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On the cross-section Structure of deoxyribonucleic acid in solution
J. Mol. Biol. (1971) 55, 311-324
On the Cross-section Structure of Deoxyribonucleic Acid in Solution STANLEY BRAM~ AND W. W. BEEMAN
Biophysics Laborato y, University of Wisconsin Madison, Wis. 53706, U.S.A. (Received 22 July 1969, and in revised form 11 September 1970) We present X-ray scattering data on dilute solutions of calf thymus DNA in a number of monovalent chlorides, particularly EaC1 and CsCI. Salt concentrations are from 0.05 to 1.0 M. The data include a range of small angles where the scattered flux is sensitive to the cross-section parameters of the molecule. Our measured mass per unit length for NaDNA is within 2 or 3% of the theoretical value for the B form. For CsDNA our measurement is about 9% below theory but within experimental error. At larger angles, where internal periodicities dominate the scattering, the data on NaDNA are in much better agreement with the B than with the A form. We observe two cross-section radii of gyration, a result characteristic of a cylindrical core of high electron density surrounded by a shell of much lower electron density. The larger radius of gyration is that of the entire structure, the smaller characterizes the core. Our results imply that the core is ionized or partially ionized DNA and that the shell is a Debye-Hiickel layer of counterions and perhaps electrostricted solvent about 20 A thick. The experimental data and the model are not accurate enough to decide what fraction of the counterions should be considered site bound to the DNA although there is some evidence to indicate that site binding, if it exists, is not large.
1. Introduction The structure of double-stranded DNA as it exists in crystalline fibers is well established. The high humidity or B form is presumably that found in dilute solution. The molecule is about 20 A in diameter and a variety of approaches give persistence of rigidity lengths of between 500 and 1000 A (Sharp Q Bloomfield, 1968). Thus, dilute solutions of DNA may be studied by X-ray techniques which furnish certain crosssection parameters of long rigid rods in a random, unoriented array. These parameters include the cross-sectional radius of gyration, the mass per unit length and some information on the electron density as a function of distance from the axis of the rod. For DNA, one may hope to verify the conformation in solution and to extract information on the structure of the surrounding ion cloud and perturbed solvent which is not easily available using other methods. Three such studies have appeared (Luzzati, Nicolaieff & Masson, 1961; Kratky, 1963; Luzatti, Masson, Mathis & Saludjian, 1967). These support the B form aa the structure in dilute solution. We here present X-ray scattering data for calf thymus DNA in a number of different salts which are in excellent agreement with the B form and which also establish that the surrounding counterions and solvent are influencing the scattering. t Present France.
address:
DQpartement
de Biochimie 311
Macromol&ulaire,
C.N.R.S.,
34 Montpellier
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2. Materials and Methods (a) Materials The calf thymus DNA used in this work was either obtained from the Worthington Biochemical Corp., Freehold, N. J., U.S.A., who use the isolation procedure of Zamenhof (1958), or isolated in our laboratory from calf thymus nucleohistones. The nucleohistones were prepared following Zubay & Doty (1959) as modified by Ris (1961). Additional details are given in the paper following this one (Bram & Ris, 1971). Our nucleohistone was deproteinized following Zamenhof (1958). This involved extraction with 2 aa-NaCl in a Waring blender, ethanol precipitation, two detergent treatments in 0.15 &r-NaCl and 0.015 M-sodium citrate at pH 7.1, and a final ethanol precipitation. The average molecular weight of the resulting DNA was at least 107. Because high viscosity is troublesome in filling sample holders most of our X-ray runs were on DNA sonicated according to the method of Cohen & Eisenberg (1966). About 25 ml. of 0.15 ar-NaCl and 0.015 M-sodium citrate containing 2 to 4 mg of DNA/ml. was irradiated in a polyethylene beaker using the T150 horn of a Branson no. 125 Sonifier. The sample was in ice and a nitrogen atmosphere. Two 30-set pulses at 125 w and 20 kc, separated by a 2-min cooling period, were used. Electron microscopy of the sonicated solution revealed well-dispersed molecules, without evidence of strand separation, and with an average length around 2000 A. To eliminate any divalent cations which might cause aggregation, and to reduce nuclease activity, most of the samples were dialyzed at 4°C against 0.075 M-NaCl, 0.01 M-EDTA (disodium salt) at pH 8.0 for as long as 3 days. All samples were then dialyzed exhaustively against the desired buffer just before the X-ray scattering experiments. Phosphorus content was determined by the method of Fiske & Subbarow (1925). DNA concentrations were calculated from the phosphorus content, an average nucleotide molecular weight of 308.6 and the atomic weight of the cation. Optical density measurements gave a molar extinction coefficient at 2590 A of 6.5 x lo6 cm2/mol P for both the Worthington preparation and our own. After sonication the ratio was 6.6 x 106. Thus no very great denaturation has occurred. The protein content, measured as histone, for both DNA’s was less than 0.4%. Our values for the extinction coefficient and protein content are in excellent agreement with those reported by Mahler, Kline & Mehrota (1964) for Worthington DNA. They also measured the RNA content and found it to be less than 0.2%. None of our X-ray scattering measurements shows any appreciable differences between Worthington DNA and our own, or between sonicated and unsonicated DNA. (b) X-ray
rneasuremertts
The X-ray source was a water-cooled, rotating copper anode tube operated at 40 kv and 160 mA. Scattered intensities were measured in symmetrical four-slit diffractometers (Ritland, Kaesberg & Beeman, 1950). An effective monochromatization of about 98% was achieved using a nickel b filter and a proportional counter with a single-channel differential pulse-height analyzer set to receive the 1.54 A CuIG radiation. Among various runs the concentration of DNA salt in the scattering sample varied from I.0 mg/ml. to about 100 mg/ml. The lower concentrations were necessary at the smaller scattering angles. In nearly all cases the sample was at 22°C. Data were taken at scattering angles from 3.5 mrad to 350 mrad. Thus the equivalent Bragg spacings sampled ranged from 440 A to 4.4 A. Measurements at the smaller angles were made in a diffractometer having a separation of successive slits of 50 cm. The slit heights were 0.75 cm and slit widths either was used. 0.03 or 0.09 cm. At the larger angles a diffractometer of much higher luminosity Successive slits were 10.0 cm apart, the slit heights were 0.60 cm and slit widths 0,09 cm. Our complete scattering curve is a composite of overlapping runs using different slit widths or different diffractometers but the detailed discussion of the radius of gyration region is based upon data taken with fixed instrumental parameters. The scattering sample was O-1 cm thick. It was contained between crystalline quartz windows each 0.001 in. thick. Background and solvent scattering were separately measured
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and subtracted from the solution scattering. The experimental scrtttering curves were corrected for the smearing effects of the slit height and width (Lake, 1967) on a CDC3000 electronic computer. Determinations of the absolute scattering power at zero angle were made by extrapolation to zero angle and (in some cases) zero concentration of the intensities measured in the radius of gyration region. These intensities were compared to those scattered, in the identical geometry, by a polystyrene sample which had been previously calibrated in our laboratory against a gas used as an absolute scattering standard. (c) General theory We interpret our data in terms of the formalism for the scattering from a long rigid rod of constant cross-section. The basic theory was first given by Porod (1948). Let L be the length of the rod and R,, the cross-sectional radius of gyration defined by
Here ni is the effective number of electrons associated with the ith atom and ri is the distance of the ith atom from a long axis of the particle through the center of charge of the cross-section. The result of interest from Porod is that if L > > 2R, there then exists a region of the scattering curve which depends only on the distribution of charge in the cross-section and not on the length of the particle. This is found in a range of h = (4n/h) sin (412) g 27#1\ for which Lh > > 1. Here h( 1.54 A) is the X-ray wavelength and $ the angle of scattering. For values of h also satisfying hR, < 1 the scattering curve is quite accurately given by M(h) = IO exp ( -haRoZ/2).
(2)
This Gaussian approximation remains useful to values of hR, appreciably greater than unity. I(h) is proportional to the observed scattered flux after correction for slit height and width effects. At the smaller scattering angles in our experiments all of the above conditions are satisfied and experimental radii of gyration are deduced from the Gaussian form given above. To somewhat larger angles, the long-rod approximation remains valid and some information on the shape of the cross-section is available. At still larger angles, internal periodicities in the molecule dominate the scattering and periodicities both perpendicular and parallel to the long axis must be considered. The following equation is useful in discussing the mass per unit length of the molecule. I, = I,(M/L)tc
N (I - P,T,Z,)~
where I,, is from equation (2), I, is proportional to the X-ray flux incident on the sample, to the forward scattering cross-section of an electron and to the luminosity of the diffractometer, M is the dry molecular weight of the molecule, c its weight concentration in solution, t is the thickness of the scattering sample, N is Avogadro’s number, 2 is the number of electrons per unit molecular weight (dalton) of the dry neutral molecule, I, is the number of electrons per d&on of solvent, pS is the density of the solvent and p the dry partial specific volume of the molecule. It is convenient to use equation (3) in the following form: I,(I,tcN)-’
= M’/L
= (M/L)@ - l’psZs)2 .
