J. Phys. Chem. B 1997, 101, 1419-1428
1419
Pulsed Electric Linear Dichroism of Double-Stranded Antiparallel Poly(rA)‚Poly(rU) and Poly(dA)‚Poly(dT) Helices in Solution† Kiwamu Yamaoka,* Noriyuki Ojima, and Yoshimasa Fujita Department of Materials Science and Graduate Department of Gene Science, Faculty of Science, Hiroshima UniVersity, 1-3-1 Kagamiyama, Higashi-Hiroshima 739, Japan ReceiVed: July 16, 1996X
Reduced electric linear dichroism (ELD), ∆/, of the title duplexes in ionic solutions was measured at 7 °C in the 1.5-24 kV/cm field strength and 300-190 nm wavelength regions. The rodlike (rA)n‚(rU)n and (dA)n‚(dT)n samples, whose counterion was Mg2+ in most cases, were prepared by sonication and subsequent fractionation. The weight-average molecular weight and molecular weight distribution of each fraction, determined by the GPC/LALLS method, were taken into account in the analysis of the field strength dependence of ∆/ values. These values were fitted to theoretical orientation functions to evaluate the saturated reduced dichroism, (∆/)s, at absorption peaks. The wavelength dependence of (∆/)s, the ELD spectrum, was undulatory in the 300-190 nm region. The isotropic absorption and second-derivative spectra of each duplex were decomposed into eight component bands, which were assigned to constituent bases. The analysis of ELD spectrum revealed that the individual bases are both tilted and rolled in the rA‚rU and dA‚dT base pair and that the planes are bent. From transient dichroism signals, the weight-average rotational relaxation time, τw, was obtained, from which the axial translation per base pair, h, was evaluated. The limiting h values were found to be ca. 2.6 Å for (rA)n‚(rU)n and ca. 3.0 Å for (dA)n‚(dT)n. Thus, both duplexes were concluded to belong to the A-form family.
Introduction The secondary structure of double-stranded helical DNA and related polynucleotides has been classified into a few major groups.1-4 The concept of the originally proposed planarity of base pairs has been revised by recent advances in computeraided X-ray diffraction analysis of single crystals of synthetic oligomeric nucleotides.3,5,6 X-ray studies on high molecular weight DNA and other polynucleotides were carried out in the oriented fiber or gel state, but they are powerless for the solution conformation in aqueous media containing added salts. Therefore, more direct physicochemical approaches are needed for the structural determination of those high molecular weight helices in solutions at an expense of atomic resolutions. There are two quantitative methods in the study of solution conformations of polymers; one is the flow dichroism,7,8 and the other is the electric dichroism.8-10 Both methods utilize external fields to orient the polymers in solution. The flow dichroism apparatus can be constructed more easily than the electric counterpart and attached to a commercial spectrophotometer,11,12 which covers a wide wavelength range. Hence, a flow dichroism spectrum can often be scanned in the time span of minutes. This feature is an advantage over the wavelengthby-wavelength manually scanning electric dichroism apparatus, which must be constructed in a laboratory.13-15 The flow dichroism method, however, has some drawbacks of the nonuniform flow field in a measuring cell and the turbulence at high flow rates for orienting a rodlike DNA sample of low molecular weight. A serious problem is often associated with an unequivocal estimation of the saturated (intrinsic) dichroism value for completely oriented solutes in solution, though some ingenious means have been advanced to circumvent this difficulty.8,11,12 † ELD Studies of Nucleic Acid Structure 2. * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, February 1, 1997.
S1089-5647(96)02123-2 CCC: $14.00
In contrast, pulsed electric dichroism is practically free from the above drawbacks.9,10,13-15 Uniform and high-voltage pulse fields with a variable duration can be applied to a solution, which contains either a high molecular weight calf thymus DNA with base pairs in millions16,17 or sonicated DNA fragments with base pairs of about 100.18 The average degree of orientation at any given field strength and, hence, the intrinsic dichroism of solute polymers can now be evaluated quantitatively even for the polydisperse system, by using theoretical orientation functions.18,19 In addition, if a pulsed field is used, the transient electric dichroism signal can be measured to evaluate the average chain length of the helical solutes. In the present work, pulsed electric dichroism measurements were carried out in ionic solutions with two double-stranded poly(rA)‚poly(rU) and poly(dA)‚poly(dT) helices, which are said to belong to different A and B′ forms from X-ray studies,4 on a comparative basis. A new analytical procedure was proposed and utilized to evaluate the electrooptical properties of these duplexes and the structural parameters, such as the tilt and roll angles of individual bases constituting base pairs, from the field strength and wavelength dependence of reduced dichroism data. Experimental Section Materials. A high molecular weight double-stranded poly(riboadenylic acid)‚poly(ribouridylic acid) sample (hereafter abbreviated as (rA)n‚(rU)n), Lot No. 2-7, was purchased from Yamasa Shoyu Co. (Choshi, Japan). Another double-stranded poly(deoxyriboadenylic acid)‚poly(deoxyribothymidylic acid) sample (abbreviated as (dA)n‚(dT)n), Lot No. 2127860031, was purchased from Pharmacia Biotech (Uppsala, Sweden). The concentration of each sample was determined photometrically at 25 °C with the molar absorption coefficient (dm3 mol-1 cm-1) in terms of mononucleotide units at the absorption peak. For (dA)n‚(dT)n, ) 6000 at 259-260 nm,20,21 but for (rA)n‚(rU)n, values vary between 7000 at the peak of 257 nm,20 6680 at 260 nm,22 5640 at 260 nm (determined by phosphorus © 1997 American Chemical Society
1420 J. Phys. Chem. B, Vol. 101, No. 8, 1997
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TABLE 1: Weight-Average Molecular Weight, Mw, Weight-Average Number of Base Pair, 〈bp〉w, and Degree of Polydispersity, Mw/Mn, of Fractionated (rA)n‚(rU)n and (dA)n‚(dT)n Duplexes duplex
fraction
Mw/104 g mol-1
〈bp〉wa
Mw/Mn
(rA)n‚(rU)n
F3 F7 F2 F3 F4
38.5 12.1 28.4 22.2 15.7
567 178 429 336 237
1.35 1.46 1.17 1.16 1.10
(dA)n‚(dT)n
a The weight-average number of base pair is defined as the weightaverage molecular weight divided by the residue weight of a base pair, which is 679.4 g mol-1 for an rA‚rU base pair and 661.4 g mol-1 for a dA‚dT base pair as the disodium salt.
