6896
J . Phys. Chem. 1990, 94, 6896-6903
Electric Field Orientation of Nucleic Acids in Aqueous Solutions. 2. Dependence of the Intrinsic Electric Dichroism and Electric Dipole Moments of Rodlike DNA on Molecular Weight and Ionic Strength’ Kiwamu Yamaoka* and Kiyohiro Fukudome Faculty of Science, Hiroshima University, Higashisenda-machi, Naka- ku, Hiroshima 730, Japan (Receiued: Nocember 27, 1989; In Final Form: April 6 , 1990)
The electric linear dichroism of four sonicated and fractionated calf thymus DNA samples with different molecular weights ( M , = (7.0-24.6) X IO4) in aqueous solutions was measured at 7 OC and at 260 nm in the presence of NaCl and Tris/HCl buffer, whose concentrations, C,, were 0.13-7.1 mM, over a wide range of appplied electric fields ( E 5 26 kV/cm). The steady-state reduced dichroism ( & / A ) obeyed the “Kerr” law in the limiting low-field region and monotonically approached a constant level at high fields. The field-strength dependence of M / A was analyzed satisfactorily with the SUSID orientation function which is based on the saturable ( A u E ) and unsaturable (Aa’E) induced dipole moment mechanism, the former transforming to a permanent-like dipole moment AuEO at the critical field strength E,. By the curve-fitting method, the intrinsic reduced dichroism ( M I A ) , of DNA was evaluated to be -1.06 f 0.03, which differs from -1.5 for the B form DNA, regardless of the chain length and ionic strength. The polarizability anisotropies Act’ and Au also varied with M , and C,, Au being 3-4 times larger than Act‘. A linear relationship was found between In (AuEo) and In (M,) with a slope less than unity. Being 1200-6400 in debye units, the magnitude of AuE, increased with the increase in M , but decreased with the increase in C,. This ionic moment was concluded to be principally responsible for the field orientation of DNA.
Introduction Electric (linear) dichroism and electric birefringence are now generally accepted as the important electrooptic technique capable of determining the conformation of biopolymers, bioaggregates, and complexes with various low-molecular-weight ionic compounds in the dissolved state, where the X-ray diffraction method is least powerful, as extensively reviewed recently.2” In particular, the pulsed electric dichroism method has been shown to be suited for the study of the helical structure and conformational transitions of D N A and polynucleotides in solution. Measurements of the reduced dichroism, A A / A , or the birefringence, An, over a wide range of applied electric fields lead in principle to quantitative interpretation of the secondary and higher order structures and electric properties or rodlike biopolymers with axial symmetry. In order to achieve this goal, a quantity, ( A A I A ) , , often termed the intrinsic or saturated reduced dichroism, must be estimated with high accuracy. The intrinsic reduced dichroism represents the optical property of a chromophoric group(s) contained in a polymer chain and corresponds to the A A / A value of a solution in which all orientable polymer molecules are aligned parallel to the direction of applied electric field. Such a complete orientation of molecules would never be attained, unless an extremely high electric field is applied to the solution. An extrapolation of measured A A I A values to infinitely high fields is usually made for estimating the ( M I A ) , value. However, this extrapolation method is ambiguous, because the dependence of observed A A I A values on applied field is complex.’ The field orientation of polymer molecules is described by the orientation function +(E), which depends on the interaction between the electric moments of those molecules and the external field E . Since the complete orientation of rodlike polymers corresponds to the approach of the orientation function to unity, ( I ) Part I of this series: Yamaoka, K.; Fukudome, K. J . Phys. Chem. 1988, 92, 4994-5001, (2) OKonski. C. T.,Ed. Molecular Electro-optics; Marcel Dekker: New
York. 1976 (Part I ) , 1978 (Part 2). (3) Jennings. B. R., Ed. Electrc-Optics and Dielecrrics of Macromolecules and Colloids; Plenum: New York, 1979. (4) Krause, S., Ed. Molecular Electro-Opitcs, Electro-Optic Properties of Macromolecules and Colloids in Solution; Plenum: New York, 1981, ( 5 ) Charney, E. Q.Rer. Biophys. 1988, 21, 1-60. (6) Watanabe, H., Ed. Dynamic Behauior of Macromolecules, Colloids, Liquid Crystals and Biological Systems by Optical and Electrooptical Merhods: H i r o k a w Tokyo, 1989.
0022-3654/90/2094-6896$02.50/0
TABLE I: Characteristics of DNA Samples Used for Electric Dichroism
sample no. 1 (200)e
I 1 (105) I11 (200) IV (105)
Mwu/104 [qlb/dL g-l
24.6 ( 3 7 3 ) f 17.9 (271) 14.2 (215) 7.0 (106)
1.65 1.15 0.87 0.28
M,/M,E 1.29 1.18 1.08 1.17
T m d / T Hd/% 33.8 35.5 35.3 35.8
39.1 36.2 38.2 33.7
The weight-average molecular weight.I7 bThe intrinsic viscosity in O C . I 6 ‘The ratio of weight-average to number-average molecular weights.I6 “The melting temperature and the hyperchromicity of DNA in 0.2 mM NaCI/Tris/HCI, respectiveIy.l6 ‘Values in parentheses are the nominal power output in watts of a Tommy Model UR-2OOP sonicator transmitted to the DNA solution.I6 /The average number of base pairs in parentheses. a
0.2 M NaCl solution at 25
A A / A values measured over a wide field-strength range may be fitted to an appropriate theoretical function to evaluate the ( M I A ) ,value. This fitting method was utilized with the so-called classical orientation function quite successfully for a number of nonconducting polymers, which possess only permanent and induced electronic dipole moments.’ I f theoretical orientation functions are available for ionizable macromolecules in solution, the above fitting method would make it possible to evaluate ( A A I A ) ,values of nucleic acids or proteins. Such orientation functions have been derived on the basis of several different orientation mechanisms, e.g., the i o n - c o n d e n ~ a t i o n , ~ ~ ~ the ionic atmosphere and more recently the electric field induced ionic polarization which is saturated at an As an extension of the last concept, electric field strength E0.12*t3 a theoretical orientation function was derived on the basis of the saturable and unsaturable induced dipole (SUSID) mechanism.’ This SUSID orientation function was compared with the exper( 7 ) O’Konski, C . T.; Yoshioka, K.; Orttung, W. H.J. Phys. Chem. 1959, 63, 1558-1 565. (8) Kikuchi, K.; Yoshioka, K. Biopolymers 1976, 15, 583-587. (9) Matsuda, K.; Yamaoka, K . Bull. Chem. SOC. Jpn. 1982, 55, 1777-1733 . - . __ ( I O ) Rau, D. C.; Charney, E. Macromolecules 1983, 16, 1653-1661. ( 1 1 ) Charney, E.; Chen, H . H.; Henry, E. R.; Rau, D. C. Biopolymers 1986, 25, 885-904. (12) Diekmann, S.; Hillen, W.; Jung, M.; Wells, R. D.; Porschke, D. Biophys. Chem. 1982, 15. 157-167. (13) Yoshioka, K. J . Chem. Phys. 1983. 7 9 . 3482-3486.
