The secondary structure of DNA in solution and in nucleohistone

J. Mol. Biol. (1971) 58, 277-288

The Secondary Structure of DNA in Solution and in Nucleohistone STANLEY BRAM , Dkpartment de Biochimie Macromoldculaire (CNRX) BP 1018 34--Montpellier, France and Biophysics Laboratory, University of Wisconsin Madison, Wise., U.X.A.

(Received 6 July 1970, and in revised form 19 January 1971) Solutions and gels of calf thymus DNA and nucleohistone were studied using wide-angle X-ray scattering. The experimental scattering curves were compared to those calculated by computer from various atomic models. The structure of DNA in solution (0.05 to 0.15 M-monovalent salt) was found to be of the B kind. A structure which is derived from the B form (as determined from fiber diffraction by decreasing the turn angle to 0.575 radian from O-628 radian per residue (to give a pitch = 37 8)) is most consistent with the results. A comparison of the scattering for DNA and nucleohistone, and the scattering calculated from the B form, show that there is a family of structures of the B kind. The results are in good agreement with the Watson-Crick base-pairing scheme and the atomic co-ordinates given by Arnott, Dover & Wonacott (1969). We find that the secondary structure of the DNA in nucleohistone is also of the i3 family. A turn angle per residue of 0.65 radian (pitch, 32 A) gives the best agreement with our data.

1. Introduction In this paper, we present X-ray scattering results on DNA, unoriented in solution, and then calculate the spherically averaged X-ray scattering curve for various models and attempt to fit them to the experimental data. A fit to the experimental curve is taken as a necessary condition for a model’s correctness but this model may not be unique. Our technique provides information on the over-all secondary structure but by itself this is not sutlicient to determine the exact atomic structure of a complex macromolecule; it is possible to determine only the distribution of the magnitudes, but not the directions, of the Patterson vectors. However, the technique can be used to fund which of several alternate models based upon X-ray fiber diagrams is in best agreement with the experimental X-ray scattering in gels or isotropic solutions. Previous studies (Bram & Beeman, 1971; Bram, 1968) have shown that the scattering from NaDNA in solution is similar but not equal to that expected from DNA in the B form. It was thought that differences could be explained by the scattering contribution of the counterions. The experiments described in this report on Li, Na, Rb and CsDNA show that this variance cannot result from the counterions and must reflect a structural change. Our results are in qualitative aggreement with many physical-chemical studies on DNA indicating that the structure changes with the environmental conditions (Emanuel, 1960; Bode & MaoHattie, 1968).

278

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Hitherto, very little has been known about the secondary structure of DNA in nucleohistone. We find that the X-ray scattering from the DNA in the nucleohistone is similar with that expected from the B form of DNA. This is the first detailed structural study of DNA and DNA in nucleohistone by wide-angle X-ray scattering. The methods and analysis should be of value in other X-ray scattering investigations of nucleic acids in solution.

2. Materials and Methods The calf thymus sodium DNA used was isolated from nucleohistone (Bram & Beeman, 1971) or purchased from the Worthington Biochemical Corp., Freehold, N. J. Preoipitation with 60% ethanol from a large volume of the monovalent chloride was used to obtain other salts of DNA. The sample was then dissolved in the desired buffer and extensively dialyzed against it. Dialysis was not performed on our most concentrated gel containing 72 ye LiDNA. Our nucleohistone was isolated from calf thymus by a procedure based on the method of Zubay Q Doty (1959). The preparation, physical and chemical charaoteristics and small-angle X-ray scattering of this nucleohistone have been described by Bram & Ris (1971). For our most concentrated gel (28%), the final dispersal in distilled water and dialysis against buffer were omitted. Calf thymus histone (unfractionated) was from Worthington Biochemical Corporation. The experiments were carried out at the University of Wisconsin. The X-ray sonrce was a rotating copper anode tube operated at 40 kv and 160 mu. Scattering intensities were measured in a symmetrical four-slit diffractometer (Schafer, 1964). Successive slits were 10.0 cm apart, 0.6 cm high and 0.03 cm wide. An effective monochromatization of 98% was achieved with a nickel j3 filter and pulse-height analyzer set to pass 1.54 A radiation. The solution or gel to be analyzed was sealed between thin mica windows in a sample holder 0.1 cm thick. Sample transmissions were measured before and after each experiment. Several independent runs on the sample were averaged for each scattering curve. Background and solvent scattering were separately measured and subtracted from that of the sample. Some of the results were corrected for smearing effects, due to the finite slit size, with the aid of a computer. Corrections were found not to be important in the wide-angle region examined in this study.?

