time than the neutral mesityl oxide marker. It was observed that the electroosmotic mobility, i.e. the electroosmotic velocity per unit field strength, was not a function of electrical field strength. A complete discussion of electroosmotic flow and the procedure that is used to measure electrophoretic mobility values using capillary electrophoresis is presented in ref 15. The reproducibility of the mobility measurements was such that the percent relative standard deviation (% RSD) was between 0.5% and 1.0% (n = 3) for all mobility measurements. The tobacco mosaic virus used in these experiments was purchased from the American Type Culture Collection (Rockville, MD). This material was supplied as a solution containing 10 mM

*

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ANALYTICAL CHEMISTRY, VOL. 62, NO. 15, AUGUST 1, 1990

phosphate at pH 7. The concentration of TMV was approximately 1.0 mg/mL. Before using TMV sample in any electrophoresis experiments, it was transferred to the electrophoresis running buffer using a prepacked PD-10 gel filtration column containing G-25 Sephadex (Pharmacia, Piscataway, NJ). This was done to ensure that the TMV sample was equilibrated with the electrophoresis running buffer. Prior to injection the TMV solution was further diluted with running buffer to a concentration of approximately 100 pg/mL. The final concentration was determined by UV absorbance measurements at 260 nm using an extinction coefficient (@:2)of 3.0 (16). The spheres that were used were 0.364 pm diameter (coefficient of variation 0.7%) styrene-butadiene Latex microspheres (Duke Scientific, Palo Alto, CA). The spheres were supplied as a 10%(vol)aqueous suspension. Before use, they were equilibrated to the electrophoresis running buffer by gel filtration in the same manner as that used for the TMV solutions. All buffers were prepared according to the protocol of Clarks and Lubbs (17). The electrophoresis running buffer used in all experiments was 2.0 mM borate pH 8.35. Two millimolar borate might be considered a low ionic strength for preserving the integrity of the TMV. However, concentrations as much as 1order of magnitude lower than the one used in this study were employed in the electric birefringence studies presented in ref 4 with no evidence of the disintegration of the TMV particle. Furthermore, if the virus had decomposed during the electrophoretic experiments, one would not expect to see a single, sharp reproducible peak. Instead, one would expect to see a broad poorly defined peak or the appearance of a number of new peaks in the electropherogram resulting from breakdown products. Neither of these effects were observed in this study.

RESULTS AND DISCUSSION The model solute used in these studies is the tobacco mosaic virus (TMV) particle. TMV is a rigid, cylindrically shaped molecule approximately 3400 A in length and 150 A in diameter (3). A t the alkaline pH values used in these studies the surface of the particle has a negative charge of approximately 7000 charge units per particle ( 4 ) . TMV was chosen as the model solute because it has a number of characteristics that make the interpretation of the electrophoretic mobility data in terms of theoretical models unambiguous. These characteristics include conformational stability, homogeneity, and well-defined surface charge at the experimental conditions used in this study. Furthermore, because TMV has been extensively studied by electric birefringence, parameters describing the electrical properties of the TMV particle are readily available ( 3 ) . To explore the influence of molecular orientation on the electrophoretic mobility of TMV, we considered the influence of electric field strength on the electrophoretic mobility. As can be seen from the definition of p (eq 6), if the net charge and the translational friction coefficient of a solute are not changed, p should remain independent of electric field strength. However, according to eqs 7 and 13, as the field strength is increased, the TMV particle will become more aligned with the direction of motion and its translational friction coefficient f will decrease. The net result would then be an increase in the electrophoretic mobility of the TMV particle. Figure 2 shows the results of such an experiment. Note that the electrophoretic mobility of TMV does indeed increase with electric field strength. In fact, the mobility of TMV increases by over 6% when the electric field is varied from 60 to 400 V/cm. To help confirm that the observed increase in the electrophoretic mobility of TMV was in fact a result of molecular orientation, the experimental data in Figure 2 were compared with predictions of eqs 7-13. First, by use of eq 13 a value of ( 0 ) was calculated for each value of E using a value of 7.0 X cm3 for the polarizability of TMV; 7.0 X cm3 is the maximum value predicted by O'Konski based on theoretical arguments and electric birefringence studies ( 5 ) . Next,

1

7

5.1 -. .