(4)
Here M’/L is directly determined by the experimental measurements and is simply related to the mass-per-unit-length M/L and partial specific volume P of the dry molecule. I, is determined from a plot of log, [M(h)] oerm ha and extrapolation of the resulting straight line to h = 0. The measurement of the absolute scattering power by comparison to a gas scatterer is essentially a determination of Ie. Equation (3) is correct only for a two-component system. For a multicomponent system a discussion directly in t#erms of density fluctuations is more convenient. The problem is thoroughly treated by Casassa & Eisenberg (1964). However, equation (3) is the morn
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useful link to the non-thermodynamic information contained in the shape of the scattering curve and we discuss briefly how it must be corrected for a three-component system. Imagine, in a two-component systam, a volume of solution containing one macromolecule but large enough so that all solvent perturbations associated with the macromolecule are within the volume. The insertion of the macromolecule introduces E electrons/dalton into the volume. At the same time Pp,Z, electrons/daltons are expelled through the surface of the volume. Thus (I - Pp,ZJ is a measure of the number of effective scattering electrons in the volume. At sufficiently low concentrations of the macromolecule the volumes scatter independently and equation (3) follows. This prescription fails if the system contains added salt since, in general, the macromolecule interacts preferentially with salt or water and the material expelled from the volume has not the same composition as the unperturbed solvent. In the solvation of DNA additional electrons are expelled from the volume because of the reduced concentration of salt in the Debye-Htickel layer around the DNA. Their number per dalton of DNA is approximately f3(Z3 - P, psZs) where f3 is tho number of daltons of salt which must be removed per dalton of DNA added, to maintain constant chemical potential of the salt, and I, and P, are, respectively, the number of electrons per dalton and the partial specific volume of the salt. A more complete discussion may be found in Vrij & Overbeek (1962) and Eisenberg & Cohen (1968). It appears that for globular proteins and nucleoproteins near the isoelectric point the two-component formalism is usually adequate even when the buffer salts are present. But DNA has a high surface to volume ratio and surface charge density and, as Eisenberg & Cohen (1968) show, the three-component equations must be used.
(d) The radius
of gyration
region.
At sufficiently small angles the spherically averaged intensity scattered by a particle has a Gaussian dependence on the angle of scattering. For a long rod there is also, as we have discussed, a region where h I(h) is Gaussian and depends only on parameters of the cross-section. In either case, if the sample consists of a mixture of two particles of different sizes or different cross-sections, the appropriate quantity is approximated by the sum of two Gaussians. The customary plot of log,[l(h)], or log,@ I(h)], wersu4 ha may exhibit two easily distinguishable straight lines if the radii of gyration of the two particles differ sufficiently. Luzzati, Witz & Nicolaieff (1961), and also Kratky, Pilz, Schmitz & Oberdorfer (1963) for the cross-section case, have pointed out that a double straight line in the customary plot may have a quite different cause. Consider a long rod consisting of a central core of high effective electron density surrounded by an extended shell of low electron density and assume the total number of effective electrons associated with the shell is small compared to the number in the core. We must sum the amplitudes (not intensit,ies) scattered by the core and shell to obtain the amplitude scattered by the entire cross-section. At the smallest angles the angular dependence of h I(h) is determined by R,, the radius of gyration of the entire cross-section. However, the amplitude contributed by the shell is never large compared to that from the core and is decreasing more rapidly with angle since the shell is more extended. Thus at somewhat larger angles the total scattered amplitude is almost entirely from the core and, in the customary plot, we transfer to a new straight line whose slope gives R, the radius of gyration of the core. The scattering we measure from DNA in fact gives two straight lines which we shall interpret in terms of a core and shell. While the above arguments are qualitatively convincing it is difficult to give any general quantitative treatment. We instead calculate the scattered intensity for a simple model with approximately the parameters we deduce for DNA. Assume a long rod of circular cross-section, with an effective electron density p0 for 0 < P < T, and an effective electron density ps for r0 < T < r,. The scattered intensity is given by
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Actual and graphical cross-section parameters for certain long cylinders
POIPS = 72
pc~ps= 32
0.975 r. 0.95 r,
1.18 r, 1.16 r,
0.707 rc 0.76 rc
0.707 To 0.72 r,
Electrons per unit length ratio (actual)
0.90
VJIOP
0.89
0.80 0.72
R, (actual) R. (graph) RI (actual)
R1 (graph)
Finite cylinder, axial ratio 10 T, = r.
0.707 r, 0.69 rc
where K is a constant independent of h and J1 is the first-order Bessel function. See Burge & Draper (1967) for a discussion of this and other models. In Fig. 1 we plot log&h I(h)] versus (h~,)~ for r,/r, = 3 and two different values of pc/ps.The predicted double straight line is observed. To the extent that the second straight line (larger values of h) is free of scattering contributions from the shell its slope measures RI, the radius of gyration of the core. The extrapolation of this line to h. = 0 determines an I, associated with the core only and (I,)* is a measure of the effective number of electrons per unit length of the core. (lo)’ is the corresponding measure for the core and shell together. This is the 1, of equations (2), (3) and (4). In Table 1 the validity of the double straight line approximation is assessed. We compare R, and RI as determined from straight lines drawn through the plotted points to the corresponding quantities calculated directly from the model (equation (1)). We also compare [I1,lo]* from the plot to the electron-per-unit-length ratio from the model. The actual and graphical RO agree within 2 or 30/o. This is a measure of how accurately we have drawn and measured the slope of a line through the plotted points. The actual and RI agree less well and the graphical R, are greater. This implies that the shell graphical scatbering contimles to make a contribution in the core region. In Fig. 1 we plot also the scattering from a right circular cylinder of finite length and of uniform electron density (without as hell). The length-to-diameter ratio is 10. The known scattering function for the entire cylinder has been used but the plot is confined to the cross-section region. Only one straight line is observed and the graphical radius of gyration is in good agreement with theory. This reassures us that the double straight lines we find in the experimental data are not some unforeseen effect of finite cylinder length. DNA is reasonably straight and rigid over lengths greater than 10 diameters. One notes that the plot for the finite cylinder has a maximum at an (hr,J2 g 0.2. Such a maximum is expected for a cylinder of finite length (Luzzati & Benoit, 1961). Similar maxima are observed in the experimental data of Fig. 4 but these are of instrumental origin. At the very smallest angles slit-edge scattering rises rapidly and the proper subtraction of this background scattering becomes very difficult. At angles greater than the experimental maxima our background scattering is small compared to sample scattering and the results are reliable. At sufficiently small angles, of course, a plot of 1&1(h) must decrease toward zero. Lightscattering measurements (Eisenberg & Cohen, 1968; Mauss, Chambron, Daune & Benoit, 1967) on DNA preparations similar to ours show that this occurs at values of h about 0.1 as large as in Fig. 4.
3. Results Measurements of X-ray scattering were made on DNA dialyzed against a variety of salts. Usually only a single run was made and data do not extend much beyond the radius of gyration region. 22
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‘ I
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I
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/
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(hr,?
FIG. 1. TheoretiaaJ spherically averaged scattering curves (the dots) in the cross-se&ion region for certain solid circular cylinders. The straight lines are drawn through the points. Curve A, core and shell struoture of infinite length, rs/ro = 3, pc/ps = 72; curve B, core and shell structure of infinite length, T,/T,, = 3, p,/p, = 32; curve C, core only, radius = T,,, finite length L = 20 T,,. The relative vertical placements of the curves are without significance.