3. Model calculations The atomic co-ordinates for the bases in the B form were taken from either Arnott, Dover & Wonacott (1969) or from Langridge et al. (1960). In this work we define the B form as having a base pair spacing of 3.36 A and an angular rotation between bases, or turn angle of O-628 radian. The co-ordinates for a given model were used in the Debye equation

(1) to calculate the scattering curves for a given model, where h = 4 n/X * sin (4/Z), C$is the scattering angle, A = 1.54 A and rmn, the vector distance between the mth and nth atom, was calculated from the

atomic co-ordinates by a UNIVAC 1108 computer at the Baculte des Sciences, Orsay, France. f,,, is the scattering factor of the w&h atom, the values being calculated as by Langridge et al. (1960). t Note added in proof. When an improved method that the first maximum of the curves can be shifted

of slit correction was employed it was found by about 3% towards larger angles.

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279

The shape and positions of the maxima in the calculated wide-angle scattering curve were rather insensitive to large changes in the value off,,, . For example, caloulations using the atomic number for fm or the values given by Langridge et al. (1960) or a rather different method of water subtraction for j’,,, (Ninio, 1971) do not appreciably alter the positions of the maxima and minima in the calculated curve, but do affect relative intensities. It was difficult to determine experimentally the relative intensities of the maxima and minima, because of uncertainty in the sample thickness; also the theoretical relative intensities were found to be a strong function of the length of the DNA model used in the calculations. As we only used the general shape and position of the scattering maxima and minima, the simpler method of Langridge et al. (1960) was employed. Calculations for our scattering curves were made with acleninethymine base pairs without oounterions. The angular values in f! (equivalent Bragg spacings) are obtained from the following equation :

S-l = X/2 sin (42).

(2)

4. Results (a) Effect of concentration, solvent, counterion, ionic strength and histone scattering The concentrations used in our study range from 3 to 15% DNA and 2 to 28% by weight nuoleohistone. In this range of concentration, it was observed that the wideangle scattering curves were independent of the concentration. In order to reduce the relative contribution of water scattering for the far-angle curve, a concentrated gel containing 72% LiDNA was used. In Figure 3 is shown the relative scattering from 0.05 M-LiCl and a sample containing 72% LiDNA minus the contribution from solvent. At this high concentration, the ordered aggregation results in a sharp maximum at 22 A and a secondary maximum with exactly one-half TABLE 1

Equivalent Bragg spacings of the jirst three scattering maxima DNA

NaDNA LiDNA DNA models with B form base pairs Turn angle = 0.628 rad (pitch = 33.6 A) Turn angle = O-575 rad (pitch = 363 A) Turn angle = 0.660 rad (pitch = 32.4 A) DNA in nucleohistone

First maximum

s - 1 value of Second maximum

Third

maximum

(4

(4

9.5 9.4

5.6 5-5

12.6

9.3

5.65

13.4

9.6

5.60

12-o

8.9

5.65

12.0

8.9

13-5 13.5

(A)

Not observed or very weak

The results for NaDNA represent the average values of three independent runs on NaDNA, three on nucleohistone, and one on LiDNA. The positions of the maxima varied less than 2% between independent runs.

