J. Phys. Chem. 1992, 96, 7 131-7 136 of stretching, scissoring, and wagging modes of water between DPDM-H20 and DPDM.'/2H20 arise from the difference of hydrogen bond strengths, while the frequencies of the rocking, overtone, and combination modes are affected by a collision interaction Occurring in a pairs of water molecules in DPDM-H20. Acknowledgmenr. I thank Professors T. Takenaka and S. Hayashi and Dr. J. Umemura of this laboratory for their invaluable guidance and encouragement during this work. I am grateful to Professor T. Kobayashi of this institute for the use of the X-ray diffractometer and to Professor K. Machida and Dr. T. Taga of the Faculty of Pharmaceutical Science, Kyoto University, for the crystal structure analysis.
References and Notes (1) Kimura, N. J. Phys. Chem. 1991, 95, 3527. (2) Taga, T.; Machida, K.; Kimura, N.; Hayashi, S.; Umemura, J.;
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Takenaka, T. Acta Crystallogr. 1986, C42, 608. (3) Malliaris, A.; Christias, C.; Margomenou-Leonidopoulou,G.; Palm, C. M. Mol. Crvst. Lia. Crvsr. 1982. 82. 161. (4) Ichida, K.;Ku;oda,Y.; Nakamura, D.; Kubo, M. Spectrochim. Acra 1972,28A, 2433. (5) Lutz, H.D.; Klu~pel, Pobitschka. W.: Baasner. B. Z . Natur.. H.-J.: jorsch. 1974, 298, 723. (6) Eriksson, A.; Lindgren, J. J. Mol. Strucr. 1978, 48, 417. (7) Tayal, V. P.; Srivastava, B. K.; Khandelwal, D. P.; Bist, H. D. Appl. Spectrosc. Rev. 1980, 16, 43. (8) Lutz, H.D. Srruct. Bonding 1988, 69, 97. (9) Bonner, 0. D.; Choi, Y. S.J . Phys. Chem. 1974, 78, 1723. (10) Giguere, P. A.; Harvey, K. B. Can. J . Chem. 1956, 34, 798. (11) Bertie, J. E.; Whalley, E. J . Chem. Phys. 1964, 40, 1637. (12) Brink, G.; Falk, M.Can. J . Chem. 1970, 48, 2096. (13) Thomas, G. H.;Falk, M.;Knop, 0. Can. J . Chem. 1974,52, 1029. (14) Chidambaram, R.J . Chem. Phys. 1962, 36, 2361. (15) Taga, T.; Machida, K.; Kimura, N.; Hayashi, S.; Umemura, J.; Takenaka, T. Acra Crystallogr. 1987, C43, 1204. (16) Falk, M.; Knop, 0. In Water: A Comprehensive Treaties; Franks, F., Ed.; Plenum Press: New York, 1973; Vol. 2, Chapter 2.
Electric Field Orientation of Nucleic Acids in Aqueous Solutions. 3. Non-Kerr-Law Behavlor of High Molecular Weight DNA at Weak Fields As Revealed by Electric Birefringence and Electric Dichroismt Kiwamu Yamaoka,* Kiyohiro Fukudome, and Koichiro Matsudat Faculty of Science, Hiroshima University, 1-3- 1 Kagamiyama, Higashi-Hiroshima 724, Japan (Received: March 30, 1992)
In order to ascertain the non-Kerr-law behavior of a high molecular weight (M,= 4.4 X lo6) calf thymus DNA (hDNA), the steady-state electric birefringence (EB) at 535 nm and electric dichrosim (ED) at 260 nm were measured in aqueous solutions at 7 OC in a range of applied electric field (E) up to 10 kV/cm, with emphasis on the effect of counterions on the fieldstrength dependence. In the low-field region, the EB and ED values of hDNA with the sodium counterion, together with other additives, did not obey the Kerr law, being proportional to the first power of E, whereas those values of hDNA with the divalent magnesium and calcium counterions obeyed the Kerr law, first being proportional to the second power of E and then transforming to the first power with an increase in field strength. This peculiar behavior of field orientation could be explained with the recently developed theoretical SUSID orientation function. Comparison between the experimental data and theoretical SUSID curva, plotted against E on a double-logarithmic scale, revealed that the saturable ion-induced dipole moment (AuE) is saturated at very low critical electric fields (EoC 100 V/cm) and, thereafter, behaves like a permanent dipole moment ( A d o ) for Na-hDNA, whereas the AaE moment is saturated at much higher Eo values (Eo> 2 kV/cm) for Mg- and Ca-hDNA.