analysis in this laboratory), and 5550 at 260 nm23 (supplied by the manufacturer). The last value was most hypochromic and hence adopted in this work. Sonication. To prepare short rodlike samples suitable for electric dichroism measurements, the molecular weight was reduced by sonication in 0.1 M NaCl without any ruptures of the double-stranded helical structure.17,24 Sonication was carried out in an ice bath under a helium gas atmosphere with two Tomy Seiko sonicators at 20 kHz: Model UR-200P with a standard tip attached to the horn at a power level of 200 W for 40 burstbubbling cycles (total of 20 min) in a large amount (900 mg, 2 mg/mL) for (rA)n‚(rU)n and Model UD-200 with a microtip at a power level of 52 W for 20 cycles (total of 10 min) in a minute amount (6 mg, 0.84 mg/mL) for (dA)n‚(dT)n. Fractionation and Purification. The sonicated (rA)n‚(rU)n sample was fractionated to seven fractions (F1-F7) by successive precipitational fractionation with acetone as the precipitant.24 The sonicated (dA)n‚(dT)n sample was fractionated at 20 °C to four fractions (designated as F1-F4 in order of elution) by gel permeation chromatography with Sephacryl S-500HR gel.25 Each fraction was purified through a column (ca. 50 mL) packed with a DEAE Bio-Gel A resin, to remove remaining contaminants.26 Prior to GPC/LALLS (gel permeation chromatography/low-angle laser light scattering) and electric dichroism measurements, each fraction was exhaustively dialyzed at 7 °C for 3 days against 0.1 M NaCl with Na2EDTA (disodium ethylenediaminetetraacetate), total of 6 L (eight batches), at a concentration equimolar to nucleotide residue to remove heavy metal ions. The fractionated (rA)n‚(rU)n samples were similarly treated for purification. Table 1 gives the data on fractions of both samples utilized in the present measurement. GPC/LALLS Determination of Molecular Weight and Distribution. In order to determine the molecular weight M, the distribution f(M), and the polydispersity in terms of the ratio of weight- to number-average molecular weights Mw/Mn of solutes in solution, each fraction was subjected to GPC/LALLS measurements. A flow-type GPC/LALLS system (Tosoh Co., Tokyo, Japan) was used for the measurements of light scattering at 30 °C and refractive index at 35 °C. A sample solution (0.5 mL) was injected into a Tosoh G-DNA-PW tandem column and eluted at a flow rate of 0.6 mL/min. Both Mw and Mw/Mn values were determined for each fraction according to the procedure cited elsewhere.24,25 The molecular polydispersity is an important parameter in the structural determination of any polydisperse systems in solution, though often ignored previously. The data pertinent to the present work are given in Table 1. Electric Dichroism Measurement. Solutions for electric dichroism were further dialyzed against MgCl2 buffered with Tris/HCl solution at appropriate concentrations, whenever needed. The counterion replacement from Na+ to Mg2+ was necessary to keep the double-helical structure of the samples stable.27 The ionic strengths, Is, were kept at 0.0004 and 0.0008
for Mg(rA)n‚(rU)n at pH 6.1-6.0 and at 0.0004 and 0.0012 for Mg(dA)n‚(dT)n at pH 7.8. At room temperature, the helical structures of Na(rA)n‚(rU)n and Na(dA)n‚(dT)n were not stable at ionic strengths lower than 0.01 and 0.0004 with Na+ ions, respectively, so an Na(dA)n‚(dT)n solution was also prepared at Is ) 0.0012 for comparison. The electric dichroism apparatus was designed and constructed in this laboratory: a UV-vis instrument with a Glan-Taylor calcite polarizer,13 which has been modified in several aspects, and a far-UV instrument with a Rochon-type magnesium fluoride polarizer, whenever needed.14 Each system consists of a 200 W deuterium lamp light source for the UV region, a