280

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the Bragg spacing and intensity. Perhaps these maxima are an indication of the presence of very closely packed DNA duplexes in this sample. Since the first maximum of the scattering (see Table 1) has been eliminated, we cannot compare directly the scattering to that of our more dilute samples, but the shapes and positions of the 4.2 and 11 to 9 A maxima indicate that a minor structural transition has taken place. It was found that the wide-angle scattering curves for DNA were the same in 0.05 M- and 0.15 M-Nacl. This was also the case for nucleohistone in 0.8 mM-potassium phosphate, pH 6.8, and in 0.075 M-Nacl, 0.024 M-EDTA, pH 6.5. Thus, the ionic strength in these ranges does not affect the scattering curves. Our scattering curves were quite reproducible. A comparison of two independent scattering curves for NaDNA between 20 and 5 A has already been presented (Bram & Beeman, 1971; Bram, 1968). The scattering curves from Li- and NaDNA were the same within the error due to solvent correction (Fig. 1). The relatively high solvent scattering compared to that of this dilute LiDNA sample causes appreciable error in the relative intensity of the

on a

A

5% l-4 d 7 0 \ , I t ? u

6 .O-

I, : \

, 4 c: 0.10

I

I

1

\‘--v I\ O-20

7 B I I

I

I

I

0.30

y5 (radians)

51

7.7 s-1 (8,

15 4

FIG. 1. The scattering curve for typical rumson N&DNA (0) (142mgjml. in 0.03 M-NaCI, 0.012 m-EDNA, pH 6.5); LiDNA (A) (32 mg/ml. in 0,050 M-LiQ) oompared to simple helical models with 4 points per cross-section

that are described

in the text.

Curve b, B form of Amott et al.; curve c, phosphorus point rotated B form unturned

to 0.57 rrtdian.

further

by IO’; curve a,

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OF DNA

maxima in the 10 to 5 A region. With Rb- and CsDNA, the relative intensity of the first maximum is reduced, but its position in the scattering curve is like that for Liand NaDNA to within f 2%. It may be concluded that the kind of counterion bound to DNA is not responsible for changes in the position of the maxima in the scattering curve. The ‘H’ in Figure 3 denote our scattering curve for calf thymus histone. The curve has a strong maximum at 4.6 A, indicative of the presence of helical regions (Mantik, 1967). In the Bragg region 20 to 8 A, the intensity curve shows a weak inflection centered at 12.8 A. The histone scattering will not change the positions and general shape of the maxima in the 20 to 8 A portion of the scattering curve for nucleohistone. This is because the variations in intensity for both DNA and nucleohistone in this wide angle region are greater than lOOo/owhile the histone intensity falls by about 30% (see Figs 1 and 3) and the relative scattering power of the histone is about half of that of the DNA in nucleohistone. Histone scattering on the other hand, may affect the details of the curve to a minor extent by reducing the sharpness of the maxima. I

I

I

3 * L

I-

10 4 (radians)

FIG. 2. The scattering curve for typical runs on NaDNA (0) and LiDNA (A) (conditions the same as Fig. 1); and nuoleohistone (*) (260 mg/ml. in 0.075 ix-NaCl, 0.024 M-EDTA, pH 6.5) compared to 4 models described in the text; 25 B-form base pairs. Curve a, turn angle = 0.675 rad; curve b, turn angle = 0.628 rad (B form); curve c, turn angle = O-65 rad. L L L, 25 base pairs with Langridge et al. atomic co-ordinate, turn angle = 0.53 rad.

-..-...-..

.-..... .-

7-7 s-’ (8,

$ (rodions) 5.1

3.8

---

---- ------------ --,

FIU. 3. The scattering cnrves from a LiDNA gel, (A), corrected for solvent (72% in 0.05 M-Lick), 0.05 M-Lick, (S), at the observed relative intensity, and histone scattering curve, (H) compared to the cnrves c&x&ted, using the co-ordinates of Arnott et al. (curve a) and Langridge et al. (curve b). The effective electron numbers of Langridge et al. for spacings of 10 A were used at angles less than 275 milliradians and the values given for 4 A Bragg spacings for the rest of the curve.

