BIOPOLYMERS
VOL. 15, 373-382 (1976)
Nonlinear Electric Properties of DNA Solutions C. MARION and J. C. BERNENGO, Laboratoire de Chimie Biologique 11, Uniuersit6 Claude Bernard, 6962l-Villeurbanne, France; and M. HANSS, Laboratoire de Biophysique, Facult6 d e M6decine, 93000--Bobigny,
France
Synopsis DNA solutions are shown to present a nonlinear electric behavior. This property is measured through the third harmonic current intensity, which appears when the solution is placed in a sinusoidal electric field of moderately high strength (about 100 V-cm-'1. T h e influence of different parameters has been examined: fundamental frequency, field strength, concentration, molecular weight, and conformation. By progressive sonication, it is shown that the harmonic current is linearly proportional to the DNA molecular weight, but under an M , of approximately lofi,the nonlinear electrical property decreases sharply and its spectrum shows a drastic change. It is thought that the harmonic current is not related to an orientational phenomenon; an explanation based on the electrical deformation of the molecule is suggested.
INTRODUCTION DNA molecules in solution are known to have a high electric polarizability.l-" Nonlinear electric properties can then be predicted when a n electric field of moderately high amplitude is applied to these molecules. For instance, if the polarization originates from the orientation of permanent dipoles, the nonlinearity will be explained by the well-known saturation phenomenon.* On the other hand, if the polarization originates from induced dipoles, their orientation creates a n excess nonlinear orientation polarizability which, though vanishingly small for molecules or spherical macromolecules, can be noticeable for highly polarizable elongated macromolecules such as We have already reported on nonlinear properties of DNA solution^.^,^^^ In order to find their correct explanation, a systematic investigation has been undertaken, the main results of which are presented here.
MEASUREMENT OF THE NONLINEAR ELECTRIC PROPERTIES The polarization P of a nonlinear dielectric can be written: P ( E ) = aE PE2 y E 3 + . . . (1) where a is the polarizability for E 0 and P, y,. . . are coefficients that depend on the polarization mechanism. For the two above-mentioned nonlinearity mechanisms, Eq. (1)is a n odd function of E .
+
-+
373 0 1976 by John Wiley & Sons, Inc.
374
MARION, BERNENGO, AND HANSS
For an alternating electric field E = EOejwt, the displacement current will be the sum of a fundamental component a t frequency F = w/2x, and of odd harmonics 3F, 5F, . . . . In all our experiments, only the third harmonic 3F could be detected and measured, the higher order harmonics having negligible amplitudes. By measuring the peak value Zh,o of the harmonic current Ih, it is possible to determine a coefficient y that is characteristic of the polarization mechanism:I0 Id
y = (13/3NtosV&d)z~,,
(2)
where I and S are the length and cross-sectional area of the measuring cell, Vo is the peak value of the alternating voltage of frequency F applied to the cell electrodes, and N is the number of molecules per unit volume. Ih,o is determined by a differential harmonic bridge, which is described elsewhere.6,a10 It can measure harmonic currents of a few nanoamperes in the frequency range 3 Hz-10 kHz; the maximum applied electric field is 700 V-cm-l; solutions with conductivities reaching 1 mMho-cm-l can be studied; the electrode polarization errors have been eliminated.
MATERIALS The following DNA samples were studied: 1) soft roe (lot D 1876): S ~ O= .14, ~ [ q ] = 29.5 dl/g, M,,,, = 3.8 X 2) salmon testes (lot D 1626): S ~ O= 17.5, , ~ [q] = 42 dl/g, M , ,= 6.3 X lo6; 3) calf thymus (lot D 1751): S ~ O= 17, , ~ [q] = 40.5 dl/g, M,,, = 5.8 X lo6; 4) calf thymus (lot TV 371): S ~ O= 22.8, , ~ [q] = 65 dl/g, M,, = 11.6 X lo6; 5) calf thymus (lot TV 23): S ~ O= 21.6, , ~ [q] = 62 dl/g, M,,, = 10.4 X lo6.
lo6;
Samples 1-3 .are commercial (Sigma). Samples 4 and 5 have been prepared a t the C.R.M. (Strasbourg). M?,, is the average M , determined from viscosity and sedimentation measurements and by using Eq. (3). M NaCl solution a t a The fibrous state DNA is diluted in a 5 X concentration of about 0.5 g/l. After 24 hr of gentle stirring a t 4"C, this stock solution is centrifuged (1 hr, 30,000 g) and kept in the cold after M NaCl solution (by its conductivity has been adjusted to that of a adding small amounts of concentrated NaCl solution). M NaCl The final DNA solutions are prepared by dilution with solutions; the exact DNA concentration is determined by optical-density measurements a t 260 nm ( e p = 6600).
