Proc. Nati. Acad. Sci. USAVol. 87, pp. 7405-7409, October 1990Biochemistry

The structure of DNA in a nucleosomeJEFFREY J. HAYES*, THOMAS D. TULLIUSt, AND ALAN P. WOLFFE**Laboratory of Molecular Biology, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Building 6, Room 131,Bethesda, MD 20892; and tDepartment of Chemistry, The Johns Hopkins University, Baltimore, MD 21218

Communicated by Martin Gellert, June 8, 1990 (receivedfor review March 28, 1990)

ABSTRACT We describe the application of the hydroxylradical footprinting technique to examine the histone-DNAinteractions of a nucleosome that includes part of the 5Sribosomal RNA gene ofXenopus borealis. We establish that twodistinct regions ofDNA with different helical periodicities existwithin the nucleosome and demonstrate a change in the helicalperiodicity of this DNA upon nucleosome formation. In par-ticular, we find that on average the helical periodicity of DNAin this nucleosome is 10.18 ± 0.05 base pairs per turn. Thesame DNA, when bound to a calcium phosphate surface, has aperiodicity of 10.49 ± 0.05 base pairs per turn, similar to thatof random sequence DNA. Modulations in minor groove widthwithin the naked DNA detected by the hydroxyl radical aremaintained and exaggerated in nucleosomal DNA. These fea-tures correlate with regions in the DNA previously suggested tobe important for nucleosome positioning.

The basic repeating unit of eukaryotic chromatin is thenucleosome (1, 2). Crystallization of nucleosome core parti-cles reveals a histone core around whichDNA is wrapped (3).Two central concepts have been proposed from a consider-ation of the constraints imposed on DNA by the histone core.First, DNA curvature may be a major determinant of nucle-osome positioning (4). This is presumed to be a consequenceof the fact that DNA is wrapped around the histone core ina shallow helical path with one complete turn comprising only80 base pairs (bp). Second, the helical periodicity of nucle-osome-wrapped DNA is thought to be different from that infree DNA. Such a difference in helical period would resolvethe so-called linking-number paradox (5). This apparentdiscrepancy, that 1.75 turns ofDNA around the nucleosomelead to only one DNA supercoil, has been explained by achange in helical periodicity from 10.5 bp per turn in solutionto 10.0 bp per turn over the 146 bp of DNA believed to beassociated with the histone core (6). Both of these conceptsrequire alterations to the structure ofDNA in a nucleosomecompared to its state free in solution. These structuralalterations are likely to affect the interaction of other DNA-binding proteins with nucleosomal DNA (7, 8).Whether or not a change in the helical periodicity ofDNA

occurs following incorporation into a nucleosome andwhether this explains the linking-number paradox has led tomuch discussion (8-11). Measurements of the helical perio-dicity ofDNA in the nucleosome with enzymatic probes suchas DNase I have shown that cleavage sites are spaced with anaverage periodicity of about 10.4 bp, not 10.0 bp as expectedfrom theoretical predictions (5, 12). This discrepancy mightbe explained by steric hindrance of nucleases from attackingat all sites at an angle normal to the nucleosome surface (5).This explanation is supported by the sequence analysis ofcloned nucleosomal DNA (13).

In this work, we detail a more direct approach to investi-gate the interaction of DNA with the histone core, using auniquely positioned nucleosome that includes DNA from a

Xenopus borealis 5S RNA gene (14) and the hydroxyl radicalas a probe ofDNA structure (15). A major advantage of thismethod is that hydroxyl radical cleavage ofDNA avoids theproblems associated with the large size and sequence spec-ificity of enzymatic probes of DNA structure (5, 16). Thus itis now possible to analyze the structure of any uniquesequence of DNA within a nucleosome at single-nucleotideresolution. The hydroxyl radical footprinting technique al-lows us to measure the helical periodicity of DNA in anucleosome and reveals a clear change in the helical periodof5S DNA upon nucleosome formation. We also confirm andextend the concepts ofDNA bending as a major determinantof nucleosome positioning.

