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Langmuir 1998, 14, 3512-3516
Dynamic Mobility of DNA Mikael Rasmusson and Bjo¨rn A° kerman* Department of Physical Chemistry, Go¨ teborg University and Chalmers University of Technology, S-41296 Go¨ teborg, Sweden Received September 22, 1997. In Final Form: December 3, 1997 The dynamic mobility (µd) of double-stranded DNA (at 1 MHz) has been measured for the first time, by measurements of the electrokinetic sonic amplitude (ESA) and the hydrated density. Calf thymus DNA (average size 3000 base pairs) and herring sperm DNA (300 bp) have been used as models for a flexible polymer and a semirigid rod, respectively. In both cases the ESA is proportional to the DNA concentration at least up to 1.5 mg/mL, allowing µd of noninteracting DNA molecules to be determined from the slopes. For calf thymus DNA µd is very similar to literature values on the steady-state mobility, available between 50 and 4 mM NaCl. Unexpectedly, the dynamic mobility at 1 mM NaCl is lower than that at 4 mM, and thermal melting experiments rule out denaturation as a cause for this nonmonotonic dependence of µd on ionic strength. Using the free-draining approximation valid in steady-state electrophoresis of DNA, we evaluate the charge fraction R from the dynamic mobility. Above 4 mM NaCl R is essentially constant at 0.60 ( 0.05, indicating that DNA can be viewed as a constant-charge cylinder also in the dynamic mobility, but at 1 mM the charge fraction drops to 0.2. The herring sperm DNA has a considerably lower dynamic mobility than calf thymus DNA, which is confirmed by measurements of the ultrasonic vibration potential. Part of the lower dynamic mobility of the herring sperm DNA can be ascribed to partial denaturation. The fact that the charge fraction is smaller than that calculated from steady-state mobilities of completely denatured DNA indicates, however, that the smaller size also contributes to the low mobility of the herring sperm DNA.
Introduction When an alternating electric field is applied to a colloidal suspension of charged particles, a sound wave is generated.1 This electrokinetic sonic amplitude (ESA) is proportional to the dynamic mobility µd of the particles. For dilute suspensions O’Brien2 has derived the following expression:
ESA(ω) ) A(ω) φ(∆F/F) µd
(1)
where ESA is measured in Pa/(V/cm-1), A(ω) is an instrument factor, φ is the volume fraction of the particles, and ∆F is the density difference between the particle density and that of the solvent (density F). ESA is a complex quantity and is usually presented in terms of an amplitude and a phase angle with respect to the applied oscillatory field.3 The obverse effect also occurs: when a high-frequency sound wave passes through an ionic suspension, it causes a macroscopic alternating voltage difference called the ionic vibration potential (IVP). This was predicted by Debye already in 1933.4 When the sample instead is a colloidal suspension, the effect is called the colloid vibration potential (CVP). The IVP and CVP effects are referred to jointly as ultrasonic vibration potential (UVP). O’Brien2 has shown that the ESA and UVP are linked by the reciprocal relation
ESA(ω) ) K*(ω) UVP(ω)
(2)
where UVP is in volts per unit pressure gradient and K* * Corresponding author. Phone: 46317723052. Fax: 46317723858. E-mail:
[email protected]. (1) Oja, T.; Petersen, G.; Cannon, D. W. U.S. patent no. 4,497,207, 1985. (2) O’Brien, R. W. J. Fluid Mech. 1988, 190, 71. (3) O’Brien, R. W.; Cannon, D. W.; Rowlands, W. N. J. Colloid Interface Sci. 1995, 173, 406. (4) Debye, P. J. Chem. Phys. 1933, 1, 13.
is the complex conductivity. From this relation one can see that it is more convenient to measure the dynamic mobility using the ESA effect than the UVP effect, because no information about the complex conductivity is needed to obtain information about the particles in the ESA case. To our knowledge, only one investigation5 has been performed which verifies the reciprocal relation cited above. Most ESA studies so far have been performed on rigid particles. We were however interested in investigating the application of this technique to flexible polymers, using double-stranded DNA as a well-characterized polymer. We have measured the ESA signal for two different DNA samples. One contained highly polymerized calf thymus DNA (about 3000 base pairs), which can be considered flexible, since the persistence length of DNA is between 150 and 300 bp in the present range of ionic strengths. The other sample consisted of sonicated herring sperm DNA (about 300 bp), a procedure commonly used to obtain DNA molecules short enough to hydrodynamically behave like rods. The dynamic mobility of the smaller herring sperm DNA was also studied by complementary UVP measurements. Materials and Methods Calf thymus DNA was from Sigma, and sonicated herring sperm DNA was from Promega. Gel electrophoresis (5 V/cm, 1% agarose gel) showed that about 90% of the calf thymus DNA was between 1000 and 6000 bp with an average size of 3000 base pairs (the maximum of the distribution), and about 90% of the herring sperm DNA was between 200 and 600 base pairs, with an average size of 300 bp. The DNA concentrations were determined by using a molar extinction coefficient for DNA of 20 (mg/mL)-1 cm-1 at 260 nm. DNA samples were dialyzed to each ionic strength using large excess volumes of the appropriate concentration of NaCl at pH 7.0. (5) O’Brien, R. W.; Garside, P.; Hunter, R. J. Langmuir 1994, 10, 931.