ELECTRIC PROPERTIES OF DNA
375
The native state is verified by measuring the 260-nm hyperchromicity profile recorded during the thermal denaturation. We have thus verified that the prolongated application of electric fields did not denature the DNA molecules. The protein content is measured by the Lowry et al. method;'l it is always less than l%for all the samples. In order to obtain lower molecular-weight DNA molecules, some samples (100 ml of the final solution) were sonicated a t 20 kHz with a Mullard 3100 apparatus (acoustic power: 5.4 W; sonication duration: between 15 sec and 8 min according to the desired degree of degradation). Under these conditions, no denaturation is detected (unchanged thermal denaturation profiles). The molecular weights of native samples are determined by viscosity and sedimentation measurements, and by using the empirical Crothers and Zimm relation:12
Mv,s = 14,400(~0~o,w - 2.7)"/'([7] + 5)"2
(3)
For the sonicated samples, the following empirical simplified relation is applied:12 0.665 log &Iv = 2.863 + log ([7] + 5)
(4)
is always slightly higher than For a given sample, A modified automatic Crothers and Zimm viscometer is used.i3 It allows viscosity measurements on highly diluted solutions' (c 5 mg/l in 0.1 M NaC1). The sedimentation coefficients are obtained with an MSE type E analytical centrifuge (35,000 rpm, 20"C, c = 25 mg/l in 0.1 M NaCl).
-
RESULTS Frequency The harmonic current Ih = Ih,O/& is measured after balancing the bridge a t the fundamental frequency F . The frequency range is 3 Hz d F d 600 Hz. Figures 1 and 2 show the variations of Ih versus F for different concentrations [sample 3), 50 mg/l d c d 400 mg/l] and field strengths (80 V-cm-l d E d 240 V-cm-'). Ih decreases rapidly a t high frequencies (>400 Hz). Under 10 Hz, a plateau appears in the Ih dispersion curve.
Field Strength A logarithmic plot of Ih as a function of E is given for different values of F (Fig. 3) and c (Fig. 4). Straight lines are obtained with a slope of 3, as is required by Eq. (2). However, for the highest values of E a slight curvature appears a t 8 Hz, which can be explained by the solution heating, as bridge balancing is more difficult (and therefore takes longer) to achieve a t low frequencies.
MARION, BERNENGO, AND HANSS
376
300
0
Fig.1. Frequency dispersion of the harmonic current for different concentrations [sample 3, E = 240 V.cm-'].
I
lhgnA
Fig. 2. Frequency dispersion of the harmonic current for different field strengths [sample 3, c = 400 mg/l].
Concentration Figure 5 shows how I h varies with the DNA concentration for different frequencies. Note the linear dependence of I h with c up to high concentrations (c 400 mg/l). This property has been verified for field strengths ranging from 80 V-cm-' to 240 V-cm-'. When c increases above about 400 mg.l-l, the distorsion level begins to saturate. The same linearity between Ih and c has been found for every DNA
-
ELECTRIC PROPERTIES OF DNA .lh
9
377
nA 20 nz 40 Hz
80 Hz
200 nz
10
E,Vcm-'
1
50
100
200
400
Fig. 3. Field strength dependence of Ih for different frequencies [sample 3, mg/l].
50
100
200
c = 400
400
Fig. 4. Field strength dependence of Ih for different concentrations [sample 3, F = 40 Hz].
sample. However, the obtained slopes are different for reasons to be shown below.
Molecular Weight and Conformation The molecular-weight dependence of the nonlinear properties can be studied either on different native DNA samples, or on fractions of the same sample, which have been sonicated for different durations. The results are summarized in Figures 6 and 7. For each solution, we have
MARION, BERNENGO, A N D H A N S S
378
30(
150
0
I
I
200
400
Fig. 5. Concentration dependence of Ih for different frequencies [sample 3, E = 240 V. cm-l].
1 : 2 3 4 5
:
: : :
3.8.106 6,3.10' 5,8.106
ll,B .lo6 10.4.10'
Fig. 6. Frequency dispersion of I h for different native DNA samples (c = 50 mgh, E = 240 Vscm-').