0

100

200

300

400

500

E (V/cm) Figure 2. Electrophoretic mobility of TMV as a function of electrical field strength. Experimental c o n d i i i s are the same as Fiiwe 1 except for variations in E . The solid curve is a plot of the function p = po f,/f where f , and fare calculated using eq 7 and bo is the mobility extrapolated to zero field strength. See text for details.

with this value for ( 0 ) and eq 7, a value o f f was calculated as a function of field strength. Finally, from eq 6 a mobility was calculated using the fact that P/Po = f o / f (14) where po is the limiting mobility of TMV as E vanishes and f o is the translational friction coefficient calculated from eq 7 assuming no preferred orientation (i.e. CP = 0). The value used for po is 5.18 X lo4 cm2/(Vs), obtained by extrapolation of the experimental data using a third-order polynomial fit. On the basis of this model, the observed increase in the electrophoretic mobility corresponds to a change in the average orientation angle of approximately 8 O , from 54.7" at zero field to 46.8" at a field of 400 V/cm. One would expect that at some value of E the TMV would become completely aligned and thus the mobility would reach a maximum value at which further increases in E would have no additional influence on mobility. On the basis of the above model, this saturation should occur a t a field strength of approximately loo0 V/cm. However, because of limitations of the present experimental apparatus, we were not able to observe saturation behavior. Two other possible explanations for the observed increase in p with field strength must be addressed before we can have confidence in the above interpretation in terms of molecular orientation. The first is that the increase in p is due to the Wien effect (18). The Wien effect occurs at very high electric field strengths when the macroion of interest is moving so fast through the supporting medium that the counterion atmosphere usually surrounding it has no time to form. As a result, the surface charge on the macroion is no longer shielded by a counterion atmosphere; therefore, the net charge of the macroion is greatly increased. Thus the mobility of the ion would increase. To determine whether or not this is a realistic possibility, we followed the calculations of Harned (19) which compare the relaxation tine of the counterion atmosphere, T , with the thickness of the atmosphere and the velocity of the macroion. According to Harned, the relaxation time of the counterion cloud can be determined from the relationship r = fi/K2kT

(15) where f i is the translational friction coefficient of the counter-ion, in this case potassium, 1 / is~the Debye double layer thickness, k is the Boltzmann constant, and T is the absolute temperature. Using a value of 0.236 x g/s for fi (19)and 6.8 X cm for 1,'. (20),we obtain a value of 2.65 x s for the relaxation time of the counterion atmosphere.

ANALYTICAL CHEMISTRY, VOL. 62, NO. 15, AUGUST 1, 1990

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Table I. Parameters Used in Equation 18 for the Calculation of the Temperature Rise in the Capillary parameter

value

units cm

25 X lo4 173 X lo4 187 X lo4 2.11 x 10-6 5.94 x 10-3 1.55 x 10-3 15.0 x 10-3 3.84 X

cm

cm R-' cm-' W cm-' K-l W cm-' K-'

W cm-' K-' W cm-2 K-l

"The values for R1,R2,R3,k,, and k , were obtained from ref 23. k, was calculated using current-voltage measurements (see eq 19). kb was obtained from ref 24 assuming that the value for the buffer is the same as that for water. h was calculated by using a correlation for the average heat transfer coefficient for gasses flowing normal to single cylinders (25). Based on fan specifications, an air velocity of 500 cm/s was used in the correlation. Given that the mobility of TMV is 5.5 X lo4 cm2/V s at 400 V/cm, during this time the TMV particle will have traveled 5.83 X lo4 cm, or only about 1%of the thickness of the double layer. Thus under these conditions of ionic strength and electric field the Wien effect does not appear to be significant. This conclusion agrees with the experimental observations of Harned which indicate that fields on the order of 100000 V/cm are necessary to induce the Wien effect to any great extent. A second effect that could result in an increase in the electrophoretic mobility of TMV with increasing field strength is the temperature increase within the capillary caused by additional Joule heating as a result of the increased electric current. Because the electrophoretic mobility of a solute in an aqueous solution is a strong function of temperature, approximately 2 % / O C (21),any increase in the buffer temperature would reflect itself in a higher observed mobility of the solute. In order to estimate the temperature rise inside the capillary as a function of field strength, the following energy balance equation in cylindrical coordinates was solved: Id --(rqJ = S e r dr where q, is the energy flux a t the radial position r and Se is the rate of power generation within the conducting fluid per unit volume. In order to find the total temperature difference between the buffer in the center of the capillary, To, and the surrounding air, T,, eq 16 must be solved in each of the four regions: buffer, glass wall, polymer coating, and surrounding air. In the electrically conductive buffer region, Se is given bY