0 1990 American Chemical Society
Electric Dichroism of Rodlike DNA
The Journal of Physical Chemistry, Vol. 94, No. 1 7 , 1990 6897
A d Eo 0 +
.“.-T”‘’,-Time
E
0 Figure I . Digitized signals of the parallel dichroism (11) and perpendicular dichroism ( I ) of a sonicated DNA ( M , = 24.6 X lo4) solution at 7 OC and at 260 nm. Applied electric field strength E, 18.8 kV/cm. Concentration of DNA: 0.13 m M in 0.2 mM Tris/HCl/NaCI at pH 7.2. Sampling time was set at 50 ns. Four signals were accumulated and averaged. The vertical scale of signal is given in volts. Note that AVliSt and AVLStare not linearly proportional to MIland PA,, respectively.
imentally obtained electric birefringence data and concluded to be a reasonable one for the fitting method. In the present paper, a detailed electric dichroism study was carried out with four well-fractionated and relatively small molecular weight DNA samples at widely different ionic strengths. The experimental results were analyzed with the SUSID function to evaluate both the electric and the optical parameters.
Experimental Section Materials. The low-molecular-weight calf thymus DNA samples in 0.2 M NaCl solutions were prepared by sonication and the subsequent precipitational fractionation with acetone. The details of these preparative procedures have been described elsewhere.lJ4-17 Table I shows the characteristics of the DNA samples used in the present work. As values of M,,,/M,, T,, and H (%) in Table I indicate, those closely monodisperse samples are in the native state after the sonication and fractionation. The DNA solution for electric dichroism measurements was prepared by an extensive dialysis at 4-7 OC against the solvent containing both NaCl and Tris/HCl buffer at a desired ionic strength (0.13-7.1 mM) and a pH (7.3-7.2). The concentration of DNA was kept at 0.13-0.12 mM in the mononucleotide unit. The complete nativeness of all DNA solutions subjected to electric dichroism measurements was confirmed with the T, and H values. Measurements. The electric dichroism of DNA solutions was measured at 260 nm on an apparatus constructed in our laborawith a “Kerr” cell thermostated at 7 O C , applied electric pulse fields being variable up to 26 kV/cm. The pulse duration was usually set at about 20 ps in the medium-to high-field range but set much longer to the 40-350 ps range at low fields. The Kerr cell was of cylindrical type,ls the optical path length being either 1 .O (0.20) or 2.0 (0.35) cm with the electrode (stainless steel) gap given in the parentheses. Instead of the conventional photographic recording of a single pulse and a signal form which were displayed on the cathode-ray tube of an oscilloscope, a new digitized signal detection system was used to improve signal-tonoise ratios by accumulating and averaging dichroism signals.’.21,22
I
/!
/
Eo -E
Figure 2. Schematic presentation of electric dipole moments, m, versus applied electric field E for the SUSID orientation. Saturable ionic induced dipole moments, PuE and AaE,. Unsaturable induced dipole moment, Aa‘E. Critical electric field, Eo.
The present apparatus could measure both the parallel dichroism Ull and the perpendicular dichroism AA, separately.l*-2’ Figure 1 shows a set of both signals of a DNA solution. Data Analysis. Provided that a solute polymer is rigid and rodlike, containing a single chromophoric group whose optical transition moment makes an angle of 8 with respect to the orientation axis, the reduced dichroism, A A / A , is expressed from the parallel specific dichroism, A A I I / A= ( A l l- A ) / A , and the perpendicular specific dichroism, AA,/A = ( A , - A ) / A , of a dilute polymer solution under an orienting field E as19.23
where @(E)is called the orientation function, which describes the orientational behavior of the solute polymers, and a complex function of the electric field. It should be noted that both quantities AAll and AA, at the same wavelength are needed to check if the electrochromic effect is involved for a particular set of experimental conditions (ionic strength, field strength, molecular weight, et^.);'^,^^ this caution should not be considered lightly. The relation, AAll/A = -2AA,/A, must be confirmed to hold over a field-strength range to be covered. In other words, if only UlI, AAL, or A A / A is measured, the electric field effect on the structural deformation of polymer may be undetected. In fact, the above relation often breaks down for high molecular weight DNA solutions at low ionic strengths and at high applied fields.24 In the first paper,] a new theoretical orientation function, the SUSID function @(y,yo,y’),was derived for the rodlike and ionized polymer without permanent dipole moment. It was shown that this function reproduces satisfactorily the field-strength dependence of rigid rodlike DNA over an entire field regi0n.l In order to avoid the confusion which may arise regarding the notations now widely used for the classical orientation function, @(p,y),’ a new set of symbols is introduced here in the following manner: @(y,yo,y’)is revised to @(p,,p,y’), where y = p + y’. Accordingly, the new notations are
The parameters are expressed as
(14) Charney, E.; Yamaoka, K. Biochemistry 1982, 21, 834-842.