S0743-7463(97)01059-7 CCC: $15.00 © 1998 American Chemical Society Published on Web 06/02/1998
Dynamic Mobility of DNA
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(a) ESA and UVP. The ESA and UVP measurements were performed on an ESA 8000 instrument (Matec Applied Sciences) using the high-sensitivity PPL-80 cell, which requires about 4 mL of sample. Each data point is the average of 10 measurements. The field strength is about 500 V/cm, and the field frequency is 0.9-1.0 MHz. It was found that the measurements were sensitive to the presence of bubbles in the sample chamber, so for each sample the measurement was made twice with the sample being taken out of the cell and reinserted in it, to check that the measured values were the same (within 4% or less of each other). To obtain the ESA signal for the DNA, the measured ESA signals were corrected for the background signal (from the electrolyte) according to the procedure outlined by Desai et al.7 The measured ESA (ESAmeas) is a vector sum of the true ESA for the DNA (ESAtrue) and the ESA for the background electrolyte (ESAbkgd).
ESAmeas ) ESAtrue + ESAbkgd
(3)
This equation can be resolved into its two components:
|ESAmeas| cos θ ) |ESAtrue| cos β + |ESAbkgd| cos φ
(3a)
and
|ESAmeas| sin θ ) |ESAtrue| sin β + |ESAbkgd| sin φ
(3b)
where θ, φ, and β are the phase angles of the measured, background, and true ESA signals, respectively. It was found that the (corrected) magnitude of the ESA signal increased linearly with increasing DNA concentration, at least up to 1.5 mg/mL of DNA. (b) Density Measurements. As pointed out by Wade et al.,8 the product φ(∆F/F) in eq 1 is equal to (Fsuspension - Fsolvent)/Fsolvent, so the individual values of volume fraction and density of the DNA are not required to calculate the dynamic mobility. This means that, in order to obtain the data on the DNA concentration necessary for the evaluation of the dynamic mobility, we do not need to rely upon absorption, which may give too high a value in the case of the herring sperm DNA which is partially denatured (see below). The density of the different DNA suspensions was measured using an Anton Paar densitometer. (c) Thermal Denaturation. Thermal denaturation followed by absorbance at 260 nm was measured in a Cary-4 spectrophotometer, using a temperature gradient of 0.4 °C/min. (d) Conductivity. The conductivity of the electrolyte was measured using a CDM 83 conductivity meter from Radiometer, Copenhagen, operating at a frequency of 4.69 kHz.
Results and Discussion (a) µd, the dynamic mobility. Figure 1 shows the variation of the (corrected) ESA signal for calf thymus DNA as a function of DNA concentration up to 0.8 mg/ mL. The scatter seems to increase slightly with increasing electrolyte concentration, but this is not unexpected, since the magnitude of the electrolyte signal increases in proportion to electrolyte concentration. Nevertheless, the linear response obtained after correction suggests that phase angles can be measured with high accuracy ((2°) in the PPL-80 cell and that the background correction produces reliable results. The constancy of the calculated β for any given electrolyte concentration (independent of DNA concentration) also validates the phase angle measurements, as well as the background correction procedure.7 From the slope of the curves of Figure 1 the dynamic mobility can be calculated, provided that the product φ(∆F/F) is known. As described in the Materials and (6) Hartford, S. L.; Flygare, W. H. Macromolecules 1975, 8, 80. (7) Desai, F. N.; Hammond, H. R.; Hayes, K. F. Langmuir 1993, 9, 2888. (8) Wade, T.; Beattie, J. K.; Rowlands, W. N.; Augustin, M.-A. J. Dairy Res. 1996, 63, 387.
