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Structural plasticity of single chromatin fibers revealed by torsional manipulation Aure´lien Bancaud1, Natalia Conde e Silva2, Maria Barbi3, Gaudeline Wagner1, Jean-Franc¸ois Allemand4, Julien Mozziconacci3, Christophe Lavelle2,3, Vincent Croquette4, Jean-Marc Victor3, Ariel Prunell2 & Jean-Louis Viovy1 Magnetic tweezers were used to study the mechanical response under torsion of single nucleosome arrays reconstituted on tandem repeats of 5S positioning sequences. Regular arrays are extremely resilient and can reversibly accommodate a large amount of supercoiling without much change in length. This behavior is quantitatively described by a molecular model of the chromatin three-dimensional architecture. In this model, we assume the existence of a dynamic equilibrium between three conformations of the nucleosome, corresponding to different crossing statuses of the entry/exit DNAs (positive, null or negative, respectively). Torsional strain displaces that equilibrium, leading to an extensive reorganization of the fiber’s architecture. The model explains a number of long-standing topological questions regarding DNA in chromatin and may provide the basis to better understand the dynamic binding of chromatin-associated proteins.

The genetic material of eukaryotic cells is organized into chromatin, a nucleoproteic structure whose repetitive unit is the nucleosome1. The core particle of the nucleosome consists of 147 bp of DNA wrapped 1.65 times around an octamer containing two copies each of the four core histones, H2A, H2B, H3 and H4 (ref. 2). This leads to both compaction and topological deformation of the DNA by one negative turn per nucleosome (DLk B –1, Lk being the linking number3). In vivo, regularly distributed nucleosome arrays with a repeat length of B200 base pairs1 fold into 30-nm fibers, whose modulated compaction is thought to be associated with a differential accessibility of DNA4 to interactions with various factors, as required for DNA activity. A better knowledge of chromatin organization is thus expected to improve our understanding of the regulation of DNA transactions in vivo. Bona fide nucleosome arrays can be reconstituted in vitro, and single-molecule techniques now offer a direct approach to study their molecular dynamics in real time. Force micromanipulation has revealed the existence of an internucleosomal attraction that maintains the higher-order chromatin structure under physiological conditions5 and shown a reversible peeling of B80 bp of nucleosomal DNA below 15 pN (ref. 6), presumably associated with the destabilization of H2A– H2B dimers. Above this force, discrete disruption events of 25 nm each, attributed to the dissociation of tetrasomes ((H3–H4)2–DNA complexes)6,7, have been observed. In this study, we performed the first torsional nanomanipulation of single chromatin fibers using magnetic tweezers8. We observed that nucleosome arrays reconstituted on 5S tandemly repeated positioning

sequences9 with core histones purified from chicken erythrocytes can accommodate large amounts of negative or positive supercoiling without much change in their length. We propose a quantitative model based on a dynamic equilibrium between the three conformations of the nucleosome previously identified through the minicircle approach (a single nucleosome reconstituted on a DNA minicircle)10. In these states, the nucleosome entry/exit DNAs can cross negatively (as in the canonical structure2) or positively, or not cross at all. The model fits the chromatin length-versus-torsion response at various levels of compaction and under stretching forces ranging from 0.09 to 5 pN. It also shows how the torsional constraint can force nucleosomes to switch conformation and can induce a large and reversible reorganization of the fiber architecture. These findings provide simple answers to long-standing topological puzzles about DNA in chromatin. Moreover, the ability of chromatin to undergo fast and reversible structural reorganizations, revealed by this study, may underlie the dynamic nature of the binding of numerous chromatin-associated proteins11,12. RESULTS Torsion Nucleosome arrays were reconstituted by stepwise dilution using a linear DNA containing 36 tandemly repeated 208-bp 5S positioning sequences9 and purified core histones. These fibers were then flanked by two naked DNA spacers, to avoid histone-mediated hydrophobic interaction with the surfaces, and by two ‘stickers’ that link the fiber to

1Institut Curie, UMR 168, 75231 Paris, France. 2Institut Jacques Monod (UMR 7592), 2 Place Jussieu, 75251 Paris, cedex 05, France. 3Laboratoire de Physique The´orique de la Matie`re Condense´e (UMR 7600), 4 Place Jussieu, 75252 Paris, cedex 05, France. 4Laboratoire de Physique Statistique (UMR 8549), 24 Rue Lhomond, 75231 Paris, cedex 05, France. Correspondence should be addressed to J.-L.V. ([email protected]) or A.P. ([email protected]).