15.4

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283

(b) Comparison of DNA curves to B form and nucleohistone curves The major difference between our DNA experimental curves and the scattering curve calcuIated with equation (1) for the B form is that the first and second maxima are shifted to smaller angles. This can be seen in Figure 2. However, the position of the third maxima coincides with that calculated for B form. Here the B form coordinates of Arnott et al. (1969) and the atomic scattering factors of Langridge et al. (1960) for 10 A spacings were employed. The 8-l values corresponding to the first three maxima of the scattering curves are given in Table 1. We believe the differences between the calculated B form and experimental curves, although small, represent a real structural change, and not an error or insensitivity in our methods. In support of this conclusion, we present for comparison the experimental scattering curve from nucleohistone. Figure 2 displays a typical scattering curve from a gel containing 26% by weight nucleohistone in 0.075 i?f-Nacl, O-024 M-EDTA, pH 65. The important points here are that the general shape is close to that of B form and that the first and second maxima are at smaller spacings (X-l) than in the calculated curve for B form (see Table 1). We will begin our analysis of the nature of the structural changes in DNA by examining the relationships between the maximum in the scattering curve and the structural features of DNA. The first maximum of the scattering curve corresponds primarily to vectors between opposite strands across the large groove. Thus, we see that the shift of the first maximum to larger equivalent Bragg spacings results from a loosening of the helical structure. This can be made more precise by taking into account helical diffraction theory. For a single or double helix in solution, strong maxima will be observed only when the following relation is satisfied (Schmidt, 1970) :

where x, is first maximum of the Bessel function of order la, and R and P are the radius and pitch. Since DNA is a family of about 40 helioes having the same pitch, but different radii, this relation cannot be applied quantitatively. However, it can be shown that the first scattering maximum can occur only after equation (3) is satisfied by those helices of largest radii. Thus, the only way the spacing of the first scattering maximum observed in nuoleohistone can be increased to the value observed in solution is by 10 to 15% increase in radius or pitch. From a sterioohemical point of view, such an increase in the radius is unreasonable. We will show that this is also unlikely in view of the resultant effect on the scattering curve. (c) Cornparkm of the DNA scattering curves to simple discontinuous helical models

In this section we shall show that a good analysis for wide-angle scattering curves can be obtained using four points on discontinuous helices to represent a nucleotide pair. (Models with two points per base (simulating two coaxial, discontinuous helioes) did not fit well to the experimental curve, especially in the small- (near 100 A) and far-angle (near 6 A) regions.) We chose to use for our four points the co-ordinates of the phosphorus atom and the center of mass for a B-form base pair (adenine and

284

8. BRAM

thymine) given by Arnott et al. (1969) (9.22 A, 94”, I.9 A; 2.9 A, EGO”, O-14 A). The best agreement to the scattering curve was obtained when the scattering power of the point representing the phosphate was about 30% higher than that of the base point. This assignment agrees approximately with the relative sum of the effective electron numbers of the phosphate and ribose compared to a base (Langridge et al. 1969). It also yields a cross-section radius of gyration, 7.2 A, in accord with that calculated with the entire Arnott et al. set, 7-O A; and with that determined from small-angle X-ray scattering, ‘7.8 + 0.5 A (Bram & Beeman, 1971). The scattering curve for this double helical B-form model was calculated using equation (1) and is shown in Figure l(b). The curve is very similar to that of DNA in solution and to that calculated with the complete Arnott et al. set, which is exhibited in Figure 2(b). It was found that the shape of the calculated curve in the 20 to 7 A region was very sensitive to small variations in the angular or radial co-ordinate of the phosphate point, but rather insensitive to changes in the base point. In Figure l(c), the dotted curve represents the scattering calculated when the angular co-ordinate of the phosphorus of a base was increased by 10” (9.22, 104”, l-9; 2.9, 80” O-14) with a B-form double helix. One observes the disappearance of the second maximum. The curve calculated with a four-point model employing the set of co-ordinates given by Langridge et al. (1960) to calculate the phosphorus and base points was very similar to the curve calculated using the entire set of atomic co-ordinates, but it fits poorly to the experimental curve. It was observed that raising the z co-ordinate of a phosphate to 4 A in order to simulate a tilting of the base pairs, resulted in a curve with features similar to that calculated for the A form, which is shown in Figure 4. A comparison of the curves in Figure 1 shows that the experimental maxima and minima are shifted to smaller angles when compared to the simple B-form helical models. We found that a re-arrangement of the four scattering points in a helical unit could not simultaneously produce a correlation in the positions of the first three maxima of the experimental curve. A change in pitch of the helices from 33.6 to about 37 A was required to produce a good fit. The best fit was obtained for a model with a pitch of 37 A, achieved by decreasing the turn angle between the bases (which had the Arnott et al. phosphorus and base positions) to 0.56 radians. This curve is presented in Figure l(a). The fact that the scattering curve in the 20 to 8 A region is primarily dependent on the phosphate position limits the scope of the information obtainable, but greatly simplifies our analysis. The equivalent region of the X-ray fiber diagrams for DNA was also found to be dependent mainly on the phosphate (Langridge et al., 1960). Thus, an X-ray scattering experiment on a solution of a helical polynucleotide can approximately furnish the helical parameters and the position of the phosphate groups. As previously discussed, the changes in the spacing of the first maximum can only be interpreted by a variation of the helical parameters. We shall show that a model invoking changes in pitch gives a very good agreement with the total scattering. We feel that mechanisms featuring changes in radius are improbable. Whatever the nature of the variations from form B it would have to shift the first and second spacing to larger spacings without altering their relative intensities or the spacing of the third maxima. Increasing the radii of the phosphates in the four-point calculations can shift the first maximum to larger spacings, but a concurrent change in curve shape and in the position of the third maxima is always observed.

