J. Phys. Chem. B 1997, 101, 837-845
837
A Comparative Study on the Structure of Double-Stranded Antiparallel Poly(riboguanylic acid)‚Poly(ribocytidylic acid) and Poly(deoxyriboguanylic acid)‚Poly(deoxyribocytidylic acid) Helices in Solution by Pulsed Electric Linear Dichroism† Kiwamu Yamaoka,* Yutaka Yamamoto, Yoshimasa Fujita, and Noriyuki Ojima Department of Materials Science and Graduate Department of Gene Science, Faculty of Science, Hiroshima UniVersity, 1-3-1 Kagamiyama, Higashi-Hiroshima 739, Japan ReceiVed: August 21, 1996; In Final Form: NoVember 7, 1996X
The sonicated and fractionated poly(rG)‚poly(rC) (I) and poly(dG)‚poly(dC) (II) samples mostly with Na+ counterions were studied, on a comparative basis, to determine the spatial arrangement of the constituent G and C bases with respect to the double-stranded helical axis in ionic aqueous solutions. The reduced electric linear dichroism, ∆/, was measured at 7 °C in 1.5-24 kV/cm field strength and 300-190 nm wavelength regions. By analyzing the field strength dependence of observed ∆/ values with theoretical orientation functions, the saturated reduced dichroism, (∆/)s, at 260 nm was evaluated to be -0.96 ( 0.02 for I and -0.93 ( 0.01 for II. The electric linear dichroism (ELD) spectra of these duplexes are very close to each other, being undulatory, but not constant, in the whole wavelength region. The (∆/)s values are never as high as -1.5, indicating that the optical transition moments of the nucleic acid bases responsible for the UV absorption bands are not normal to the helix axis. By analyzing the ELD spectra with a newly developed technique, the inclination angle R, the roll angle θR, and the tilt angle θT were evaluated for the indiVidual bases. The most likely values are 24°, 1°, and 24° for rG; 26°, 1°, and 26° for rC in the rG‚rC base pair; 26°, 2°, and 26° for dG; 29°, 3°, and 29° for dC in the dG‚dC pair. Thus, the base pairs are only slightly bent and propeller twisted, being nearly coplanar. Both duplexes were concluded to exist in the same conformation and to belong to the same A-form family in solutions in spite of the different sugar structure, contrary to X-ray results in the solid state.
Introduction In a comprehensive review article, pulsed electric linear dichroism (hereafter abbreviated as ELD) has been shown to be a powerful technique to clarify the secondary structure of biopolymers, in particular DNA and related polynucleotides, in aqueous ionic solutions.1 This technique was also compared with other physicochemical methods for solution conformation.2 An earlier ELD work was initiated in our laboratory on sonicated and rodlike DNA and its dye complex in 1981,3 although three major problems remained to be resolved for the quantitative analysis of the experimental data. Since then, efforts were made to solve these problems for structural determination of polynucleotides. The first problem was how to evaluate the saturated or (intrinsic) reduced dichroism of polyions like DNA and its synthetic analogues at infinitely high fields from the field strength dependence of observed reduced dichroism values at a given wavelength. This problem was resolved by introducing a new set of theoretical SUSID orientation functions based on the mechanism of saturable and unsaturable induced dipole moments.4 The second one was how to treat the polydispersity of molecular weight or chain length of the DNA preparations. This problem was solved by the sonication and fractionation techniques in combination with the determination of the molecular weight and the distribution even for minute samples by the GPC/LALLS (gel permeation chromatography/low-angle laser light scattering) method.5 The third one was how to analyze the observed ELD spectrum for the structural parameters. This problem was resolved by developing an analytical procedure to evaluate the parameters, which specify the ar-
rangement of individual bases with respect to the axis of the double- or triple-stranded helix.6 Since DNA contains four bases or two base pairs, the ELD data are complex.3 Although the elucidation of the secondary structure of DNA in solution is the final goal of our pulsed ELD study, much simpler constituent duplex polymers should first be worked out to gain insight into the structural features. With the above problems resolved for quantitative analysis of ELD results, two structural studies are recently carried out with the following well-characterized rodlike samples in aqueous ionic solutions on a comparative basis. One study was on the double-stranded poly(rA)‚poly(rU) and poly(dA)‚poly(dT),7 which were said to belong to the A and B′ forms, respectively,8-10 and the other was on the triple-stranded poly(dA)‚poly(dT)‚ poly(dT) and poly(rA)‚poly(rU)‚poly(rU),11 both of which were proposed to be in the A′ forms from X-ray diffraction studies.8,12 In the present work, the remaining two antiparallel doublestranded DNA analogues, poly(rG)‚poly(rC) and poly(dG)‚poly(dC), were studied by the same pulsed ELD method as above. These duplexes have been studied less extensively than their A‚T and A‚U base-paired counterparts, but an X-ray work reported that poly(dG)‚poly(dC) undergoes an A to B transition with the change in relative humidity, just as the natural DNA.13 By measuring the electric field and wavelength dependence of carefully-prepared and fractionated samples in the UV region, the observed data were analyzed to evaluate the roll and tilt angles of the indiVidual bases in the duplexes with the preceding procedure.6,7 Experimental Section
* To whom correspondence should be addressed. † ELD Studies of Nucleic Acid Structure 3. Part 2 is ref 7. X Abstract published in AdVance ACS Abstracts, January 1, 1997.