square-wave high-voltage pulser, a Kerr cell holder, an optical assembly, and a digitized signal detector. The pulser can deliver an electric pulse up to 26 kV/cm with a variable duration (5 µs and 5 ms). The apparatus can detect both parallel (∆A|) and perpendicular (∆A⊥) dichroism signals separately. In this work, usually 4-36 signals (occasionally up to 100, when a sample solution stood against electric pulses) were accumulated and averaged to improve signal-to-noise ratios. The field-off isotropic absorption spectrum, A, of the same sample solution was measured on a Shimadzu UV-250 spectrophotometer. Both electric dichroism and absorption were measured at 7 °C under the nitrogen gas purge. Electric Dichroism Data Analysis Steady-State Electric Dichroism. The difference in absorptions by a sample solution in the presence and the absence of an applied electric pulse field, E, is defined as ∆A| ) A|E - A in terms of absorbances or ∆| ) |E - in terms of molar absorption coefficients for the monochromatic light beam linearly polarized parallel to the field direction.13 ∆A| ) ∆|/ Cpd, where Cp is the mononucleotide concentration of a polymer solution and d is the path length of a Kerr cell in centimeters. Similarly, the difference for the perpendicularly polarized light is defined as ∆A⊥ ) A⊥E - A or ∆⊥ ) ⊥E - . The reduced (electric linear) dichroism is defined as ∆A/A ) (∆A|/A) (∆A⊥/A) ) (A|E - A⊥E)/A or ∆/ ) (|E - ⊥E)/.13,16 If there appears no electrochromism in the sample, the following relationship holds: 3 ) |E + 2⊥E. Since a polynucleotide chain contains the chromophores, i.e., bases, each of which shows several overlapping absorption bands, the observed absorption spectrum is a composite of a number of partial bands. Then, the reduced dichroism at a given wavelength λ is given as13,28
∆ )
( ) ∆
s
Φ(E) )
∑j ∑k j,k[(∆/)s]j,k ∑j ∑k
Φ(E)
(1)
j,k
where (∆/)s is the saturated or intrinsic reduced dichroism at infinitely high fields, j,k is the jth partial band of the kth chromophore, and Φ(E) is the orientation function, which gives the average degree of orientation of solutes at a field strength E. Saturated Reduced Dichroism. The field orientation of polymer chains in a system, each of which possesses electric moments, is described by the function Φ(E). If the polymer system is polydisperse, this orientation function must be substituted by the weight-average orientation function 〈Φ(E)〉w.19 In the present work, use was made of the well-tested theoretically derived SUSID orientation function.18,19 The permanent dipole moment was unnecessary for consideration, because an antiparallel double-stranded helix showed no such moment.19,26 The (∆/)s value was evaluated, by fitting experimental (∆/ ) points, measured over a wide field strength range, to one of
Electric Dichroism of (rA)n‚(rU)n and (dA)n‚(dT)n
J. Phys. Chem. B, Vol. 101, No. 8, 1997 1421 saturated reduced dichroism in eq 1 is expressed as follows: 13,28
∑j ∑k j,k(ν)(3 cos2 θj,k - 1)
( ) () ∆
3
(5)
)
) (3/2){
s
∑j ∑k j,k(ν)
2
∑j ∑k j,k(ν)[3(-cos θTk sin θRk sin ξj,k + sin θTk cos ξj,k)2 - 1]}/[∑∑j,k(ν)] j k
Let Rk be the angle between the helix axis and the normal to the plane of the kth chromophore; then
cos |Rk| ) cos θRk cos θTk
Figure 1. Coordinate system for a single base in a duplex. In the upper half, the Cartesian coordinates (x,y,z) are set up, in which a base plane lies with the x axis as the tilt axis and the y axis as the roll axis, prior to rotational operation (the initial state). In the lower half, the coordinates of the base is first rolled around the roll axis by θR to the new (x′,y′,z′) coordinates (the intermediate state) and finally 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.28 Angles θ, ψ, and ξ are defined in the text.