Se = P / k ,

(17)

where I is the current density and k , is the electrical conductivity of the buffer. In the glass, polymer film and air regions, Se = 0. The method of solution is given in ref 22. The resulting equation describing the total temperature rise from the center of the capillary to the surrounding air is

TO- T. =

SeR1'( - + 2

2kb

In

(2)+ (2) + &) In

(18)

where kb, k,, and k , are the thermal conductivities of the buffer, glass, and polymer coating with radii R1, R2, and R3, respectively, and h is the heat transfer coefficient between the outer surface of the capillary and the surrounding air. According to eq 18, the maximum temperature rise that would be expected under the conditions of these experiments is approximately 0.015 "C. (See Table I for the values of the

5P---4 5.0

4.9'

0

I

I

100

I

200

I

'

300

400

'

J 500

E (V/cm) Flgure 3. Electrophoretic mobility of TMV (m) (data are the same as in Figure 2) and 0.364-pm Latex spheres (0)as a function of electrical field strength. Experimental conditions are the same as Figure 2.

parameters used in this calculation.) Given that p increases of the order of 2?70/~C,it is clear that the observed increase in electrophoretic mobility is most probably not caused by temperature effects. Furthermore, if there were a significant increase in the temperature of the buffer, one would expect to see an increase in the value of the electrical conductivity of the buffer, k,, where

k, = Li/AV

(19)

where L is the total capillary length, i is the total current, A is the cross-sectional area of the capillary, and V is the total voltage across the capillary. No such increase in k, was observed. ( k , = 2.05 X R-l cm-' f 0.01 X a t all field strengths used in this study.) A control experiment to confirm that the observed increase in p is attributable to an orientational effect was performed on a spherical Latex particle. The experimental conditions were identical with those used for the TMV experiments. The Latex particle was chosen to have comparable dimensions to TMV. This spherical particle system was subject to the same effects of temperature, electroosmotic flow, and ion atmosphere distortion, however, its spherical symmetry precludes it from exhibiting any orientational effects. Thus, if the Wien effect, an increase in the buffer temperature or variations in the electroosmotic flow velocity, were responsible for the observed increase in the electrophoretic mobility of TMV, this would also have been reflected in the mobility of the Latex particle. On the other hand, if the mobility increase of TMV is due only to orientational effects, the mobility of the Latex particle should not change with increasing field strength. As Figure 3 shows, the mobility of the spherical particle does not appear to increase with increasing field strength; in fact there appears to be a slight decrease in p as E increases. This decrease in p with increasing field strength is most likely due to the "relaxation effect" (26). Because the center of the counterion atmosphere lags behind the particle, there is an electrical force acting on the particle in a direction opposite to its direction of motion, thus reducing the net forward force. As the particle velocity increases, this effect becomes more exaggerated. Also in Figure 3, the behavior of the spherical particle is contrasted with that of the TMV particle. The fact that the electrophoretic mobility of the spherical particle does not increase with increasing electric field strength provides strong evidence that the observed increase in p for TMV is in fact a result of molecular orientation. It was observed that the dependence of electrophoretic mobility on the electric field strength could be enhanced if

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ANALYTICAL CHEMISTRY, VOL. 62, NO. 15, AUGUST 1, 1990

6.0)

I

I

I

I

1

I

I

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I

1

h

capillaries provided that the sample buffer does not equilibrate with the running buffer within the time frame of electrophoresis.

u)

ACKNOWLEDGMENT We gratefully acknowledge D. Eden and C. T. O’Konski for their helpful comments and discussions. Further thanks are expressed to J. C. Colburn for reviewing this manuscript prior to submission.

i

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0 7

LITERATURE CITED

X 3.