More extensive measurements were made on NaDNA dialyzed against O-05 M-NaCl and to a lesser extent on NaDNA against 1.0 M-NaCl and CsDNA against O-05 M-CsCl. The discussion will center on these cases. Our complete scattering curve for NaDNA dialyzed against O-05 M-NaCl is shown in Figure 2. This is a composite of several runs, overlapping in angular range, made with the different DNA concentrations and instrumental parameters appropriate to each angular range. In Figure 3 the peak region of the same curve is compared to the spherically averaged scattering caloulated for the A and l3 forms of DNA. The atomio co-ordinates for the calculation were taken from Fuller, Wilkins, Wilson & Hamilton (1965) and Langridge et al. (1960), respectively, and atomic scattering factors appropriate to the solvated molecule from Langridge et al. (1960). These were used in the evaluation of the Debye expression :
I(h) =
CEfmfny=
BR
(6)
where n,,,,, is the distance between the nath and nth atoms and f,,, is the scattering factor of the n&h atom. The calculations were made for double helices 30 base pairs
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FIG 2. The complete soattering curve for NaDNA dialyzed against 0.05 x-NaC1. The curve is a composite of several partial runs with different DNA concentrations and different instrumental parameters.
long. This is reasonably fast on a CDC3600 computer if one exploits the symmetry of the molecule. The calculation is for the ionized core. No counterions are included. It is clear that the experimental results are in much better agreement with the B form. This is one of the more direct indications that the B form is that found in solution. In Figure 4 we plot the radius of gyration region for NaDNA and CsDNA. Two radii of gyration are observed which we believe imply a core and shell structure for the solvated molecule. It seems unlikely that a fraction of the DNA molecules in close lateral association is introducing the larger radius of gyration. We see no such association in our electron micrographs. In addition, such an association might be expected to be concentration dependent but experimental curves on NaDNA in the concentration range 1-Oto 12 mg/ml. show very similar double straight-line plots. Finally, as we shall discuss, the mass per unit length determined from the extrapolation to zero angle of the first, or steeper, straight line is very close to the theoretical value for the B form. This would not be the case if the first straight line were due to aggregates. There remains the possibility that the double straight line represents some characteristic feature of the DNA scattering curve which has nothing to do with a core and shell structure. In particular we must remember that DNA has perisdicities along the axis which are ignored in the theory of the cross-section scattering of long rigid rods. The greatest of these periods is 34 A. The angular region in which we measure our first radius of gyration is between 10 and 30 mrad which samples equivalent Bragg spacings between 150 and 50 A. Internal periodicities can contribute no appreciable intensity in this region. Our second radius of gyration terminates at roughly 50 mrad or 31 A. No doubt the scattering seen on the first layer line of the fiber pictures is here making some contribution to our measurements but we believe this contribution is small. In the fiber diagrams the scattering seen on the second and higher layer lines is more intense than that on the first. It is the higher layer lines which contribute to our peak region of Figure 2 beginning at about 100 mrad. We point out that our measured intensity in this region is about one-tenth of what we observe at 50 mrad. In addition the
S. BRAM
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I
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200
250
300
350
Scattering angle ( m rad )
FIG. 3. The observed scattering at larger angles from NaDNA dialyzed against 0.06 M-Nacl is Bragg spacing. compared to theory for the A and B forms, 100 mrad = 15.4 A equivalent B form, theory; - - -, A form, theory; A, 107 mg DNA/ml., not sonioated (a gel); 0, 3G’DNA/ml., sonicated. Vertical positioning is arbitrary, for maximum visibility.
calculations of the scattering from the 30 base-pair model of the B form, which are shown in Figure 3, have been extended into the radius of gyration region. We find no hint of two radii of gyration. It is perhaps not impossible that some slight supertwisting of the molecule would simulate a core and shell structure in projection along the axis or introduce additional intensity at small angles from long axial periods. No evidence for such a structure is seen in fiber diagrams and this, and most other models, leave unexplained that we observe the theoretical mass per unit length. Scattering measurements on solutions containing less than 5 mg of DNA/ml. are somewhat tedious and can be uncertain, therefore careful checks of concentration dependence were made only on NaDNA dialyzed against 0.05 M-Nacl. These are illustrated in Figure 5. Fortunately, the concentration dependence is small. The results we quote are not extrapolated to zero concentration but the error thus introduced is appreciably less than that from other sources. Note that the data of Figure 5 are
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FIQ. 4. Some measured scattering curves in the radius of gyration region. Curve A, NaDNA, 12 mg/ml., 0.05 M-N&I; curve B, NeDNA, 5.55 mg/ml., 1.0 M-N&~; curve C, CsDNA, 7.83 mg/ml., 0.05 an-CsCl. The relative vertical positions are without significance.
before slit corrections. The radii of hydration will not agree with the final results in Table 2. In Table 2 we collect the principal results of the measurements. The more reliable NaDNA and CsDNA data are given at the top of the Table. The parameters have been extracted from the measurements as described under Materials and Methods. Where a value of R, is not given, the experimental data were not good enough to permit a clear resolution of two radii of gyration. DNA concentrations are calculated for the neutral salt. We estimate that the R, of the more careful runs are reliable to 3 or 4% and for the salts other than NaCl and CsCl perhaps 5%. The I, which come from the extrapolation to zero angle of the first (or R,) straight line have about this same reliability. However M’IL depends not only on I, but on an absolute intensity calibration in which there might be an additional systematic error of as large as 4%. On most of our curves R, can be determined as accurately as R, but for R, and (IJI,,)’ the question is rather one of interpretation. How realistic is the particular core and shell model we choose; to what extent are scattering contributions from the shell influencing the measured values of R, and I, ? The last two columns of Table 2 compare measured and theoretical values of the mass per unit length. The measured values are calculated by Eisenberg & Cohen (1968) from M’IL in the thesis of Bram (1968), upon a part of which thesis this paper is based. Eisenberg & Cohen (1968) use the correct three-component formalism and the partial specific volumes and density increments from their own recent work, Cohen & Eisenberg (1968). Readers of Eisenberg & Cohen (1968) and this paper are warned that our M’/L are the M’ of Table 1 of Eisenberg & Cohen (1968), divided by Avogadro’s number.
320
FIO. 5. The extrapolations to zero DNA concentration of R, and [h I(h) Jbx o for NaDNA dialyzed against 0.05 M-NaCl. The solid circles are sonicated DNA, the open circles are unsonicated. These results are before slit corrections. TABLE
2
Experimental cross-section parameters of calf thymes DNA
Buffer
salt
04% M-NaCl 0.05 ~-Nacl 1.0 M-NaC1 o&-i
M-cd!1
0.5 ix-LiCl 1.0 M-LiCl 1.0 M-NH&I 0.05 ~-Kc1 0.10 ~-Kc1 0.05 M-RbCl 0.10 M-RbCl 0.54 xu-RbCI
DNA concn (mglml.)
2.21 12.2 5.55 7.83 2.08 1.99 2.09 8.24 9.25 8.03 8.02 8.1
(MI-V
R&9
R,(A)
9.6 9.0 8.9 10.4 8.5 8.8 8.9 9.4 9.6 10.8 10.4 9.5
7.9 7.8 7.7 9.0 7.3 8.0 9.0 8.3
M’lL
9.15 9.06 7.76 11.1 6.98 6.98 6.55 8.96 7.89 10.2 8.30 7.64
VJLIP
0.92 0.92 0.93 0.93
M/L
daltons/A
193 191 204 240
B-structure theoretical daltons/A
197 197 197 263
0.95 0.94 0.93 0.94
A few measurements on NaDNA dialyzed against 0.05 M-NaCI were made at 4°C and 35°C. Both M’JL and R, decrease with increasing temperature. M’IL decreases about lo%, R, appreciably less. Our observations do not permit a choice from among the several possible explanations.
4. Discussion In Table 2 we give theoretical M/L only for the B form. For the A form they are, of course, about 30% greater. The measured M/L are in excellent agreement with those calculated for the neutral salts in the B form. In fact if, with the O-05 M-NaCI preparation, we use the I, determined by an extrapolation to zero DNA concentration we
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FIG. 6. The slit-corrected experimental data at 22°C for N&DNA dialyzed against 0.05 M-N&~ are compared to the scattering from certain models. Squares, 6.09 mg NaDNA/ml. ; circles, 12.0 mg NaDNA/ml. ; long-dash line, right circular cylinder, no shell ; solid line, a Gaussian scattering ourve, exp [ -haR,a/2]; short-dash line, core and shell model r,/r,, = 3, 10% of electrons in shell. All curves are normalized to unity at h = 0 and the R, is the total cross-sectional radius of gyration of each. Such 8 plot makes the curves coincident in the radius of gyration region.