Received 23 December 2005; accepted 14 March 2006; published online 16 April 2006; doi:10.1038/nsmb1087

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Figure 1 Schematic of the experiment. A single nucleosome array (B7.5 kbp), sandwiched between two naked DNA spacers (B600 bp each), is linked to a coated surface and to a magnetic bead. A pair of magnets placed above this molecule exerts controlled torsional and extensional constraints8.

the coated bottom of the flow cell and to the paramagnetic bead, respectively (Fig. 1, blue and orange segments). A pair of magnets was placed above this construction, and different torsions were applied by rotating the magnets about the vertical axis. The magnets’ vertical position specifies the stretching force, that is, the fiber extension, which was measured by recording the three-dimensional position of the bead8. The typical torsional behavior of a single chromatin fiber in low-salt buffer B0 (see Methods) is shown in Figure 2a at 0.34 pN (blue curve). After chemical dissociation of the nucleosomes, the response of the corresponding naked DNA was obtained (red). This latter curve displays a mechanical effect of torsion and an asymmetry for negative supercoiling. These features are the signatures of an unnicked singleduplex DNA8. Compared to naked DNA, chromatin is shorter by B1.35 mm, and its center of rotation is shifted by –24 ± 2 turns. This corresponds to a shortening of B–55 nm per negative turn, as expected for one nucleosome, as 50 nm corresponds to 150 bp. Nucleosomes were also disrupted mechanically by increasing the tension, after supplementing B0 with 50 mM NaCl and 2
10–3 % (w/v) nucleosome assembly protein-1 (NAP-1; gift from S. Leuba, University of Pittsburgh). At 7.7 pN, 14 individual lengthening steps with an average height of 24.2 ± 1.9 nm were detected (Fig. 2b), in agreement with ref. 6. Thanks to the presence of NAP-1, which interacts with core histones in vitro13 and favors their release, this process occurred at a lower force than in ref. 6. Notably, it was partially reversible, as also reported in ref. 6. In the course of two successive pulling phases at 7.7 pN, separated by a 50-s pause at

Figure 2 Micromanipulation of single chromatin fibers. (a) Extension-versusrotation curves at 0.35 pN for an intact fiber (blue) in buffer B0 (see Methods), for the same fiber after partial nucleosome disruption as shown in b (green) and for its corresponding naked DNA after complete nucleosome dissociation (red). (b) Individual nucleosome disruption events at 7.7 pN of the fiber in a in B0 plus NAP-1 and 50 mM salt (see Results). The force was temporarily lowered to 0.67 pN between the arrows. (c) Maximal extension versus topological departure from DNA for ten fibers at 0.3 ± 0.07 pN in B0. Black straight line shows the relationship predicted by our three-state model (see Supplementary Discussion). Fibers on the line are referred to as regular and those off as irregular. Arrowheads correspond to the fibers studied in a (black) and d (blue). Numbers in green refer to fibers studied in Figure 6. (d) Extension-versus-rotation curves of the chromatin fiber corresponding to the blue arrowhead in c at 0.25 pN (blue) and of its corresponding renormalized DNA (red). Smooth curves were obtained assuming an elastic response in bending, stretching and twisting (worm-like rope model)15.

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Stretching The fiber described in Figure 2d and its corresponding DNA were also compared, again in B0, with respect to their stretching behaviors