S1089-5647(96)02590-4 CCC: $14.00
Materials. A sample of poly(riboguanylic acid), potassium salt (hereafter abbreviated as (rG)n), with a molecular weight © 1997 American Chemical Society
838 J. Phys. Chem. B, Vol. 101, No. 5, 1997
Yamaoka et al.
TABLE 1: Characterization and Conditions of Sonicated and Fractionated (rG)n‚(rC)n and (dG)n‚(dC)n Duplexes Used for Electric Dichroism Measurements duplexes
Mwa/g‚mol-1
Mw/Mna
〈bp〉wb
τw/µs
Lwc/Å
h/Å
counterions
Isd/10-3
pHe
(rG)n‚(rC)n F1
185000
1.58
266
7.8
608 (572) 547 (512) 511 (478) 476 (444)
2.3 (2.2) 2.1 (1.9) 1.9 (1.8) 1.8 (1.7)
Na+
0.8
7.4
Na+
1.2
7.8
Mg2+
0.8
7.8
Mg2+
1.2
7.9
Na+
1.0
7.4
Na+
1.0
7.4
Na+
1.0
7.4
6.0 5.1 4.3 (dG)n‚(dC)n F1
1.1
8.0
F2
4.5
F3
4.3
643 (618) 516 (494) 508 (485)
a The weight-average molecular weight, Mw, and the degree of polydispersity in terms of Mw/Mn, as determined by the GPC/LALLS method.14 A likely value of 1.1 was assumed for (dG)n‚(dC)n with due consideration of the (dA)n‚(dT)n sample in the previuos work.7 b The weight-average number of base pairs defined as Mw divided by the residue weight of a base pair (694.3 g‚mol-1 for an rG‚rC and 662.3 g‚mol-1 for a dG‚dC as the disodium salt). c The weight-average length of a helix was calculated with an assumed diameter of 20 or 26 Å (in parentheses). d The ionic strength is expressed on the basis of the total ionic species present in a solution including the buffer reagent and counterion. e pH was adjusted with NaH2PO4/Na2HPO4 for Na(rG)n‚(rC)n and with MgCl2/Tris/HCl for Mg(rG)n‚(rC)n, while it was adjusted with 0.1 mM NaCl/Tris/HCl for Na(dG)n‚(dC)n.
higher than 150 000, lot no. 18F-4026, was purchased from Sigma Chemical Co. A sample of poly(ribocytidylic acid), sodium salt (hereafter abbreviated as (rC)n), with a sedimentation coefficient s020,w of 8.7, lot no. S-301, was supplied from Yamasa Shoyu Co. (Choshi, Japan). In order to prepare a double-stranded (rG)n‚(rC)n helix sample, both (rG)n and (rC)n samples (ca. 2 mg/mL in 0.1 M NaCl, 200 mL each) were mixed slowly and synchronously at 1:1 molar ratio (in terms of the mononucleotide concentration) with stirring, and then a sodium phosphate buffer was added to this mixture to adjust the pH of the solution to 7.8, the total ionic strength (abbreviated as Is) being kept at 0.151. The solution was incubated at 37 °C for 115 h prior to sonication.14,15 This annealing process was needed to prepare a stable double-helical sample free from precipitates or triple-stranded helix. A double-stranded poly(deoxyriboguanylic acid)‚poly(deoxyribocytidylic acid) sodium salt sample (hereafter abbreviated as (dG)n‚(dC)n), lot no. 24HO8671, was purchased from Sigma Chemical Co. A (dG)n‚ (dC)n solution was prepared for sonication, by dissolving the commercial sample (ca. 1.5 mg/mL, 15 mL) in 0.2 M NaCl. The concentrations of all duplex samples were determined photometrically in terms of mononucleotide units with a molar absorption coefficient in mol-1 dm3 cm-1 of 7490 at 260 nm for (rG)n‚(rC)n16 and 7060 at 260 nm for (dG)n‚(dC)n.17 Sonication and Fractionation. In order to prepare rigid and rodlike samples with relatively uniform molecular weights for ELD measurements, the above duplexes were subjected to sonication, as described previously.4,5,14 Sonication was carried out in an iced bath with two Tomy Seiko sonicators under helium gas atmosphere; a Model UR-200P sonicator with a standard tip attached to the horn at a power level of 200 W for 40 burst-bubbling cycles (totally 20 min, one complete cycle with 30 s burst and 5 min bubbling of helium gas) for the stock (rG)n‚(rC)n solution in a three-way rosette vessel (100 mL each)14 and a Model UD-200 sonicator with a microtip at a power level of 97 W for 40 cycles (totally 20 min) for the stock (dG)n‚(dC)n solution in a polypropylene centrifuge tube (7 mL each).5,7 In order to prepare closely monodisperse samples, the sonicated (rG)n‚(rC)n solution was fractionated to five fractions (F1-F5) by successive precipitational fractionation with acetone as the precipitant.14 The sonicated (dG)n‚(dC)n solution was fractionated through a gel permeation chromatographic column