obtain M/L = 196 daltona/& an agreement with theory which must be considered somewhat fortuitous. Note that M'/L shows a strong dependence on salt concentration. This is expected since Cohen & Eisenberg (1968) find a compensating dependence of V on salt concentration. Their V are also appreciably lower than the values around 055 cm3/g for NaDNA which are common in the literature. M/L should be independent of solution conditions. If the M/L had been calculated using equation (4) they would have been 15 or 20% less than those listed. Thus the number of effective scattering electrons per unit length is reduced roughly 10% by preferential interactions between the DNA and the components of the solvent. We have not calculated M/L for the other salts since accurate partial specific volumes and density increments are not available. We now discuss the additional information available in the shape of the scattering curve in the radius of gyration region. We think it clear that the slope of the first
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straight line, giving R,, represents information about the molecular cross-section plus its perturbed solvent environment. This is emphasized by the fact that it is the extrapolation of this straight line to zero angle which furnishes the correct values of M/L. In addition, R, is always considerably larger than the theoretical cross-section radius of gyration of ionized DNA which is about 7.0 A. Thus one must assume the existence of an extended shell whose average electron density exceeds that of the solvent. Even the unlikely neutral structure in which a metal ion is tightly bound close to each phosphorus will give (in the absence of solvent contributions) an R, of at most 8 8. It is equally clear that R, depends on more than just the ionized DNA core. The R, we measure are definitely greater than 7 A. They also show an increase with increasing atomic number of the counterion. This is understandable if counterions close to the DNA surface are making a contribution to the core scattering. Such a contribution from the shell is present even in the calculations on our idealized model. However, if we assume the validity of our core and shell model, the measured R, and R, permit a calculation of the radial extent of the shell. Using R, == 9.6 A and R, = 7.8 A, the parameters for the 0.05 al-NaCl measurements, and taking a core radius rc = 10 A for the DNA, we find that the shell is approximately 20 A thick, i.e. it extends from r, = 10 A to an r, = 30 8. The absolute intensity measurements imply about 150 effective scattering electrons per base pair (3.4 A) of the NaDNA. The measured (1,/I,,)* = 0.92 then assigns S:h of these, or 12 electrons per base pair, to the shell. We may ask to what extent these results agree with expectations for solvated DNA. The Debye-Hiickel length in 0.05 M-NaCl is 13.6 A. Most of the shielding counterions will be found within a couple of Debye-Hiickel lengths. Presumably the counterions, with perhaps a contribution from water electrostricted in the field of the DebyeHiickel shell, are providing the scattering electrons of the shell. It must be remembered that the 12 electrons per base pair just mentioned is the net, above unperturbed solvent. Since some salt is preferentially pushed out of the shell about 25 electrons per base pair must be provided by counterions and electrostriction. Depending on the partial specific volume one assumes, 15 to 20 of these might come from the two Na+ counterions. On the other hand all 25 could be furnished by a 1% increase in density of the water in the shell. The X-ray data for the 0.05 M-CsCI give an r, = 29 A and for I.0 M-NaCl, r, = 24 8. The latter shell thickness of 14 A is greater than we would expect if the usual expression for the Debye-Hiickel length were to remain valid at so high an ionic strength. An unsatisfactory feature of the results is the assignment of about the same fraction of scattering electrons to the shell for different DNA salts. The counterions, in fact, represent a much larger fraction of the total scattering in CsDNA than in NaDNA. No doubt a partial explanation is the evidence that some shell scattering is contributing to the core parameters. The purpose of this discussion is to show that the core and shell implications of the X-ray data are in reasonable agreement with expectations. The data are not good enough to justify a more realistic and complex model, for instance one in which the density of shell electrons decays exponentially from the core. Nor can we shed much light on the problem of site binding versus ion clouds except to remark that site binding appears not to be necessary to explain our data. In this connection we call attention to Figure 3 where, at larger angles, the scattering calculated for the ionized core is compared to experiment. We did a number of calculations placing Na+ in
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fixed positions near the phosphorus. The agreement with experiment was always poorer. This can be taken as evidence against site binding. Data of a quality which is probably technically feasible, but time consuming, might very well answer some of these questions. In summary both our mass per unit length determinations and the shape of the scattering curve in the peak region at larger angles are in excellent agreement with predictions for the B form of DNA. The former measurements give simultaneous support to our determinations of absolute X-ray intensities and to the recent careful partial specific volume and density increment measurements of Cohen & Eisenberg (1968). We find two cross-sectional radii of gyration which strongly support a core and shell structure for solvated DNA and, within the somewhat limited resolution of the data, the parameters deduced are in satisfactory agreement with an ionized DNA core surrounded by a Debye-Hiickel layer of counterions. We close with a brief comparison of our results and those of Luzzati et al. (1961, 1967) and Kratky (1963). Neither of these authors observed more than a single radius of gyration and neither made measurements in the peak region at larger angles. For NaDNA both measured radii of gyration between 8.0 and 8.5 A, values which fall between our R, and R,. For CsDNA Luzzati et al. (1967) measure a value very close to our R,. Both authors made absolute intensity measurements and determined M/L but used a two-component formalism equivalent to our equation (3). The recent V measurements of Cohen & Eisenberg (1968) were not then available. Eisenberg & Cohen (1968) have recalculated the M/L of Luzzati et al. (1961,1967) using the three-component equations. The resulting M/L are about 20% below the theoretical values. Luzzati et al. treat their experimental data in a way which may obscure the presence of two radii of gyration. Their experimental scatterin, u curves, taken with slits of effectively infinite height, are presented as log I(h) vers?Cslog h. In such a plot comparisons with calculated curves permit the extraction of a radius of gyration and an extrapolated forward intensity. In Figure 6 we plot some of our NaDNA data (but slit corrected) against the scattering calculated for various models in this way. The agreement is best with the core and shell model and in fact would have been better if a model assigning 8% of the electrons to the shell had been used. The model plotted is the first one of Figure 1 which assigns 10% of the electrons to the shell. We note that the presence of two radii of gyration is not obvious in these plots. However there are other important differences in the two experiments. Luzzati et al. (1961,1967) did not dialyze against buffer, their DNA concentrations were almost a factor of ten greater than we have used and their measurements did not reach such small angles. These factors also would make more difficult the observation of two radii of gyration. It is interesting that if we extrapolate to zero angle using the straight line representing our second and smaller radius of gyration we obtain an M/L within 5% of that’ reported by Luzzati et al. We thank Professor Hans Ris and Professor J. W. Anderegg for numerous helpful suggestions and Dr V. Luzzati for several very constructive comments on the manuscript. We were greatly assisted by the manuscripts of Eisenberg & Cohen (1068) which the authors kindly made available to us before publication. This work was supported by research and training grants of tha National Institutes of Healtll.
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REFERENCES Bram, S. (1968). University of Wisconsin, Ph.D. Thesis. Bram, S. & Ris, H. (1971). J. Mol. Biol. 55, 325. Burge, R. E. & Draper, J. C. (1967). Acta Cryst. 22, 6. Casassa, E. F. & Eisenberg, H. (1964), Advanc. Protein Chem. 19, 287. Cohen, G. & Eisenberg, H. (1966). Biopolymers, 4, 429. Cohen, G. & Eisenberg, H. (1968). Biopolymers, 6, 1077. Eisenberg, H. & Cohen, G. (1968). J. Mol. BioZ. 37, 355. Fiske, C. H. & Subbarow, Y. (1925). J. Biol. Chem. 66, 375. Fuller, W., Wilkins, M. H. F., Wilson, H. R. & Hamilton, L. D. (1965). J. Mol. BioZ. 12, 60. Kratky, 0. (1963). Progress in Biophysics, 13, 107. Kratky, O., Pilz, I., Schmitz, P. J. & Oberdorfer, R. (1963). 2. Naturj. 18b, 180. Lake, 5. A. (1967). Acta Cryst. 23, 191. Langridge, R., Marvin, D. A., Seeds, W. E., Wilson, H. R., Hooper, C. W., Wilkins, M. H. F. & Hamilton, L. D. (1960). J. Mol. BioZ. 2, 38. Luzzati, V. & Benoit, H. (1961). Actrc Cryst. 14, 297. Luzzati, V., Masson, F., Mathis, A. & Saludjian, P. (1967). Biopolymers, 5, 491. Luzzati, V., Nicolaieff, A. & Masson, F. (1961). J. Mol. BioZ. 3, 185. Luzzati, V., Witz, J. & Nicolaieff, A. (1961). J. Mol. BioZ. 3, 379. Mahler, H. R., Kline, B. & Mehrota, B. D. (1964). J. Mol. BioZ. 9, 801. Mauss, Y., Chambron, J., Daune, M. & Benoit, H. (1967). J. Mol. BioZ. 27, 579. Porod, G. (1948). Acta Pity. Austriuca., 2, 255. Ris, H. (1961). Canad. J. Genet. 3, 95. Ritland, H. N., Kaesberg, P. & Beeman, W. W. (1950). J. AppZ. Phys. 21, 838. Sharp, P. & Bloomfield, V. A. (1968). J. Chem. Phys. 48, 2149. Vrij, A. & Overbeek, J. Th. G. (1962). J. CoZZ. Sci. 17, 570. Zamenhof, S. (1958). Biochemical Preparations, 6, 8. Zubay, G. & Doty, P. (1959). J. Mol. BioZ. 1, 1.