MATERIALS AND METHODSDNA Fragments. Radiolabeled DNA fragments contained

the X. borealis somatic 5S RNA gene inserted in eitherorientation within the vector pSP64 at a BamHI site (17).These were used to reconstitute nucleosomes and for hy-droxyl radical footprinting. A 583-bp Hha I-EcoRI fragmentfrom plasmid pXP-10 (17) was radiolabeled at the EcoRI site.The axis ofdyad symmetry of the nucleosome on the 5S RNAgene (14) is -72 bp from the radiolabel. A 293-bp HindIII-EcoRI fragment from plasmid pXP-14 (17) was radiolabeledat the HindIII site. In this case the axis of dyad symmetry ofthe nucleosome on the 5S RNA gene is -84 bp from theradiolabel. Only a single nucleosome will bind to this partic-ular DNA fragment (18).A Hpa II-Rsa I fragment from pXbs-1 (19), which extends

from position -102 to +75 with respect to the start oftranscription of the 5S gene, was used in the calcium phos-phate experiments to investigate the helical periodicity of theupstream half (-80 to -3) of the nucleosome binding site.Likewise, the HindIII-BamHI fragment from pXbs 201 (20)(-50 to +196), labeled at the HindIII site, was used toinvestigate the periodicity of the downstream half (-3 to+70) of the nucleosome binding site (see Fig. 2B).Nucleosome Reconstitution and Footprinting. Chicken

erythrocyte histones were reconstituted onto the radiola-beled DNA fragments to form nucleosomes by salt/ureadialysis (21-23). The efficiency of reconstitution was moni-tored by electrophoresis (4, 24). We found that >95% of thelabeled DNA needed to be reconstituted into nucleosomes toallow the appearance of a hydroxyl radical footprint (data notshown). Cleavage ofDNA in nucleosomes by DNase I or thehydroxyl radical was accomplished as described for otherprotein-DNA complexes (16).

Quantitative Analysis. Autoradiographs were scanned witha Joyce-Loebl Chromoscan 3 densitometer fitted with anaperture wide enough to allow measurement of the opticaldensity across a whole lane. The area of each band wasdetermined by integration using software included with thedensitometer. Integrals ofbands from the control (free DNA)samples were subtracted from the integrals of correspondingbands in the nucleosome samples. The resulting values,which represent the amount of cleavage at each nucleotide inthe nucleosome, were then smoothed by performing a three-bond running average throughout the entire data set. Data

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sets were fitted with a sine function by using the programPASSAGE on a Macintosh computer. Data sets were alsoanalyzed by Fourier transformation. The errors quoted in thetext are ±2cr.

RESULTS AND DISCUSSIONThe Helical Periodicity of DNA in the SS Nucleosome. The

small size and lack of sequence specificity of the hydroxylradical compared to enzymatic probes prompted us to at-tempt to analyze the structure of DNA in a nucleosome byusing this reagent. Nucleosomes made up of histone coresassembled on 5S DNA were "footprinted" with both thehydroxyl radical and DNase I. A clear modulation of cleav-age is seen with both reagents (Fig. 1). The DNase I footprintis identical to those previously reported for this gene (14).Regions of maximum hydroxyl radical cleavage coincideapproximately with the DNase I cleavage sites in the nucle-osome (Fig. 1). Experiments in which the opposite strand wasradiolabeled revealed a stagger in the positions of maximalcutting of 1-3 bases, characteristic of the minor groove-centered cleavage chemistry of hydroxyl radical (data notshown; ref. 16). Densitometric analysis (Fig. 2) of these

Proc. Natl. Acad. Sci. USA 87 (1990)

autoradiographs shows that the hydroxyl radical cleavagepattern is modulated with a period of -10.0 bases overextended regions on either side of the center of dyad sym-metry of the nucleosome (14), which is marked by the large

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FIG. 1. Hydroxyl radical footprints of a nucleosome incorporat-ing the X. borealis 5S RNA gene. (A) For this experiment, the 583-bpfragment of pXP-10, radiolabeled on the noncoding strand of the 5SRNA gene, was used. Cleavage patterns are shown for naked 5SDNA generated by DNase I (lanes 1 and 2) and by the hydroxylradical (lane 6) as well as for DNA in the nucleosome generated byDNase I (lanes 3 and 4) and by the hydroxyl radical (lane 7). Lane5 contains G+A markers generated by chemical cleavage of5S DNA.DNA fragments were separated by electrophoresis on a 6% poly-acrylamide gel containing 7 M urea. Cleavage patterns resulting fromDNase I digestion for 30 sec (lanes 1 and 3) and 2 min (lanes 2 and4) are shown. (B) The same set of samples was electrophoresed fora shorter time to highlight the smaller DNA fragments. The positionof the axis of dyad symmetry of the nucleosome on the 5S RNA geneis indicated, as is the internal control region of the 5S RNA gene(stippled bar covering positions +45 to +95). The footprint of thenucleosome that is positioned over the beginning of the 5S gene isindicated by the black bar next to the autoradiograph. The approx-imate positions of two other nucleosomes detected by the hydroxylradical, which are located downstream of the 5S nucleosome, areindicated by the black bars labeled N2 and N3.