the most appropriate orientation functions, which take into account the molecular weight distribution curve obtained from the GPC/LALLS data.19 Angle between Optical Transition Dipole Moment Direction and Helix Axis, Tilt and Roll Angles of Base. If an absorption spectrum consists of a single band, the saturated (intrinsic) reduced dichroism in eq 1 is expressed in terms of the angle θ between the optical transition dipole moment direction |m| and the molecular orientation axis, which should coincide with the helix axis z of a rodlike duplex, as follows:16
(∆) ) (23)(3 cos θ - 1) 2
s
(2)
The angle θ is in general related with the tilt angle θT and the roll angle θR of a planar chromophore as28
cos θ ) -cos θT sin θR sin ξ cos ψ + sin θT cos ξ cos ψ + cos θT cos θR sin ψ (3) where ψ is the angle between |m| and its projection onto the chromophore plane and ξ is the angle between the projected moment |mb| and the roll axis (y), the signs of ψ and ξ being positive for clockwise rotation, as shown in the upper half of Figure 1. The signs of θT and θR are positive for clockwise rotation, as viewed from the negative to positive directions of the x (or x′) and y axes in the lower half of Figure 1. The angle θ can be expressed as a function of θT and θR, if both ξ and ψ are known. If the chromophore possesses only in-plane π f π* transition moments with no out-of-plane n f π* transition moment (ψ ) 0), eq 3 reduces to a much simpler form29
cos θ ) -cos θT sin θR sin ξ + sin θT cos ξ
(4)
If a double-stranded polynucleotide has k chromophores, in each of which j partial absorption bands are involved, the
(6)
The angle ζ between the direction of an in-plane transition moment and the reference axis of a base is related to ξ as ξ ) 103.4° + ζ for adenine and ξ ) 56° - ζ for uracil and thymine. The reference axis is defined as the line bisecting atoms C(4) and C(5) for adenine and N(1) and C(4) for uracil and thymine.30 The sign of angles θT and θR can now be determined from eq 5. The wavelength dependence of measured (∆/)s was simulated according to the procedure previously reported.28 The bestfitted angles of θT and θR in eq 5 were searched for iteratively by the nonlinear least-squares method.28,31 In this procedure, angles of ξ in eq 4 were selected from the diverse literature values of ζ, which introduce uncertainties in the final results (cf. Figure 7 in Results and Discussion). In the present work, the profile of an absorption band j,k in eq 5 was approximated by the Gaussian function based on wavenumber ν (not wavelength) as15,32
{
[
j,k(ν) ) max,j,k(ν) exp -(4 ln 2)
]}
ν - νmax,j,k δj,k(ν)
2
(7)
where j,k(ν) is the molar absorption coefficient of the jth partial band of the kth chromophore at ν, max,j,k(ν) is the maximum absorption coefficient, νmax,j,k is the position of the band maximum, and δj,k(ν) is the half-intensity bandwidth, 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 lessen ambiguities and to facilitate a unique deconvolution, the second-derivative spectrum, d2j,k(ν)/dν2, was also utilized.28 Transient Dichroism Decay Process. In order to evaluate the relaxation time τ of a rodlike molecule from dichroism decay signal, the signal at time t after removal of an applied electric field is normalized by the steady-state signal at t ) 0 and plotted against t. For a polydisperse system containing molecules with various molecular weights, the dichroism-average relaxation time 〈τ〉ED is defined as the area surrounded by the normalized signal and the time axis.33 At infinitely high fields, 〈τ〉ED reduces to the weight-average relaxation time τw as33
τw )
∫τ(M) fw(M) dM ∫fw(M) dM
(8)
where τ(M) and fw(M) are the rotational relaxation time and the weight fraction (obtained from GPC/LALLS) of solute molecules with molecular weight M. A rigid and rodlike duplex
1422 J. Phys. Chem. B, Vol. 101, No. 8, 1997
Yamaoka et al.
Figure 2. GPC/LALLS-determined molecular weight distribution profiles of Na(rA)n‚(rU)n in (a) and Na(dA)n‚(dT)n in (b) in terms of the weight fraction gw(log M) against the logarithm of molecular weight M. Numerals are fractions used for electric dichroism. The area of each profile was normalized to unity.
molecule may be assumed to be a cylinder with length L and radius b. The Broersma equation (eq 9) was used to calculate the length L, which is proportional to M, with an assumed value for b:34
[ ()
(
)]
πη0L3 L 1 - 0.28 τ) ln - 1.57 + 7 18kT b ln(L/b)
2 -1
(9)
where η0 is the viscosity of solvent, k is the Boltzmann constant, and T is the absolute temperature. L is related to the axial translation (or the rise) per base pair h, an important quantity for characterizing the solution conformation of a helix, and is given as L ) h × (bp), where bp is the number of base pair. Results and Discussion Characterization of Duplex Samples. Molecular Weight Distribution. Figure 2 shows the weight fractions of sonicated (rA)n‚(rU)n and (dA)n‚(dT)n samples used for electric dichroism measurements. The GPC/LALLS-determined data are plotted in terms of the gw(log M) vs log (M), where the area surrounded by the distribution curve and the abscissa is normalized to unity.24,25 Each fraction shifts successively to the lower molecular weight side with a mutual overlap. The degree of polydispersity and the weight-average molecular weight of each fraction are given in Table 1. The GPC-fractionated (dA)n‚(dT)n sample gives a smaller Mw/Mn value than the precipitationally fractionated (rA)n‚(rU)n sample. If a once-fractionated sample is available in a large quantity, the molecular weight distribution can be narrowed by further fractionations. As presented here, the sonication-fractionation procedure is a recommendable technique to prepare well-characterized nucleic acid samples for studying the dependence of the physical properties on molecular weight.17-19,24
Figure 3. Circular dichroism (a) and absorption spectra (b) of sonicated and fractionated Na(rA)n‚(rU)n (F3) (- - -) and Na(dA)n‚(dT)n (F2) (s) at 25 °C in 0.1 M NaCl. The ordinates are the molar ellipticity [θ] and the molar absorption coefficient . The CD spectra were measured on a JASCO Model J 600 spectropolarimeter.