(IS) Fukudome, K.; Yamaoka, K.; Nishikori, K.; Takahashi, T.; Yamamoto, 0.Polym. J . (Tokyo) 1986, 18, 71-79. (16) Fukudome, K.; Yamoka, K.; Nishikori, K.; Tatehata, H.; Yamamoto, 0.Polym. J . (Tokyo) 1986, 18, 81-88. (17) Fukudome. K.: Yamaoka, K.; Ochiai, H. Polym. J . (Tokyo) 1987, 19, 1385-1394. (18) Yamaoka, K.; Matsuda. Chem. 1980, 43, 185-203.
K. J . Sci. Hiroshima Unio., Ser. A : Phys.
(19) Yamaoka, K.; Matsuda, K . Macromolecules 1981, 1 4 , 595-601. (20) Matsuda, K.; Yamaoka, K. Bull. Chem. SOC.Jpn. 1982.55.69-76, (21) Yamaoka, K.; Ueda, K.; Kosako, I. J . Am. Chem. SOC.1986, 108,
4619-4625. (22) Yamaoka, K.; Yamamoto, 19, 951-963.
S.;Kosako, I . Polym. J . (Tokyo) 1987,
&E2 __ 2kT ’
E AuEo2 p: E * = -Eo’ Yo = 2kT - 4P’
Aa’E2 2kT (3)
and y’ = -
where p3 is the permanent dipole moment along the longitudinal axis, Ao is the saturable, ionic polarizability anisotropy, Aa is the electronic or covalent polarizability anisotropy, Pa’ is the unsa(23) Yamaoka, K.; Charney, E. J . Am. Chem. SOC.1972,94,8963-8974. (24) Pollak, M.; Glick, H. A. Biopolymers 1977, 16, 1007-1013.
6898 The Journal of Physical Chemistry, Vol. 94, No. 17, 1990
Yamaoka and Fukudome
TABLE 11: Optical and Electric Properties of Sonicated DNA at 260 nm and at 7 “C sample no. CJmM -(AA/AL Au’/IO-’~ F m2 AU/IO-’~ F m2 I 0.13 1.08 5.86 19.5 I 0.2 1.10 5.15 17.2 i 0.5 1.11 2.63 8.77 I 0.8 I .07 I .98 6.61 I I .2 1.04 4.38 1.34 1 1.8 I .05 4.00 0.600 1 4.! 1.05 1.30 0.391 i 7.I I .07 0.781 0.234 13.0 II 0.13 I.04 3.91 11.6 II 0.2 1.10 3.48 I1 1.8 0.98 0.948 3.16 111 Ill Ill Ill Ill IV
IV
Iv IV IV
0.13 0.2 0.8 1.8
4.1 0.13 0.2 0.8 1.8
4.1
1.08 1.11
1.08 1.10 1.10 0.96 1.02 1.07 1.08 I .02
3.07 2.43 1.45 0.806 0.358 0.889 0.823 0.516 0.336 0.209
E J k V cm-‘ 1.09 1.16 I .63 I .87 2.28 2.41 4.22 5.45
AaEn/10-26C m
2.13 (6400)u 2.00 (6000) I .43(4300) I .24(3700) 1.02(3100) 0.964 (2900) 0.549 ( 1 700) 0.426 (I 300) 1.73 (5200) 1.64(4900) 0.856 (2600) I .54(4600) 1.37(4100) 1.08 (3200) 0.791 (2400) 0.525 (1600) 1.17 (3500) 1.13 (3400) 0.892(2700) 0.724(2200) 0.568( 1 700)
1.33 1.41
2.71 1.51 1.69 2.19 2.94 4.41 3.30 3.43 4.33 5.36 6.80
10.2 8.1 I
4.83 2.69 1.19 3.56 3.29 2.06 1.35 0.836
“Values in parentheses are the saturated moments in debye units turable, ionic and electronic polarizability anisotropy (vide infra), k is the Boltzmann constant, and T i s the absolute temperature. Integrals I , to in eq 2 are complex expressions‘ and are given in the Appendix. As shown in Figure 2, the electric moment m in the saturable-unsaturable induced dipole (SUSID) mechanism consists of the saturable induced ionic dipole moment AaE, which is saturated at the critical electric field Eoand, thereafter, behaves as the permanent-like dipole moment AaEo, and the unsaturable induced dipole moment Aa’E, which is not saturated at any experimentally attainable field strengths.’ Conceptually, Aa‘ (or y’) differs from Aa (or y ) in the classical orientation function.’ As advanced by Tinoco and Y a m a ~ k a Aa’ , ~ ~ consists of both electronic and ionic parts: A d = Aa(e1ectronic) + Aa(ionic). The field-strength dependence of the steady-state y’ is identical with that of 7, but the time dependence differs from each other.25
Results and Discussion Steady-State Dichroism over a Wide Field Range. Figure 3 shows the field-strength dependence of both AAl,/Aand -2AA,/A for DNA samples I-IV. The relation I1AII/A= -2AA,/A holds for all samples over the entire field range regardless of the concentration of added NaCl and Tris/HCl salts, C,; hence, any possible electrochromic effect is ruled out at the lowest C,of 0.13 mM (comparable with the DNA base concentration), where a high field was about 26 kV/cm, or at the highest C, of 7.1 mM, where the maximum attainable field was about 6 kV/cm. The sign of reduced dichroism is negative in all cases, the angle 0 being more than f54.7’. The experimentally determined dependence of U / A values on field strength shows a monotonic increase and a subsequent level-off, as commonly observed in previous reports. In all cases the &/A versus E2 plots exhibit no maximum or even its onset, in contrast with the prediction of a recent Debye-Huckel ion atmosphere polarization theory.I0 Within the experimental limits reported in the present work, the stripping of the ion atmosphere on the DNA rod is unlikely to occur. Therefore, it is reasonable to compare those AA/A data with the theoretical orientation functions which were derived on the basis of the saturation of induced dipole moments or condensed counterion polarization. Solid lines in Figure 3 represent the theoretical SUSID orientation function. The use of this function is most appropriate,’ since the double-stranded, antiparallel DNA helix possesses no intrinsic permanent dipole moment in aqueous solutions, as revealed by reversing-pulse electric birefringence
0
200
LOO
E2
600
/ (kVicm)’
800
Figure 3. Dependence of steady-state dichroism at 260 nm of sonicated DNA on applied electric field strength E at various added NaCl/buffer concentrations. DNA samples: I in (a), I 1 in (b), 111 in (c), and 1V in (d). Ordinate: the parallel specific dichroism . b , , / A (open symbols) and the perpendicular specific dichroism & , / A , multiplied by a factor of -2 (filled symbols). Concentrations of added NaCl and buffer in mM: 0.13(0,0),0.2(A,A),0.8(0,~),1.8(V,~),and4.1 (0,D). Solid lines are theoretical SUSID curves (see text). Inserts: the low-field behavior on expanded scales.
