Structure of Chromatin and the Linking Number Of

Proc. Nati. Acad. Sci. USA Vol. 78, No. 3, pp. 1461-1465, March 1981 Biochemistry

Structure of chromatin and the linking number of DNA (DNA supercoiling/nucleosomes/chromatin fiber) ABRAHAM WORCEL*, STEVEN STROGATZt, AND DONALD RILEYt *Department of Biochemical Sciences and tDepartment of Mathematics, Princeton University, Princeton, New Jersey 08544; and +Division of Genetics, The Fred Hutchinson Cancer Research Center, 1124 Columbia Street, Seattle, Washington 98104 Communicated by Bruno H. Zimm, November 20, 1980

ABSTRACT Recent observations suggest that the basic su- the strands intact). Moreover, it is related to the writhing num- pranucleosomal structure of chromatin is a zigzag helical ribbon ber W and the twist number T by the equation (18-21) with a repeat unit made of two nucleosomes connected by a relaxed spacer DNA. A remarkable feature of one particular ribbon is that L = W + T. it solves the apparent paradox between the number of DNA turns per nucleosome and the total linking number of a nucleosome-con- W is a real number that measures the shape of the duplex axis; taining closed circular DNA molecule. We show here that the re- it is a geometrical, not a topological, invariant. One may con- peat unit of the proposed structure, which contains two nucleo- veniently represent a ccDNA as a twisted ribbon (21). Then, somes with - 13/4 DNA turns per nucleosome and one spacer whereas W is a crossover per repeat, contributes -2 to the linking number of property of the ribbon axis, the twist number closed circular DNA. Space-filling models show that the cylindri- T depends on the entire ribbon. Like W, T does not have to be cal 250-A chromatin fiber can be generated by twisting the ribbon. an integer and is not a topological invariant. The more usual term for T in the biochemical literature is "duplex winding num- It is now well-established that the unit structure of chromatin, ber" or "number of duplex turns"; for native DNA in solution, the nucleosome (1-3), is a flat cylindrical particle (110 X 110 T = bp/10.4 (22). x 57 A) with DNA wrapped around a histone octamer in a left- A ccDNA that lies flat on a plane will have W = 0 and L handed toroidal supercoil of approximately 80 base pairs (bp) = T. This is the case of the relaxed ccDNA. The experimentally per turn (4). There are 146 bp of DNA in the nucleosome core observed AL after nucleosome assembly with histones and nick- describing -13/4 superhelical turns (5) and 20-95 bp of spacer ing-closing enzyme [AL = - n, where n = the number of nu- DNA between neighboring nucleosome cores (6). cleosomes, (14)] could be due to AW, AT, or a combination of The nature of the supranucleosomal structure of chromatin the two according to is less clear. Electron microscopic studies of eukaryotic nuclei AL = AW + AT. have revealed a "thin" 100-A chromatin fiber and a "thick" 250- A fiber (7-9). Many past models have assumed that neighboring For instance, if the duplex winding number of DNA in solution nucleosomes are stacked side by side to generate a 100-A nu- and on the nucleosome were not the same, ATwould contribute cleofilament, which is further coiled into a 250-A "solenoid" to AL according to the equation. (10, 11). The unstacked 100-A fiber ("beads on a string") can be Recent careful measurements of the DNase I cutting pattern readily observed in nuclei and chromatin preparations spread in chromatin and on the nucleosome (5, 23, 24) reveal that the under isotonic conditions (1, 2, 12). A stacked 100-A nucleofila- observed DNA periodicity equals 10.4 bases and not 10.0 as ment also has been detected, but only at high salt concentrations previously thought (25). The simplest interpretation of this re- (11). Although the 100-A fiber is present in histone Hi-depleted sult is that the helical repeat of DNA on the nucleosome is 10.4 chromatin, the 250-A fiber is never observed under these con- bp per turn. Because the coiling of the DNA on the nucleosome ditions (11, 12). Thus, histone HI must play a role in the further apparently does not change T (5, 22, 23), AT = 0, and compaction of the linear chain of beads (12, 13). Reconstitution studies with the four intranucleosomal his- AL = AW tones and small circular DNAs in the presence of nicking-clos- W(nucleosomal DNA) - W(relaxed DNA) ing enzyme have revealed that the DNA coiling around a nu- =W(nucleosomal DNA) cleosome changes the DNA linking number by -1 (14). The histone Hl-induced compaction of the "beads on a string" into In other words, the geometry