Circular Dichroism (CD) and Absorption Spectra. Figure 3 shows both CD and absorption spectra of sonicated (rA)n‚(rU)n and (dA)n‚(dT)n samples. While the absorption spectra are close to each other, the CD profiles are characteristic. This feature has been attributed to different conformations of these duplexes.35 The present sonication-fractionation process does not alter the optical property and helical conformation of nucleic acids.17-19 Electrooptical Property of Duplexes. Field Strength Dependence of Reduced Dichroism. Figure 4 shows the reduced dichroism at absorption peaks for samples of (a) Mg(rA)n‚(rU)n, (b) Mg(dA)n‚(dT)n, and (c) Na(dA)n‚(dT)n with different molecular weights at various ionic strengths over a wide range of applied field strength. The field orientation is more pronounced at lower Is and at higher Mw. Dichroism values tend to be saturated regardless of Mw and Is, but never reach a saturation (i.e., complete orientation) even at very high field strengths. In the low-field region (cf. inserts of Figure 4), dichroism values are nearly proportional to the second power of field strength.36 Thus, Kerr’s law (E-2 dependence) definitely holds for the field orientation of duplexes (rA)n‚(rU)n and (dA)n‚(dT)n, as already verified for rodlike sonicated DNA samples.17,18 Both values of ∆|/ and -2∆⊥/ coincide with each other over the entire field (0-24.5 kV/cm) region (not shown), indicating that the backbone conformation remains unaltered by applied highvoltage pulsed fields (no electrochromic effect).13,18 Reduced Dichroism and Orientation Function. Since a reversing-pulse electric birefringence study has verified that antiparallel (rA)n‚(rU)n possesses no net permanent (electric) dipole moment,19 as calf thymus DNA fragments,26 the field dependence of observed ∆/ values was fitted to theoretical SUSID orientation functions, which take into account the molecular polydispersity.18,19 Figure 4 shows the best-fitted theoretical curves with solid lines. In each case, the agreement between measured points and calculated curves is excellent over
Electric Dichroism of (rA)n‚(rU)n and (dA)n‚(dT)n
J. Phys. Chem. B, Vol. 101, No. 8, 1997 1423 TABLE 2: Saturated Reduced Dichroism, (∆E/E)s, and Weight-Averages of Electric Properties of (rA)n‚(rU)n and (dA)n‚(dT)n in Mg2+ and Na+ Solutions with the Total Ionic Strength Is at 7 °C duplex (fraction) (rA)n‚(rU)n F3(Mg2+) F7(Mg2+) (dA)n‚(dT)n F2(Mg2+) F2(Na+) F3(Mg2+) F3(Na+) F4(Mg2+) F4(Na+)
I s/ 10-3 (∆/)sa
〈∆R〉w/ 〈∆σ〉w/ 〈E0〉w/ 〈∆σ〉w〈E0〉wb/ 10-32 10-32 D F m2 F m2 kV cm-1
0.4 0.8 0.4 0.8
-1.03 -1.05 -1.00 -1.00
3.45 2.40 1.04 1.28
10.36 7.20 3.47 2.14
1.93 2.32 2.59 3.30
5990 5010 2690 2120
0.4 1.2 1.2 0.4 1.2 1.2 0.4 1.2 1.2
-1.10 -1.07 -1.10 -1.10 -1.10 -1.10 -1.08 -1.08 -1.07
3.36 3.07 2.78 2.87 2.69 2.76 1.74 1.74 1.31
8.39 3.83 4.63 7.16 3.36 4.60 5.80 2.18 4.35
1.92 2.01 2.24 2.08 2.15 2.24 2.00 2.67 2.31
4830 2310 3110 4460 2160 3100 3480 1740 3010
a These values were measured at 256 nm for (rA)n‚(rU)n and at 260 nm for (dA)n‚(dT)n b This quantity is only close, but not equal, to the weight-average ionic induced dipole moment 〈∆σE0〉w.18,19 1 D ) 3.336 × 10-30 C m.
Figure 4. Field strength dependence of reduced dichroism of (a) Mg(rA)n‚(rU)n at 256 nm, (b) Mg(dA)n‚(dT)n at 260 nm, and (c) Na(dA)n‚(dT)n at 260 nm and curve fittings to theoretical SUSID orientation functions (solid lines). (a) F3 (O) and F7 (4) at Is ) 0.0004; F3 (b) and F7 (2) at Is ) 0.0008. (b) F2 (O) and F4 (4) at Is ) 0.0004; F2 (b) and F4 (2) at Is ) 0.0012. (c) F2 (0) and F4 (]) at Is ) 0.0012. The saturated reduced dichroism is indicated with arrows on the right ordinate. Inserts are the same plots in the low-field region on an expanded scale.
the entire field region. The saturated reduced dichroism (∆/ )s at infinitely high fields was evaluated from this curve fitting. Values of (∆/)s are given in Table 2, together with electric parameters obtained from the curve fitting. With these values, the electric property and field orientation of the antiparallel double-stranded helices in ionic solutions may be discussed, but such discussions are beyond the scope of this work.18,36 The saturated reduced dichroism and, hence, the corresponding angle θ (cf. eq 2) was found to be -1.02 ( 0.03 and about 70.9° at 256 nm for (rA)n‚(rU)n and -1.09 ( 0.03 and 72.4° at 260 nm for (dA)n‚(dT)n, as an average, regardless of Mw and Is. This result strongly indicates that the duplex conformation remains nearly constant under the present conditions. It should be noted that an average value of -1.06 ( 0.03 (θ ) 72°) has been obtained for many sonicated and fractionated DNA samples18 or -(0.87-1.05) (θ ) 68-72°) for sonicated but unfractionated DNA samples.17 Thus, the 260 nm in-plane transition moments are probably inclined at angles of θ given above with respect to the axis of the double-stranded helix. Consequently, the constituent bases or base pairs should be inclined relative to the helix axis by nearly the same angles for (rA)n‚(rU)n and (dA)n‚(dT)n, and also for DNA, in spite of the chemical differences in the base and sugar structures. WaVelength Dependence of (∆ε/ε)s. Figure 5 shows the wavelength dependence of saturated reduced dichroism, (∆/ )s, i.e., the ELD spectrum, for Mg(rA)n‚(rU)n, Mg(dA)n‚(dT)n,
Figure 5. Wavelength dependence of saturated reduced dichroism of (rA)n‚(rU)n and (dA)n‚(dT)n duplexes. (a) Mg(rA)n‚(rU)n: F3 (O) and F7 (0) at Is ) 0.0004 and F7 (]) at Is ) 0.0008. (b) Mg(dA)n‚(dT)n: F2 (O) at Is ) 0.0004 and F2 (0) and F4 (]) at Is ) 0.0012. (c) Na(dA)n‚(dT)n (b) and Mg(dA)n‚(dT)n (O) (F2 at Is ) 0.0012) and Mg(rA)n‚(rU)n (0) (F7 at Is ) 0.0008).