ELECTRIC PROPERTIES OF DNA
379
Fig. 7. Frequency dispersion of I), for different sonicated fractions of sample 3 ( c = 200 mg/l, E = 240 Vecrn-').
1
2
4
6
Fig. 8. Molecular-weight dependence of I), (c = 200 mg/l, E = 240 Vecm-', F = 10 Hz) for sonicated fractions of sample 3.
controlled the concentration and field strength dependence of Ih. I t can be seen that increases with M,,. The molecular-weight dependence of Ih is h e a r when different fractions of the same sample are examined, and if @, > lo6 (Fig. 8). For lower molecular weights, a discontinuity in the Ih, M,, curve appears, which is followed by a major change in the distortion spectrum (Fig. 7).
380
MARION, BERNENGO, AND HANSS
200
100
0 0
50
100
Fig. 9. Melting profiles of sample 3 determined by OD measurements (50 mgh, 260 nm) and z h studies (c = 300 mgh, E = 240 Vacm-', F = 4 Hz).
To give an estimation of the signal-to-noise ratio of the distorsion measurements, we have given in Figure 7 the results when both cells are M NaCl solution (curve NaCl). filled with the same The nonlinear electric properties depend on the conformation of DNA, as is demonstrated by thermal denaturation experiments. They are carried on by keeping DNA solutions a t the desired temperature for 30 min, then cooling them in an ice-water mixture, and lastly by measuring the optical density (260 nm) and Ih a t room temperature. Figure 9 shows that the nonlinear property disappears when the DNA is heatdenatured. The low melting temperature (45OC) is explained by the low ionic strength.14
DISCUSSION The reported results show that DNA solutions have nonlinear electric properties, the evidence being the production of a third harmonic curreIlt I h when an alternating field is applied to the solutions. This nonlinear effect was sought for, as it can be predicted by a theory based on the orientation polarization of induced dipole moments (hyperpolarization). As the magnitude of the induced dipole moment is directly proportional to the electrical polarizability a, any factor modifying a will also alter the nonlinearity. For instance, when the DNA molecule is heat-denatured, a becomes very small in the melting temperature range,15-17so that the harmonic distorsion becomes vanishingly small.
ELECTRIC PROPERTIES OF DNA
381
However, we think that the initial explanation of the phenomenon is directly propormay not be correct. Indeed, Figure 5 show9 that tional to the concentration, even at the highest values of c (about 500 mg/l). A t such high concentrations, the intermolecular interactions become important, as is shown by the usual hydrodynamic properties of or other polyelectrolyte solutions. Therefore, it is difficult to accept any explanation based on the orientation of the whole molecule. Another reason is the molecular-weight dependence of the nonlinear effect. As is shown in Figure 8, for a given DNA sample, Zh is directly proportional to M,,. In the hyperpolarization mechanism applied to long rigid macromolecules,5 y is proportional to a2. As it is generally assumed20-22that for a rigid elongated polyelectrolyte of length L , a is proportional to L2,I h should vary as M V 4 . This deduction is not experimentally verified; the hyperpolarization mechanism, which was initially proposed, seems therefore inadequate for high M , DNA. Another explanation could be the elongation of the molecule by the electric field. If one assumes as a first order approximation that the molecular lengthening is proportional to E , an E3 term in the polarization could appear, because of the L 2 dependence of a. Further experiments are being carried on to verify that the harmonic distorsion comes from the electrical deformation of the DNA molecule. Experimental results supporting this hypothesis have already been obtained and will be proposed for publication. Other nonlinearity mechanisms can be suggested. In fact, any modification of the electrical polarizability or of the counterions mobility through conformational changes (electric deformation, local denaturation) or through a saturation of the induced polarizability or of the surface mobility, will generate harmonics in sinusoidal field experiments. Therefore, theoretical quantitative results of these mechanisms are needed in order to establish clearly the origin of the nonlinear behavior of high M , DNA solutions. In any case, whatever the nonlinearity origin is, our results show a field dependence of the electric properties, which can be demonstrated on DNA solutions by using electric-field strengths as low as a few 10 Vcm-'.