Introduction In 1880, J. Kerr concluded that the optical phase retardation of glass was proportional to the second power of the applied electric field strength E (the famous Kerr law, Le., the E2 dependence).' Since then, this electrooptic Kerr effect has been verified for a great number of gases and organic liquids.2 For nonionic macromolecular solutions, theories predict that the steadystate electric birefringence (EB) and electric dichroism (ED) are proportional to the second power of E at weak fields, if a solute polymer possesses either, or both, of the permanent dipole moment I.( and the electronic (or covalent) polarizability anisotropy Act, regardless of the shape of the solute, e.g., an axially symmetric ~ y l i n d e r , ~ a disk4a flexible chain,+' or an asymmetric ellipsoid! The electric fwld orientation of these molecules is described by the so-called classical orientation f u n c t i ~ n ,whose ~ , ~ mathematical expression starts from the E2term at weak fields. This Ez dependence of the electrooptic properties at wegk fields has long been established experimentally for a large variety of rigid or flexible polymer^.^."^ Some ionized polymers of relatively small molecular sizes have also been confirmed to obey the Kerr law, if a sufficient amount 'Part of this work was submitted by K. Matsuda in partial fulfillment of requirements for the D.Sc.degree. Part 2 of this series, ref 26. ;Present address: Horiba, Ltd., Kyoto, Japan.
of salt was added to the solution. Examples for the E2 dependence are some proteins and polypeptide~,'~J~ double-stranded helical DNA,'"20 and other polynucleotides.21.2ZHowever, some groups of workers have insisted on the dependence of ED on the first power of E (the E' dependence) for small-size DNA on the basis either of the ion-flow orientation model23 or of the saturated induced-momentmodeLZ4 Recently, the field dependence of sonicated DNA samplts of smaller molecular weights was thoroughly examined over a wide range of field strength (0.2 IE I22.4 kV/cm) at various ionic strengths, with special emphasis on the weak-field behavior of steady-state values of EB and ED.25,26 These studies confirmed beyond doubt that the Kerr law holds for all those samples at extremely low fields, even if the ionic strength was as low as 1.3 X lo4 and the molecular weights up to 3 X los. The experimental data were analyzed with the theoretical SUSID orientation function, which was newly proposed on the basis of the orientation mechanism of saturable and unsaturable induced ionic dipole moments. Hence, the E2 dependence of EB and ED now seems to be an accepted fact. Nonetheless, some serious, though occasional, studies have disclosed an apparent breakdown of the Kerr law; the steady-state EB values were nearly proportional to the first power of E.27-32 This peculiar phenomenon was observed mostly for ionized polyelectrolytes of high molecular particularly for DNA
0022-3654/92/2096-7131$03.00/0 0 1992 American Chemical Society
7132 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992
and its dye c o m p l e x e ~ . ~ ~Yamaoka - ~ ’ ~ ~ ~and Charney reported a careful work on a high molecular weight DNA (hDNA) and its methylacridinium dye complex by means of EB and ED.3S Contrary to the result for the corresponding small-size systems,17 they found that both EB and ED values are proportional to the first power of field strength over a wide range (0.7 I E I8 kV/cm), apparently disobeying the Kerr law. They also verified that the parallel specific dichroism M I I / Aequals the perpendicular specific dichroism M J A multiplied by a factor of -2 for both samples. This is the general relationship that should hold, if no electrochromic effect, Le., the field-induced structural change, is i n v o l ~ e d . Thus, ~ ~ . ~ both ~ hDNA and its dye complex in salt solutions were concluded to remain unaffected by applied electric fields. The long-puzzling problem is now resolved experimentally and theoretically in the present work. We will report an apparent linear field dependence of the data of EB and ED for a high molecular weight DNA sample under various conditions, and we will analyze the results by utilizing the recently proposed SUSID orientation function, which contains both El and E2 terms at weak field^.^^^^^ By changing its counterions from monovalent to divalent species, we can observe experimentally that the field strength dependence of the EB and ED of hDNA becomes either linear or quadratic in the measurable low-field region.
Yamaoka et al.
externally applied electric pulse field, A is the isotropic absorbance in the absence of the field, 6 is the angle between the direction of an optical transition moment and the molecular axis of symmetry, and CP ( E ) is the orientation function, by which the average degree of orientation (or alignment) of solute molecules is specified at a given field strength E. The importance of a general relationship, U I I / A= -2AA,/A, cannot be o v e r e m p h a s i ~ e d ; ~ ~ * ~ ~ ~ ~ ~ indeed, it was found to hold in the present work.