and Na(dA)n‚(dT)n duplexes over the UV and far-UV regions. Values of (∆/) were measured for each duplex mostly at an interval of 2 nm and at a fixed field strength and converted to the corresponding ELD spectrum with the aid of eq 1. These detailed ELD spectra are reported for the first time and reveal many suggestive features. (1) Each ELD spectrum is not
1424 J. Phys. Chem. B, Vol. 101, No. 8, 1997 constant but undulatory throughout the 300-190 nm region; thus, the corresponding isotropic spectrum is a composite of many partial bands. (2) The (∆/)s values never reach a low value of -1.5 at any wavelengths; thus, the θ angles never in the vicinity of 90°, and consequently, the in-plane transition moments or the base-pair planes are not normal to the helix axis in disagreement with the B-form model. (3) The counterion species, Na+ or Mg2+, and also ionic strength do not affect the ELD spectra of (dA)n‚(dT)n duplex; thus, the secondary structure remains unaltered under the present conditions. (4) Mg(rA)n‚(rU)n shows the ELD spectra, which slightly depend on the ionic strength of Mg2+ (0.0004 vs 0.0008); thus, the helical structure of (rA)n‚(rU)n may be less rigid, changing slightly at low Is values. (5) The molecular weights do not affect the ELD spectra of (rA)n‚(rU)n and (dA)n‚(dT)n; thus, the conformation of each duplex remains unaltered by applied electric field in spite of the difference in chain lengths. (6) The ELD spectrum of the (dA)n‚(dT)n duplex is more undulatory and distinctly different from the one observed for the (rA)n‚(rU)n duplex; thus, these spectra reflect the optical characteristics of two different base pairs. (7) The dichroism values of (rA)n‚(rU)n samples happen to coincide each other near 240 nm regardless of Mw and Is; thus, a careless comparison of dichroism data at a single wavelength would lead to a misinterpretation on the relative arrangement of a given base pair in the helical structure. The (∆|/) and -2(∆⊥/) values of each duplex again coincide with each other over the entire 300-190 nm region (not shown); thus, the applied high electric pulse fields induce neither strand separation nor unsymmetric internal motion of particular bases in this wavelength region. The results in this section lead to the conclusion that the observed ELD spectra are qualitatively suggestive, but still unable to allow any accurate discussions, on the arrangement of bases in a helix. The ELD spectra must be analyzed quantitatively in terms of the optical property of constituent bases or base pairs, as shown below. DeconVolution of Isotropic Spectra and Simulation of ELD Spectra. Figure 6a shows the result of the deconvolution of a field-off isotropic absorption spectrum (bottom), a secondderivative spectrum (middle), and a field-on ELD spectrum (top) for Mg(rA)n‚(rU)n. The deconvolution principle is to decompose the observed isotropic spectrum to a minimum number of constituent bands according to eq 7 under due consideration with the second-derivative spectrum. Each deconvolution was actually performed in terms of wavenumbers (eqs 5 and 7), but the results were converted and expressed in terms of wavelengths. The isotropic spectrum was decomposed into eight bands, which were numbered from the longer wavelength side. The sum of these constituent bands or the second-derivative bands reproduced the experimental spectrum (drawn with circles to distinguish it from the fitted curve (solid lines)) quite well over the entire wavelength region. Since the partial bands of the constituent single-stranded (rA)n and (rU)n were found to be seven and six, respectively, the total of eight uncovered bands for (rA)n‚(rU)n indicates that some of 13 partial bands are merged or overlapped one another.37 By selecting an appropriate θ value to each component band, without changing the deconvoluted optical parameters given in Table 3, the ELD spectrum (top) was simulated with the first part of eq 5. A good agreement was found between measured and calculated ELD spectra with slightly varying angles (θ ) 73-66°), as shown in parentheses. Figure 6b shows the deconvolution of the spectra of Mg(dA)n‚(dT)n in the same manner as applied to Mg(rA)n‚(rU)n. The isotropic spectrum was again decomposed into eight component bands as numbered in the bottom figure. Angles θ
Yamaoka et al.