References 1. Takashima, S. (1966) J . Phys. Chem. 70,1372-1380. 2. Hornick, C. & Weill, G. (1971) Biopolyrners 10,234552358, 3. Hanss, M. & Bernengo, J. C. (1973) Biopolyrners 12,2151-2159. 4. Debye, P. (1929) Polar Molecules, Dover, New York. 5. Hanss, M. & Bernengo, J. C. (1966) J . Chirn. Phys. 63,1474-1476. 6. Hanss, M., Bernengo, J. C. & Sadron, C. (1968) C. R. Acad. Sci. 266,1263-1266. 7. Hanss, M. & Roux, B. (1972) Ann. Phys. Eiol. M6d. 3, 133-163. 8. Bernengo, J. C. (1970) ThBse, Universitk de Lyon. 9. Hanss, M. & Bernengo, J. C. (1969) presented a t the 3rd Int. Congress Biophysics (IUPAB), Cambridge, Mass.
382
MARION, BERNENGO, AND HANSS
10. Hanss, M. & Bernengo, J. C. (1975) J. Chim. Phys. 72,724-728. 11. Lowry, 0. H., Rosebrough, N. J., Farr, A. L. & Randall, R. J. (1951) J. Biol. Chem. 193,265-275. 12. Crothers, D. M. & Zimm, B. H. (1965) J. Mol. Biol. 12,525-536. 13. Bernengo, J. C., Marion, C. & Roux, B. (1973) Reu. Sci. Instr. 44,311-313. 14. Marmur, J. & Doty, P. (1962) J . Mol. Biol. 5,109-118. 15. Hanss, M., Viovy, R. & Sadron, C. (1963) C. R. Acad. Sci.256,4510-4513, 16. Mesnard, G. & Vasilescu, D. (1964) Biochim. Biophys. Acta 91,531-533. 17. Takashima, S. (1966) Biopolymers 4,663-676. 18. Eigner, J., Schildkraut & Doty, P. (1962) Biochem. Biophys. Acta 55,13-21. 19. Bloomfield, V. A. (1968) Macromolecules 1,255-316. 20. McTague, J. P. & Gibbs, J. H. (1966) J. Chem. Phys. 44,4295-4301. 21. Oosawa, F. (1970) Biopolymers 9,677-688. 22. Van der Touw, F. & Mandel, M. (1974) Biophys. Chem. 2,231-218.
Received May 23,1975 Returned for revision July 21,1975 Accepted September 29,1975
VOL. 15, 373-382 (1976)
Nonlinear Electric Properties of DNA Solutions C. MARION and J. C. BERNENGO, Laboratoire de Chimie Biologique 11, Uniuersit6 Claude Bernard, 6962l-Villeurbanne, France; and M. HANSS, Laboratoire de Biophysique, Facult6 d e M6decine, 93000--Bobigny,
France
Synopsis DNA solutions are shown to present a nonlinear electric behavior. This property is measured through the third harmonic current intensity, which appears when the solution is placed in a sinusoidal electric field of moderately high strength (about 100 V-cm-'1. T h e influence of different parameters has been examined: fundamental frequency, field strength, concentration, molecular weight, and conformation. By progressive sonication, it is shown that the harmonic current is linearly proportional to the DNA molecular weight, but under an M , of approximately lofi,the nonlinear electrical property decreases sharply and its spectrum shows a drastic change. It is thought that the harmonic current is not related to an orientational phenomenon; an explanation based on the electrical deformation of the molecule is suggested.
INTRODUCTION DNA molecules in solution are known to have a high electric polarizability.l-" Nonlinear electric properties can then be predicted when a n electric field of moderately high amplitude is applied to these molecules. For instance, if the polarization originates from the orientation of permanent dipoles, the nonlinearity will be explained by the well-known saturation phenomenon.* On the other hand, if the polarization originates from induced dipoles, their orientation creates a n excess nonlinear orientation polarizability which, though vanishingly small for molecules or spherical macromolecules, can be noticeable for highly polarizable elongated macromolecules such as We have already reported on nonlinear properties of DNA solution^.^,^^^ In order to find their correct explanation, a systematic investigation has been undertaken, the main results of which are presented here.
MEASUREMENT OF THE NONLINEAR ELECTRIC PROPERTIES The polarization P of a nonlinear dielectric can be written: P ( E ) = aE PE2 y E 3 + . . . (1) where a is the polarizability for E 0 and P, y,. . . are coefficients that depend on the polarization mechanism. For the two above-mentioned nonlinearity mechanisms, Eq. (1)is a n odd function of E .
+
-+
373 0 1976 by John Wiley & Sons, Inc.