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0.67 pN, the fiber contracted by –28.5 nm during the pause, roughly corresponding to one individual nucleosome reassociation. The response in torsion of the partially disrupted fiber was then probed in B0 at low force and, as expected, it was intermediate between the responses of the original fiber and of DNA (Fig. 2a, green). The shifts in length and in topology between the new fiber and DNA were respectively B700 nm and –13 ± 1.5 turns, or B54 nm per turn, identical to the values derived for the initial fiber. Assuming that each step corresponds to the dissociation of one nucleosome, the topological deformation per nucleosome can be estimated as –(11 ± 1.5)/14 ¼ –0.8 ± 0.1 turn. The rotational behavior of ten fibers was then compared by plotting their maximal length at 0.3 ± 0.07 pN versus the rotational shift of those maxima relative to their corresponding naked DNAs (Fig. 2c). A linear trend was observed, with most data points well aligned and a slope close to 55 nm per turn. This is the expected behavior for regular nucleosome arrays with a variable number of nucleosomes. The corresponding nucleosome arrays were therefore referred to as regular. A few fibers, however, deviated from this linear trend. We show in the Supplementary Discussion online that these deviations can be attributed to the presence of variable proportions of clustered nucleosomes devoid of linker DNA (see also Supplementary Fig. 1 online). Hence, these fibers were termed irregular. A direct comparison between chromatin and DNA requires a derivation of the torsional response of a DNA molecule having the same maximal length under the same force. Taking advantage of the invariance in length of the DNA torsional response8, one can obtain the renormalized curve of the DNA by dividing both lengths and rotations by the ratio of the maximal length of DNA to the maximal length of chromatin. The resulting renormalized DNA curve was further displaced parallel to the abscissa to superimpose its rotation center onto that of the fiber (Fig. 2d). Compared to DNA, nucleosome arrays seem extremely resilient, being able to accommodate a much larger amount of supercoiling without substantial shortening.

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(Fig. 3a). Whereas chromatin is more rigid than DNA below 1 pN (the curve is steeper) in its entropic stretching regime (see below), beyond that force it becomes more flexible. This feature can be understood qualitatively as a consequence of the chromatin’s three-dimensional arrangement: bending a wire in a spring-like shape can reduce its stretching modulus by orders of magnitude, a property extensively used in engineering. The dependence of the rotational behavior on the applied force was also studied (Fig. 3b; with forces ranging from 0.09 pN to 0.34 pN). The torsional response always seemed more asymmetric at lower forces, and the curve’s apex shifted toward negative values. This latter feature, which was not observed for naked DNA (not shown), indicates a larger topological deformation per nucleosome at lower force. Salt effects Several buffer conditions were investigated, and two of them, representative of the general trend, are documented here: B0 plus 25 mM NaCl and B0 plus 40 mM NaCl and 2 mM MgCl2. Compared to the results with B0, the fibers always seemed more compact at higher salt concentrations (by B15% in the first condition and B30% in the second; Fig. 4a and b, respectively). Notably, the condensed fiber in salt could be extended to the length observed in B0 by the transient application of a force of several pN. When the tension was released, the force-versus-length behavior became virtually identical to that obtained in B0. This property is consistent with the hysteresis loop observed in Figure 4c: the fiber was always longer upon decreasing the force than upon increasing it. A hysteresis was also observed in the rotational behavior: if a force of B2–3 pN was exerted immediately before a torsional manipulation (typically performed at 0.3 pN), the response of the fiber was nearly identical to that previously recorded in B0 at the same force (data not shown).

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The reference behavior in B0 therefore seems to correspond to a maximal extension of the fiber, in agreement with earlier observations that nucleosome arrays are decondensed in low salt14. The condensation and the hysteretic behavior in higher salt conditions presumably reflect short-range attractive nucleosome-nucleosome interactions mediated by histone tails, which can be temporarily broken by a transient force increase. These results are quite consistent with those reported in ref. 5, in which native chromatin was micromanipulated in tension under different salt conditions. Despite a scattering intrinsic to the length measurements, a shift of the center of rotation toward more negative values was always observed in higher salt (Fig. 4b), as was also observed at lower force (Fig. 3b). For instance, the shift from B0 to B0 plus 40 mM NaCl and 2 mM MgCl2 was –6 turns, that is B–0.25 turns per nucleosome (Fig. 4b). Worm-like rope modeling and canonical chromatin The fiber’s mechanical properties were first fitted using the worm-like rope model. This model, widely used for DNA15, represents a molecule (or, here, the chromatin fiber) as an isotropic elastic rod with defined bending, twisting and stretching moduli. This model fits well the length-versus-torsion and force-versus-length responses in Figures 2 and 3. The best-fit values of the bending persistence length and stretching modulus (28 nm and 8 pN, respectively) were in agreement with previous studies5,6 and models of the chromatin fiber16,17. In contrast, the torsional persistence length, which was measured here for the first time, was exceptionally low (B5 nm, compared to B80 nm for DNA). As a first attempt to interpret this torsional resilience, we modeled two-angle nucleosomes18,19 with their entry/exit DNAs crossed negatively, as inferred from the core particle crystal structure2 and observed with crystallized tetranucleosomes20. Connecting these canonical nucleosomes by flexible DNA linkers led to the ‘all-negative’ fiber in