Figure 1. Corrected ESA signal for calf thymus DNA as a function of DNA concentration at indicated NaCl concentrations. Table 1. Comparison of Electrophoretic and Dynamic Mobility of Calf Thymus DNA and the Dynamic Mobility of Herring Sperm DNA cNaCl (mM)
µd(calf thymus) (×10-8 m2 V-1 s-1)
1 4 10 20 50 100
4.3 5.4 5.0 4.5 3.8
a
µ ea (×10-8 m2 V-1 s-1) 5.9 5.0 4.4 3.3 2.8
µd(herring sperm) (10-8 m2 V-1 s-1) 3.9 3.4 3.0 3.0 2.5
From Hartford and Flygare6.
Methods section, this product is equal to (Fsuspension - Fsolvent)/ Fsolvent, an experimentally accessible quantity. We have measured this dimensionless quantity for different buffers (10 mM phosphate and 50 mM Tris-borate), ionic strengths (1-50 mM NaCl), and DNA types (herring sperm and calf thymus), and we find this quantity to be virtually constant for any given DNA concentration (a typical value is 2.31 × 10-4 for a DNA concentration of 0.517 mg/mL) and to be proportional to the DNA concentration in the investigated range. Using eq 1, the measured values of (Fsuspension - Fsolvent)/Fsolvent, and the corresponding ESAtrue data for calf thymus DNA at different ionic strengths (Figure 1) resulted in the values of the dynamic mobility µd presented in Table 1. Included for comparison are the electrophoretic light-scattering data of Hartford and Flygare on calf thymus DNA,6 and it can be seen that the agreement between the two sets of data is good. This suggests that the magnitude of the dynamic mobility is very similar to that of the constant-field electrophoretic mobility in the case of calf thymus DNA. It is noteworthy, however, that at 1 mM NaCl µd deviates from the trend that µd increases with decreasing ionic strength. To our knowledge no constant-field electrophoretic mobilities of DNA at this low salt concentration have been published. The ESA signal for the herring sperm DNA with a median size around 300 bp is shown as a function of DNA concentration in Figure 2. It is seen that at any given electrolyte concentration the (background-corrected) ESA signal for herring sperm DNA is not as high as that measured for calf thymus DNA. The resulting dynamic mobilities for herring sperm DNA calculated from the slopes are also presented in Table 1. We have verified these results by measuring the UVP signal for the herring sperm DNA (Figure 3). In Table 2 the |K*| values obtained from eq 2 by dividing the slope from the ESA measurements by the slope obtained from the UVP measurements are compared with the background electrolyte conductivity K∞ (which is the same at low frequencies and 1 MHz within
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3514 Langmuir, Vol. 14, No. 13, 1998
Figure 2. Corrected ESA signal for herring sperm DNA as a function of DNA concentration at indicated NaCl concentrations. Figure 4. Thermal melting profiles for calf thymus and herring sperm DNA at indicated NaCl concentrations. Table 3. Melting Temperature and Hypochromicity of Calf Thymus DNA and Hypochromicity of Herring Sperm DNA cNaCl (mM) 1 4 10 20 50
Figure 3. Corrected UVP signal for herring sperm DNA as a function of DNA concentration at indicated NaCl concentrations. Table 2. Comparison of the Measured Bulk Electrolyte Conductivity (K∞) and |K*| (at 1 MHz), As Calculated by Eq 2 cNaCl (mM)
K∞ (mS/cm)
|K*| (mS/cm)
1 4 10
0.124 0.485 1.187
0.231 0.523 1.199
experimental uncertainty). The results confirm eq 2, since the calculated magnitude of the complex conductivity is very similar in magnitude to the electrolyte conductivity. Only for the lowest electrolyte concentration is there a clear deviation, and in this case the conductivity contribution (at 1 MHz) of the DNA is significant. A similar trend was found in a study of poly(acrylic acid).5 The status of the DNA samples was monitored by thermal denaturation studies. The calf thymus DNA exhibited a distinct melting behavior, with a hypochromism of about 35% (Figure 4). This shows that the DNA is double-stranded at all ionic strengths employed in this work. The melting temperature increased with increased salt concentration, as expected for doublestranded DNA (Table 3). By contrast, the herring sperm DNA showed a wide transition profile and a considerably lower hypochromicity than the 35-40% expected for intact double-stranded DNA. The large width of the transition could partly be due to the wide distribution of DNA sizes in this sample,9 but the degree of hypochromism is insensitive to DNA size above approximately 20 bp,9 so the low value for the hypochromism shows that the herring sperm DNA is partially denatured. The transition profile was very similar at 1 and 4 mM salt but became less wide (9) Bloomfield, V. A.; Crothers, D. M.; Tinoco, I., Jr. Physical Chemistry of Nucleic Acids; Harper & Row: New York, 1974; p 339.