374
MARION, BERNENGO, AND HANSS
For an alternating electric field E = EOejwt, the displacement current will be the sum of a fundamental component a t frequency F = w/2x, and of odd harmonics 3F, 5F, . . . . In all our experiments, only the third harmonic 3F could be detected and measured, the higher order harmonics having negligible amplitudes. By measuring the peak value Zh,o of the harmonic current Ih, it is possible to determine a coefficient y that is characteristic of the polarization mechanism:I0 Id
y = (13/3NtosV&d)z~,,
(2)
where I and S are the length and cross-sectional area of the measuring cell, Vo is the peak value of the alternating voltage of frequency F applied to the cell electrodes, and N is the number of molecules per unit volume. Ih,o is determined by a differential harmonic bridge, which is described elsewhere.6,a10 It can measure harmonic currents of a few nanoamperes in the frequency range 3 Hz-10 kHz; the maximum applied electric field is 700 V-cm-l; solutions with conductivities reaching 1 mMho-cm-l can be studied; the electrode polarization errors have been eliminated.
MATERIALS The following DNA samples were studied: 1) soft roe (lot D 1876): S ~ O= .14, ~ [ q ] = 29.5 dl/g, M,,,, = 3.8 X 2) salmon testes (lot D 1626): S ~ O= 17.5, , ~ [q] = 42 dl/g, M , ,= 6.3 X lo6; 3) calf thymus (lot D 1751): S ~ O= 17, , ~ [q] = 40.5 dl/g, M,,, = 5.8 X lo6; 4) calf thymus (lot TV 371): S ~ O= 22.8, , ~ [q] = 65 dl/g, M,, = 11.6 X lo6; 5) calf thymus (lot TV 23): S ~ O= 21.6, , ~ [q] = 62 dl/g, M,,, = 10.4 X lo6.
lo6;
Samples 1-3 .are commercial (Sigma). Samples 4 and 5 have been prepared a t the C.R.M. (Strasbourg). M?,, is the average M , determined from viscosity and sedimentation measurements and by using Eq. (3). M NaCl solution a t a The fibrous state DNA is diluted in a 5 X concentration of about 0.5 g/l. After 24 hr of gentle stirring a t 4"C, this stock solution is centrifuged (1 hr, 30,000 g) and kept in the cold after M NaCl solution (by its conductivity has been adjusted to that of a adding small amounts of concentrated NaCl solution). M NaCl The final DNA solutions are prepared by dilution with solutions; the exact DNA concentration is determined by optical-density measurements a t 260 nm ( e p = 6600).
ELECTRIC PROPERTIES OF DNA
375
The native state is verified by measuring the 260-nm hyperchromicity profile recorded during the thermal denaturation. We have thus verified that the prolongated application of electric fields did not denature the DNA molecules. The protein content is measured by the Lowry et al. method;'l it is always less than l%for all the samples. In order to obtain lower molecular-weight DNA molecules, some samples (100 ml of the final solution) were sonicated a t 20 kHz with a Mullard 3100 apparatus (acoustic power: 5.4 W; sonication duration: between 15 sec and 8 min according to the desired degree of degradation). Under these conditions, no denaturation is detected (unchanged thermal denaturation profiles). The molecular weights of native samples are determined by viscosity and sedimentation measurements, and by using the empirical Crothers and Zimm relation:12
Mv,s = 14,400(~0~o,w - 2.7)"/'([7] + 5)"2
(3)
For the sonicated samples, the following empirical simplified relation is applied:12 0.665 log &Iv = 2.863 + log ([7] + 5)
(4)
is always slightly higher than For a given sample, A modified automatic Crothers and Zimm viscometer is used.i3 It allows viscosity measurements on highly diluted solutions' (c 5 mg/l in 0.1 M NaC1). The sedimentation coefficients are obtained with an MSE type E analytical centrifuge (35,000 rpm, 20"C, c = 25 mg/l in 0.1 M NaCl).
-
RESULTS Frequency The harmonic current Ih = Ih,O/& is measured after balancing the bridge a t the fundamental frequency F . The frequency range is 3 Hz d F d 600 Hz. Figures 1 and 2 show the variations of Ih versus F for different concentrations [sample 3), 50 mg/l d c d 400 mg/l] and field strengths (80 V-cm-l d E d 240 V-cm-'). Ih decreases rapidly a t high frequencies (>400 Hz). Under 10 Hz, a plateau appears in the Ih dispersion curve.