(because of a minute amount), which was packed with Sephacryl S-500HR gel, and three major fractions (F1-F3) were separated. Each sonicated duplex solution was dialyzed exhaustively against 0.2 M NaCl containing disodium ethylenediaminetetraacetate (Na2EDTA) before or after fractionation, to remove metal-ion contaminants. Fractions used for ELD measurements are given in Table 1, together with the data pertinent to the present work. Absorption and ELD Measurements. Sample solutions for ELD measurements were further dialyzed against either NaCl or MgCl2 at appropriate concentrations buffered with sodium phosphates or Tris/HCl, as given in Table 1, in order to adjust the ionic strength to low levels and to examine the effect of counterion species. Both (rG)n‚(rC)n and (dG)n‚(dC)n solutions were found to be stable at a pH range 7-10 and between 7 and 40 °C for the Na+ counterion but between 7 and 80 °C for the Mg2+ counterion. By the optical titration method, these samples were verified to exist solely in the double-stranded conformation without the presence of triple-stranded helices under the present conditions.14,15 The absorption spectra were measured with a Shimadzu UV-250 spectrophotometer at 7 °C. Electric dichroism was measured at 7 °C on two apparatus, which can detect both parallel (∆A|) and perpendicular (∆A⊥) dichroism signals separately. Since the details were described in previous papers,3,7 no repeated citation is necessary here. Steady-State Electric Dichroism. The reduced electric linear dichroism (∆A/A) of a solution is defined as3,7 ∆A/A ) (A|E - A⊥E)/A or ∆/ ) (|E - ⊥E)/, where ∆A| ) A|E - A or ∆| ) |E - , expressed in terms of absorbances or molar absorption coefficients in the presence and in the absence of the electric field for the monochromatic light beam linearlypolarized parallel to the field direction, ∆A| ) ∆|/Cpd, where Cp is the mononucleotide concentration of a polymer solution and d is the path length of a Kerr cell. Similarly for the perpendicularly polarized light, the difference is defined as ∆A⊥ ) A⊥E - A or ∆⊥ ) ⊥E - . Since a polynucleotide chain contains some bases, each of which consists of several overlapping absorption bands, the observed absorption spectrum is a composite of a number of these partial bands. Then, the reduced dichroism of a solution, which contains cylindrically-symmetric rigid double-stranded helices, at a given wavelength λ and in an orienting electric field E is expressed as6,7
Electric Dichroism of (rG)n‚(rC)n and (dG)n‚(dC)n
( ) ∆
∆ )
Φ(E) )
J. Phys. Chem. B, Vol. 101, No. 5, 1997 839
∑j ∑k j,k[(∆/)s]j,k
s
Φ(E)
∑j ∑k
(1)
j,k
where (∆/)s is the saturated or intrinsic reduced dichroism at infinitely high field strengths, j,k is the molar absorption coefficient of the jth partial band of the kth base, and Φ(E) is the orientation function, which gives the average degree of orientation of solute polymers at a given field strength E, and should be independent of wavelength. Saturated Reduced Dichroism. The saturated reduced dichroism in eq 1 is expressed as follows:6,7
j,k(ν) (3 cos2 θj,k - 1) ∑ ∑ 3 j k
( ) () ∆
)
s
2
∑j ∑k
j,k(ν)
() 3
)
2
×
∑j ∑k j,k(ν)[3(-cos θTk sin θRk sin ξj,k + sin θTk cos ξj,k)2 - 1] ∑j ∑k j,k(ν) (2) where θj,k is the angle between the direction of the jth optical transition dipole moment of the kth base and the molecular orientation axis, which should coincide with the helix (z) axis of a rigid rodlike duplex, and related with the roll angle θR and the tilt angle θT of a planar base, which possesses only in-plane π f π* transition moments with no out-of-plane n f π* transition moment; the angle θ is given as6,7
cos θ ) -cos θT sin θR sin ξ + sin θT cos ξ
(3)
ξ is the angle between a transition moment, projected onto the base plane, |mb|, and the roll (y) axis, the sign being taken to be positive for clockwise rotation from the positive y axis around the z axis, as indicated in Figure 1a. The signs of θR and θT are taken to be positive for clockwise rotation, as viewed from the negative to positive directions of the x (x′) and y axes in Figure 1b. The angle ξ is related to the the angle ζ between the direction of an in-plane transition moment and the reference axis of a base.6,7 The most probable values and signs of angles θR and θT may be determined, as cited in the next heading. An important quantity is the angle Rk in Figure 1b, the angle between the z axis and the normal (the z′′ axis) to the plane of the kth base, that describes the inclination of the plane of individual base, G or C, with respect to the axis of the (rG)n‚(rC)n or (dG)n‚(dC)n helix. This angle can be evaluated from angles θR and θT:
cos |Rk| ) cos θRk cos θTk
Figure 1. Coordinate system of a base for rotational operations. (a) The base plane lies on the Cartesian coordinates (x,y,z) with the x axis as the tilt axis and the y axis as the roll axis, prior to the rotational operations (the initial state). (b) The coordinates of the base (x,y,z) is first rolled around the roll axis by θR to the new (x′,y′,z′) coordinates (the intermediate state) and then tilted around the tilt axis by θT to the (x′′,y′′,z′′) coordinates (the final state). The z′′ axis is normal to the rolled and tilted base plane. The thick double-headed arrow denotes the direction of a transition moment m. R is the inclination angle between the helix axis (z) and the z′′ axis. Single-headed arrows of angles ξ, ψ, θR, and θT denote the positive direction of rotation.