THE r-

B

A B

B

E AB % EB

I

/ 3%

’

C

SECONDARY

285

OF DNA

-

I

I

/

c TT

‘A B

c C

B B

cB C

* A AA

A I 0.10

FIG. 4. A comparison the atomic co-ordinates B, and C.

1

1

B B

AA

c El

.O

BBEEB

% cccc cficc ‘c

A

A

I

’ EA

C

STRUCTURE

I

, CB 0.20 $(radians)

c0 I

,

B

AAAkn

B b c’” AA A A

A* * A

B

,

cB C c 0.30

of the sc&ttttering curve for nucleohistone to the curves calculated with of the A, B and C forms of DNA, denoted respectively by the letters A,

(d) Comparison of DNA curves to atomic models of varying pitch The simplest mechanism which more or less maintains the base stacking is a change in the turn angle between base pairs. When the turn angle between adjacent base pairs is decreased by about 10% (to 0.575 & 0.01 radian), keeping the atomic coordinates and base-pair separation the same as B form, the shape and positions of the first two minima and three maxima in the computer-calculated scattering curve agree with those of the experimental curve. As is pbserved in Figure 2(a), indeed an excellent fit to the experimental curve is obtained. The most important criteria for agreement are a jit in the positions of the maxima and minima, next is the shape of the maxima, and then the relative intensities of the maxima and minima. We point out in passing that this turn angle is equivalent to about 11 base pairs per turn. As there is no reason to expect an exact repeat, it is less misleading to state our results in terms of the helix pitch. The pitch for this model is 37 A. If the pitch is increased by allowing the distance between base pairs to equal 3.7 A, while maintaining a turn of 0.628 radian, the first two maxima are also brought into coincidence. However, the third maximum is shifted to 53 A. Thus, both curve fitting and the requirement for maintenance of base stacking would tend to eliminate this as a possibility. In addition, small-angle X-ray scattering experiments show the mass per unit length