Field Strength A logarithmic plot of Ih as a function of E is given for different values of F (Fig. 3) and c (Fig. 4). Straight lines are obtained with a slope of 3, as is required by Eq. (2). However, for the highest values of E a slight curvature appears a t 8 Hz, which can be explained by the solution heating, as bridge balancing is more difficult (and therefore takes longer) to achieve a t low frequencies.
MARION, BERNENGO, AND HANSS
376
300
0
Fig.1. Frequency dispersion of the harmonic current for different concentrations [sample 3, E = 240 V.cm-'].
I
lhgnA
Fig. 2. Frequency dispersion of the harmonic current for different field strengths [sample 3, c = 400 mg/l].
Concentration Figure 5 shows how I h varies with the DNA concentration for different frequencies. Note the linear dependence of I h with c up to high concentrations (c 400 mg/l). This property has been verified for field strengths ranging from 80 V-cm-' to 240 V-cm-'. When c increases above about 400 mg.l-l, the distorsion level begins to saturate. The same linearity between Ih and c has been found for every DNA
-
ELECTRIC PROPERTIES OF DNA .lh
9
377
nA 20 nz 40 Hz
80 Hz
200 nz
10
E,Vcm-'
1
50
100
200
400
Fig. 3. Field strength dependence of Ih for different frequencies [sample 3, mg/l].
50
100
200
c = 400
400
Fig. 4. Field strength dependence of Ih for different concentrations [sample 3, F = 40 Hz].
sample. However, the obtained slopes are different for reasons to be shown below.
Molecular Weight and Conformation The molecular-weight dependence of the nonlinear properties can be studied either on different native DNA samples, or on fractions of the same sample, which have been sonicated for different durations. The results are summarized in Figures 6 and 7. For each solution, we have
MARION, BERNENGO, A N D H A N S S
378
30(
150
0
I
I
200
400
Fig. 5. Concentration dependence of Ih for different frequencies [sample 3, E = 240 V. cm-l].
1 : 2 3 4 5
:
: : :
3.8.106 6,3.10' 5,8.106
ll,B .lo6 10.4.10'
Fig. 6. Frequency dispersion of I h for different native DNA samples (c = 50 mgh, E = 240 Vscm-').
ELECTRIC PROPERTIES OF DNA
379
Fig. 7. Frequency dispersion of I), for different sonicated fractions of sample 3 ( c = 200 mg/l, E = 240 Vecrn-').
1
2
4
6
Fig. 8. Molecular-weight dependence of I), (c = 200 mg/l, E = 240 Vecm-', F = 10 Hz) for sonicated fractions of sample 3.
controlled the concentration and field strength dependence of Ih. I t can be seen that increases with M,,. The molecular-weight dependence of Ih is h e a r when different fractions of the same sample are examined, and if @, > lo6 (Fig. 8). For lower molecular weights, a discontinuity in the Ih, M,, curve appears, which is followed by a major change in the distortion spectrum (Fig. 7).
380
MARION, BERNENGO, AND HANSS
200
100
0 0
50
100
Fig. 9. Melting profiles of sample 3 determined by OD measurements (50 mgh, 260 nm) and z h studies (c = 300 mgh, E = 240 Vacm-', F = 4 Hz).
To give an estimation of the signal-to-noise ratio of the distorsion measurements, we have given in Figure 7 the results when both cells are M NaCl solution (curve NaCl). filled with the same The nonlinear electric properties depend on the conformation of DNA, as is demonstrated by thermal denaturation experiments. They are carried on by keeping DNA solutions a t the desired temperature for 30 min, then cooling them in an ice-water mixture, and lastly by measuring the optical density (260 nm) and Ih a t room temperature. Figure 9 shows that the nonlinear property disappears when the DNA is heatdenatured. The low melting temperature (45OC) is explained by the low ionic strength.14
DISCUSSION The reported results show that DNA solutions have nonlinear electric properties, the evidence being the production of a third harmonic curreIlt I h when an alternating field is applied to the solutions. This nonlinear effect was sought for, as it can be predicted by a theory based on the orientation polarization of induced dipole moments (hyperpolarization). As the magnitude of the induced dipole moment is directly proportional to the electrical polarizability a, any factor modifying a will also alter the nonlinearity. For instance, when the DNA molecule is heat-denatured, a becomes very small in the melting temperature range,15-17so that the harmonic distorsion becomes vanishingly small.