(4)
The reverse calculation to estimate the tilt and roll angles from the inclination angle is, however, difficult; thus, the present analytical technique is advantageous over previous ones.2,17,18 Optical Transition Dipole Moment Directions. The wavelength dependence of measured (∆/)s is simulated with the aid of eq 2, by searching iteratively for the best-fitted angles of θR and θT with reported values of ξ and trial sets of θR and θT by the nonlinear least-squares method.6,7,18 In this procedure, however, angles ξ and, hence, ζ must be known for each transition moment involved in an isotropic absorption spectrum, which is to be decomposed into the component bands of G and C. Values of ζ are selected from the literature, but they are
often contradictory, inevitably introducing uncertainties in the final results. In the present work, reported ξ values are grouped into four sets:7 set 1 from single crystal data,19,20 set 2 from stretched-film dichroism data,21,22 set 3 from theoretically calculated data,23,24 and set 4 from expediently chosen out of sets 1-3 (cf. Table 3). Figure 2 shows the directions of transition moments in these sets. The profile of an absorption band j,k in eq 2 was approximated by the Gaussian function based on wavenumbers (not wavelengths) as6,7,11
{
[
j,k(ν) ) max,j,k exp -(4 ln 2)
]}
ν-νmax,j,k δj,k
2
(5)
where j,k(ν) is the jth partial band of the kth base at a wavenumber of ν, max,j,k is the maximum absorption coefficient, νmax,j,k is the position of the band maximum, and δj,k is the halfintensity band width, i.e., j,k ) (1/2)max,j,k. An isotropic absorption band j,k(ν) was decomposed into partial bands, each being specified with a set of parameters (max, νmax, and δ). In order to remove ambiguities and to facilitate a unique deconvolution, the second-derivative spectrum, d2j,k(ν)/dν2, was utilized.6 Results and Discussion Circular Dichroism and Absorption Spectra of Duplex Samples. Figure 3 shows the circular dichroism and absorption spectra of (rG)n‚(rC)n (upper half) and (dG)n‚(dC)n (lower half) samples used for the ELD measurement. The spectra of a sonicated and precipitationally-fractionated sample of (rG)n‚ (rC)n are quite superimposable with those of a high molecular
840 J. Phys. Chem. B, Vol. 101, No. 5, 1997
Figure 2. Directions of optical transition moments of bases, guanine (G) and cytosine (C), denoted with double-headed arrows for sets 1-3 (the first, second, and third rows) reported in the literature. See text for details. Numerals in each set denote the approximate peak wavelengths in nm for the transition moments.
Figure 3. Circular dichroism and absorption spectra of (rG)n‚(rC)n in (a) and (dG)n‚(dC)n in (b) before sonication (filled circles) and after sonication and fractionation (open circles). Fractionated samples: (a) F1 and (b) F3. The pH, counterion species, and ionic strength in (a) and (b): 7.8, Na+ and phosphates, and 0.02. The molar ellipticity [θ] (deg cm2 dmol-1) in CD and the molar absorption coefficient (dm3 mol-1 cm-1) in absorption. The CD and absorption spectra were measured at 20 °C on a JASCO Model J-720 W spectropolarimeter and a Shimadzu UV-250 spectrophotometer, respectively.
weight sample not subjected to sonication. This result indicates that the optical properties and, hence, the structural features, are not affected by sonication in the molecular weight range of (20-10) × 104, as already documented for natural DNA samples.25 The (dG)n‚(dC)n samples are sensitive to pH in the neutral range, showing a minor discrepancy in both CD and absorption spectra before and after sonication, probably because of an easier protonation on cytosine residue. The sonicated and chromatographically-fractionated smaller molecular weight sample
Yamaoka et al.
Figure 4. Field-strength dependence of steady-state reduced dichroism of sonicated and fractionated Na(rG)n‚(rC)n in (a), Mg(rG)n‚(rC)n in (b), and Na(dG)n‚(dC)n in (c). Samples: (a) and (b) F1; (c) F1 (O), F2 (4), and F3 (0). Ionic strengths Is: (a) and (b) 0.0004 (O), 0.0008 (4), and 0.0012 (0); (c) 0.001 for F1-3. Solid-line curves are the best-fitted theoretical SUSID orientation functions. Arrows indicate the saturated reduced dichroism values at infinitely high electric fields. The F1 sample of Na(rG)n‚(rC)n was rather unstable at Is ) 0.0004, so that the data were given only here for reference. Insets: Low-field plots of ∆/ against E2 on an expanded scale.