286

S. BRAM

for DNA in solution to be equal to that of the fiber B form (Bram & Beeman, 1971). This would rule out models featuring a change in average rise per residue. In Figure 2, one observes that the 9 to 10 A shoulder, which is quite strong in both the experimental and the curve calculated with the Arnott et ?l. (1969) co-ordinates, is much less pronounced with the Langridge et al. (1960) co-ordinates. When a turn angle of 0.53 radian is used with the Langridge et al. values, the first maximum of the calculated curves agrees well with the experimental curve, but the 9 to 10 A shoulder is observed at smaller angles than in experimental curves as a very weak inflection (see Fig. 2). Thus, we are unable to obtain a correspondence to both the first and second maxima of the experimental curve using the Langridge et al. co-ordinates. In the far-angle region, the experimental curve for our concentrated gel fits the calculated scattering curve slightly better when the more recent set of co-ordinates is used (Fig. 3). Although the fit is not too good, using a turn angle of 0.628 radian results in the best agreement with the experimental curve. This indicates that a transition from the secondary structure in solution to a conformation similar to that in a fiber at high relative humidity takes place in our gel at this very high DNA concentration. This is expected since the concentration is like that used in the fiber experiments. We remind the reader that a change in turn angle will result in some distortion of the phosphate bonds. However, our own model building and that of Langridge et al. show that the phosphate group may take a wide range of stereochemical positions if the bond angles are slightly distorted. Such minor intra-base pair distortions would not result in observable changes in the scattering curve. In fact, it seems that a decrease in the turn angle of 10% would tend to relieve torsional strain in the published B-form models (Sundaralingam, personal communication). (e) Nucleohtitone The same arguments applied to the structure of DNA in nucleohistone, the predominate state of DNA in higher organisms, show that the structure is very similar to, but somewhat more compact than, form B. As can be seen in Figure 2(c), the positions of the first maxima in the experimental scattering curve coincide with those from a model with a larger turn angle per residue (turn angle 0.65 radian, pitch 32.4 8). In Figure 4 we compare the nucleohistone scattering curve to those calculated with the atomic co-ordinates of the A form (Arnott et al., 1969), B form (Arnott et al.) and C form (Marvin, Spencer, Wilkins & Hamilton, 1961). A cursory analysis shows that the scattering curve is quite different from that of the A form which has its first minimum at 0.07 radian and the second maximum at O-205radian. The nucleohistone scattering cnrve is rather similar to that of the B form, but different from the related C form. As discussed above, a better correspondence can be obtained by increasing the turn angle to 0.65 radian from 0.628 radian for form B. However, the correspondence could not be improved with A- and 0 forms. The intense maxima found at about 5.5 A in both DNA and in all our model calculations are either very weak or not observed in nucleohistine. Tertiary supercoiling of the DNA, which is consistent with small-angle X-ray scattering (Bram & Ris, 1971) and X-ray fiber diffraction (Pardon, Wilkins & Richards, 1970) might explain the absence of this maximum.

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287

It is known that the DNA in nucleohistone is almost completely inactive for protein synthesis. whereas DNA in solution is quite active (Huang & Banner, 1962). One possible function of the histone is to keep the DNA in its compact form by lowering the hydration about its surface. Low hydration seems to result in a more compact structure-form B-in the fiber at high humidity and high salt and also in nucleohistone. The structure becomes even more compact in a fiber at lower humidity. (f) Alternative models The resolution is limited by errors in the model calculations due to uncertainty in the atomic structure factors and in the published atomic coordinates. and by colimination smearing. With this in mind, the structure of either DNA in solution or in nucleohistone may be closer to that of form B than as discussed here. But it is certain that the structure of DNA in these two states is appreciably different, and a change in turn angle per base pair seems to provide the best explanation. However, it is worth mentioning that the number of sugar-phosphate conformations observed in nature is very limited (Sundaralingam, L969) and the models presented here by and large maintain the B-form intra-base co-ordinates.

5. Discussion Although there is little other direct structural information for DNA in solution, our conclusions are consistent with several physical studies on DNA solutions under various conditions. Wang, Baumgarten & Olivera (1967) have postulated that a change in the number of base pairs per turn with ionic environment could be an explanation for the origin of tertiary turns in cyclic DNA molecules. Electron microscopy and sedimentation experiments on circular DNA at various NaCl concentrations support this model (Bode & MaoHattie, 1968). The optical rotatory dispersion of DNA changes with increasing salt concentration and follows roughly the decrease in hydration with water activity (Tunis & Hearst, 1968). The optical rotatory dispersion of DNA in water-alcohol mixtures at room temperature (Brahms & Mommaerts, 1964) and at low temperature (Travers, Michelson & DOUZOU,1970) is similar to that observed in concentrated salt solutions. The hypochromism of DNA decreases by as much as 10% in the presence of high salt concentrations (Emanuel, 1960) and in 80% ethanol (Brahms & Mommaerts, 1964). All these results are consistent with a further turning of the double helix with respect to the structure in dilute salt solution (which results in a decreased pitch) as the hydration or water activity is lowered by the addition of salt or alcohol. (They are inconsistent with a decrease in base separation.) An overturned structure would have less base overlap, which would be manifested by a decrease in hypochromism. Our nucleohistone diffraction work strongly indicates that the DNA double helix is further turned with respect to solution. A pitch of 32 .& gives the best agreement with our results. The recent work of Permogorov, Debakov, Sladkova & Rebentish (1970) and Hensen & Walker (1970) shows that the circular dichroism of DNA in nucleohistone is almost identical with DNA in 2 M-NaCl. This finding tends to conErm our interpretation.? t Note added in proof. Reoent wide-angle X-ray scattering experiments on DNA in 2 M-N&I and LiCl yield & pattern similrar to that of DNA in nucleohistone and to that of overturned B-kind models.