In each case, the agreement between experimental values and theoretical curve is excellent over the entire field-strength range (also see inserts). From this curve fitting, the following parameters were evaluated: the intrinsic reduced dichroism (AA/A)s, the polarizability anisotropies A d and Aa, and the critical field Eo. These values are all summarized in Table 11. For a given molecular weight, dichroism values are generally saturated more slowly at the higher ionic strength. For a given ionic strength, dichroism values and, hence, the degree of orientation are lower with the smaller molecular weights of DNA.
( 2 5 ) Tinoco, I . , Jr.; Yamaoka, K. J . Phys. Chem. 1959,63, 423-427.
(26)Greve. J.; de Heij, M . E. Biopolymers 1975,14. 2441-2443.
(27) Yamaoka. K.; Matsuda, K. Macromolecules 1980. 13, 1558-1 560.
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990 6899
Electric Dichroism of Rodlike DNA E’ 0 6.01
4 I
8
/
I
(kV/cm)‘ 12
16
20
I
I
24
32
LO
1.2,
I
0
2
I
I
I
I
L.5
3.0
4
a
0.8 0 0.9
0.6
0.3 0
8
16 E‘
/
(kV/cm)’
L
E-2/
Figure 4. Low-field behavior of steady-state reduced dichroism at 260 nm per square of field strength, (hA/A)(I/E2), of sonicated D N A at various added NaCl and buffer concentrations. DNA samples: I in (a), I 1 in (b), I I I in (c), and IV in (d). Concentrations of added NaCl and buffer in m M : 0.13 (0),0.2 (A), 0.8 ( 0 ) ,1.8 (V), and 4.1 (0). Solid lines are theoretical SUSID curves. Note that the abscissa scale of (d) differs from the remainder.
.
6 8 10-3(kV/cm)-2
IO
Figure 5. High-field behavior and extrapolation of steady-state reduced dichroism of sonicated DNA at various added NaCl and buffer concentrations. Reduced dichroism is plotted against the reciprocal of the D N A samples: I in (a), where ( 0 ) second power of field strength, E2. and ( 0 )denote the added NaCl and buffer concentrations of 0.5 and 1.2 m M ,respectively, I1 in (b), 111 in (c), and IV in (d). Other symbols and notations are the same as those in Figure 4. Solid lines are theoretical SUSID curves.
Quite interestingly, however, the intrinsic ( M / A ) , values at infinitely high fields were found to be nearly constant (see Figures almost disappears, values of ( M I A ) (1/ E 2 )being nearly constant 7b and 8b later), as previously r e p ~ r t e d . ’ ~ * ~These * * ~ ~results in the low-field region. The intercept of the ordinate yields a finite altogether imply that the electric dipole moments of D N A are value without exception, i.e., decreased either with the decrease in the molecular weight or with the increase in the concentration of added NaC1.’2,’4,28,3b33The individual electric and optical properties will be discussed quantitatively in the later sections. This fact suggests that the reduced dichroism is proportional to Field-Strength Dependence of Reduced Dichroism at Low Fields. As often emphasized by the present a ~ t h o r s ~ and , ~ ~ * ~the ~ *second ~ ~ power of field strength in the low-field region (cf. eq 12 of ref l), Le., the Kerr law is obeyed, and also that the saturable also by other ~ o r k e r s , ’ J O *the ~ ~ *low-field ~~ behavior of the reduced ionic dipole moment AoE is not saturated spontaneously at a very dichroism divided by field strength, e.g., ( M I A ) (1/E2),must be weak pulse field. The possibility of the spontaneous saturation compared with theoretical orientation function to verify the field of AoE can be ruled out, because the ( A A / A ) ( l / E )versus E plots orientation mechanism of polymers. In general, the plot of converge to the origin of the coordinate in all cases (not shown ( & / A ) ( 1 / E 2 ) versus E2 in the low-field region (E2 0) for the here). Hence, the critical field strength E, is not too low for the nonconducting polymer shows either a slight maximum for the present D N A samples (cf. Table 11). pure induced dipole orientation or a monotonic decrease for the Solid lines in Figure 4 are theoretically calculated curves with pure permanent dipole orientation.’ For the ionizable macrothe SUSID orientation function by use of the parameters ( p , p, molecule which orients according to the SUSID mechanism, the y’, Eo) which were evaluated in Figure 3 and given in Table 11. same plot generally shows a maximum whose position and height The agreement between these curves and experimental points is are varied by an interplay between the parameters: p,2/4p, p,2/2yr, good under consideration of experimental difficulties at extremely and (p: 27’) (see Figure 2 of ref 1). low fields. In many cases, the theoretical curve shows a weak but Figure 4 shows the plots of ( A A / A ) (1 / E 2 ) versus E2 at low definite maximum. The dependence of ( M I A ) (I / E 2 ) Evalues ~ fields for four DNA samples. Although experimental