ELECTRIC PROPERTIES OF DNA
381
However, we think that the initial explanation of the phenomenon is directly propormay not be correct. Indeed, Figure 5 show9 that tional to the concentration, even at the highest values of c (about 500 mg/l). A t such high concentrations, the intermolecular interactions become important, as is shown by the usual hydrodynamic properties of or other polyelectrolyte solutions. Therefore, it is difficult to accept any explanation based on the orientation of the whole molecule. Another reason is the molecular-weight dependence of the nonlinear effect. As is shown in Figure 8, for a given DNA sample, Zh is directly proportional to M,,. In the hyperpolarization mechanism applied to long rigid macromolecules,5 y is proportional to a2. As it is generally assumed20-22that for a rigid elongated polyelectrolyte of length L , a is proportional to L2,I h should vary as M V 4 . This deduction is not experimentally verified; the hyperpolarization mechanism, which was initially proposed, seems therefore inadequate for high M , DNA. Another explanation could be the elongation of the molecule by the electric field. If one assumes as a first order approximation that the molecular lengthening is proportional to E , an E3 term in the polarization could appear, because of the L 2 dependence of a. Further experiments are being carried on to verify that the harmonic distorsion comes from the electrical deformation of the DNA molecule. Experimental results supporting this hypothesis have already been obtained and will be proposed for publication. Other nonlinearity mechanisms can be suggested. In fact, any modification of the electrical polarizability or of the counterions mobility through conformational changes (electric deformation, local denaturation) or through a saturation of the induced polarizability or of the surface mobility, will generate harmonics in sinusoidal field experiments. Therefore, theoretical quantitative results of these mechanisms are needed in order to establish clearly the origin of the nonlinear behavior of high M , DNA solutions. In any case, whatever the nonlinearity origin is, our results show a field dependence of the electric properties, which can be demonstrated on DNA solutions by using electric-field strengths as low as a few 10 Vcm-'.
References 1. Takashima, S. (1966) J . Phys. Chem. 70,1372-1380. 2. Hornick, C. & Weill, G. (1971) Biopolyrners 10,234552358, 3. Hanss, M. & Bernengo, J. C. (1973) Biopolyrners 12,2151-2159. 4. Debye, P. (1929) Polar Molecules, Dover, New York. 5. Hanss, M. & Bernengo, J. C. (1966) J . Chirn. Phys. 63,1474-1476. 6. Hanss, M., Bernengo, J. C. & Sadron, C. (1968) C. R. Acad. Sci. 266,1263-1266. 7. Hanss, M. & Roux, B. (1972) Ann. Phys. Eiol. M6d. 3, 133-163. 8. Bernengo, J. C. (1970) ThBse, Universitk de Lyon. 9. Hanss, M. & Bernengo, J. C. (1969) presented a t the 3rd Int. Congress Biophysics (IUPAB), Cambridge, Mass.
382
MARION, BERNENGO, AND HANSS
10. Hanss, M. & Bernengo, J. C. (1975) J. Chim. Phys. 72,724-728. 11. Lowry, 0. H., Rosebrough, N. J., Farr, A. L. & Randall, R. J. (1951) J. Biol. Chem. 193,265-275. 12. Crothers, D. M. & Zimm, B. H. (1965) J. Mol. Biol. 12,525-536. 13. Bernengo, J. C., Marion, C. & Roux, B. (1973) Reu. Sci. Instr. 44,311-313. 14. Marmur, J. & Doty, P. (1962) J . Mol. Biol. 5,109-118. 15. Hanss, M., Viovy, R. & Sadron, C. (1963) C. R. Acad. Sci.256,4510-4513, 16. Mesnard, G. & Vasilescu, D. (1964) Biochim. Biophys. Acta 91,531-533. 17. Takashima, S. (1966) Biopolymers 4,663-676. 18. Eigner, J., Schildkraut & Doty, P. (1962) Biochem. Biophys. Acta 55,13-21. 19. Bloomfield, V. A. (1968) Macromolecules 1,255-316. 20. McTague, J. P. & Gibbs, J. H. (1966) J. Chem. Phys. 44,4295-4301. 21. Oosawa, F. (1970) Biopolymers 9,677-688. 22. Van der Touw, F. & Mandel, M. (1974) Biophys. Chem. 2,231-218.
Received May 23,1975 Returned for revision July 21,1975 Accepted September 29,1975