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FIG. 2. (A) Densitometer scans of the hydroxyl radical footprintof the 5S nucleosome. Cleavage patterns for the noncoding strand of5S DNA are shown. The upper tracing is the hydroxyl radicalfootprint of the nucleosome, and the lower tracing is the pattern ofhydroxyl radical cleavage of this same DNA when free in solution.The small arrows mark the positions of maximum hydroxyl radicalcleavage of nucleosomal DNA, which were determined after sub-traction of the trace of naked DNA. Nucleotide positions arenumbered relative to the start of the 5S RNA gene. Note that thereis no zero position in this figure. The corresponding positions onnaked DNA are shown for reference. The large vertical arrowsindicate the position ofthe axis ofdyad symmetry of this nucleosomeas previously determined (14). The horizontal black bar indicates theregion that appears to be internucleosomal. (B) Plots of the hydroxylradical cleavage frequency at each nucleotide of the noncodingstrand of the X. borealis 5S RNA gene free in solution, bound tocalcium phosphate, and assembled in a nucleosome. Sites arenumbered relative to the start of transcription of the 5S gene (+1).Positions -n (upstream) actually correspond to positions -(n - 1) inthe usual numbering scheme for upstream sequences, due to thenecessity of the plotting program to include a point at 0. Note that the"DNA on Calcium Phosphate" data are actually comprised of twoindependent data sets, which were joined at position -3 as indicatedby a horizontal dash. Each data set covers one-half of the nucleo-some binding site and is not expected to have any relation to theother. The horizontal bar above the curve indicates the approximateposition of the 5S gene internal control region (ICR). The verticallines are included to highlight the change in helical periodicitybetween DNA bound to calcium phosphate and in the nucleosome.They also show how the periodic features in the cleavage pattern ofnaked DNA correlate with the other two patterns.

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Proc. Natl. Acad. Sci. USA 87 (1990) 7407

vertical arrow in Fig. 2A. It is also clear from this scan thatthe 10.0-base periodicity does not extend across the center ofdyad symmetry, because the modulation patterns to eitherside of the center are not in phase with each other (see below).We assume that the modulation of the cleavage pattern

gives directly the helical repeat of the DNA (16) in the localframe of reference [i.e., with respect to the surface of thehistone core (6, 25)]. Cleavage by the hydroxyl radical can beattenuated by alterations in minor groove width as a conse-quence of DNA bending (26) or by the presence of proteinbound to the helix (16). The hydroxyl radical cleavage data(Fig. 2) was quantitated (see Materials and Methods). Toevaluate the periodicity for the entire core DNA within the 5Snucleosome, it is most convenient to treat separately thethree turns of DNA that span the center of dyad symmetry(located at position -3), since this region has a helicalperiodicity that clearly differs from that in the rest of thenucleosome. Fig. 2A shows that regions to either side of thedyad have a periodicity of 10.0 bp that are out of phase by -2bp if extended across the center of dyad symmetry. Cleavagedata from each of the flanking regions, which cover positions+14 to +72 and positions -17 to -75 in the 5S gene, wereanalyzed independently by Fourier analysis of the smootheddata (Fig. 3A) or by the fitting of a sine function to the dataset (not shown). Both analyses yield identical results. We findthat both of the flanking regions have a periodicity of 10.05± 0.04 bp per helical turn.The helical period of the small central region can be most

accurately determined by comparing the phases of sinefunctions that were fitted to the adjoining flanking regions.The difference in phase between these regions was found tobe 68 ± 20, or about 0.2 turns (680/3600) of the DNA helix.Therefore, the region ofDNA that contains the central 32 bpin the 5S nucleosome (positions -17 to + 15) has a periodicityof 10.68 ± 0.06 bp per turn. The entire core DNA region isthen calculated to have an average periodicity of 10.18 ± 0.05bp per turn, in close agreement with earlier estimates fromsequence analysis of mixed-sequence nucleosome cores,which gave a periodicity of 10.17 bp per turn (4, 13, 27).The Helical Periodicity of 5S DNA Changes Upon Nucleo-