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0.8 Figure 4 Salt-dependence of the fiber’s 0.8 mechanical behavior. (a) Extension-versus0.6 1 rotation behavior of a fiber in B0 (black) and 0.6 0.4 in B0 plus 25 mM NaCl (blue crosses; blue 0.4 line shows filtered average) at 0.35 pN. 0.2 0.2 (b) Extension-versus-rotation behavior of a fiber 0.1 in B0 (black) and in B0 plus 40 mM NaCl and 0.0 0.0 – 60 – 40 – 20 0 20 40 – 60 – 40 – 20 0 20 40 0.0 0.5 1.0 1.5 2.0 2 mM MgCl2 (blue crosses; blue line shows Rotation (turns) Rotation (turns) Fiber length (µm) filtered average) at 0.2 pN. In high salt, an increased variability in the measurements is observed and the apex of the average curve shifts toward more negative rotation values, reflecting a displaced equilibrium with more nucleosomes in the negative state. (c) Response in force versus extension of the fiber in a at its center of rotation. In this experiment, we describe ‘force cycles:’ first, the force on the fiber is increased step by step, and for each step the length of the fiber is recorded (dark blue and black). Once a constraint of B5 pN is reached, the process is reversed, and the force is progressively lowered to its initial value (B0.05 pN; gray and cyan). The fiber does not show any hysteresis in B0 (black and gray). In contrast, the fiber in B0 plus 25 mM NaCl (dark blue and cyan) is initially more compact, but it can be extended to the B0 level by a force of a few pN. Upon decrease in force, it behaves the same way as in low salt.

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Figure 3 Tension dependence of the fiber behavior. (a) Force versus extension curves in B0 of the fiber in Figure 2c,d (squares) and of the corresponding naked DNA (crosses) at their respective centers of rotation. Smooth curves were obtained as in Figure 2d. (b) Extension versus torsion of a regular fiber (same as charted in blue in Fig. 2a) in B0 under tensions of 0.09 pN (triangles), 0.17 pN (circles) and 0.34 pN (crosses). Strong asymmetry in the mechanical response for positive compared to negative torsional constraints is observed at low forces. This is presumably a consequence of the different energies of the nucleosome’s positive and negative states (see Results). The apex also shifts toward negative torsion at lower forces, presumably as a consequence of a shift in the equilibrium favoring nucleosomes in the negative conformation.

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Figure 5 Three-state model of the chromatin fiber. (a) Diagrams of individual nucleosomes in the negative (a B 541; blue), open (a B –301; yellow) and positive (a B 301; cyan) states. (b) Torsional data (from same fiber as in Fig. 2d; squares) fitted by our three-state nucleosome model. The model fits the response over 30 turns around the apex (bold line). For higher torsion (on the positive and negative sides), a thin line representing the best fit using the plectoneme model is plotted. Under the curve are shown typical structures of a 208-bp repeat fiber at torsions marked by black circles (structures 1, 2 and 3). In structure 1, at the apex, 65%, 20% and 15% of nucleosomes, on average, are in the open, positive and negative conformations, respectively; in structure 2, the transition to the plectoneme regime on the negative side, 100% are negative, on average; in structure 3, the transition to the plectoneme regime on the positive side, 80% are positive and 20% are open, on average. (c) Torque as predicted by the three-state model (bold line) and by the plectoneme model (thin lines). Dashed line corresponds to the predicted evolution of the torque in the absence of plectonemes.