points at on molecular weight and ionic strength will be discussed quanextremely low fields are inevitably scattered due to weak signal titatively in the later sections. intensity, a slight maximum is discernible for some plots at low Intrinsic Dichroism at Infinitely High Fields. A major aim C,.’As the ionic strength is increased, however, this maximum of the present study is to resolve if the intrinsic dichroism ( M I A ) , can be separated with the least ambiguity from the electric pa(28) Hogan, M.; Dattagupta, N.; Crothers, D. M. Proc. Narl. Acod. Sci. rameters. Figure 5 shows the plots of reduced dichroism, -AA/A, U.S.A. 1978, 75, 195-199. versus the reciprocal of the second power of field strength, E2. (29) Dattagupta, N.; Hogan, M.; Crothers, D. M . Proc. Narl. Acad. Sci. U.S.A. 1978, 75, 4286-4290. Symbols are observed points above 10 kV/cm, which were taken (30) Stellwagen, N . C. Biopolymers 1981, 20, 399-434. from Figure 3. These plots immediately reveal the f o l l o ~ i n g : ’ ? ’ ~ (31) Elias, G.; Eden, D. Macromolecules 1981, 14, 410-419. (1) the simple extrapolation to infinitely high fields is impossible (32) Yamaoka, K.; Matsuda, K.; Takarada, K. Bull. Cfiem. SOC.Jpn. 1983, 56, 927-928. for each DNA solution if the concentration of added salts exceeds (33) Diekmann, S.; Jung, M.; Teubner, M . J . Chem. Phys. 1984, 80, approximately 1 mM, since A A / A values are not measurable at 1259-1262. high fields and (2) the linear extrapolation with a few higher field (34) Yamaoka, K.; Ueda, K. Bull. Cfiem.SOC.Jpn. 1983,56, 239C-2395. points clearly yields an intercept often much higher or lower than (35) Stellwagen, N. C. Biopfiys. Cfiem. 1982, I S , 311-316. the intrinsic ( A A / A ) , value. (36) Rau, D. C.: Charney, E. Biopfiys. Chem. 1983, 17, 35-50.
-
+
6900 The Journal of Physical Chemistry, Vol. 94, No. 17, 1990
Yamaoka and Fukudome
-L, l
1
5
I
‘n
I
I
I
4
a
Figure 7. Dependence of experimentally evaluated electrooptical quantities at 260 nm of sonicated DNA with different molecular weights on the added NaCl and buffer concentrations, C,, on a semilogarithmic scale. DNA samples: I ( O ) , I1 (A),111 ( O ) , and IV (v). 0
3
6
9
1 2 1 5
/ 10-2(kV/cm)-’
E-’
Figure 6. High-field behavior and extraplation of steady-statereduced dichroism of sonicated DNA at various added NaCl and buffer concentrations. Reduced dichroism is plotted against the reciprocal of the first power of field strength, E’. DNA samples: I in (a), 11 in (b), 111 in (c), and IV in (d). Symbols and notations are the same as those in Figures 4 and 5 . Solid lines are theoretical SUSlD curves.
Solid lines are theoretical SUSlD orientation curves which were calculated with the original sets of parameters (cf. Table 11). Since the agreement between experimental points and theoretical curves is all excellent in Figure 5, and also in Figure 3, the intercepts on the ordinate can be taken as the ( A A I A ) , values with some confidence. These values are rather close to one another for each DNA sample. It should be noted that the curvature for extrapolation is large and unpredictable if the salt concentrations of DNA solutions are high. In such cases, the graphical extrapolation would be quite uncertain, even if measurements over very high fields ( E >> 8 kV/cm) should have been performed. Some workers prefer the A A / A versus E’ plot either to the above-mentioned extrapolation or to the curve fitting with some empirical formula^.]^^]^^*^^^^'^ Figure 6 shows the plot of AA/A versus the reciprocal of the first power of field strength, El. As was pointed out in ref I , the graphical extrapolation would often yield much higher values of ( A A / A ) , up to -1.5 and beyond. Unless the ionic strength is very low, each theoretical curve plotted against E-‘ clearly shows a sigmoidal change with an inflection point a t a high electric field which is often located in the experimentally unattainable region. In this case, the A A / A versus El plots should actually level off; here again, a linear extrapolation is unfeasible and unreliable.] In some previous studies, the theoretical curves, calculated from the classical orientation function +(@,r), were employed to evaluate ( A A I A ) , values with remarkable success, on the understanding that the function is illogical for DNA solutions but acceptable as an empirical formula. By this curve-fitting method, ( A A I A ) , values were found to be in the range between -0.9 and (37) Ding, D.-W.: Rill, R.; Van Holde, K. E. Biopolymers 1972, I / . 2109-21 24. (38) Sokerov, S.; Weill, G . Biophys. Chem. 1979, 10, 161-171. (39) Hogan, M.; Dattagupta, N.; Crothers, D. M. Biochemistry 1979, 18, 280-288. (40) Lee, C.-H.; Charney, E. J . Mol. Biol. 1982, 161, 289-303.