some Formation. The average helical periodicity of 10.18 bpper turn found for the DNA in the 5S nucleosome would bestrong evidence for a change in helical period upon nucleo-some formation, if, as would be expected, the periodicity ofthis same DNA is different when free in solution (8, 25). Thehelical periodicity of naked DNA in solution has been mea-sured by cleaving DNA bound to calcium phosphate crystalswith DNase I (28-30), or with the hydroxyl radical (15).These experiments have yielded a range of values for thehelical period of random sequence DNA from -10.6 ± 0.1 bpper turn (28), to 10.5 bp per turn (15), to 10.4 bp per turn (29,30). The average value from these experiments for the helicalperiodicity of DNA, -10.5 bp per turn, is in good agreementwith the value of 10.54 ± 0.01 bp per turn that was determinedby a completely different experimental approach (31).We consequently have analyzed the hydroxyl radical

cleavage pattern of 5S DNA bound to calcium phosphatecrystals to determine the helical periodicity of this DNA. Fig.2B shows plots of the hydroxyl radical cleavage frequency of5S DNA when free in solution, bound to calcium phosphate,and bound in a nucleosome. The frequency of a sine curvefitted to the cleavage pattern in 5S DNA bound to calciumphosphate yields a value of 10.49 ± 0.05 bp per turn for thehelical repeat of the 150 bp of 5S DNA (positions -80 to +70)that associates with the histone core (Fig. 3). To test ourmethod of analysis, we have treated in the same way DNaseI cleavage data for random-sequence nucleosomal DNAbound to calcium phosphate (15). For this DNA we derive ahelical periodicity of 10.5 bp per turn (results not shown), insubstantial agreement with previous measurements (15, 28).

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FIG. 3. (A) Plots of the frequency spectra from Fourier analysisof hydroxyl radical cleavage data. The data set analyzed for the peaklabeled "DNA on Calcium Phosphate" was derived from the datashown in Fig. 2 for the DNA downstream of the start site of the 55gene. The peak labeled "DNA in Nucleosome" is derived from datacovering positions +16 to +74 in the "DNA in Nucleosome" data setshown in Fig. 28. The width of the Fourier transform peak is afunction of the size of the data set used to calculate the modulus ofthe transform and is that expected for these particular data sets. (B)Least-squares fit of a sine function to a portion of the "DNA onCalcium Phosphate" data set (Fig. 2B), which corresponds to thedownstream half (positions -3 to +72) of the nucleosome bindingsite on the 55 gene. A similar analysis of the part of the "DNA onCalcium Phosphate" data set that corresponds to the upstream halfof the nucleosome binding site (-3 to -78) yields an identical result.Shown is a plot of the original data set and the fitted sine curve. Thefitted period, which gives the helical periodicity of this segment ofDNA in solution, is indicated.

We conclude that the segment of 55 DNA that forms anucleosome, when free in solution, has a helical periodicityvery close to that found for random sequence B-form DNAin solution.Comparison of the cleavage patterns of 55 DNA in the

nucleosome and bound to calcium phosphate demonstratesdirectly that the helical periodicity of 55 DNA changes sig-nificantly as a consequence of its interaction with the histonecore. The change in periodicity is clearly evident in Fig. 28,where peaks in the hydroxyl radical cleavage frequency in thecalcium phosphate and nucleosome plots are roughly alignedat approximately position +20, but are clearly out of phase afew helical turns away at +50 or +60. In the region encom-passing positions +15 to +75 in the 55 gene, the helical periodchanges from about 10.50 bp per turn in solution to 10.05 bpper turn in the nucleosome (Fig. 3A). However, the averagehelical periodicity of DNA in the nucleosome is not as dras-tically different. The three helical turns that cross the center of

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dyad symmetry, which have a periodicity of - 10.7 bp per turn,make the average periodicity of 5S DNA in the nucleosomecore 10.18 bp per turn. Evidence for the existence of a centralregion of altered periodicity in the bulk population of nucle-osomes and the consequences for the linking-number paradoxare discussed below.