and only the geometry of the a 250-A-diameter supranucleosomal structure (15) does not -DNA coiling around the nucleosome -repeat must account for cause further changes in the linking number (16). Because the the change in the linking number of the DNA. nicking-closing enzyme relaxes the spacer DNA (16), the ob- The DNA coils for -13/4 turns around the histone octamer served change in the linking number must be due to the par- (4). If neighboring nucleosomes were to stack in a linear array, ticular DNA structure in the nucleosome. AL would approach -2n and not - n. In the stacked 100-A nu- The linking number L of a closed circular DNA (ccDNA) cleofilament (10, 11), in which the DNA follows a regular su- molecule is the number of topological revolutions made by one perhelical path, AL will be equal to the number of DNA turns strand about the other [counted after the molecule is con- around the linear chain of nucleosomes. However, the regular strained to lie in a plane (17)]. L is a topological invariant (i.e., superhelix is a particular and rather exceptional case. In most an integer which is unchanged by all deformations that leave other cases, AL is not equal to the number of superhelical turns around the nucleosomes. The value of AL will very much de- The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertise- Abbreviations: ccDNA, closed circular DNA; bp, base pair(s); L, DNA ment" in accordance with 18 U. S. C. §1734 solely to indicate this fact. linking number. 1461 Downloaded by guest on September 24, 2021 1462 Biochemistry: Worcel et aL Proc. Natl. Acad. Sci. USA 78 (1981)

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.-. FIG. 1. Electron micrographs r z z e * < f of partially unravelled chromatin fibers. Embryonic chicken eryth- H~i rocyte nuclei (4 days old) were eweVrid w 4~~ mildly digested with endogenous nuclease for 10 min at 37TC. Nuclei were rinsed in buffer (0.01 M Tris-HCl, pH 7.5/0.01 M NaCl/3 in .1-, l *e mM MgCl2) and allowed to spread e in 0.2 mM EDTA (pH 7.0) (28). The chromatin was fixed for 1-2 min in 1.5% (vol/vol) formaldehyde. Sam- ples were applied to glow-dis- i, . 1$* -I charged carbon-coated grids for 30 t *r/ sec followed by rinsing in 0.4% pho- toflow (29). The grids were air dried, stained with 5 mM uranyl- acetate, and rotary-shadowed with platinum.

pend on the path of the spacer*SvInDNA between nucleosomes (see used, the negatively charged DNA is attracted to the charged ref. 21 for examples and discussion). grid surface and the fragments spread open, revealing the in- A stacked 100-A nucleofilament, with AL = -2n, is not con- dividual nucleosomes and the spacer DNA between them. sistent with available data. Furthermore, such a nucleofilament Careful analysis of many such gently spread chromatin frag- is not observed under isotonic conditions. On the contrary, ments has revealed a recurring pattern: the nucleosomes are not electron microscopic observations suggest that under isotonic arranged in a linear fashion but instead appear to be "two-track" or low ionic strength conditions the nucleosomes are arranged arrays, with the spacer DNA going back and forth in a zigzag in a zigzag helicalb W *ribbon * * (see figures 1, 4, and 6 in refs. 26, 12, manner between the two nucleosome tracks. Obviously, the And show here that one ribbon-like zigzag pattern is the result of an artefactual unstack- and 27, respectively). We shall particular ribbon has the required AL = - n. ing of the packed nucleosomes. Such aconsistent pattern cannot be simply discarded but must be explained, somehow in terms of a conformational change from the native structure. METHODS AND RESULTS Fig. la shows long 250-A chromatin fibers from chicken Electron Microscopy of Gently Spread Chromatin Frag- erythrocytes. At many places (see arrowheads) the nucleosomes ments. Gentle digestions with nucleases release chromatin frag- appear to be slightly unstacked, revealing a ribbon-like, struc- ments which contain histone HI and the four nucleosomal his- ture. The zigzag pattern is the only recurring structural theme tones. In the electron microscope, they appear to be fragments that can be detected in these fibers. A fiber is shown at a higher of a cylindrical, bumpy, 250-A-diameter fiber (26). It is not pos- magnification in Fig. lb. The ribbon-like structure is clearly sible to ascertain the path of the DNA in such compacted struc- evident. The arrowhead points to a more compacted segment tures. When glow-discharged electron microscope grids are of the fiber where the alternating nucleosomes appear to be Downloaded by guest on September 24, 2021 Biochemistry: Worcel et al. Proc. Natl. Acad. Sci. USA 78 (1981) 1463