This finding has been interpreted as being that the @(@,y)function should be very similar, in a mathematical form, to the SUSID orientation function, in spite of the fact that the latter lacks in the parameter P.l4 This interpretation is now verified below. The SUSlD orientation function can be expanded to power series at higher fields if the moment AuE has already been saturated at a much lower field ( E L Eo): 3 @(y’>>l,p,>>l)= 1 - -1.1.14J9920,30,35
Ps
+ 2Y‘
This is eq 16 of ref 1 and becomes formally identical with the classical function at high fields, Le., @(P>>l,y>>l)= 1 - ( 3 / ( p 2y)), derived by O’Konski et al. (eq 25 of ref 7), by setting p s p and y’ y or SUE, p and ha’ E A a . That is, the saturated induced ionic dipole moment AuEo behaves just like the permanent dipole moment 1.1. These results lead to two important conclusions. First, the AA/A versus El plot would permit a linear extrapolation to yield the value of ( A A / A ) s ,only if the field orientation is predominantly due to the saturated induced ionic dipole moment AuEo (cf. eq 17 of ref 1). On the other hand, the A A / A versus E-* plot would be appropriate, if the unsaturable induced dipole moment Aa‘E is mostly responsible for the orientation (cf. eq 15 of ref 1). Second, the classical orientation function may be employed empirically to evaluate the ( & / A ) , value of DNA or other related nucleic acids in solution, if no physical meaning is attached to the parameters p and y. Ionic Strength Dependence of Electric and Optical Properties. On the basis of the parameters that were evaluated by the curve-fitting method in the preceding sections (cf. Figures 3, 4, and 5), the variation of the electric and optical properties of four DNA samples with the concentration of added salts is now discussed quantitatively. The ( A A / A ) (1/E2)E2-o value of electric dichroism (eq 4) may be considered equivalent to the Kerr constant of electric birefringence, since eq 4 is the product of the optical term and the electric term and, hence, the electrooptic property. Figure 7a shows the dependence of ( A A / A ) (1/E2)€+, which was evaluated in Figure 3 , on salt concentration, C,. For a given molecular weight, those extrapolated values are decreased with increasing C,, the effect being more pronounced with higher molecular weight samples. Figure 7b summarizes the intrinsic reduced dichroism ( M I A ) , of DNA samples. It should be pointed out that ( A A I A ) , values are nearly constant over a very wide range of C, (0.13-7.1 mM)
+
Electric Dichroism of Rodlike DNA
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990 6901
I I I regardless of molecular weights. Though slightly scattered, these values remain between -0.96 and - I . I3 with the mean value of -1.06, which is in good agreement with previously reported v a l u e s . ’ 2 ~ ’ 4 ~ ’ 9 ~ 2 0 ~ 2 8Hence, ~ 2 9 ~ 3the 7 ~ angle 3 ~ 1 8 (cf. eq 1) remains nearly constant at approximately f72O; Le., the optical transition moment (or moments) at 260 nm of DNA base pairs makes this angle with respect to the orientation axis of the double-stranded DNA helix. This angle alone, however, allows no unique determination of the tilt, roll, and/or propeller twist of the plane of 1.31 (b) the DNA base pairs.5.4246 To resolve this difficult problem, the dependence of ( A A I A ) , on wavelength, or the electric linear dichroism spectrum, must be measured in the ultraviolet region.19,4446A preliminary result of D N A in alcoholic solutions has already been pre~ented.4~It should be noted that the average value of ( A A I A ) , at 260 nm was -1.06 (e = 72O), but not -1.5 (e = 9 0 O ) ; the latter has occasionally been reported in earlier and is usually assigned for the B-form DNA.5v45 Considering the discussion in the preceding section, the discrepancy in evaluating the ( A A I A ) , value probably results from the long extrapolation of measured AA/A values to infinitely high fields exercised by different workers. It is surprising that, notwithstanding the semiflexible backbone conformation of longer DNA in solution in the absence of an external electric field, the ( A A I A ) , values remain nearly constant over a 50-fold or more increase in NaCl concentrations. This result clearly indicates that Figure 8. Dependence of experimentally evaluated electrooptical quanthe secondary structure of DNA is unaltered under an orienting tities at 260 nm of sonicated DNA on the weight-average molecular electric field, although higher salt concentrations are believed to weights, M,. at various salt concentrations. Added NaCl and buffer lower the persistence length of the backbone helix or to increase 0.2 (A),0.5 ( O ) , 0.8 ( O ) , 1.2 ( O ) , 1.8 concentrations in mM: 0.13 (0). the fle~ibility.~ Therefore, it is likely that the slightly bending (V), 4.1 (O), and 7.1 ( A ) . backbone may be straightened out by an electric field (not necessarily elongated or stretched out) and that the field-on conformation or the secondary structure of rodlike DNA samples is probably unaffected by ionic strength, if their molecular weights are in the (7-25) X IO4 range. Figure 7c shows the plot of (AA/A)(1/E2)E2,0(Figure 7a) divided by ( A A I A ) , (Figure 7b) versus C,. The ordinate is the quantity equal to ( 1 /15kT)(Aa’ + Au) (cf. eq 4), indicating that 2oI-0. I I I 1 the magnitude of electric moments (Aa‘E and AuE) is decreased with increasing ionic additives in the bulk solution. Although it is undeterminable from Figure 7c if the electric moments vanish at much higher ionic strengths, e.g., above I O mM, the experimental points all seem to converge into a single value, perhaps smaller than 0.001. This result may be taken as evidence (1) that the electric moments are predominantly due to the ionic polarization of the counterion (Na+) on the DNA surface, (2) that the electronic polarizability anisotropy (Act) contribution to the electric field orientation is very small, and (3) that DNA samples possess no intrinsic permanent dipole moment, as supported p r e v i ~ u s l y . ~ ~ * ~ It would be interesting to extend the present work to longer, but not too long, and slightly bending DNA samples with molecular weights up to a million or ~ 0 . ~ ~ 3 ~ ~ Molecular Weight Dependence of the Electric and Optical Properties. Figure 8 shows the molecular weight dependence of the electrooptic (a), optical (b), and electric (c) properties of four DNA samples at various salt concentrations. The intrinsic reduced W 20.51 dichroism ( A A I A ) , in Figure 8b remains nearly constant (the - 0 mean value = -1.06 f 0.03; 0 = 72’); hence, the field-on sec0.1 0.5 1 5 10 ondary structure of those D N A samples is independent of both Cs/ m M molecular weight and ionic strength. Figure 8c also shows that Figure 9. Dependence of the electric properties of sonicated DNA with the electric moment terms, ( A A / A ) (1 / E 2 ) p 4 divided by different molecular weights, Mw, on the concentration of added salt and ( M I A ) , , increase with increasing molecular weights, if the ionic buffer, C,, on a semilogarithmic scale. Ordinates: Unsaturable (a) and
4
(41) Wu, H. M.; Dattagupta, N.; Crothers, D. M. Proc. Natl. Acad. Sci. U.S.A. 1981, 78, 6808-6811. (42) Charney, E.; Chen, H . H. Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 1546-1549. (43) Norden, B.; Seth, S. Biopolymers 1979, 18, 2323-2339. (44) Causley, G.; Johnson, W . C., Jr. Biopolymers 1982, 21, 1763-1780. (45) Matsuoka, Y.; Norden, B. Biopolymers 1982, 21, 2433-2452. (46) Edmondson, S. P.; Johnson, W. C., Jr. Biopolymers 1985, 24, 825-841. (47) Yamaoka, K.; Fukudome, K.; Sekiguchi, J. Presented at 9th International Biophysics Congress held at Jerusalem, Israel, Aug 23-28, 1987; Abstr. p 109.