Relevance to Other Nucleosomes. It has been suggested thata nucleosome including 5S DNA may be an unusually stablestructure and thus not representative of the bulk of nucleo-somes (32). However, other results discussed below supportthe generality of our conclusions. The periodicities ofDNaseI and DNase II cleavage sites at the two ends of the DNA innucleosomes containing mixed DNA sequences were close to10.0 bp, while the spacing of those cleavage sites toward thecenter of the nucleosome was closer to 10.5 bp (13, 33).Photofootprinting of nucleosomes containing mixed-se-quence DNA shows that thymidine dimer formation is mod-ulated with a periodicity of about 10.0 bp on either side of acentral region, which has a periodicity of about 10.5 bp. Thiscentral region, which spans the axis of dyad symmetry in thenucleosome core, offsets the phases of the outer regions byabout 2-3 bp (34). Sequence analysis ofDNA cloned from 177nucleosome cores detects, near the dyad symmetry axis, adiscontinuity in the periodic fluctuation of sequence contentfound in the rest of the nucleosomal DNA (13). Moreover, ithas been noted that these modulations in sequence have aperiod of 10.02 bases in regions on each side of the axis ofdyad symmetry, which implies that the periodicity in thecentral region must average 10.7 bases to obtain the mea-sured overall periodicity of 10.17 bp per turn (27). Themodulation patterns of sequence and thymidine dimer for-mation in the nucleosome thus closely parallel the structuralmodulations that are detected directly by the hydroxyl radicalin the present work.The Change in Linking Number Upon 5S Nucleosome For-

mation and the Linking-Number Paradox. With the detailedinformation we have obtained on the helical periodicity of SSDNA in the nucleosome and in solution, we can now evaluatethe structural changes that occur in SS DNA upon nucleo-some formation. The linking-number paradox refers to thediscrepancy in the change in linking number (ALk) observedupon nucleosome formation (-1) and expected from knowl-edge of the structure of the nucleosome (-2). The equationmost often used to understand this process is

ALk=ATw + AWr, [1]

where ATw is the change in twist and AWr the change inwrithe experienced by the DNA (6). The experimental de-termination of nuclease accessibility (or hydroxyl radicalcleavage rate, as we do here) gives information on the helicalrepeat in the local frame ofreference [i.e., with respect to thesurface of the nucleosome core (6)]. The helical repeat ofDNA in the local frame is related to the quantity 4), called thewinding number, defined as the number oftimes that a vectorassociated with the DNA backbone rotates past the surfacethat is the reference frame (6). The helical repeat h, definedas the number of base pairs per unit winding number, or h =N/4), is the quantity measured in the experiments reported inthis paper. 4) is not the same as the quantity Tw in Eq. 1. Theyare simply related, though, by the following equation (25):

Tw=STw+ ), [2]

where STw, the surface twist, is calculated from the geometryof the system. The corresponding equation for relating thechanges in these quantities that occur upon nucleosomeformation from DNA in solution is

ATw= ASTw + A4).

ASTw, the change in surface twist upon forming the nucle-osome, is calculated to be -0.19 (6).

In the experiments described in this paper, we havedetermined that the average helical repeat of 5S DNA boundin a nucleosome is 10.18 ± 0.05 bp per turn, a value thatagrees very well with the average helical periodicity ofrandom sequence nucleosomes inferred by sequence analysis(4, 13, 28). Substituting this value into Eq. 3 along with thevalue for ASTw for the nucleosome and the value we deter-mined for the helical repeat ofSS DNA bound to a precipitateof calcium phosphate, and considering that there are 146 bpof DNA in the nucleosome core, we obtain

ATw = ASTw + A(N/h) =

- 0.19 + (146/10.18 - 146/10.49) = +0.23. [4]

The change in writhe calculated for DNA assembling ontothe nucleosome is -1.65 (25), so, using Eq. 1, the change inlinking number for formation of the 5S nucleosome is -1.42± 0.13 (assuming an error of +0.1 in the calculated change inwrithe). Although ALk for formation of a nucleosome onXenopus 5S DNA has not been experimentally measured, thevalue we calculate above may be compared with the exper-imental value of -1.01 ± 0.08 per nucleosome observed forLytechinus variegatus 5S nucleosome arrays (35).