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Supplementary Figure 2 online. Its very large torsional persistence length (35 nm, compared to 5 nm for the experimental value; see above) prompted us to turn to other concepts. Mononucleosomes assembled on DNA minicircles Previous studies have demonstrated that mononucleosomes thermally fluctuate between three discrete conformational states corresponding to different crossing statuses of entry/exit DNAs (with DLko B –0.7 (open, no crossing), DLkn B –1.4 (closed negative, negative crossing) and DLkp B –0.4 (closed positive, positive crossing) for the 5S positioning sequence (Fig. 5a)). The transition between these states involves a rotation of the nucleosome around its dyad relative to the loop10,21. Notably, cryo-EM visualization of reconstituted fibers in low-salt conditions has also suggested the occurrence of such states22. In contrast, they do not appear in the tetranucleosome crystal structure20, presumably because the high-salt conditions used for crystallization and the crystal packing energies favor closed conformations10. The existence of the open state was first documented in minicircles23, but it was only after the core particle crystal structure was disclosed2 that the reason for such an easy unwrapping of the nucleosome edges became clear. DNA is attached to the octamer at 14 specific binding sites. These 14 sites are spaced every B10 bp and are defined by their super-helix location (SHL) relative to the dyad2. The SHL ± 6.5 sites are located at the nucleosome entry/exit and have the weakest binding energy24. The existence of discrete open and closed states therefore results from the status of these sites, which can be only ‘on’ or ‘off.’ The closed positive state shows a positive crossing of entry/ exit DNAs. Although counterintuitive given the left-handed wrapping around the histone octamer, this state has been extensively documented using the minicircle approach through ethidium bromide fluorescence titration25 and relaxation21,26,27. We recently confirmed that SHL ± 6.5 binding sites are ‘on’ in this closed positive conformation. Indeed, the substitution of H3 Arg49 by a lysine, which, in contrast to arginine, cannot intercalate its basic lateral chain into the small groove of the DNA2, equally affects the energies of the closed negative and closed positive states (N.C.eS. & A.P., unpublished data).

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New model of the chromatin fiber We constructed a new molecular model for the fiber (208-bp repeat length), assuming a thermodynamic equilibrium between the three different states of the nucleosome described above (Fig. 5a). A standard statistical mechanical analysis (free energy minimization based on the partition function) could then predict the fiber lengthversus-torsion behavior at constant force, as a function of the energy differences between the states (see details in Supplementary Discussion and Supplementary Equations 1–3 online). The upper part of the rotational response of a regular nucleosome array (corresponding to the blue arrowhead in Fig. 2c) was accurately fit by this model (Fig. 5b, bold line), using the number of nucleosomes (31) and the energy differences between the negative and open states (Un ¼ +0.4 kcal mol–1, that is +0.7 kBT per molecule, where kBT is the thermal energy), and between the positive and open states (Up ¼ +1.2 kcal mol–1, that is +2 kBT) as adjustable parameters. The low energies involved imply that nucleosomes in the fiber are in a dynamic equilibrium and this equilibrium is displaced by the applied torsion. Three typical structures of fibers under specific rotational constraints are marked by black circles in Figure 5b. Structure 1 has the maximal extension and most of its nucleosomes in the open state. Structure 2 is 34 31 27 22

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Figure 6 Single-parameter fitting. The torsional behavior of four regular fibers (corresponding to data labeled 1–4 in Fig. 2c) at 0.3 ± 0.07 pN in B0 is plotted, together with their best fits using the three-state model. Each fit assumes a single set of energy differences for both the negative versus open state (Un ¼ +0.4 kcal mol–1) and the positive versus open state (Up ¼ +1.2 kcal mol–1) and adjusts the number of nucleosomes only; upper left key gives best-fit number of nucleosomes.

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ARTICLES Figure 7 Chromatin as a topological buffer. Shown are schematics of the twin-supercoiled domain model of transcription38 adapted to chromatin within the three-state model. Assuming that the fiber has clamped ends and that the transcription machinery cannot rotate around the helical axis of chromatin, the progression of the enzyme generates a positive torsional stress ahead of it (to the right) and a negative one in its wake (to the left). In vivo, proteins can ensure immobilization of the fiber ends, as in chromatin loops, for example. Blue box represents the transcription bubble, but does not denote any assumption regarding the fates of nucleosomes under transcription. (a) At the onset of transcription, the whole fiber is torsionally relaxed (Supplementary Fig. 4). Once started, the polymerase will keep moving until the increasing torques exerted by the left and right parts of the fiber balance the torque generated by the enzyme. (b) At the end of the elongation phase, the right part of the fiber is in a most-positive state (Fig. 5b, structure 3), whereas the left part is in an all-negative state (Fig. 5b, structure 2).