I-

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(1) Kerr, J. Phibs. Mag. 1875, 50, 337. (2) O’Konski, C. T.; Zirnm, B. H. Science 1850, 111, 113-116. (3) O’Konski, C. T.; Haltner, A. J. J. Am. Chem. SOC. 1856, 78, 3604-3610. (4) O’Konski, C. T.; Haltner, A. J. J . Am. Chem. SOC. 1857, 79, 5634-5649. (5) O’Konski, C. T.; Yoshioka, K.; Orttung, W. H. J. Phys. Chem. 1858, 63,1558-1565. (6) Elias, J. G.; Eden, D. Macromolecules 1881, 14, 410-419. (7) Eigen, M.; Schwartz, G. J. Colbid. Sci. 1857, 72, 181-194. (8) Ise, N.; Eigen, M.; Schwartz, G. BlOpo/ymefs 1863, 1 , 343-352. (9) Hogan, M.; Dattagupta, N.; Crothers, D. M. Proc. Natl. Acad. Sci. 1878, 75, 195-199. (10) Jorgenson, J. N.; Lukacs, K. D. Science 1883, 222, 266-272. (11) Lauer, H. H.; McManlgill, D. Anal. Chem. 1886, 58, 166. (12) Cantor. C. R.;Schimrnel, P. R. Biophysical Chemistry, Part 11; W. H. Freeman and Company: New York, 1980; Chapter 10. (13) Happel, J.; Brenner, H. Low ReynoMs Number Hydrodynamics; Martinus Nijhoff Publishers: The Hague, 1983; Chapter 5. (14) de Gennes, P. G. The Physics of Liquid Crystals; Clarendon Press: Oxford, 1974; Chapter 2. (15) Grossman, P. D.; Colburn, J. C.; Lauer, H. H. Anal. Biochem. 1888, 179, 28-33. (16) Brakke, E. I n Methods in Virology; Mararnorosch, K., Koprowski, H., Eds.; Academic Press: New York, 1967; Vol 2, pp 104. (17) Dean, J. A. Langes Handbook of Chemistry, 11th ed.; McGraw-Hill: New York, 1973; Chapter 5. (18) Atkins, P. W. Physical Chemistry; W. H. Freeman and Company: San Francisco, CA, 1978; p 830. (19) Harned, H. S. Physical Chemistry of Electrolytic Solutions; Reinhold: New York, 1950: p 95. (20) Hiemenz, P. C. Principles of Colloid and Surface Chemlstry, 2nd ed.; Marcel Dekker: New York, 1986; Chapter 12. (21) Hjerten, S. Chromatogr. Rev. 1867, 9 , 122. (22) Bird, R. B.; Stewart, W. E.; Lightfoot, E. W. Transpo~Phenomena; John Wiley 8, Sons: New York, 1960; Chapter 9. (23) From Data Sheet supplled by Polymlcro Technologles tor their “Flexible Fused Silica Capillary Tubing” (Polymicro Tecnologies Inc., Phoenix, AZ). (24) Perry, R. H.; Chilton, C. H. Chemical Enigineers Handbook, 5th ed.; McGraw-Hili: New York, 1973; pp 3-214. (25) Chapman, A. J. Heat Transfer, 3rd ed.;Macmillan: New York, 1974; p 351. (26) Overbeek, J. I n Electrophortesis; Bier, M., Ed.; Academic Press: New York, 1967; Vol 2, Chapter 1.

5.0F 0 100 200 300 400 500 E (Vkm) Flgure 4. Influence of sample buffer composition on the dependence of the electrophoretic mobllhy of TMV on the electrical field strength. Samples are dissolved in running buffer (A)and in a 1OX dilution of running buffer (0).The lower solid curve was generated by using the same procedures as in Figure 2, while the upper solid line used a modified procedure where the value of E in eq 11 was replaced with 1.4E.

the TMV sample was dissolved in a buffer having a lower ionic strength than the electrophoresis running buffer. Figure 4 compares the data obtained from such an experiment with the data of Figure 2, where in the upper curve the TMV sample was dissolved in a 1OX dilution of the runner buffer. We suggest that this enhancement of the orientation effect is due to the fact that a zone surrounding the TMV particle is created which has a lower conductivity than the running buffer. This lower conductivity causes the electric field strength within the zone to be higher than the average field strength, resulting in more effective orientation of TMV. The data in Figure 4 can be modeled by using the same relationships as before if, instead of using the average field strength in eq 11 (E = V / L ) ,one uses an enhanced field strength of 1.4E.Presumably this effect could be further exaggerated by increasing the conductivity difference between the running buffer and the sample buffer. It should be noted that, because of the small size of the sample zone, the magnitude of the average field outside of the sample zone is not appreciably affected. This method of enhancing the orientation effect by dissolving the sample in a lower conductivity buffer could potentially provide a powerful way to magnify these nonlinear effects without having to resort to higher voltages or shorter

RECEIVED for review January 11,1990. Accepted May 7,1990. The financial support of the University of Califorina Berkeley BRSG Fund and a generous research grant from Applied Biosystems, Inc., are greatly appreciated.