It would thus seem that the observed alteration in thehelical periodicity of SS DNA upon nucleosome formationdoes not, by itself, completely explain the linking-numberparadox as currently formulated (6). This is entirely due tothe difference in the helical periodicity of nucleosomal DNAof 10.0 bp per helical turn assumed in theoretical work (6) andthe actual helical periodicity of 10.18 bp per turn measureddirectly in this work and inferred from sequence analysis (4,13). One reason for this discrepancy may be that in nucleo-somal arrays (35) other sources of writhe and surface twistthan the nucleosome exist. Moreover, it has been suggestedthat the nucleosome itself might not be best represented as asimple cylinder and that alternative paths of DNA maycontribute to the experimentally observed change in linkingnumber (36). The calculation above considers only the lengthofDNA found in the nucleosome core particle as isolated bymicrococcal nuclease digestion of chromatin. More than 146bp of DNA may be in contact with the histone core innucleosome arrays. Inspection of the hydroxyl radical foot-prints (Figs. 1 and 2) reveals a modulation of cleavageextending more than 90 bp from the center ofdyad symmetryof the nucleosome (14), whereas the modulation of DNase Icleavage only extends as far as position +70.The Positioning of Nucleosomes on DNA. Considerable

evidence exists in support of sequence-directed positioningof nucleosomes on DNA (13, 14, 18, 37). Chicken, frog, andyeast histones recognize the same structural features of a 5SRNA gene, leading to the same nucleosome position. How-ever, it should be noted that whether or not a nucleosome ispositioned on the X. borealis somatic SS gene in vivo is notknown. Mutagenesis experiments using sea urchin 5S DNAindicated that a region comprising 20-30 bp to either side ofthe center of dyad symmetry of the nucleosomal DNAcontained the major elements necessary for positioning (38).In addition, Ramsay (39) located two regions, centered about1.5 helical turns to either side ofthe center ofdyad symmetry,that are important for positioning of a bacterial DNA frag-ment on a histone core.The hydroxyl radical detects variations in minor groove

width (26). Such variations are apparent in the hydroxylradical cleavage pattern of naked DNA containing the 5SRNA gene from X. borealis (Fig. 2). Quantitative analysisindicates a periodic reduction in minor groove width every10-11 bp (Fig. 2B, "Free DNA" trace) and therefore raises

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the possibility that this stretch of DNA bends toward thenarrowed grooves. More importantly, the features present innaked DNA are retained and exaggerated in the hydroxylradical cleavage pattern of the nucleosome (Fig. 2B, compare"DNA in Nucleosome" to "Free DNA'' data sets). Thus,positions of reduced minor groove width in the naked DNA,located where sequence-directed positioning elements areexpected, are also places where the minor groove is narrowedwhen the DNA is bent around the histone core. Comparisonof sequences found at these positions reveals few similarities,except for some A+T-rich character. Our results imply thatthese different sequences can adopt similar secondary struc-tural conformations. We conclude that the hydroxyl radicalprovides a simple means to detect structural elements in freeDNA that are likely to be functional in the positioning of anucleosome.

CONCLUSIONSWe have used hydroxyl radical footprinting to obtain high-resolution data concerning the structure of a particular se-quence of DNA in a nucleosome. From our results weconclude that the helical periodicity of 5S DNA is changedfrom 10.49 ± 0.05 bp per turn in solution to 10.05 ± 0.05 bpper turn over extensive regions on either side of the center ofdyad symmetry of the nucleosome. Because a shorter regionaround the center of dyad symmetry changes its helicalperiodicity in the other direction, to 10.7 bp per turn, theaverage helical periodicity of DNA in the 5S nucleosome is10.18 ± 0.05 bp per turn. Calculation ofthe contribution thesechanges in helical periodicity make to the change in linkingnumber expected upon formation of the 5S nucleosomedemonstrates that changes in helical periodicity do not com-pletely explain the linking-number paradox as currently for-mulated (6). Detection by the hydroxyl radical of structuralfeatures in naked DNA that are maintained in nucleosomalDNA supports the assertion that the capacity ofDNA to bendis a major determinant of nucleosome positioning. Thesestudies demonstrate that the hydroxyl radical footprintingtechnique will prove a powerful analytical tool in determiningthe structural details of DNA in large nucleoprotein assem-blies.

We thank D. D. Brown, M. E. A. Churchill, D. J. Clark, H. R.Drew, G. Felsenfeld, M. Gellert, A. Klug, R. Morse, D. Rhodes,R. T. Simpson, and A. A. Travers for critical reading of the manu-script. We also thank T. Flatley for the Fourier algorithm. We aregrateful to V. Thuy for the preparation of the manuscript.

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