exhibits the CD spectrum resembling previously reported spectra.16,17,26 Field-Strength Dependence of Steady-State Dichroism. Reduced Dichroism and Orientation Function. Figure 4 shows the field-strength dependence of reduced dichroism, ∆/, plotted against E2, for Na- and Mg(rG)n‚(rC)n in (a) and (b) and for Na(dG)n‚(dC)n in (c). The field orientation of these duplexes is more pronounced at lower ionic strengths. In all cases, dichroism values tend to be saturated but never reach a saturation even at very high fields. In the low-field region (cf. Figure 4, insets), the dichroism values are nearly proportional to the second power of field strength. Thus, the Kerr law (the E2 dependence) holds for the field orientation of the present duplexes, as observed for other double-stranded nucleic acids.4,7 It should be noted that the parallel-specific dichroism, ∆|/, and perpendicular-specific ∆⊥/, coincide with each other over the entire field strength range examined, if the latter is multiplied by a factor of -2. This fact supports the notion that the backbone conformation of the present duplexes remains unaltered by applied pulse field, as already confirmed for DNA3,4 (no electrochromic effect).27 In order to analyze the wavelength dependence of reduced dichroism ∆/, the average degree of molecular orientation in solution must be computed at a given field. For this purpose, the saturated or intrinsic reduced dichroism (∆/)s, must be known (cf. eq 1). Measurements of ∆/ values at very high fields are experimentally difficult and possibly introduce a separation of the double strands or an unexpected decline of ∆/ values. To circumvent these difficulties and to accurately evaluate the saturated value, fitting of observed ∆/ values to a set of appropriate orientation functions was recommended.4 The antiparallel double-stranded helices possess no permanent electric dipole moment, as verified by a recent reversing-pulse electric birefringence study.28 Therefore, the theoretical SUSID orientation functions4 can be employed to fit observed data, by
Electric Dichroism of (rG)n‚(rC)n and (dG)n‚(dC)n
J. Phys. Chem. B, Vol. 101, No. 5, 1997 841
TABLE 2: Saturated Reduced Dichroism, (∆E/E)s, and Weight Averages of the Electric Properties of (rG)n‚(rC)n and (dG)n‚(dC)n in Mg2+ and Na+ Solutions with the Total Ionic Strength Is at 7 °C duplexes (rG)n‚(rC)n F1(Na+) F1(Mg2+) (dG)n‚(dC)n F1(Na+) F2(Na+) F3(Na+)
Isa/10-3
(∆/)sb
〈∆R〉w/10-32F m2
〈∆σ〉w/10-32F m2
〈E0〉w/kV cm-1
〈∆σ〉w〈E0〉wc/D
0.8 1.2 0.8 1.2
-0.98 -0.98 -0.95 -0.93
0.75 0.51 0.47 0.43
5.66 3.80 3.51 3.23
2.34 2.85 2.97 3.09
3970 3250 3120 2990
1.0 1.0 1.0
-0.94 -0.94 -0.92
1.15 0.99 0.80
2.87 1.65 0.99
3.28 3.75 5.58
2820 1850 1660
a The sum of added salt and buffer reagent. b These values were measured at 260 nm for both duplexes. c This quantity is close, but not equal, to the weight-average ionic induced dipole moment 〈∆σE0〉w. 1 debye (D) ) 3.336 × 10-30 C m.
taking into account the polydispersity in terms of the weightaverage to number-average molecular weights, Mw/Mn, and the molecular weight distribution of the present polymer system (cf. Table 1).29 In Figure 4, the best-fitted theoretical curves are shown with solid lines, together with arrows at infinitely high fields. In each case, the agreement between measured points and calculated curves is excellent over the entire field strength region. The (∆/)s values and the electric parameters, evaluated from these curve fittings, are given in Table 2. The (∆/)s values are -0.96 ( 0.02 at 260 nm for (rG)n‚ (rC)n and -0.93 ( 0.01 for (dG)n‚(dC)n, as an average, regardless of molecular weights and ionic strengths, being slightly smaller than those found for the (rA)n‚(rU)n and (dA)n‚ (dT)n duplexes in the preceding paper.7 It should be noted that an average value of -1.06 ( 0.03 was obtained for many sonicated and fractionated DNA samples4 and -(0.8-1.05) for sonicated but unfractionated DNA fragments.30 If a base pair is normal to the axis of the double-stranded helix, the (∆/)s value should be close to -1.5.31 Thus, the 260-nm transition moment of the rG‚rC or dG‚dC base pair is probably inclined at angles of 69°-70° relative to the axis. Extrapolation of Reduced Dichroism to Infinitely High Fields. As shown above, an accurate (∆/)s value is essential for determining the inclination of bases in a nucleic acid helix. It has usually been estimated by visual extrapolation or by nonlinear least-squares fitting to the ordinate from a ∆/ vs E-1 (or E-2) plot. No matter how elaborate these extrapolation techniques may be, the extrapolated value is often over- or underestimated due to the unknown curvature of the plot.4 Figure 5 presents examples of this problem, where the observed ∆/ vs E-1 plots appear to increase monotonically in the experimentally attainable field region. In contrast, each SUSID orientation curve (solid line) levels off, showing an inflection point at higher fields, where actual measurements are rather difficult. If visual extrapolation was carried out linearly with few points at a high-field range (broken lines), the (∆/)s value would be higher than -1.1. If a smooth extrapolation is performed with a large curvature, the value would be as misleadingly high as -1.5. Thus, the importance of the curvefitting technique cannot be overemphasized here for evaluating a correct (∆/)s value. Wavelength Dependence of Saturated Reduced Dichroism. ELD Spectra. At a fixed electric field strength, values of reduced dichroism, ∆/, were measured at each wavelength (mostly at an interval of 2 nm) in the absorption region. The wavelength dependence of saturated reduced dichroism (∆/ )s, which is termed the electric linear dichroism (ELD) spectrum, was calculated from the ∆/ values according to eq 1. Figure 6 shows the ELD spectra of Na- and Mg(rG)n‚(rC)n in (a) and Na(dG)n‚(dC)n in (b), their spectra being compared with each other in (c). An apparent angle θ between a transition moment and the helix axis was calculated from the expression (∆/)s ) (3/2)(3 cos2 θ - 1) and plotted on the right-hand
Figure 5. High-field behavior of reduced dichroism plotted against E-1 of Na- and Mg(rG)n‚(rC)n in (a) and Na(dG)n‚(dC)n in (b). Samples: (a) F1 at Is ) 0.0008; (b) F1 and F3 at Is ) 0.001. Solidline curves are the same theoretical SUSID orientation function as in Figure 4. Dashed lines are drawn for the linear extrapolation of experimentally obtained high-field ∆/ values to infinitely high fields.