Figure 6. Deconvolution of isotropic (bottom) and second-derivative (middle) spectra and ELD spectrum (top). (a) Mg(rA)n‚(rU)n: F3 at Is ) 0.0008. (b) Mg(dA)n‚(dT)n: F2 at Is ) 0.0012. Circles: experimental spectra. Solid lines: the deconvoluted component bands and the resultant sum of these bands. Numbers 1-5 denote the individual bands from the longer wavelength side. A, U, or T stands for the base to which the particular band was assigned. Numerals in parentheses are angles of θ in degrees to reproduce the experimental ELD spectrum.
were also found to be in the 74-61° range, reproducing the observed ELD spectrum quite well over the entire wavelength region. The fact that values of θ are not close to 90° throughout
Electric Dichroism of (rA)n‚(rU)n and (dA)n‚(dT)n
J. Phys. Chem. B, Vol. 101, No. 8, 1997 1425
TABLE 3: Optical Characteristics, Angle ξ between the Roll Axis and Transition Moment Direction, and Assignment of Component Bands to Constituent Bases in (rA)n‚(rU)n and (dA)n‚(dT)n duplex base
λmax,j,k/ nm
(rA)n‚(rU)n rA 285.0 (A1)b 263.4 (A2) 235.6 (A3) 207.5 (A4) 186.0 (A5) rU 276.8 (U1) 251.1 (U2) 218.5 (U3) (dA)n‚(dT)n dA 281.6 (A1) 259.9 (A2) 233.8 (A3) 201.6 (A4) 187.0 (A5) dT 271.1 (T1) 251.3 (T2) 212.6 (T3)
max,j,k/ δj,k/ 103 M-1 103 cm-1 cm-1 set 1
ξj,ka/deg 2
3
4
0.50 3.64 1.50 5.20 8.86 1.40 3.80 2.10
1.50 75.4c 94.2e 148.4g 75.4c 3.00 3.4c 116.2e 58.4g 116.2e 3.50 118.4c 32.2e 132.4g 32.2e 5.00 118.4c 185.4f 34.4g 118.4c 7.80 223.4c 185.4f 34.4g 223.4c 2.20 65d 75f 66.5g 65d 3.00 47* 67e 66.5g 67e 3.60 -3d -15f 46.5g -3d
1.80 2.90 1.35 3.55 9.00 2.75 3.50 4.20
1.90 75.4c 94.2e 148.4g 75.4c 2.80 3.4c 116.2e 58.4g 116.2e 3.80 118.4c 32.2e 132.4g 32.2e 5.20 118.4c 185.4f 34.4g 118.4c 7.00 223.4c 185.4f 34.4g 223.4c 2.30 65d 75f 66.5g 65d 3.30 47* 87e 66.5g 87e 3.80 -3d -15f 46.5g -3d
a
Letters c-g denote the reference number from which ξ values are taken: (c) refs 39 and 40; (d) ref 38; (e) ref 42; (f) ref 41; (g) ref 43. Asterisk (*) is the angle for U2 or T2, which is assumed to be symmetric to that for U1 with respect to the reference axis of U. b Numerals in parentheses correspond to the numbered component bands in Figure 6.
this region immediately suggests that the planes of individual bases A and T, or their base pair, are not nearly normal, but inclined at about 70°, with respect to the helix axis. Further structural information on the tilt and roll angles of the individual bases constituting a duplex helix can be extracted in the following section. Estimation of Angle ξ and Assignment to Component Band. In order to evaluate both tilt θT and roll θR angles for bases constituing a base pair in a helix from a deconvoluted ELD spectrum in Figure 6a,b, two difficulties must be overcome. (1) Knowledge is limited as regards the exact angles of ξ or ζ between the roll or reference axis of a purine or pyrimidine and the directions of electronic transition moments. Figure 7 shows the directions of bases A, U, and T reported by previous workers.38-43 (2) The assignment of an angle ξ or ζ to a component band deconvoluted in the preceding section is often subjective. Since no reliable ζ values are available for a hydrogen-bonded base pair, the literature values for each isolated base must be used (problem 1). Four sets of the reported values, given in Table 3, were used as trials: set 1 from single-crystal data,38-40 set 2 from film dichroism data,41,42 set 3 from data based on molecular orbital calculations,43 and set 4 from data expediently chosen from sets 1-3. The numerical agreement among these sets is rather poor, as noted in Table 3. The assignment of ξ value to each decomposed component band (problem 2) must be made as self-consistently as possible. EValuation of Tilt Angle θT and Roll Angle θR. By substituting ξ values of each set in Table 3 to the second part of eq 5, the most likely tilt and roll angles θTk and θRk were searched iteratively for each base, until the standard deviation was minimized. Figure 8 shows some simulations of experimental ELD spectra of Mg(rA)n‚(rU)n (circles) (a) and Mg(dA)n‚(dT)n (squares) (b) with ξ values from sets 1-3. The spectrum of (rA)n‚(rU)n is reproduced by set 2 (dash-dot) slightly better than other sets, while the ELD spectrum of (dA)n‚(dT)n is fitted by set 1 (solid) better than the others. In any case, the portions fitted to each observed spectrum are limited; thus, the overall fitting is barely satisfactory probably because of the two
Figure 7. Reported transition moment directions of constituent bases, A, U, and T. For each base, the roll axis (y) is denoted by a singleheaded arrow and the direction of moments by dual-headed arrows with the corresponding peak wavelengths in nanometers for sets 1-3.