calf thymus hypochr Tm 0.35 0.30 0.33 0.33 0.34
51.8 56.8 63.8 64.9 74.8
herring sperm hypochr 0.17 0.15 0.21 0.16 0.25
with increasing salt concentration (Figure 4). This indicates that the sample is more denatured at the lowest ionic strength and becomes progressively more doublestranded as the ionic strength increases, although at 50 mM NaCl the DNA is still about 30% single-stranded according to the hypochromism. (b) Relationship between µd and ζ. Several investigations10,11 have shown that in constant-field electrophoresis DNA can be modeled as an (infinite) cylinder rather than the porous sphere model.12 The latter should be valid only when the overlap of double layers of different polymer segments is significant, which will not occur if the polymer is stiff on a length scale which is considerably longer than the Debye screening length,11 as is the case for double-stranded DNA. We assume that the cylinder model approximation holds also for the dynamic mobility. This question has not been investigated rigorously, but it seems to be a reasonable assumption that the cancellation of hydrodynamic interactions between any pair of segments which are far apart compared to the Debye screening length (which effect underlies the free-draining behavior in constant fields) will occur to a large extent also in nonconstant fields. The relation between mobility and the ζ potential has not been investigated theoretically to the same extent for the dynamic mobility as for constant-field electrophoresis in general, and in particular not for cylinders. This is partly because the ESA technique is relatively new and partly because the theoretical calculations are rather complicated. For spherical particles, Mangelsdorf and White13 have provided a numerical solution which relates (10) Schellman, J. A.; Stigter, D. Biopolymers 1977, 16, 1415. (11) van der Drift, W. P. J. T.; de Keizer, A.; Overbeek, J. Th. G. J. Colloid Interface Sci. 1979, 71, 67. (12) Hermanns, J. J.; Overbeek, J. Th. G. Rec. Trav. Chim. Pays-Bas 1948, 67, 761. (13) Mangelsdorf, C. S.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1992, 88 (24), 3567.
Dynamic Mobility of DNA
µd to ζ for any given particle radius and double-layer thickness. Loewenberg et al.14-16 have calculated µd for a spheroidal particle, but this analysis is restricted to thin double layers (κa . 1). For cylinders, Ohshima17 recently showed that µd for a cylinder of infinite length is roughly equal to the dynamic mobility of a sphere with a radius of 1.5 times the cylinder radius. Ohshima’s ruleof-thumb agrees with the results of Loewenberg’s and O’Brien’s14 study of a prolate particle with a thin double layer, but his result is valid for any κa (a is the cylinder radius), albeit only for low ζ potentials. Investigations have shown that the hydrodynamic radius of double-stranded DNA is between 9.6 and 12.5 Å,18,19 and we will here model DNA as a cylinder with a radius of 10 Å. Thus, according to Ohshima,17 the dynamic mobility of this cylinder is roughly equal to the mobility of a sphere with a radius of 15 Å, provided that ζ is low. However, for spheres with a radius of 200 Å or less the magnitude of the dynamic mobility is equal to that of the electrophoretic (constant-field) mobility;13 i.e., µd (1 MHz) ) µe. If we assume that µd (1 MHz) ) µe holds also at the comparatively high ζ values relevant for DNA, we can calculate ζ from classical electrokinetic theory for spheres following Wiersema et al.,22 as later extended by O’Brien and White.23 The use of the theory of Wiersema-O’Brien-White for spheres for a problem involving a cylindrical geometry gains further support from the work of Stigter et al.10,20 Stigter20 solved the nonlinear Poisson-Boltzmann equation for a cylinder of infinite length. He included the relaxation effect (polarization of the double layer) for the case where the cylinder was oriented perpendicularly in an external field, whereas in the parallel case he assumed that the Smoluchowski equation (eq 21) is valid. Stigter compared his result with the corresponding calculations of Wiersema22 for a