ordinate. The ELD spectra of (rG)n‚(rC)n are not constant but wavelength-dependent over the 300-190 nm range with distinct extrema in the 260 and 220 nm regions, being affected slightly by counterions (Na+ vs Mg2+) and ionic concentrations. This undulatory behavior of ELD spectra is also noted for all three (dG)n‚(dC)n fractions. Both (rG)n‚(rC)n and (dG)n‚(dC)n duplexes show the nearly identical and undulatory, though not superimposable, ELD spectra in spite of the possible difference in their sugar conformations. This is an unexpected result that was unraveled for the first time by electrooptic measurements. The above results lead to several important conclusions concerning the solution structure of the duplex composed of G and C. (1) Surprisingly, the arrangement of dG‚dC base pair with respect to the helix axis is practically the same as that of rG‚rC pair; hence, the solution structure of these two duplexes should be closely related to each other. (2) The planes of paired bases are not perpendicular to the axis of double helix (θ * 90°), but clearly inclined, as indicated with the angle θ; hence, the solution structure should be different from the classical B form but close to A form. (3) In spite of the difference in the chain length, the number of base pairs, or the valence of counterions, the backbone structure remains unaffected as judged from the fact that the relation ∆|/ ) -2(∆⊥/) holds over the entire wavelength region (not shown); hence, an applied
842 J. Phys. Chem. B, Vol. 101, No. 5, 1997
Figure 6. ELD spectra of Na- and Mg(rG)n‚(rC)n in (a) and Na(dG)n‚ (dC)n in (b), and a comparison of ELD spectra of these duplexes in (c). Samples: (a) F1 at ionic strengths of 0.0008 (O) and 0.0012 (4) (Na+) and 0.0008 (b) and 0.0012 (2) (Mg2+); (b) F1 (O), F2 (4), and F3 (0) at an ionic strength of 0.001. In (c) three samples are taken from (a) and (b) with the corresponding symbols.
electric field may only straighten, but not stretch or deform, the backbone chain (no electrochromism).27 (4) The observed ELD spectra are composed of a number of absorption bands of component bases (the component bands), as judged from the undulatory nature; hence, the directions of the transition dipole moments of these bands must be available for quantitative discussion for the solution structure. Deconvolution of Isotropic Absorption and ELD Spectra. Figure 7 shows the deconvolution of the observed absorption spectrum of an Na(rG)n‚(rC)n duplex in the absence of applied electric field into component bands of rG and rC (solid lines in the bottom), together with the most likely assignment to the individual bases (G1 to G5 for rG and C1 to C4 for rC) (cf. Table 3). This assignment was carried out by using the result of the deconvolution of the absorption spectra of guanosine, cytidine, and also single-stranded polynucleotides (rG)n and (rC)n.7,32 The deconvolution of the duplex was aided with the second derivative of the observed absorption spectrum (middle). By giving an appropriate value of the angle θ, as indicated with a numeral in parentheses, to each component band G or C according to the first part of eq 2, the observed ELD spectrum was simulated (top). The agreement between the observed (circles) and calculated (solid line) results is excellent in each spectrum. The principle of the deconvolution was to make the number of partial bands minimal to reproduce the observed spectrum; therefore, some partial bands are probably composed of more than one component band, but no further attempt of decomposition was made in this work. Figure 8 shows the deconvolution of the observed isotropic spectrum of an Na(dG)n‚(dC)n into nine component bands of dG and and dC and the spectrum summed up therewith. The number and assignment of individual component bands are the same as those for Mg(rG)n‚(rC)n, except for the relative intensity and peak positions (cf. Table 3). Here again, the agreement between the three observed (circles) and calculated (solid lines) spectra in the top, middle, and bottom parts is excellent over the entire wavelength. It should be noted that the angle θ for each component band always falls in the range between 61°
Yamaoka et al.
Figure 7. Deconvolution and synthesis of isotropic absorption (bottom), second-derivative (middle), and ELD (top) spectra of Na(rG)n‚ (rC)n. Sample: F1 at Is ) 0.0008. Experimental data (O) and simulated data (solid line). In the bottom, the decomposed component bands with their optical parameters in Table 3 were assigned to either guanine (G1-5) or cytosine (C1-4) with values of angle θ in degrees in parentheses, with which the ELD spectrum was synthesized (solid line in the top).