Figure 8. Comparison between observed and simulated ELD spectra. (a) Mg(rA)n‚(rU)n and (b) Mg(dA)n‚(dT)n with three sets of optical parameters: set 1 (s), set 2 (- - -), and set 3 (- ‚ -). (c) (rA)n‚(rU)n (s) and (dA)n‚(dT)n (- - -) with expediently chosen set 4 for better fitting. Numerical parameters are given in Table 3. Other conditions are the same as in Figure 6.
problems cited above. Fittings with set 3 (dotted), based on quantum-mechanical calculations, seem to be worse than other two, revealing the difficulty involved in theoretical prediction of transition moment directions. Figure 8c shows the simulation
1426 J. Phys. Chem. B, Vol. 101, No. 8, 1997
Yamaoka et al.
Figure 9. Projection onto the initial coordinates (x,y,z) of rolled and tilted base pairs A‚U and A‚T in the final state (x′′,y′′,z′′), as calculated with four sets (1-4) of angles ξ for transition moment directions. Both roll and tilt angles in degrees are shown with numerals. The new roll angle θR′ is expressed as cos θR′ ) cos θR/(cos2 θR + cos2 θT sin2 θR)1/2 with values of θR and θT in Table 4, the sign being positive for the clockwise rotation from the negative to positive direction (front to rear of the paper) of the roll (y) axis. The tilt angle θT is positive for clockwise rotation from the negative to positive direction of the tilt (x) axis.
TABLE 4: Angles r, θR, and θT for Bases in (rA)n‚(rU)n and (dA)n‚(dT)n Evaluated by Simulation of Observed ELD Spectra duplex bases (rA)n‚(rU)n rA rU (dA)n‚(dT)n dA dT
R/deg set 1 2 3
4
1
θR/deg 2 3
4
1
θT/deg 2 3 4
31 20
25 31 36 19 9 -30 7 25 23 -6 35 34 29 25 -20 -16 -4 -12 1 30 29 22
32 19
26 22 32 33 25 29
25 -17 1 -3 21 20 22 31 -9 -21 -16 -19 17 26 20 22
with the aid of set 4, in which angles ξ were expediently chosen from sets 1-3 for better fitting to observed ELD spectra. Fittings are now much improved, as compared with those in (a) and (b), but still far from being perfect. The best-fitted values of θT and θR are given for each set in Table 4. Figure 9 shows the tilt and roll of individual bases in base pairs rA‚rU and dA‚dT projected onto the tilt (x) and roll (y) axes with respect to the z axis (cf. Figure 1). The projected tilt and roll angles were calculated from the data given in Table 4 for sets 1-4. The following two important features were clarified. (1) The tilt and roll angles are 25° and 12° for rA but 1° and -20° for rU in rA‚rU base pair from set 1, for example, whereas they are 21° and 17° for dA but 21° and -12° for dT in dA‚dT pair. The base pairs in the (rA)n‚(rU)n helix as well as in the (dA)n‚(dT)n are evidently not coplanar; the bases are inclined indiVidually and differently with respect to the helical axis, as also indicated by the angle R, which were calculated from eq 6 and given in Table 4. Therefore, the rigid planarity of the base pair probably breaks down at the hydrogenbonded hinge, though the bending is not too large. (2) The differences in roll angles is ca. 32° (set 1) and 22° (set 2)
Figure 10. Field strength dependence of rotational relaxation time 〈τ〉ED of Mg(rA)n‚(rU)n in (a) and Mg(dA)n‚(dT)n in (b). (a) F3 (O) and F7 (0) at Is ) 0.0004. (b) F2 (O), F3 (4), and F4 (0) at Is ) 0.0004. Inserts are the dependence of 〈τ〉ED values on the reciprocal of the second power of field strength. Solid lines were drawn by the least-squares method.
between rA and rU and 33° (set 1) and 3° (set 2) between dA and dT. Thus, the bases in both base pairs are undoubtedly propeller-twisted around the roll axis. Granted that a large uncertainty is involved in the reported directions of transition moments, the tilt and roll angles in Table 4 may be taken as evidence that the helical structure of (rA)n‚(rU)n and (dA)n‚(dT)n duplexes both belong to A-form family in ionic solutions (the sugar puckering cannot be resolved by the present method), contrary to the X-ray results that the former belongs to A form but the latter to B′ form.4 The sign of angles θT and θR could be determined unequivocally by the ELD method (Table 4). Values of the inclination angle R (cf. Table 4) of individual bases are surprisingly close to those found from flow dichroism.31 These findings are quite significant, manifesting the advantage of the present ELD analytical procedure. Poor fittings to the measured ELD spectra and the disagreement among three simulated ones in Figure 8a-c are mostly based on inaccurate ξ values. These angles were determined for isolated bases, but they should be altered by hydrogen-bonding or stacking interactions. In any case, experimental sets 1 and 2 gave more reasonable paired values of θT and θR than the theoretical set 3. Decay Process of Dichroism Signals. Dependence of Relaxation Time on Electric Field. Figure 10 shows the dependence of electric dichroism average relaxation time 〈τ〉ED on field strength for (a) Mg(rA)n‚(rU)n and (b) Mg- and Na(dA)n‚(dT)n at various ionic strengths. In all cases, 〈τ〉ED values decrease considerably at initial low fields (