S. BRAM

288

Pardon, Wilkins & Richards (1970) have described several mechanisms which might introduce regular supercoiling in nucleohistone. In one of their models, histone molecules form links at regular points along the DNA. These links impose restraints on the DNA analogous to those present in closed circular viral DNA such that subsequent changes in the pitoh of the double helix introduce supercoiling. Our results furnish support for this mechanism. If the turn angle for a base pair before the addition of histone was O-57 radian and 0.65 after, one left-handed superhelical turn could be achieved in a minimum contour length of 250 A. This would be a rather compact superhelix in agreement with the model proposed by Bram & Ris (1971) (pitch 45 A, radius 30 A). I am greatly indebted to Dr W. W. Beeman for valuable suggestions and discussions, to Drs E. Zuckerkandl and H. Ohlenbusch for encouragement and advice and to Mr R. D. Carlson and Mr J. Ninio for technical assistance and suggestions. Financial support for this work was provided by the Centre National de la Recherche Scientifique, the U.S. National Institutes of Health, and the Ligue Nationale Franpaise contre le Cancer. REFERENCES Arnott, S., Dover, S. D. & Wonacott, A. J. (1969). Acta Cry&. B25, 2192. Bode, V. C. & MaeHattie, L. A. (1968). J. Mol. Biol. 32, 673. Bram, S. (1968). Ph.D. Thesis, University of Wisconsin. Bram, S. & Beeman W. W. (1971). J. Mol. BioE. 55, 311. Bram, S. & Ris, H. (1971). J. Mol. Biol. 55, 325. Brahms, J. & Mommaerts, W. F. H. M. (1964). J. Mol. Biol. 10, 73. Emanuel, E. C. F. (1960). Biochim. biophys. Acta, 42, 60. Henson, R. & Walker, I. 0. (1970). Biochemical Jouwud. Proc. Biochem. Sot., 503rd Meeting. Huang, R. C. & Bonner, J. (1962). Proc. Nut. Acad. Sci., Wash. 48, 1216. Langridge, R., Marvin, D. A., Seeds, W. E., Cooper, C. W., Wilkins, M. H. F. & Hamilton, L. D. (1960). J. Mol. Biol. 2, 38. Mantik, D. W. (1967). Ph.D. Thesis, University of Wisconsin. Marvin, D. A., Spencer, M., Wilkins, M. H. F. & Hamilton, L. D. (1961). J. Mol. Biol. 3,547.

Ninio, J. (1971). Ph.D. Thesis, University of Paris. Pardon, J. F., Wilkins, M. H. F. & Richards, B. W. (1970). In Biological Macromoleclules, ed. by G. Fasman & S. Timasheff, vol. IV. New York: Marcel Dekker. Permogorov, B. I., Debakov, V. G., Sladkova, I. A. & Rebentish, B. (1970). Biochim. biophys.

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Schafer, L. (1964). Ph.D. Thesis, University of Wisconsin. Schmidt, P. W. (1970). J. App!. Cry&. 3, 257. Sundaralingam, M. (1969). Biopolymers, 7, 821. Travers, F., Michelson, A. M. & Douzou, P. (1971). Biochim. biophys. Acta, in the press. 6, 1218. Tunis, M. J. B. & Hearst, J. E. (1968). Biopolymers, Wang, J. C., Baumgarten, D. & Olivera, B. M. (1967). Proc. Nat. .&ad. Sci., Wash. 58, 1852. Zubay, G. & Doty, P. (1959). J. Mol. Biol. 1, 1.