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shorter, and essentially all of its nucleosomes are in the closed negative state. Structure 3 has an intermediate length and contains a mixture of open and closed positive nucleosomes (for comparison, ‘all-open’ and ‘all-positive’ fibers are shown in Supplementary Fig. 3 online; see also Supplementary Discussion). The model also provides a prediction of the torque as a function of torsion (Fig. 5c; for a comparison with the curve obtained when considering the fiber as an isotropic elastic rod, see Supplementary Fig. 4 online). The torque is less than 3 pN nm rad–1 over B30 turns around the center of rotation, that is, substantially smaller than that exerted by polymerases (45 pN nm rad–1)28 or than the value predicted for nucleosome torsional ejection (9 pN nm rad–1)29. Notably, the behavior of all regular nucleosome arrays can be described with the same set of energy values by fitting the number of nucleosomes only (Fig. 6). The fitted energies (Un ¼ +0.4 kcal mol–1 and Up ¼ +1.2 kcal mol–1; see above) are close to those obtained in the minicircle system under conditions of maximal repulsion of entry/ exit DNAs (Un ¼ +0.5 kcal mol–1 and Up ¼ +2.2 kcal mol–1 (ref. 10)). Considering the differences in geometry and ionic environment between the two systems, our best-fit values seem to be fully consistent with minicircle data. Response to high torsional stress Once B–20 turns have been applied starting from the apex, the model predicts that all nucleosomes should be in the closed negative state (Fig. 5b, structure 2). Because the fiber in the model cannot accommodate more negative turns by nucleosome transitions, the torque then increases abruptly (Fig. 5c, dotted line). In the experimental curve, a marked change in the length-versus-rotation curve is indeed observed beyond B–20 turns, associated with a constant slope of B–25 nm per turn. By analogy with naked DNA8, we interpret this constant slope as a consequence of plectoneme formation. Notably, 25 nm per turn is much smaller than the 90 nm per turn obtained for naked DNA at the same force, which indicates a lower torque (3 pN nm rad–1 for chromatin compared to 6 pN nm rad–1 for naked DNA; see Supplementary Discussion). Hence, plectonemes cannot form in the DNA spacers flanking the nucleosome array (Fig. 1); they must form in the fiber itself. Indeed, plectoneme formation may be facilitated in chromatin for two reasons. First, the energy cost of bending is a major component of the free energy of formation of plectonemes on naked DNA. This cost should be reduced by nucleosomes, which are natural DNA benders. (The bending persistence length of the fiber is indeed smaller than that of DNA; see above.) Second, the DNA charge screening of entry/exit DNAs through interactions with H3 N-terminal tails30,31 may also contribute to reduction of electrostatic repulsion and thus may favor compact

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‘twisted-pairs’ conformations that occur in plectonemes. This process is expected to extrude nucleosomes away from the plectoneme axis (Supplementary Fig. 5 online). Plectonemes should also develop on the positive side of the rotation curve, and indeed, a transition to a linear slope of B25 nm per turn occurs at B+10 turns from the apex. This corresponds to a supercoiling substantially lower than on the negative side. Our model, however, predicts that the corresponding torque should still be B3 pN nm rad–1 (see Supplementary Discussion), a value similar to that obtained on the negative side. This discrepancy between the negative and the positive behavior is a direct consequence of the higher energy of the positive state as compared to the negative one. Our model consistently indicates that only a fraction of the nucleosomes are in the closed positive state at the onset of plectoneme formation (Fig. 5b, structure 3); the torque necessary to drive the fiber into an all-positive conformation is higher than the critical torque for plectoneme formation. DISCUSSION Nucleosome transitions and chromatin topology These nanomanipulation experiments show that regular chromatin fibers are torsionally resilient structures that can accommodate large positive and negative supercoiling without developing strong torques or undergoing much shortening. We interpreted this resilience, typically five times higher than that predicted for a canonical fiber of closed negative nucleosomes, as being the consequence of a dynamic equilibrium occurring between three conformational states of the nucleosome. A molecular model based on this equilibrium quantitatively accounts for the data and delineates the energy landscape involved in the nucleosome transitions. This dynamic nature of chromatin provides simple explanations to several long-standing puzzles about the topology of DNA in chromatin. The most well known is the so-called ‘linking-number paradox:’ why does a 2-turn particle reduce the DNA linking number by 1 instead of 2 (refs. 10,32,33)? At first, the DNA was proposed to become overtwisted upon wrapping on the histone surface32, but it was later recognized that, even if some overtwisting may occur, it is by no means sufficient to explain the discrepancy4. The true explanation may, therefore, lie in a dynamic topological compensation occurring between negatively and positively crossed nucleosomes. Several other pending questions find simple answers thanks to our results. (i) The shift of the DLk per nucleosome observed for a minichromosome reconstituted on the same 5S repeats as used here, from –1.0 with control histones to –0.8 with hyperacetylated histones (that is, under high mutual repulsion of linker DNAs)34 is due to a displacement of the dynamic equilibrium toward more nucleosomes