stacked on top of each other. The path of the spacer DNA as 2a, is greatly diminished (although never completely elimi- it zigzags from one nucleosome to the next is also visible in Fig. nated) by helically twisting the ribbon about the midline parallel ic. Electron micrographs such as this one and previously ptib- to the nucleosome columns. Experimentation with space-filling lished ones are compelling enough to warrant a careful analysis models demonstrated the feasibility and enhanced symmetry of the implications of such ribbon structure on the linking num- of this higher-order coiling (Fig. 3). In this way, the flat struc- ber of DNA and on the internucleosome contacts in the 250- ture of Fig. 2a could also acquire the "volume" characteristic A chromatin fiber. of the 250-A chromatin fiber. The 250-A Chromatin Fiber As a Twisted Ribbon. Fig. 2a The Proposed Structure Has AL = -n. Methods for com- shows one of the many possible ribbons. As we shall show be- puting the linking number of DNA have been discussed else- low, this is the only simple helical ribbon with AL = - n. The where (20, 21). A straightforward approach involves modeling spacer DNA remains relaxed as it moves from one nucleosome the ccDNA as a ribbon and then counting edge crossovers as to the next, and there are -13/4 DNA turns per nucleosome. described (21). This empirical approach led us to the realization Alternating nucleosomes are stacked on their flat, histone sur- that the ribbon in Fig. 2 has AL = - n. To show this, we use faces. These are the only surfaces of the nucleosome that could the repeat unit in the proposed structure, the dinucleosome. participate in stereospecific, symmetrical internucleosome con- Several copies of this unit are joined end-to-end in the overall tacts (4, 30). The arrangement of the nucleosome cores in Fig. structure. We now seek to isolate the contribution made to L 2a is similar to the one observed in the crystals of nucleosome by each dinucleosome. The approach is to substitute a dinu- cores (4); the only thing that is new in this diagram is the path cleosome for a segment of spacer DNA and to compute the re- of the spacer DNA connecting the stacked nucleosome cores. sulting change in L. There are two other reasonable ways to build a stacked rib- Fuller has indicated some of the pitfalls involved in decom- bon. One of those resembles the ribbon shown in Fig. 2a except posing L into contributions from various portions of a structure. that the 1 - 2 spacer DNA crosses over above, not below, the However, there is one special simple case (see figure 7 in ref. 2 3 spacer DNA, etc. Such ribbon will have AL = -2n, a 37). Suppose a "topological ball" contains the segment of spacer value that clearly is too high for chromatin. (When unstacked, DNA to be hypothetically excised and, in particular, suppose this ribbon will appear as shown below in Fig. 5 Upper Left). this ball excludes all other regions of spacer and nucleosomal The third possible ribbon can be generated by flipping over DNA. Then if the dinucleosome to be inserted also can be con- in a 180° rotation the even-numbered nucleosomes of Fig. 2a so that the DNA spacers no longer cross over. (Such a ribbon is shown below in Fig. 5 Upper Right.) Because the DNA spacers are parallel to each other, the nucleosomes will have only - 1'/2 turns of DNA (not -13/4). More important, such a ribbon will have AL = -11/2 n. Thus, for simian virus 40 DNA containing 24 nucleosomes, such a structure will result in AL = -37, not -25 as observed (there is an additional super- Uf f helical twist introduced because of the end effects of ring clo- sure as noted below). Because -37 is clearly different from the observed -25 ± 1 (14, 31, 32), this third possible ribbon also may be rejected. A ribbon is a helix with a repeat unit made of two nucleosomes. Careful analysis of Fig. 2a reveals that the two nucleo- I_, somes in the helical repeat are not exactly symmetrical. In ad- dition to the right-angle spacer crossovers resulting from the - 13/4 DNA turns per nucleosome, spacers from even-numbered nucleosomes show a down * up and up - down crossover which is not present in the odd-numbered nucleosomes. This peculiar spacer crossover is perhaps the most important feature of our proposed structure. It occurs every two nucleosomes and is responsible for the rather low AL of the resulting structure. The nucleosome asymmetry, which is quite evident in Fig.

