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) *;B { 81 ' ..,.. > * .... v v ...... .C s. r~~~~~~~~~~~~~~rt .., W.t . 5 a' " st..~~~~~~~~.dJ S;.--.X* w be sac it .. ., : r~~~~~~~~~A . 11 j~~~~~~~~~~~~~ ;. * 41- . ~~,.;--'I .. ^ A*"2.4 b_5 *~~. WI'. ~4. *w' e, .f "o 0.5. F_ t. i0 X1 i '-.- .r j.. I - e I . X -* Dr ; .-. 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.