On the Cross-section Structure of Deoxyribonucleic Acid in Solution STANLEY BRAM~ AND W. W. BEEMAN
Biophysics Laborato y, University of Wisconsin Madison, Wis. 53706, U.S.A. (Received 22 July 1969, and in revised form 11 September 1970) We present X-ray scattering data on dilute solutions of calf thymus DNA in a number of monovalent chlorides, particularly EaC1 and CsCI. Salt concentrations are from 0.05 to 1.0 M. The data include a range of small angles where the scattered flux is sensitive to the cross-section parameters of the molecule. Our measured mass per unit length for NaDNA is within 2 or 3% of the theoretical value for the B form. For CsDNA our measurement is about 9% below theory but within experimental error. At larger angles, where internal periodicities dominate the scattering, the data on NaDNA are in much better agreement with the B than with the A form. We observe two cross-section radii of gyration, a result characteristic of a cylindrical core of high electron density surrounded by a shell of much lower electron density. The larger radius of gyration is that of the entire structure, the smaller characterizes the core. Our results imply that the core is ionized or partially ionized DNA and that the shell is a Debye-Hiickel layer of counterions and perhaps electrostricted solvent about 20 A thick. The experimental data and the model are not accurate enough to decide what fraction of the counterions should be considered site bound to the DNA although there is some evidence to indicate that site binding, if it exists, is not large.
1. Introduction The structure of double-stranded DNA as it exists in crystalline fibers is well established. The high humidity or B form is presumably that found in dilute solution. The molecule is about 20 A in diameter and a variety of approaches give persistence of rigidity lengths of between 500 and 1000 A (Sharp Q Bloomfield, 1968). Thus, dilute solutions of DNA may be studied by X-ray techniques which furnish certain crosssection parameters of long rigid rods in a random, unoriented array. These parameters include the cross-sectional radius of gyration, the mass per unit length and some information on the electron density as a function of distance from the axis of the rod. For DNA, one may hope to verify the conformation in solution and to extract information on the structure of the surrounding ion cloud and perturbed solvent which is not easily available using other methods. Three such studies have appeared (Luzzati, Nicolaieff & Masson, 1961; Kratky, 1963; Luzatti, Masson, Mathis & Saludjian, 1967). These support the B form aa the structure in dilute solution. We here present X-ray scattering data for calf thymus DNA in a number of different salts which are in excellent agreement with the B form and which also establish that the surrounding counterions and solvent are influencing the scattering. t Present France.
address:
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2. Materials and Methods (a) Materials The calf thymus DNA used in this work was either obtained from the Worthington Biochemical Corp., Freehold, N. J., U.S.A., who use the isolation procedure of Zamenhof (1958), or isolated in our laboratory from calf thymus nucleohistones. The nucleohistones were prepared following Zubay & Doty (1959) as modified by Ris (1961). Additional details are given in the paper following this one (Bram & Ris, 1971). Our nucleohistone was deproteinized following Zamenhof (1958). This involved extraction with 2 aa-NaCl in a Waring blender, ethanol precipitation, two detergent treatments in 0.15 &r-NaCl and 0.015 M-sodium citrate at pH 7.1, and a final ethanol precipitation. The average molecular weight of the resulting DNA was at least 107. Because high viscosity is troublesome in filling sample holders most of our X-ray runs were on DNA sonicated according to the method of Cohen & Eisenberg (1966). About 25 ml. of 0.15 ar-NaCl and 0.015 M-sodium citrate containing 2 to 4 mg of DNA/ml. was irradiated in a polyethylene beaker using the T150 horn of a Branson no. 125 Sonifier. The sample was in ice and a nitrogen atmosphere. Two 30-set pulses at 125 w and 20 kc, separated by a 2-min cooling period, were used. Electron microscopy of the sonicated solution revealed well-dispersed molecules, without evidence of strand separation, and with an average length around 2000 A. To eliminate any divalent cations which might cause aggregation, and to reduce nuclease activity, most of the samples were dialyzed at 4°C against 0.075 M-NaCl, 0.01 M-EDTA (disodium salt) at pH 8.0 for as long as 3 days. All samples were then dialyzed exhaustively against the desired buffer just before the X-ray scattering experiments. Phosphorus content was determined by the method of Fiske & Subbarow (1925). DNA concentrations were calculated from the phosphorus content, an average nucleotide molecular weight of 308.6 and the atomic weight of the cation. Optical density measurements gave a molar extinction coefficient at 2590 A of 6.5 x lo6 cm2/mol P for both the Worthington preparation and our own. After sonication the ratio was 6.6 x 106. Thus no very great denaturation has occurred. The protein content, measured as histone, for both DNA’s was less than 0.4%. Our values for the extinction coefficient and protein content are in excellent agreement with those reported by Mahler, Kline & Mehrota (1964) for Worthington DNA. They also measured the RNA content and found it to be less than 0.2%. None of our X-ray scattering measurements shows any appreciable differences between Worthington DNA and our own, or between sonicated and unsonicated DNA. (b) X-ray
rneasuremertts
The X-ray source was a water-cooled, rotating copper anode tube operated at 40 kv and 160 mA. Scattered intensities were measured in symmetrical four-slit diffractometers (Ritland, Kaesberg & Beeman, 1950). An effective monochromatization of about 98% was achieved using a nickel b filter and a proportional counter with a single-channel differential pulse-height analyzer set to receive the 1.54 A CuIG radiation. Among various runs the concentration of DNA salt in the scattering sample varied from I.0 mg/ml. to about 100 mg/ml. The lower concentrations were necessary at the smaller scattering angles. In nearly all cases the sample was at 22°C. Data were taken at scattering angles from 3.5 mrad to 350 mrad. Thus the equivalent Bragg spacings sampled ranged from 440 A to 4.4 A. Measurements at the smaller angles were made in a diffractometer having a separation of successive slits of 50 cm. The slit heights were 0.75 cm and slit widths either was used. 0.03 or 0.09 cm. At the larger angles a diffractometer of much higher luminosity Successive slits were 10.0 cm apart, the slit heights were 0.60 cm and slit widths 0,09 cm. Our complete scattering curve is a composite of overlapping runs using different slit widths or different diffractometers but the detailed discussion of the radius of gyration region is based upon data taken with fixed instrumental parameters. The scattering sample was O-1 cm thick. It was contained between crystalline quartz windows each 0.001 in. thick. Background and solvent scattering were separately measured
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and subtracted from the solution scattering. The experimental scrtttering curves were corrected for the smearing effects of the slit height and width (Lake, 1967) on a CDC3000 electronic computer. Determinations of the absolute scattering power at zero angle were made by extrapolation to zero angle and (in some cases) zero concentration of the intensities measured in the radius of gyration region. These intensities were compared to those scattered, in the identical geometry, by a polystyrene sample which had been previously calibrated in our laboratory against a gas used as an absolute scattering standard. (c) General theory We interpret our data in terms of the formalism for the scattering from a long rigid rod of constant cross-section. The basic theory was first given by Porod (1948). Let L be the length of the rod and R,, the cross-sectional radius of gyration defined by
Here ni is the effective number of electrons associated with the ith atom and ri is the distance of the ith atom from a long axis of the particle through the center of charge of the cross-section. The result of interest from Porod is that if L > > 2R, there then exists a region of the scattering curve which depends only on the distribution of charge in the cross-section and not on the length of the particle. This is found in a range of h = (4n/h) sin (412) g 27#1\ for which Lh > > 1. Here h( 1.54 A) is the X-ray wavelength and $ the angle of scattering. For values of h also satisfying hR, < 1 the scattering curve is quite accurately given by M(h) = IO exp ( -haRoZ/2).
(2)
This Gaussian approximation remains useful to values of hR, appreciably greater than unity. I(h) is proportional to the observed scattered flux after correction for slit height and width effects. At the smaller scattering angles in our experiments all of the above conditions are satisfied and experimental radii of gyration are deduced from the Gaussian form given above. To somewhat larger angles, the long-rod approximation remains valid and some information on the shape of the cross-section is available. At still larger angles, internal periodicities in the molecule dominate the scattering and periodicities both perpendicular and parallel to the long axis must be considered. The following equation is useful in discussing the mass per unit length of the molecule. I, = I,(M/L)tc
N (I - P,T,Z,)~
where I,, is from equation (2), I, is proportional to the X-ray flux incident on the sample, to the forward scattering cross-section of an electron and to the luminosity of the diffractometer, M is the dry molecular weight of the molecule, c its weight concentration in solution, t is the thickness of the scattering sample, N is Avogadro’s number, 2 is the number of electrons per unit molecular weight (dalton) of the dry neutral molecule, I, is the number of electrons per d&on of solvent, pS is the density of the solvent and p the dry partial specific volume of the molecule. It is convenient to use equation (3) in the following form: I,(I,tcN)-’
= M’/L
= (M/L)@ - l’psZs)2 .