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ARTICLES in the open state. The same occurred in our experiment (Fig. 4b): DLk B –1 was obtained in higher salt, compared to DLk B –0.8 in B0 (also favoring entry/exit DNA repulsion). Notably, a similar B+0.2 shift in DLk was also measured in the minicircle system with acetylated mononucleosomes in phosphate, a buffer that further destabilizes interactions between histone tails and DNA10. (ii) Reconstituted minichromosomes can withstand as much negative supercoiling (s B –0.1) as the corresponding naked DNA upon treatment with DNA gyrase35. The nucleosome’s apparent ‘transparency’ to that enzyme in spite of the trapping of most DNA in the nucleosome cores can be explained by a shift of most nucleosomes to the negative state10 rather than by a forced undertwisting of the DNA on the histone surface34. (iii) Finally, the ability of positively supercoiled plasmids to withstand the reconstitution of a large number of nucleosomes, in spite of the large additional positive supercoiling expected to accumulate36, must similarly reflect the displacement of nucleosomes toward the positive state. Chromatin as a topological buffer One may question the biological relevance of conclusions about the topology of nucleosomes drawn from experiments performed on chromatin fibers devoid of linker histones (such as H1). Linker histones cannot bind nucleosomes in the open state, but they do bind nucleosomes in the negative and positive states, and this brings entry/exit DNAs together into a torsionally highly flexible stem27. Also, the binding energy of linker histones on the nucleosomes is rather low, considering the dynamics of these proteins in live cells11,12,37. The presence of linker histones may thus alter substantially the equilibrium between the three states and in particular decrease the proportion of the open state. However, this should not suppress the high resilience still associated with the equilibrium between the closed negative and the closed positive states. Consequently, even if the steady-state proportion of open-state nucleosomes is small in quiescent chromatin, H1-containing fibers with nucleosomes in the closed negative and closed positive states should remain highly resilient. Open nucleosomes may rather be more involved in active chromatin, as suggested by two observations. First, histone acetylation, which favors the open state (see above), is usually associated with transcription. Second, H2A–H2B dimers are much more easily removed by NAP-1 when nucleosomes are in the open state than in the negative state, and their removal results in further unwrapping and the formation of single-turn tetrasomes (N.C.eS. & A.P., unpublished data). Chromatin torsional resilience must have important in vivo implications, because DNA transactions usually involve topological changes. Consider, for instance, the twin–supercoiled domain model of transcription38 in the context of chromatin. Our three-state model predicts that a fiber containing 50 nucleosomes and clamped at both ends can accommodate the supercoiling generated by the transcription of about 100 bp without the help of topoisomerases and without exceeding the torque exerted by the polymerase (Fig. 7), thus acting as a powerful ‘topological buffer.’ The transcription of 100 bp would indeed induce B10 positive turns on the right part of the fiber and B10 negative turns on the left side. The Lk difference between a relaxed and an ‘all-negative’ or a ‘most-positive’ fiber is B–0.5 or B+0.4 per nucleosome, respectively (see Fig. 5b and Supplementary Fig. 4). For these two constrained states of the fiber, the torque is B3 pN nm rad–1. Hence, the total torque is B6 pN nm rad–1, close to the torque exerted by the polymerase, at least 5 pN nm rad–1 (ref. 28). We conclude that a fiber containing B50 nucleosomes (equivalent to a topological buffer of B25
0.4 ¼ 10 turns) can sustain