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FIG. 3. Space-filling model of a twisted helical ribbon. The flat 2 ribbon of Fig. 2a has been twisted along the groove parallel to the nucleosome columns; such a twist will change slightly (<10%) the overall 110A 157A3 AL. Nucleosome 1 is unstacked. The numbers are positioned at both ends of the 140-bp nucleosomal DNA coil. Black numbers, visible on ab one groove of the ribbon, indicate the DNA entering nucleosome n 1 10 A (DNA is coming from nucleosome n - 1). White numbers, visible on the other groove, pointtothe DNA leaving nucleosome n (DNA is going to nucleosome n + 1). These numbered sites are the probable places FIG. 2. Helical ribbon of stacked nucleosomes with AL = -n. (a) of histone H1-DNA interaction (33,34). Histone H1 thus bound could Nucleosomes are drawn as flat cylinders to show the symmetrical in- compact the linear string of unstacked nucleosomes into a ribbon-like ternucleosome contacts. (b) Path of the DNA in nucleosomes 2, 3, and structure. Interaction between contiguous H1 molecules along each 4 of a. Spacer DNA is relaxed and each nucleosome has 13/4 left-handed groove of the ribbon could further compact the fiber and generate the DNA turns. observed H1 homopolymers in crosslinked chromatin (35, 36). Downloaded by guest on September 24, 2021 1464 Biochemistry: Worcel et al Proc. Natl. Acad. Sci. USA 78 (1981) DISCUSSION a The proposed zigzag ribbon of stacked nucleosomes is a structure that is radically different from a linear nucleofilament. In a linear array, neighboring nucleosomes stack onto each other, whereas alternating nucleosomes interact along the two tracks of a ribbon. So far, available chromatin crosslinking data cannot b A distinguish between these two basically different structures. A ribbon and a nucleofilament will have different effects on the linking number of ccDNA. A nucleofilament with DNA wrapped in a more or less continuous superhelix will have AL = -2n (where n = number of nucleosomes). Such a nucleofilament has been observed at high salt concentrations (0.9 M NaCl) (11). Under those conditions, nonhistone proteins and histone H1 are removed from chromatin and the spacer DNA is supercoiled (39). The extra coils in the spacer DNA, which are probably responsible for stacking neighboring nucleosomes onto each other (11), could be the result of overwinding of the d A duplex DNA by the high salt concentration (30, 40, 41). Under isotonic conditions, the spacer DNA is not supercoiled (16) and neighboring nucleosomes do not stack onto each other (Fig. 1). Clearly then, a nucleofilament with AL = -2n is not a likely FIG. 4. Proof by transforma- structure for chromatin under isotonic conditions, whereas a z tion that the proposed dinucleo- ribbon with AL = -n is consistent with the available data. e some changes the linking num- Not all ribbons will have AL = - n. Fig. 5 Upper Left shows E D ~~~~~~berof ccDNA by -2. a ribbon made up of nucleosomes with -13/4 DNA turns each. This type of ribbon has appeared in a number of recent diagrams tained in the ball, there is a well-defined "contribution to L", (see figure 14 in ref. 12 and figure 5 in ref. 42) but is not a likely AL (37), associated with this change of winding path. As should structure for chromatin because it has AL = -2n. A ribbon be clear from Fig. 2b, the dinucleosomes in the helical zigzag made up of nucleosomes with - 11/2 DNA turns each is shown satisfy this condition. By using the methods described by Fuller in Fig. 5 Upper Right. Although this stacked ribbon is sym- (37), it can be proven that our dinucleosome has AL = -2 (un- metrical and rather plausible, it has AL = - 11/2 n, a value that published data), and this immediately establishes AL = -n. is also probably too high for chromatin. RoughlyFbecause two nucleosomes change L by -2, a struc- On the other hand, there are a number of zigzag ribbons that ture with n nucleosomes should have AL = -n. share AL = -n (Fig. 5 Lower). These structures are topolog- The Repeat Unit (Dinucleosome with - 13/4 Turns of DNA ically equivalent to the stacked ribbon in Fig. 2. For example, Per Nucleosome) Contributes -2 to the Linking Number of a structure proposed by Lohr and van Holde (24) for yeast chro- ccDNA. This point is illustrated graphically by the following matin (Fig. 5 Lower, structure a), can be generated by unstack- transformation. Fig. 4a shows the repeat unit of the