spherical particle. He found that, for any given electrolyte concentration, a randomly oriented cylinder with a radius a exhibits the same ζ-mobility relationship (within 10%) as a spherical particle with radius a. Thus, in practice one can use the O’Brien and White calculations for both spherical and cylindrical geometries. We have therefore used the computer program MOBILITY, which is based on the model of O’Brien and White. We fixed the sphere radius to 10 Å and varied the electrolyte concentration between 1 and 100 mM NaCl and compared the output with Stigter’s results.10,20 It was found that the difference between the two calculations was always less than 5% for this small radius. (c) Calculated ζ Potentials. The resulting ζ potentials for calf thymus and herring sperm DNA as a function of electrolyte concentration can be seen in Figure 5. The ζ potentials calculated from the data of Hartford and Flygare6 and Constantino et al.24 are also included for comparison. (14) Loewenberg, M.; O’Brien, R. W. J. Colloid Interface Sci. 1992, 150, 58. (15) Loewenberg, M. J. Fluid Mech. 1994, 278, 149. (16) Loewenberg, M. Phys. Fluids A 1993, 5 (3), 765. (17) Ohshima, H. J. Colloid Interface Sci. 1997, 185, 131. (18) Langridge, R.; Marvin, D. A.; Seeds, W. E.; Wilson, H. R.; Hopper, C. W.; Wilkins, M. H. F.; Hamilton, L. D. J. Mol. Biol. 1960, 2, 38. (19) Yamakawa, H.; Fuji, M. Macromolecules 1973, 6, 407; 1974, 7, 128. (20) Stigter, D. J. Phys. Chem. 1978, 82, 1417. (21) von Smoluchowski, M. Bull. Acad. Sci. Cracovie 1903, 182. (22) Wiersema, P. H.; Loeb A. L.; Overbeek, J. Th. G. J. Colloid Interface Sci. 1966, 22, 78. (23) O’Brien, R. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1607. (24) Constantino, L.; Liquori, A. M.; Vitogliana, V. Biopolymers 1964, 2, 1.
Langmuir, Vol. 14, No. 13, 1998 3515
Figure 5. Measured ζ potentials for calf thymus and herring sperm DNA as a function of NaCl concentration. Literature values from Hartford and Flygare6 (HF) and Constantino et al.24 (CLV).
It can be seen that the three different experimental techniques (electrophoretic light scattering,6 moving boundary electrophoresis,24 and the ESA method) yield similar ζ potentials for calf thymus DNA as a function of electrolyte concentration. The ζ potential for herring sperm DNA is considerably lower than that for calf thymus DNA. Furthermore the increase of the ζ potential with decreasing electrolyte concentration is not as large as that in the case of calf thymus DNA, and moreover the ζ potential increases also going from 4 to 1 mM NaCl, in contrast to the decrease seen with calf thymus DNA. (d) r, The Charge Fraction. The kinetic charge density σkin corresponding to the ζ potential can be calculated for any given electrolyte concentration on the basis of the cylinder model, using the modified DebyeHu¨ckel approximation25
σkin )
0κK1(κa)ζβ K0(κa)
(4)
where is the dielectric constant of the solvent, 0 is the permittivity in a vacuum, K0 and K1 are Bessel functions of zeroth and first order, respectively, and κ is the inverse Debye length. β is the correction factor (>1) which incorporates the nonlinear charge-potential relationship, as calculated and tabulated by Stigter (ref 25, p 299). The structural charge density σ0 of a cylinder is given by
σ0 ) ze/2πab
(5)
where e is the elementary charge and z is equal to 1 if b is taken as the distance between the charges. The radius a has previously been set to 10 Å, and b is known to be 1.7 Å for double-stranded (native) DNA.26 The charge density of native DNA is then σ0 ) 0.15 C/m2. Following Schellman and Stigter,10 we now define R, the charge fraction, as
R ) σkin/σ0
(6)
which is a measure of how large a fraction of counterions is located outside the surface of shear. (25) Stigter, D. J. Colloid Interface Sci. 1975, 53, 296. (26) Record, M. T., Jr.; Woodbury, C. P.; Lohman, T. M. Biopolymers 1976, 15, 893.
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Figure 6. Charge fraction R (ref 10) as a function of NaCl concentration, calculated from the mobilities of DNA in Figure 5 (same notations), as described in the text.