(4)
Here M’/L is directly determined by the experimental measurements and is simply related to the mass-per-unit-length M/L and partial specific volume P of the dry molecule. I, is determined from a plot of log, [M(h)] oerm ha and extrapolation of the resulting straight line to h = 0. The measurement of the absolute scattering power by comparison to a gas scatterer is essentially a determination of Ie. Equation (3) is correct only for a two-component system. For a multicomponent system a discussion directly in t#erms of density fluctuations is more convenient. The problem is thoroughly treated by Casassa & Eisenberg (1964). However, equation (3) is the morn
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useful link to the non-thermodynamic information contained in the shape of the scattering curve and we discuss briefly how it must be corrected for a three-component system. Imagine, in a two-component systam, a volume of solution containing one macromolecule but large enough so that all solvent perturbations associated with the macromolecule are within the volume. The insertion of the macromolecule introduces E electrons/dalton into the volume. At the same time Pp,Z, electrons/daltons are expelled through the surface of the volume. Thus (I - Pp,ZJ is a measure of the number of effective scattering electrons in the volume. At sufficiently low concentrations of the macromolecule the volumes scatter independently and equation (3) follows. This prescription fails if the system contains added salt since, in general, the macromolecule interacts preferentially with salt or water and the material expelled from the volume has not the same composition as the unperturbed solvent. In the solvation of DNA additional electrons are expelled from the volume because of the reduced concentration of salt in the Debye-Htickel layer around the DNA. Their number per dalton of DNA is approximately f3(Z3 - P, psZs) where f3 is tho number of daltons of salt which must be removed per dalton of DNA added, to maintain constant chemical potential of the salt, and I, and P, are, respectively, the number of electrons per dalton and the partial specific volume of the salt. A more complete discussion may be found in Vrij & Overbeek (1962) and Eisenberg & Cohen (1968). It appears that for globular proteins and nucleoproteins near the isoelectric point the two-component formalism is usually adequate even when the buffer salts are present. But DNA has a high surface to volume ratio and surface charge density and, as Eisenberg & Cohen (1968) show, the three-component equations must be used.
(d) The radius
of gyration
region.
At sufficiently small angles the spherically averaged intensity scattered by a particle has a Gaussian dependence on the angle of scattering. For a long rod there is also, as we have discussed, a region where h I(h) is Gaussian and depends only on parameters of the cross-section. In either case, if the sample consists of a mixture of two particles of different sizes or different cross-sections, the appropriate quantity is approximated by the sum of two Gaussians. The customary plot of log,[l(h)], or log,@ I(h)], wersu4 ha may exhibit two easily distinguishable straight lines if the radii of gyration of the two particles differ sufficiently. Luzzati, Witz & Nicolaieff (1961), and also Kratky, Pilz, Schmitz & Oberdorfer (1963) for the cross-section case, have pointed out that a double straight line in the customary plot may have a quite different cause. Consider a long rod consisting of a central core of high effective electron density surrounded by an extended shell of low electron density and assume the total number of effective electrons associated with the shell is small compared to the number in the core. We must sum the amplitudes (not intensit,ies) scattered by the core and shell to obtain the amplitude scattered by the entire cross-section. At the smallest angles the angular dependence of h I(h) is determined by R,, the radius of gyration of the entire cross-section. However, the amplitude contributed by the shell is never large compared to that from the core and is decreasing more rapidly with angle since the shell is more extended. Thus at somewhat larger angles the total scattered amplitude is almost entirely from the core and, in the customary plot, we transfer to a new straight line whose slope gives R, the radius of gyration of the core. The scattering we measure from DNA in fact gives two straight lines which we shall interpret in terms of a core and shell. While the above arguments are qualitatively convincing it is difficult to give any general quantitative treatment. We instead calculate the scattered intensity for a simple model with approximately the parameters we deduce for DNA. Assume a long rod of circular cross-section, with an effective electron density p0 for 0 < P < T, and an effective electron density ps for r0 < T < r,. The scattered intensity is given by
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Actual and graphical cross-section parameters for certain long cylinders
POIPS = 72
pc~ps= 32
0.975 r. 0.95 r,
1.18 r, 1.16 r,
0.707 rc 0.76 rc
0.707 To 0.72 r,
Electrons per unit length ratio (actual)
0.90
VJIOP
0.89
0.80 0.72
R, (actual) R. (graph) RI (actual)
R1 (graph)
Finite cylinder, axial ratio 10 T, = r.
0.707 r, 0.69 rc
where K is a constant independent of h and J1 is the first-order Bessel function. See Burge & Draper (1967) for a discussion of this and other models. In Fig. 1 we plot log&h I(h)] versus (h~,)~ for r,/r, = 3 and two different values of pc/ps.The predicted double straight line is observed. To the extent that the second straight line (larger values of h) is free of scattering contributions from the shell its slope measures RI, the radius of gyration of the core. The extrapolation of this line to h. = 0 determines an I, associated with the core only and (I,)* is a measure of the effective number of electrons per unit length of the core. (lo)’ is the corresponding measure for the core and shell together. This is the 1, of equations (2), (3) and (4). In Table 1 the validity of the double straight line approximation is assessed. We compare R, and RI as determined from straight lines drawn through the plotted points to the corresponding quantities calculated directly from the model (equation (1)). We also compare [I1,lo]* from the plot to the electron-per-unit-length ratio from the model. The actual and graphical RO agree within 2 or 30/o. This is a measure of how accurately we have drawn and measured the slope of a line through the plotted points. The actual and RI agree less well and the graphical R, are greater. This implies that the shell graphical scatbering contimles to make a contribution in the core region. In Fig. 1 we plot also the scattering from a right circular cylinder of finite length and of uniform electron density (without as hell). The length-to-diameter ratio is 10. The known scattering function for the entire cylinder has been used but the plot is confined to the cross-section region. Only one straight line is observed and the graphical radius of gyration is in good agreement with theory. This reassures us that the double straight lines we find in the experimental data are not some unforeseen effect of finite cylinder length. DNA is reasonably straight and rigid over lengths greater than 10 diameters. One notes that the plot for the finite cylinder has a maximum at an (hr,J2 g 0.2. Such a maximum is expected for a cylinder of finite length (Luzzati & Benoit, 1961). Similar maxima are observed in the experimental data of Fig. 4 but these are of instrumental origin. At the very smallest angles slit-edge scattering rises rapidly and the proper subtraction of this background scattering becomes very difficult. At angles greater than the experimental maxima our background scattering is small compared to sample scattering and the results are reliable. At sufficiently small angles, of course, a plot of 1&1(h) must decrease toward zero. Lightscattering measurements (Eisenberg & Cohen, 1968; Mauss, Chambron, Daune & Benoit, 1967) on DNA preparations similar to ours show that this occurs at values of h about 0.1 as large as in Fig. 4.
3. Results Measurements of X-ray scattering were made on DNA dialyzed against a variety of salts. Usually only a single run was made and data do not extend much beyond the radius of gyration region. 22
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‘ I
I
IO
20
I
30
/
40
50
(hr,?
FIG. 1. TheoretiaaJ spherically averaged scattering curves (the dots) in the cross-se&ion region for certain solid circular cylinders. The straight lines are drawn through the points. Curve A, core and shell struoture of infinite length, rs/ro = 3, pc/ps = 72; curve B, core and shell structure of infinite length, T,/T,, = 3, p,/p, = 32; curve C, core only, radius = T,,, finite length L = 20 T,,. The relative vertical placements of the curves are without significance.