Theoretical Section Although many efforts have been directed toward the goal, as reviewed comprehensively in a recent no complete theory has yet been developed for the field orientation of ionized polyelectrolytes such as nucleic acids and protein^.^^ Among the existing theories, some orientation functions indeed show the first-order dependence on applied field strength a t weak fields,23~24~44-46 but the agreement between experimental data and theoretical curves is rather poor.25 Considering these past developments, we recently proposed the SUSID orientation function, CP(p,p,y’), which is given as25,26 (3)
together with the following parameters: Experimental Section AuE& p = y&7*2 = AuE2 Materials. A high molecular weight ( a . 4.4 X 106) calf thymus ps = 2y&* = kT ’ 2kT ’ DNA (hDNA) sample was purchased from Worthington Biochemicals. The protein content of a purified sample was less than 1 wt All other chemicals were of reagent grade. The stock DNA solution (ca. 1 mg/cm3) containing 1 mM NaCl was diluted where Au - a l l )is the saturable ionic polarizability anand dialyzed at 4 OC for 48 h or more against distilled water isotropy ( ~ and 7 ~u1, ~ are the polarizabilities parallel and percontaining NaCl ( 5 L) at a desired ionic strength (hereafter pendicular to the symmetry axis (3-axis)), Aa’ is the unsaturable denoted as Na-hDNA). In order to substitute the sodium ionic and electronic anisotropy, k is the Boltzmann constant, T counterion by the divalent magnesium (or calcium) ion, a 1 mM is the absolute temperature, and Eo is the critical field strength. NaC1-containing Na-hDNA solution was successively dialyzed According to the SUSID mechanism, the electric moment of a against 1 M MgC12 (1 L) for 2 days, against 0.1 M (1 L) and rodlike nucleic acid polymer consists of the saturable induced ionic then 10 mM MgC12(1 L) for 1 day each, and finally against 0.333 dipole moment AuE, which is saturated at Eo and thereafter ( E mM MgC12(2 L) for 2 days (hereafter denoted as Mg-hDNA). 1 Eo) behaves as a permanent-like dipole moment AuEo, and the The Ca-hDNA solution was prepared from CaC12 in the same unraturable induced dipole moment A d E , which is not saturated way as Mg-hDNA. Other details for the preparation of DNA a t any experimentally attainable field strengths. Integrals I , to solutions in the presence and the absence of additives were given Z4 in eq 3 are complex expressions, which are not recited here since e l ~ e w h e r e . ~The ~ - ~concentration * and the hypochromicity of the they were originally derived in a previous paper25 and again DNA solution were determined in a standard manner.17,37,38 in the Appendix of ref 26. For the case that E* < Measurements. An electric birefringence (EB) a p p a r a t u ~ ~ . ~ ~summarized -~~ 1, Le., no saturation of the moment AuE occurs at any fields, the and an electric dichroism (ED) a p p a r a t ~ s ” ~ ~ ’were J ~ 3designed ~~ orientation function is reduced to ( u cos and constructed in our laboratory. The steady-state EB signal (An) was measured at 535 nm and at 7 OC under nitrogen gas @(P*T’) = flush with a quarter-wave plate in the optical system. An was (P + Y)‘12 expressed in terms of the optical phase retardation 6 (=2lrdAn/X), ( p + y’)ep+Y’- ( p + y ’ ) 1 / 2 x e“*du where d is the path length of a Kerr cell, which was either 2.0 - (5) (P + Y ’ P j cm (the electrode gap 0.33 cm) or 1.0 cm (the gap 0.207 cm), (p + y f ) 3 / 2 1 eu2du and X is the wavelength in vacuo. The steady-state ED signal was 0 measured at 260 nm under the same condition as EB. For diExpressions 3 and 5 may be expanded in a power series of field chroism, both the specific parallel ( U I , / A )and the specific strength in the extremely low-field region. If the saturation of perpendicular dichroism (M,/A)17935were measured separately. the saturable moment AuE occurs even at extremely weak fields Electric pulses of 1-0.5 ms were usually applied at least twice to (E* > l ) , eq 3 is given as each DNA solution in the Kerr cell; any irreversible EB or ED signals were rejected. 2Y&* (2r&*)2 27’ *(-l&*