proposed ing the nucleosomes of Fig. 2 and loosening 10 bp from each structure, the dinucleosome (2, 3) of Fig. 2 a and b. The ribbon end of the nucleosomal DNA coil. The resulting nucleosomes represents the DNA duplex wound -13/4 turns on each core will have - 1'/2 DNA turns (120 bp of DNA at -80 bp per turn), particle (core not shown). In Fig. 4b we reproduce the left half and the DNA spacers will be parallel to each other. Similarly, of Fig. 4a to facilitate comparison with c and d. The endpoints structure b in Fig. 5 Lower can be generated from structure a of structures in Fig. 4 b-d are taken to be fixed. The first trans- by peeling off an additional 10 bp from each end of the nu- formation occurs between b and c, where the portion of the cleosome coil, leaving 100 bp of DNA and - /4 DNA turns per duplex that lies under the DNA exiting the nucleosome (arrow nucleosome. The nucleosomes in structure c of Fig. 5 Lower in b) was imagined to have passed through and over. This dou- have 80 bp of DNA and -1 DNA turn [this structure is anal- ble-stranded passage changes AL by +2. [See ref. 37 for the sign ogous to an early proposal (43)], and those in structure d have convention used in the calculation of crossovers.]¶ The struc- 60 bp of DNA and -3/4 DNA turn. ture in Fig. 4d is topologically equivalent to that in c and, hence, It can be easily shown with a ribbon (21) that all of the struc- contributes the same amount to AL as the structure in c does. tures in Fig. 5 Lower have AL = - n. Thus, they could all be We have slackened the portion of the duplex indicated by the easily and reversibly generated by unstacking the compacted arrow in Fig. 4c and pulled it around and under the lower ring. 250-A fiber in Figs. 2 and 3. Indeed, the structures in Fig. 5 By this second transformation, we make it obvious that c is Lower are actually observed in the electron microscope as the equivalent to a structure with 13/4 right-handed turns. The re- thick chromatin fiber uncoils (Fig. 1; refs. 12 and 26). The usual sulting structure is shown in Fig. 4e. Because of its reflection "beads on a string" appearance of spread chromatin (1) likely symmetry, this structure would contribute AL = 0. Because it corresponds to the extended conformation in structure c. differs by +2 in AL from our proposed dinucleosome (Fig. 4a), Normally, the two DNA strands are not free to rotate. This the proposed dinucleosome must contribute AL = -2. statement applies not only to small ccDNA molecules but also to large, presumably linear DNA molecules which appear to be § More precise considerations show actually AL = -(n + 1) if end ef- subdivided into independent supercoiled domains both inside fects are not neglected. Following the decomposition approach (20), and outside the cell (40, 44, 45). Thus, in the absence of to- begin with a "reference" molecule containingone nucleosome. Count- poisomerase action or DNase nicking, the linking number of ing edge crossovers (21) shows that here AL = -2 [i.e., AL = DNA will not The structures shown in 5Lower will -(n + 1)]. Because insertion of dinucleosomes changes n by 2 and change. Fig. AL by -2, the formula remains valid for all odd n. Similar arguments be freely interconvertible at equilibrium for the precise reason work when n is even. that they share the same DNA linking number. I See also refs. 38 and 39 for the practical consequences of such double- Note that all of the nucleosomes in Fig. 5 Lower are sym- strand passages. metric. The final compaction to the stacked fiber with slightly Downloaded by guest on September 24, 2021 Biochemistry: Worcel et aL Proc. Natl. Acad. Sci. USA 78 (1981) 1465 structure of the type shown in Figs. 2 and 3 will generate a bumpy and discontinuous 250-A fiber, which is probably closer a 4 be4 to the correct overall structure (13). 1. Olins, A. L. & Olins, D. E. (1974) Science 183, 330-332. 2. Oudet, P., Gross-Bellard, M. & Chambon, P. (1975) Cell 4, 281-300. AL =-2n 3. Felsenfeld, G. (1978) Nature (London) 271, 115-122. 4. Finch, J. T., Lutter, L. C., Rhodes, D., Brown, R. S., Rushton, B., Levitt, M. & Klug, A. (1977) Nature (London) 269, 29-36. 5. Prunell, A., Kornberg, R. D., Lutter, L., Klug, A., Levitt, M. a I)01 & Crick, F. H. C. (1979) Science 204, 855-858. 6. Compton, J. L., Bellard, M. & Chambon, P. (1976) Proc. Natl. AL: -n Acad. Sci. USA 73, 4382-4386. b 7. Wolfe, S. L. (1969) in The Biological Basis ofMedicine, ed. Bittar, /