More extensive measurements were made on NaDNA dialyzed against O-05 M-NaCl and to a lesser extent on NaDNA against 1.0 M-NaCl and CsDNA against O-05 M-CsCl. The discussion will center on these cases. Our complete scattering curve for NaDNA dialyzed against O-05 M-NaCl is shown in Figure 2. This is a composite of several runs, overlapping in angular range, made with the different DNA concentrations and instrumental parameters appropriate to each angular range. In Figure 3 the peak region of the same curve is compared to the spherically averaged scattering caloulated for the A and l3 forms of DNA. The atomio co-ordinates for the calculation were taken from Fuller, Wilkins, Wilson & Hamilton (1965) and Langridge et al. (1960), respectively, and atomic scattering factors appropriate to the solvated molecule from Langridge et al. (1960). These were used in the evaluation of the Debye expression :
I(h) =
CEfmfny=
BR
(6)
where n,,,,, is the distance between the nath and nth atoms and f,,, is the scattering factor of the n&h atom. The calculations were made for double helices 30 base pairs
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FIG 2. The complete soattering curve for NaDNA dialyzed against 0.05 x-NaC1. The curve is a composite of several partial runs with different DNA concentrations and different instrumental parameters.
long. This is reasonably fast on a CDC3600 computer if one exploits the symmetry of the molecule. The calculation is for the ionized core. No counterions are included. It is clear that the experimental results are in much better agreement with the B form. This is one of the more direct indications that the B form is that found in solution. In Figure 4 we plot the radius of gyration region for NaDNA and CsDNA. Two radii of gyration are observed which we believe imply a core and shell structure for the solvated molecule. It seems unlikely that a fraction of the DNA molecules in close lateral association is introducing the larger radius of gyration. We see no such association in our electron micrographs. In addition, such an association might be expected to be concentration dependent but experimental curves on NaDNA in the concentration range 1-Oto 12 mg/ml. show very similar double straight-line plots. Finally, as we shall discuss, the mass per unit length determined from the extrapolation to zero angle of the first, or steeper, straight line is very close to the theoretical value for the B form. This would not be the case if the first straight line were due to aggregates. There remains the possibility that the double straight line represents some characteristic feature of the DNA scattering curve which has nothing to do with a core and shell structure. In particular we must remember that DNA has perisdicities along the axis which are ignored in the theory of the cross-section scattering of long rigid rods. The greatest of these periods is 34 A. The angular region in which we measure our first radius of gyration is between 10 and 30 mrad which samples equivalent Bragg spacings between 150 and 50 A. Internal periodicities can contribute no appreciable intensity in this region. Our second radius of gyration terminates at roughly 50 mrad or 31 A. No doubt the scattering seen on the first layer line of the fiber pictures is here making some contribution to our measurements but we believe this contribution is small. In the fiber diagrams the scattering seen on the second and higher layer lines is more intense than that on the first. It is the higher layer lines which contribute to our peak region of Figure 2 beginning at about 100 mrad. We point out that our measured intensity in this region is about one-tenth of what we observe at 50 mrad. In addition the
S. BRAM
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Scattering angle ( m rad )
FIG. 3. The observed scattering at larger angles from NaDNA dialyzed against 0.06 M-Nacl is Bragg spacing. compared to theory for the A and B forms, 100 mrad = 15.4 A equivalent B form, theory; - - -, A form, theory; A, 107 mg DNA/ml., not sonioated (a gel); 0, 3G’DNA/ml., sonicated. Vertical positioning is arbitrary, for maximum visibility.
calculations of the scattering from the 30 base-pair model of the B form, which are shown in Figure 3, have been extended into the radius of gyration region. We find no hint of two radii of gyration. It is perhaps not impossible that some slight supertwisting of the molecule would simulate a core and shell structure in projection along the axis or introduce additional intensity at small angles from long axial periods. No evidence for such a structure is seen in fiber diagrams and this, and most other models, leave unexplained that we observe the theoretical mass per unit length. Scattering measurements on solutions containing less than 5 mg of DNA/ml. are somewhat tedious and can be uncertain, therefore careful checks of concentration dependence were made only on NaDNA dialyzed against 0.05 M-Nacl. These are illustrated in Figure 5. Fortunately, the concentration dependence is small. The results we quote are not extrapolated to zero concentration but the error thus introduced is appreciably less than that from other sources. Note that the data of Figure 5 are
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3500
Squoreof scattering angle(mrod)’
FIQ. 4. Some measured scattering curves in the radius of gyration region. Curve A, NaDNA, 12 mg/ml., 0.05 M-N&I; curve B, NeDNA, 5.55 mg/ml., 1.0 M-N&~; curve C, CsDNA, 7.83 mg/ml., 0.05 an-CsCl. The relative vertical positions are without significance.
before slit corrections. The radii of hydration will not agree with the final results in Table 2. In Table 2 we collect the principal results of the measurements. The more reliable NaDNA and CsDNA data are given at the top of the Table. The parameters have been extracted from the measurements as described under Materials and Methods. Where a value of R, is not given, the experimental data were not good enough to permit a clear resolution of two radii of gyration. DNA concentrations are calculated for the neutral salt. We estimate that the R, of the more careful runs are reliable to 3 or 4% and for the salts other than NaCl and CsCl perhaps 5%. The I, which come from the extrapolation to zero angle of the first (or R,) straight line have about this same reliability. However M’IL depends not only on I, but on an absolute intensity calibration in which there might be an additional systematic error of as large as 4%. On most of our curves R, can be determined as accurately as R, but for R, and (IJI,,)’ the question is rather one of interpretation. How realistic is the particular core and shell model we choose; to what extent are scattering contributions from the shell influencing the measured values of R, and I, ? The last two columns of Table 2 compare measured and theoretical values of the mass per unit length. The measured values are calculated by Eisenberg & Cohen (1968) from M’IL in the thesis of Bram (1968), upon a part of which thesis this paper is based. Eisenberg & Cohen (1968) use the correct three-component formalism and the partial specific volumes and density increments from their own recent work, Cohen & Eisenberg (1968). Readers of Eisenberg & Cohen (1968) and this paper are warned that our M’/L are the M’ of Table 1 of Eisenberg & Cohen (1968), divided by Avogadro’s number.
320
FIO. 5. The extrapolations to zero DNA concentration of R, and [h I(h) Jbx o for NaDNA dialyzed against 0.05 M-NaCl. The solid circles are sonicated DNA, the open circles are unsonicated. These results are before slit corrections. TABLE
2
Experimental cross-section parameters of calf thymes DNA
Buffer
salt
04% M-NaCl 0.05 ~-Nacl 1.0 M-NaC1 o&-i
M-cd!1
0.5 ix-LiCl 1.0 M-LiCl 1.0 M-NH&I 0.05 ~-Kc1 0.10 ~-Kc1 0.05 M-RbCl 0.10 M-RbCl 0.54 xu-RbCI
DNA concn (mglml.)
2.21 12.2 5.55 7.83 2.08 1.99 2.09 8.24 9.25 8.03 8.02 8.1
(MI-V
R&9
R,(A)
9.6 9.0 8.9 10.4 8.5 8.8 8.9 9.4 9.6 10.8 10.4 9.5
7.9 7.8 7.7 9.0 7.3 8.0 9.0 8.3
M’lL
9.15 9.06 7.76 11.1 6.98 6.98 6.55 8.96 7.89 10.2 8.30 7.64
VJLIP
0.92 0.92 0.93 0.93
M/L
daltons/A
193 191 204 240
B-structure theoretical daltons/A
197 197 197 263
0.95 0.94 0.93 0.94
A few measurements on NaDNA dialyzed against 0.05 M-NaCI were made at 4°C and 35°C. Both M’JL and R, decrease with increasing temperature. M’IL decreases about lo%, R, appreciably less. Our observations do not permit a choice from among the several possible explanations.
4. Discussion In Table 2 we give theoretical M/L only for the B form. For the A form they are, of course, about 30% greater. The measured M/L are in excellent agreement with those calculated for the neutral salts in the B form. In fact if, with the O-05 M-NaCI preparation, we use the I, determined by an extrapolation to zero DNA concentration we
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SOLUTION
t
t
1
I
I 05
I
I
I
I
I IO
II \
. 3.0
hR.
FIG. 6. The slit-corrected experimental data at 22°C for N&DNA dialyzed against 0.05 M-N&~ are compared to the scattering from certain models. Squares, 6.09 mg NaDNA/ml. ; circles, 12.0 mg NaDNA/ml. ; long-dash line, right circular cylinder, no shell ; solid line, a Gaussian scattering ourve, exp [ -haR,a/2]; short-dash line, core and shell model r,/r,, = 3, 10% of electrons in shell. All curves are normalized to unity at h = 0 and the R, is the total cross-sectional radius of gyration of each. Such 8 plot makes the curves coincident in the radius of gyration region.