Figure 6 shows R as a function of electrolyte concentration, where it is seen that the value for calf thymus R is almost constant in the electrolyte concentration range studied here. Schellman and Stigter10 have shown that this applies also between 100 and 400 mM, although they obtained a slightly larger R because they used a slightly larger cylinder radius (12 Å). Only for the lowest salt concentration is there a significant deviation from this behavior, reflecting the same trend in the mobility data (Figure 1). For herring sperm DNA R values are considerably lower than those for double-stranded calf thymus DNA, and in further contrast the R values decrease monotonically with decreasing electrolyte concentration. The thermal melting experiments show that the herring sperm DNA is partially denatured, but this alone cannot explain the comparatively low R values obtained for this DNA at all ionic strengths. This can be seen from the following calculation of R for single-stranded (denatured) DNA based on data from the literature,6,24 using the same approach as that for doublestranded DNA. The structural charge density σ0 of single-stranded DNA is 0.12 C/m2, a decrease compared to that for doublestranded DNA which occurs as a net effect of the distance between the charges b increasing to 4.3 Å26 and the cylinder radius decreasing to 5 Å.9 As expected from this observation, the electrophoretic mobility of denatured DNA is lower than that for double-stranded DNA, by 10-15%.6,24 From these experimental mobilities we have calculated ζ and σkin, using the cylinder radius of 5 Å. Finally R was calculated using the appropriate value for σ0 for the denatured samples, and the result can be seen in Figure 5. The R values are similar to the values obtained (here and by other techniques) for DNA which is known to be double-stranded, and thus it seems that R is independent of the secondary structure of the DNA (although it should be remembered that R does depend on counterion type10). We have calculated R for the herring sperm DNA assuming that it was double-stranded, but even if it was fully denatured at all ionic strengths, this could not explain the much lower R values obtained for this DNA, since the measured mobilities are much lower than those for calf thymus DNA (Table 1). We thus conclude that the charge fraction of herring sperm DNA deviates from that of calf thymus DNA mainly because of other effects, possibly size effects. (e) Model Deficiencies. Infinite Cylinder Model. It has been shown that the electrophoretic mobility of DNA
is independent of molecular weight,27 at least down to 260 000 g/mol, which corresponds to about 400 base pairs. However, the mobility of the monomer was considerably lower, which shows that the mobility at some point should start to decrease with decreasing molecular weight. The corresponding ζ potential for the monomer (in 10 mM NaCl) is 55 mV, which agrees favorably with 61 mV, as obtained for herring sperm DNA at the same ionic strength. Since the median size of the herring sperm DNA is around 300 base pairs, there is thus the possibility that these molecules are in a size range where the mobility depends on molecular weight. To our knowledge there are no (constant field) electrophoresis data for DNA in this size range, but theoretical calculations of mobilities of wormlike chains show size effects (in terms of a decrease in mobility) for polymerization degrees of 1000 or less at 1 mM salt and 100 or less at 50 mM salt (for a polymer with a radius of 5.5 Å and a persistence length of 4.5 nm, compared to 50 nm for DNA).28 End effects are neglected in Stigter’s calculations, and their inclusion would increase the calculated ζ potentials (for a given constant-field mobility value), the more so the lower the salt concentration. Dynamic Mobility of a Cylinder. Finally it should be pointed out that the relationship between the ζ potential and the dynamic mobility of a cylinder has not yet been examined in the case of high ζ potential. In 1 mM NaCl, much lower ζ (and thereby also R) than expected is observed here for both herring sperm and calf thymus DNA. Earlier studies have avoided these low salt concentrations, claiming that DNA tends to denature when the ionic strength is as low as 1 mM.24 This possibility has been ruled out here in the case of calf thymus DNA, but again we have not found any constant-field electrophoresis data to compare with. The possibility thus remains that this decrease in mobility at very low ionic strengths is a characteristic of the dynamic mobility only and not of the constant-field mobility. It should be noted, however, that a decrease in (the constant field) mobility of polyvinyl sulfates at low ionic strengths has been observed.29 Conclusions A linear relationship between ESA signal and DNA concentration (up to 1.5 mg/mL) was obtained, indicating that the dynamic mobility of noninteracting DNA molecules can be evaluated from ESA measurements. The reciprocal relation between the ESA and UVP effects was verified by measurements on herring sperm DNA. The dynamic mobilities for calf thymus DNA are very similar in magnitude to available data on the constantfield electrophoretic mobility. The calculated ζ potentials suggest that calf thymus DNA behaves like a cylinder with a constant charge; i.e., the corresponding charge fractions R are independent of ionic strength. The dynamic mobility for herring sperm DNA is substantially lower than that for calf thymus DNA, which may be ascribed, at least partly, to denaturation and end effects. LA971059V (27) Oliveira, B. M.; Baine, P.; Davidson, N. Biopolymers 1964, 2, 245. (28) Cleland, R. Macromolecules 1991, 24, 4391. (29) Nagasawa, M.; Soda, A.; Kagawa, I. J. Polym. Sci. 1958, 31, 439.