saturable (b) polarizability anisotropies, critical field strength (c), and saturated ionic induced dipole moment (d). Symbols and notations are the same as those in Figure 7.
strength is relatively low, but the terms become almost independent of molecular weights if the ionic strength is higher (24.1 mM). This trend is in contrast with the un-ionized nonconducting helical polymers.48 (48) Ueda, K.; Mimura, M.; Yamaoka, K. Biopolymers 1984, 23, 1667-1681.
6902
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990
I
I
5
I
10 Mw x 1 6 ‘
20
30
Figure 10. Dependence of the electric properties of sonicated DNA on weight-average molecular weights, M,, at different salt concentrations. Symbols and notations are the same as those in Figures 8 and 9. Solid lines are determined by the least-squares method. Note that the plots are on a double logarithmic scale.
Dependence of Electric Moments and Critical Fields on Molecular Weight and Ionic Strength. The electric moments in Figures 7c and 8c will now be separated from the set of parameters (y’,2y0E*, and yo) to the individual components ( A d , Au, and Eo),and their dependence both on ionic strength and on molecular weight will be examined. Figure 9a shows the dependence of A d an ionic strength and molecular weight, while Figure 9b shows the same dependence of ACT. Both A d and Au clearly decrease with increasing ionic strength, but the dependence is marked only for higher molecular weight D N A samples; the changes in ha‘ and Au are very slight for sample IV whose contour length (ca. 400 A) is definitely shorter than the persistence length.5J7-3’~4e5’ It should be noted that ACTis about 3-4 times larger than A d for each DNA sample. Although both A d and Aa tend to converge to a constant level, it is difficult to confirm if either or both of them approach zero at impractically high salt concentrations. If the electronic or covalent polarizability anisotropy makes a small but finite contribution to field orientation, then A d # 0 even at much higher salt concentrations. Figure IOa,b shows that the dependence of A d and A0 on molecular weight and ionic strength may be expressed empirically as ha’ = KI(Mw)”l and
A U = K2(Mw)Y1
The proportionality between the ionic polarizability and the chain length of polyelectrolyte has been discussed in a number of studiess Depending on the mechanism of induced dipole moment, some workers proposed that the polarizability is proportional to the third power of molecular length,5253whereas others Kikuchi and proposed the second power pr~portionality.~~-~~*~* Yoshioka showed that the exponent to the chain length is 2 at low fields but transforms to 1 at high fieldse8 More interestingly, Sakamoto et a1.55956demonstrated in their dielectric dispersion measurements of DNA that the root-mean-squared dipole moment is proportional to the 1S t h power of the length, while Rau and C h a r n e ~calculated, ~~ on the basis of the ion atmosphere polarization m e c h a n i ~ mthat , ~ ~ the ionic polarizability is proportional approximately to the 1.8th power of the chain length. This subject still remains open to the further investigation. Critical Field Strength. A unique feature of the SUSID orientation mechanism resides on the concept of saturable induced ionic dipole moment AaE, which behaves just like the permanent dipole moment AoEo at applied electric fields higher than the critical field strength Eo. Figures 9c and 1Oc show the dependence of Eo values on salt concentration and on molecular weight, respectively. The critical field increases with increasing ionic strength, Le., the saturation of the moment AuE tends to occur at a higher field strength, but it decreases with increasing molecular weight of DNA (Figure l&). It is interesting to note that a qualitatively similar relationship exists between the number of DNA base pairs and the Eo value which was defined by Diekrnann et al.12J6 Although the complete saturation at a single field strength is an oversimplified idea, the saturation of the saturable electric moment seems to complete below 4-5 kV/cm at lower ionic strength, but Eo values shift upward at higher added salt concentrations, probably because of the increased exchange of counterions bound on the DNA surface with free sodium ions in the bulk solution through the electric double layer. The nature of the dependence on ionic strength is yet to be resolved in the future work. The introduction of a single critical field for a given DNA solution is undoubtedly artificial, such critical fields should spread over some confined range.33 The tractability of any mathematically rigorous orientation functions would be limited, once the blurred critical field range is taken into account. Saturated Ionic Dipole Moment. Figure 9d shows the dependence of the saturated induced (or permanent-like) ionic dipole moment AaEo on added salt concentration; AaEo is linearly proportional to the logarithm of the added salt concentration, -In (C,), in the (0.1-4.1) mM range for rodlike DNA. On the assumption that the saturable ionic moment probably vanishes at high ionic strength (Figure 9d), the dependence may be expressed as AaEo = k( 1 - u In [C,])
(7)
where k and u are constants which depend on the molecular weight of DNA. Figure 10d shows the molecular weight dependence of AaEo for four rodlike DNA samples. This dependence may be expressed as
(6)
where ( K l ,u I ) and (K2, u2) are functions of Cs;u I varies from 1.51 (0.13 mM NaCI) to 1.14 (4.1 mM NaCI), while u2 varies from 1.36 to 0.499. The plots of In ( A d ) ,and also In (Au), versus In (M,)are linear for all DNA samples in the 0.1 3-4.1 mM range. Since the contour length of rodlike DNA is proportional to the molecular weight or the number of base pairs, the results in Figures 9 and I O lead to the conclusion that the polarizability anisotropies ( A d and An) of double-helix DNA is proportional approximately to the 15th power of the contour length at low salt concentrations but the exponent is lowered to either the first power ( u ~ or ) the square root ( v 2 ) at high ionic strengths. (49) Jolly, D.; Eisenberg, H. Biopolymers 1976, 15, 61-95. (50) Hagerman, P. J . Biopolymers 1981. 20. 1503-1535. (51) Elias. J . G.:Eden, D. Biopolymers 1981, 20, 2369-2380.