obtain M/L = 196 daltona/& an agreement with theory which must be considered somewhat fortuitous. Note that M'/L shows a strong dependence on salt concentration. This is expected since Cohen & Eisenberg (1968) find a compensating dependence of V on salt concentration. Their V are also appreciably lower than the values around 055 cm3/g for NaDNA which are common in the literature. M/L should be independent of solution conditions. If the M/L had been calculated using equation (4) they would have been 15 or 20% less than those listed. Thus the number of effective scattering electrons per unit length is reduced roughly 10% by preferential interactions between the DNA and the components of the solvent. We have not calculated M/L for the other salts since accurate partial specific volumes and density increments are not available. We now discuss the additional information available in the shape of the scattering curve in the radius of gyration region. We think it clear that the slope of the first
322
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straight line, giving R,, represents information about the molecular cross-section plus its perturbed solvent environment. This is emphasized by the fact that it is the extrapolation of this straight line to zero angle which furnishes the correct values of M/L. In addition, R, is always considerably larger than the theoretical cross-section radius of gyration of ionized DNA which is about 7.0 A. Thus one must assume the existence of an extended shell whose average electron density exceeds that of the solvent. Even the unlikely neutral structure in which a metal ion is tightly bound close to each phosphorus will give (in the absence of solvent contributions) an R, of at most 8 8. It is equally clear that R, depends on more than just the ionized DNA core. The R, we measure are definitely greater than 7 A. They also show an increase with increasing atomic number of the counterion. This is understandable if counterions close to the DNA surface are making a contribution to the core scattering. Such a contribution from the shell is present even in the calculations on our idealized model. However, if we assume the validity of our core and shell model, the measured R, and R, permit a calculation of the radial extent of the shell. Using R, == 9.6 A and R, = 7.8 A, the parameters for the 0.05 al-NaCl measurements, and taking a core radius rc = 10 A for the DNA, we find that the shell is approximately 20 A thick, i.e. it extends from r, = 10 A to an r, = 30 8. The absolute intensity measurements imply about 150 effective scattering electrons per base pair (3.4 A) of the NaDNA. The measured (1,/I,,)* = 0.92 then assigns S:h of these, or 12 electrons per base pair, to the shell. We may ask to what extent these results agree with expectations for solvated DNA. The Debye-Hiickel length in 0.05 M-NaCl is 13.6 A. Most of the shielding counterions will be found within a couple of Debye-Hiickel lengths. Presumably the counterions, with perhaps a contribution from water electrostricted in the field of the DebyeHiickel shell, are providing the scattering electrons of the shell. It must be remembered that the 12 electrons per base pair just mentioned is the net, above unperturbed solvent. Since some salt is preferentially pushed out of the shell about 25 electrons per base pair must be provided by counterions and electrostriction. Depending on the partial specific volume one assumes, 15 to 20 of these might come from the two Na+ counterions. On the other hand all 25 could be furnished by a 1% increase in density of the water in the shell. The X-ray data for the 0.05 M-CsCI give an r, = 29 A and for I.0 M-NaCl, r, = 24 8. The latter shell thickness of 14 A is greater than we would expect if the usual expression for the Debye-Hiickel length were to remain valid at so high an ionic strength. An unsatisfactory feature of the results is the assignment of about the same fraction of scattering electrons to the shell for different DNA salts. The counterions, in fact, represent a much larger fraction of the total scattering in CsDNA than in NaDNA. No doubt a partial explanation is the evidence that some shell scattering is contributing to the core parameters. The purpose of this discussion is to show that the core and shell implications of the X-ray data are in reasonable agreement with expectations. The data are not good enough to justify a more realistic and complex model, for instance one in which the density of shell electrons decays exponentially from the core. Nor can we shed much light on the problem of site binding versus ion clouds except to remark that site binding appears not to be necessary to explain our data. In this connection we call attention to Figure 3 where, at larger angles, the scattering calculated for the ionized core is compared to experiment. We did a number of calculations placing Na+ in
STRUCTURE
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fixed positions near the phosphorus. The agreement with experiment was always poorer. This can be taken as evidence against site binding. Data of a quality which is probably technically feasible, but time consuming, might very well answer some of these questions. In summary both our mass per unit length determinations and the shape of the scattering curve in the peak region at larger angles are in excellent agreement with predictions for the B form of DNA. The former measurements give simultaneous support to our determinations of absolute X-ray intensities and to the recent careful partial specific volume and density increment measurements of Cohen & Eisenberg (1968). We find two cross-sectional radii of gyration which strongly support a core and shell structure for solvated DNA and, within the somewhat limited resolution of the data, the parameters deduced are in satisfactory agreement with an ionized DNA core surrounded by a Debye-Hiickel layer of counterions. We close with a brief comparison of our results and those of Luzzati et al. (1961, 1967) and Kratky (1963). Neither of these authors observed more than a single radius of gyration and neither made measurements in the peak region at larger angles. For NaDNA both measured radii of gyration between 8.0 and 8.5 A, values which fall between our R, and R,. For CsDNA Luzzati et al. (1967) measure a value very close to our R,. Both authors made absolute intensity measurements and determined M/L but used a two-component formalism equivalent to our equation (3). The recent V measurements of Cohen & Eisenberg (1968) were not then available. Eisenberg & Cohen (1968) have recalculated the M/L of Luzzati et al. (1961,1967) using the three-component equations. The resulting M/L are about 20% below the theoretical values. Luzzati et al. treat their experimental data in a way which may obscure the presence of two radii of gyration. Their experimental scatterin, u curves, taken with slits of effectively infinite height, are presented as log I(h) vers?Cslog h. In such a plot comparisons with calculated curves permit the extraction of a radius of gyration and an extrapolated forward intensity. In Figure 6 we plot some of our NaDNA data (but slit corrected) against the scattering calculated for various models in this way. The agreement is best with the core and shell model and in fact would have been better if a model assigning 8% of the electrons to the shell had been used. The model plotted is the first one of Figure 1 which assigns 10% of the electrons to the shell. We note that the presence of two radii of gyration is not obvious in these plots. However there are other important differences in the two experiments. Luzzati et al. (1961,1967) did not dialyze against buffer, their DNA concentrations were almost a factor of ten greater than we have used and their measurements did not reach such small angles. These factors also would make more difficult the observation of two radii of gyration. It is interesting that if we extrapolate to zero angle using the straight line representing our second and smaller radius of gyration we obtain an M/L within 5% of that’ reported by Luzzati et al. We thank Professor Hans Ris and Professor J. W. Anderegg for numerous helpful suggestions and Dr V. Luzzati for several very constructive comments on the manuscript. We were greatly assisted by the manuscripts of Eisenberg & Cohen (1068) which the authors kindly made available to us before publication. This work was supported by research and training grants of tha National Institutes of Healtll.
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REFERENCES Bram, S. (1968). University of Wisconsin, Ph.D. Thesis. Bram, S. & Ris, H. (1971). J. Mol. Biol. 55, 325. Burge, R. E. & Draper, J. C. (1967). Acta Cryst. 22, 6. Casassa, E. F. & Eisenberg, H. (1964), Advanc. Protein Chem. 19, 287. Cohen, G. & Eisenberg, H. (1966). Biopolymers, 4, 429. Cohen, G. & Eisenberg, H. (1968). Biopolymers, 6, 1077. Eisenberg, H. & Cohen, G. (1968). J. Mol. BioZ. 37, 355. Fiske, C. H. & Subbarow, Y. (1925). J. Biol. Chem. 66, 375. Fuller, W., Wilkins, M. H. F., Wilson, H. R. & Hamilton, L. D. (1965). J. Mol. BioZ. 12, 60. Kratky, 0. (1963). Progress in Biophysics, 13, 107. Kratky, O., Pilz, I., Schmitz, P. J. & Oberdorfer, R. (1963). 2. Naturj. 18b, 180. Lake, 5. A. (1967). Acta Cryst. 23, 191. Langridge, R., Marvin, D. A., Seeds, W. E., Wilson, H. R., Hooper, C. W., Wilkins, M. H. F. & Hamilton, L. D. (1960). J. Mol. BioZ. 2, 38. Luzzati, V. & Benoit, H. (1961). Actrc Cryst. 14, 297. Luzzati, V., Masson, F., Mathis, A. & Saludjian, P. (1967). Biopolymers, 5, 491. Luzzati, V., Nicolaieff, A. & Masson, F. (1961). J. Mol. BioZ. 3, 185. Luzzati, V., Witz, J. & Nicolaieff, A. (1961). J. Mol. BioZ. 3, 379. Mahler, H. R., Kline, B. & Mehrota, B. D. (1964). J. Mol. BioZ. 9, 801. Mauss, Y., Chambron, J., Daune, M. & Benoit, H. (1967). J. Mol. BioZ. 27, 579. Porod, G. (1948). Acta Pity. Austriuca., 2, 255. Ris, H. (1961). Canad. J. Genet. 3, 95. Ritland, H. N., Kaesberg, P. & Beeman, W. W. (1950). J. AppZ. Phys. 21, 838. Sharp, P. & Bloomfield, V. A. (1968). J. Chem. Phys. 48, 2149. Vrij, A. & Overbeek, J. Th. G. (1962). J. CoZZ. Sci. 17, 570. Zamenhof, S. (1958). Biochemical Preparations, 6, 8. Zubay, G. & Doty, P. (1959). J. Mol. BioZ. 1, 1.