and 69°, being slightly smaller than the values (66°-70°) for Mg(rG)n‚(rC)n. The fact that these angles are much less than 90° for all component bands is a strong indication of the base inclination relative to the double-helical axis. Any further information on the detailed tilting and rolling of the plane of individual base is disclosed quantitatively with the aid of the procedure cited below. Estimation of Angle ξ and Assignment to Component Band. In order to calculate the roll and tilt angles (θR and θT) of the plane of a base in the rG‚rC or dG‚dC base pair from eq 2, the angle ζ in each base must be known. Since no data of transition moments are available for G‚C base pair in a duplex, the literature value of ζ for an isolated base was utilized. Four sets of reported angles were adopted as cited in Experimental Section. The angles, ξ, were calculated as follows: ξ ) 105° + ζ for rG and dG, where the reference axis is the line bisecting the purine ring from C(4) to C(5) atoms, and ξ ) 53° - ζ for rC and dC, where the reference axis is the line bisecting the pyrimidine ring from N(1) to C(4) atoms (the DeVoe-Tinoco convention33). For set 2, slightly modified relations were used: ξ ) 110° + ζ for guanine and ξ ) 53° - ζ for cytosine, because ζ values were defined differently in ref 22. Table 3 summarizes all necessary values of these angles, together with other pertinent optical data. EValuation of Tilt Angle θR and Roll Angle θT. Angles θR and θT for the individual bases in a base pair of rG‚rC or dG‚ dC can now be evaluated. By substituting values of ξ in sets 1-4 and a trial pair of θR and θT, together with the molar absorption coefficient of each component band, to the second part of eq 2, an experimental ELD spectrum can be simulated. This procedure is repeated, until the standard deviation between observed and simulated ELD spectra is minimized, by searching for the most probable values of θR and θT iteratively. Figure 9 shows some results of fitting to ELD spectra of Na(rG)n‚(rC)n (a) and Na(dG)n‚(dC)n (b) with ξ values in sets 1 and 3. The best-simulated ELD spectra reproduce the observed ones only
Electric Dichroism of (rG)n‚(rC)n and (dG)n‚(dC)n
J. Phys. Chem. B, Vol. 101, No. 5, 1997 843
TABLE 3: Optical Characteristics, Angle ξ, and Assignment of Component Bands to Constituent Bases in (rG)n‚(rC)n and (dG)n‚(dC)n ξa/deg duplexes (rG)n‚(rC)n rG
rC
(dG)n‚(dC)n dG
dC
λmax,j,k/nm
max,j,k/M
-1
cm
-1
δj,k/cm
-1
set: 1
290.3 (G1)b 279.2 (G2) 250.5 (G3) 237.9 (G4) 179.6 (G5) 264.0 (C1) 226.6 (C2) 212.0 (C3) 197.9 (C4)
930 2070 4470 2270 13500 5500 1470 3130 8000
1600 2200 3100 3300 6400 2900 3500 5200 6200
182c 182c 140c 30c 146c 47d 88d -23d -33d
303.5 (G1)b 287.5 (G2) 275.2 (G3) 249.4 (G4) 189.0 (G5) 263.2 (C1) 234.5 (C2) 216.7 (C3) 197.2 (C4)
200 1750 3100 5400 7000 4150 2250 3350 6600
1650 2300 2400 3400 6400 2800 3700 5200 6000
182c 182c 140c 30c 146c 47d 88d -23d -33d
2
114f 22f 28f -41e
114f 22f 28f -41e
3
4
158h 181h 181h 184h 121h 35g 64g 29g 98g
158h 182c 140c 30c 146c 35g -41e -23d -33d
158h 181h 181h 184h 121h 35g 64g 29g 98g
158h 182c 140c 30c 146c 35g -41e -23d -33d
a Letters c-h denote the previous reports for ξ values: (c) ref 19, (d) ref 20, (e) ref 21, (f) ref 22, (g) ref 23, and (h) ref 24. b Assignments to the G or C component bands in the parentheses.
Figure 8. Deconvolution and synthesis of isotropic absorption (bottom), second-derivative (middle), and ELD (top) spectra of Na(dG)n‚ (dC)n. Sample: F3 at Is ) 0.001. Other notations and symbols are all the same as in Figure 7.
Figure 9. Simulation of observed ELD spectra of Na(rG)n‚(rC)n in (a) and Na(dG)n‚(dC)n in (b) with sets 1 and 3 for angles ξ and both duplexes in (c) with set 4 for comparison. Samples: (a) F1 (O) at Is ) 0.0008 and (b) F3 (0) at Is ) 0.001. ELD spectra simulated with set 1 (s) and set 3 (-‚-) in (a) and (b), and with set 4 (s) in (c).
partly in the whole wavelength region. The main reasons for this unsatisfactory fitting are (1) values of ξ reported only for isolated bases, not for bases paired by hydrogen bonds in the hydrophobic environment of a double-stranded helix, and (2) the less unequivocal assignment of decomposed partial bands to compnent base G or C. Since the optical transition moments revealed from film dichroism work are fewer than the numbers of the partial bands, no reliable assignment of angle ξ in set 2 to partial bands was possible. Figure 9c shows simulations of two observed ELD spectra with values of ξ in set 4. Needless to say, the fitting is much improved. This result should be taken as evidence that the directions of some transition moments of isolated bases are altered upon pairing. Table 4 summarizes the angles R, θR, and θT, evaluated with angles, ξ, in sets 1-4, the first being
calculated from eq 4. Since the present procedure can yield the roll and tilt of the plane of the individual base, not being limited to the plane of a base pair, no coplanarity of the paired bases is necessary to be assumed. Values of θT and θR in Table 4 reveal that both bases, rG and rC (also dG and dC), are clearly tilted by nearly 30° and rolled at a variety of angles with respect to the axis of helix and that the plane of each base is definitely inclined at an angle of R relative to the axis. Bend and Propeller Twist of G‚C Base Pairs and Comparison with PreVious Cases of A‚U and A‚T Base Pairs. Figure 10 shows schematically the arrangements of tilted and rolled base planes in the (rG)n‚(rC)n and (dG)n‚(dC)n duplexes, as projected onto the initial state (x,y,z) (cf. Figure 1), the z-axis being taken to be parallel to the helix axis. The projected tilt and roll angles were calculated with sets 1-4 in Table 4. It is interesting to
844 J. Phys. Chem. B, Vol. 101, No. 5, 1997
Yamaoka et al.