Yamaoka and Fukudome
where the exponent ug is again a function of added salt concentration, being much less than unity (u3 < 1) in the molecular weight range of (7-25) X IO4. In the low ionic strength region, AuEo appears to be linearly proportional to the 0.46th power, or approximately the square root, of the contour length, but it is nearly independent of the length in the high ionic strength region. On (52) Hornick, C.; Weill, G. Biopolymers 1971, IO, 2345-2358. (53) Weill. G.; Hornick, C. In Polyelerrrolyres; Selegny, E., Ed.; Reidel: Dordrecht, Holland, 1974; pp 227-284. (54) Charney, E. Biophys. Chem. 1980, 11, 157-166. (55) Sakamoto, M.; Hayakawa, R.; Wada, Y . Biopolymers 1978, 17, 1507-15 12. (56) Sakamoto, M.; Hayakawa, R.; Wada, Y . Biopolymers 1979, 18, 2169-2782. ( 5 7 ) Rau. D. C.; Charney, E. Biophys. Chem. 1981, 14, 1-9.
Electric Dichroism of Rodlike DNA this basis, the effect of the length distribution or polydispersity of a rodlike DNA sample on the SUSID orientation function would not be too serious, though it was derived for a monodisperse system. It is possible to derive the SUSID function for the polydisperse system,59now that the dependence of electric moments on the chain length is revealed. The effect of polydispersity on the steady-state dichroism data would also not be too serious,59 since the present DNA samples are all fractionated (cf. Table I). Furthermore, it is known that the polydispersity of molecular weights in a given polymer sample hardly affects the optical property such as (AA/& if the rodlike molecules are long and thin.’ Finally, the magnitude of AuEo deserves a comment. It amounts to several thousand debyes, depending on both ionic strength and molecular weight (cf. Table 11). It is not a mere coincidence that these AaEo values are in good agreement with the permanent or pseudopermanent dipole moments previously assigned to DNA in ionic solutions from the analysis of the steady-state dichroism or birefringence versus E2 curve on the basis of the classical orientation f u n c t i ~ and n ~ the ~ ~modified ~ ~ ~ ~funct i ~ n or, ~from ~ dielectric dispersion measurement^.^^.^^ This is probably because the saturated induced ionic dipole moment behaves as if it were a permanent dipole moment, by which the DNA molecule is oriented. This would be the case if attempts were made to fit the experimental steady-state dichroism or birefringence data to the theoretical curves only at field strengths higher than the critical field Eo (cf. Figure 7 of refl). In fact, the theoretical S U S I D orientation function is nearly superimposable on the classical orientation function above Eo,if the parameters are adjusted.’
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990 6903 approximation, to estimate ( M I A ) ,values. (6) The electrooptical properties and the conformation of a wide variety of DNA, polynucleotides, and other related biopolymers will be elucidated henceforth by the quantitative analysis of the steady-state electric dichroism data with the aid of the SUSID orientation function.
Appendix Integrals 11-14in eq 2 are explicitly given with the presently revised notations as follows:L
I, =
Conclusions
The present paper clarified the following points. (1) The SUS I D orientation function can be used successfully to evaluate the electrooptical quantities of rodlike DNA in aqueous solutions by fitting the experimental data to the theoretical function not only in the medium-to-high electric field region but also in the extremely low field region. (2) By this curve fitting, the intrinsic reduced dichroism ( A A I A ) , at 260 nm was estimated with the least ambiguity (a graphical extrapolation to infinitely high fields could thus be avoided). (3) Values of ( A A / F I )remain ~ nearly constant at -1.06 f 0.03 regardless of the concentration of added Tris/ HCI/NaCI and the molecular weight of DNA, indicating that the field-on conformation of DNA is unaltered by these factors. (4) Once the saturable ionic dipole moment AuE is saturated at the critical field strength Eo,it behaves like the permanent dipole moment AoEo at the higher fields. This permanent-like moment predominates in the electric field orientation of DNA, the magnitude ranging between 6400 and 1600 D. (5) A theoretical support is given for the curve fitting of the dichroism data with the classical orientation (P(/3,y),as a reliable and convenient (58) Manning, G. S. Biophys. Chem. 1978, 9, 65-70. (59) Yamaoka, K.; Fukudome, K. Bull. Chem. SOC.Jpn. 1983,56,60-65.
where u = cos 8 , 8 being the angle between the longitudinal axis of agolymer and the direction of an applied field, and F(x) = J”Sef dt.