TABLE 4: Angles r, θR, and θT for Bases in (rG)n‚(rC)n and (dG)n‚(dC)n Evaluated by Simulation of Observed ELD Spectra θR/deg
R/deg duplexes (rG)n‚(rC)n rG rC (dG)n‚(dC)n dG dC
θT/deg
set: 1
2
3
4
1
2
3
4
1
2
3
4
24 29
30 26
23 27
24 26
0 -2
29 6
7 -26
1 1
24 29
11 26
22 7
24 26
27 33
32 30
29 29
26 29
-3 0
30 7
19 -27
2 3
27 33
12 29
23 12
26 29
Figure 10. Projection of the rolled and tilted rG‚rC and dG‚dC base pair in the final state (x′′,y′′,z′′), onto the initial state (x,y,z). Being shown with numerals in degrees, the newly projected roll angle θR′ could be calculated as θR′ ) cos θR/(cos2 θR + cos2 θT sin2 θR)1/2 with values of θR and θT, evaluated with sets 1-4 (cf. Table 4). The roll angle θR′ (or θR) is taken to be positive for clockwise rotation from the negative to positive direction of the roll (y) axis (front to rear of the paper). The tilt angle θT is positive for clockwise rotation from the negative to positive direction of the tilt (x) axis. Since only two angles ξ for transition moment directions (j ) 1,2) are available in set 2 for either of two bases (k ) 1,2), the roll and tilt angles were calculated, by solving simultaneous equations as follows: cos θj,k ) -cos θT sin θR sin ξj,k + sin θT cos ξj,k (cf. eq 3).
note that those angles, calculated with ξ values in sets 1 and 4, indicate that the bending of two bases (rG‚rC or dG‚dC) at the hydrogen-bonded joint is small and, consequently, almost no propeller twist exists between the two bases (but the difference between the roll angles of paired bases does exist to some extent, if it is calculated from sets 2 and 3. The most significant finding in the present work is that the base pair in (rG)n‚(rC)n duplex shows nearly the same bending and propeller-twist arrangement as the counterpart in (dG)n‚(dC)n, in spite of the difference in chemical structure of sugars (ribose vs deoxyribose) in these two duplexes. The bend angle κ is defined as (θT of G) - (θT of C), i.e., the difference between the tilt angles of paired bases. The propeller-twist angle, θP, is defined as (θR of G) - (θR of C), i.e., the difference between the roll angles of paired bases. The angles κ and θP were calculated for four base pairs, i.e., rG‚rC, dG‚dC, rA‚rU, and dA‚dT, with the tilt and roll angles from ξ values in sets 1-4 in the present and previous studies.7 The results are given in Table 5. The propeller-twist angles of base pairs rG‚rC and dG‚dC are clearly much smaller than those of
the corresponding angles for the base pairs in (rA)n‚(rU)n and (dA)n‚(dT)n duplexes. This finding is quite reasonable in consideration of the fact that three lateral intrabase hydrogen bonds rigidly join the rG‚rC or dG‚dC base pair in these duplexes but only two such bonds hinge the rA‚rU or dA‚dT base pair in (rA)n‚(rU)n and (dA)n‚(dT)n duplexes with more freedom. As already noted in the previous work,7 the ξ values obtained from single-crystal polarization spectra seem to be most reliable, though the agreement between experimental and simulated ELD spectra is only fair. Theoretically calculated values of ξ in set 3 gives less reliable bend and propeller-twist angles, indicating the difficulties involved in molecular orbital treatment for the direction of optical transition moments. It is not surprising that ξ values in set 4 yield the logically acceptable bend and propeller-twist angles, since they were chosen expediently. The quantitative analysis given in this section leads to the important and definitive conclusion that the inclination of bases paired in both (rG)n‚(rC)n and (dG)n‚(dC)n duplexes is nearly the same as each other and that the base pairs are not normal to the helical axis in solution under the present experimental conditions, contrary to previous X-ray studies.9,13 Transient Decay Signal and Relaxation Time. Figure 11 shows the dependence of electric dichroism-average relaxation time, 〈τ〉ED, on field strength for Na- and Mg(rG)n‚(rC)n in (a) and Na(dG)n‚(dC)n in (b) at various ionic strengths. The quantity 〈τ〉ED was defined34 as the area surrounded by a normalized dichroism decay signal and the baseline at a given field strength and evaluated28 by the peeling method.35 In all cases, 〈τ〉ED values decrease considerably at initial low fields (