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the transcription of 100 bp with no need for relaxation by a topoisomerase. The chromatin’s capacity to accommodate torsion should therefore favor the smooth progression of tracking enzymes and protect nucleosomes from unsolicited destruction by positive supercoiling. Notably, the polymerase’s torque seems to lie just below the combined thresholds for plectoneme formation on the upstream and downstream parts of the fiber, that is, below the torque at which the fiber should begin to dramatically shorten and change its large-scale organization. Whether this is a mere coincidence or a biologically relevant feature (for example, preventing the action of polymerases from dramatically altering chromatin organization if the torque is not relaxed efficiently enough) will deserve further investigation. Nucleosome conformational transitions may also have a role in the control of DNA-protein interactions in the context of chromatin, for instance by affecting the binding of linker histones and their HMG protein competitors39. In addition, they may affect the binding of other proteins, such as remodeling or transcription factors12, in a torsion-dependent manner, by means of rearrangements in the fiber’s three-dimensional architecture (as in Figs. 5 and 7, for example). As suggested in ref. 39, dynamic binding of proteins on chromatin11,12,37 offers an efficient way to quickly react to changes in the environment. Because they depend on the fiber torsion, the transitions revealed and discussed in the present work may provide the conditions for coupling between this dynamic binding and the action of tracking enzymes. Such coupling has the notable property of being both long-range and much faster than any molecular transport process. It is thus a particularly interesting candidate for quickly responding regulatory mechanisms. METHODS Nucleosome arrays preparation. Nucleosome arrays were reconstituted by conventional stepwise dilution. The nucleosome density was checked by sedimentation in sucrose gradients40 and the nucleosome array’s reguarity probed by micrococcal nuclease digestion (data not shown). Three DNA fragments were prepared by PCR: two were amplified from the linearized template Litmus28i (NEB, positions 2008 and 2580) with modified biotin or digoxigenin nucleotides (Roche); the third was obtained by amplifying the pFOS-1 template (NEB, positions 3803 and 4539) with standard nucleotides. Appropriate restriction digestions of the PCR products led to 554- and 620-bp fragments. These fragments were ligated into two different 1,174-bp ‘hybrids,’ consisting of one part (620 bp) unmodified DNA and another part (574 bp) DNA modified with biotin or digoxigenin. The two hybrid fragments were then ligated to the nucleosome arrays to give the final construction (Fig. 1). The fibers were finally dialyzed against TE buffer (10 mM Tris-HCl (pH 7.5) and 1 mM EDTA) and stored at –20 1C after a twofold dilution with 100% (v/v) glycerol. Magnetic tweezers apparatus. A poly-di-methylsiloxane (PDMS; DowCorning) flow cell with a 2-mm-wide and 80-mm-high channel was constructed. This microfluidic cell was mounted on a glass coverslip treated with 3-mercaptopropyl-trimethoxysilane (Sigma)41. The surface-coating was performed inside the channel with nonspecific binding of anti-digoxigenin (Roche) for 1 h at 37 1C, followed by overnight BSA blocking. The PDMS flow cell was placed beneath two NdFeB permanent magnets (HPMG) separated by 0.8 mm41. Images were grabbed by a CCD camera (JAI). From the transverse fluctuations magnitude and the molecule length, the exact force acting on the bead was deduced8. Moving the magnets up and down by B5 mm permits a range of forces from 0.1 pN to 15 pN. The topological constraint was controlled by rotation of the magnets about the vertical axis. Nucleosome array injection and study. Just before the experiment, 1 ng of chromatin, previously diluted to 10 ml with TE, was mixed with 100 mg of 2.8-mm-diameter streptavidin-coated magnetic beads (Dynal). After 1 min of

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ARTICLES incubation, the solution was aspirated into the cell by a syringe pump. Data were usually acquired in TE plus 0.01% (w/v) BSA (buffer B0). The standard buffer was B0 because, at this low ionic strength, nucleosomes are very stable and do not move along DNA42, and nucleosome-nucleosome interactions are weak43. Chemical nucleosome disruption. At the end of each experiment, nucleosomes were chemically disassembled by aspirating into the flow cell a solution containing 0.01% (w/v) heparin (Dakota Pharm) in B0 for 10 min.

© 2006 Nature Publishing Group http://www.nature.com/nsmb

Note: Supplementary information is available on the Nature Structural & Molecular Biology website. ACKNOWLEDGMENTS The authors are grateful to G. Almouzni and J.P. Quivy for providing material in preliminary experiments, E. Ben-Haim and C. Bouchiat for discussions and K. Dorfman and A. Sivolob for critical reading. A.B., N.C.eS., G.W., C.L. and J.M. thank the French Ministry of Research for AC-MENRT fellowships. This work was supported by the Centre National de la Recherche Scientifique (A.P.’s and J.M.V.’s laboratories) and by grants from the Centre National de la Recherche Scientifique/Ministe`re de l’Education Nationale de la Recherche et de la Technologie DRAB programs and the Institut Curie Physics of the Cell cooperative program (J.L.V.’s laboratory). COMPETING INTERESTS STATEMENT The authors declare that they have no competing financial interests. Published online at http://www.nature.com/nsmb/ Reprints and permissions information is available online at http://npg.nature.com/ reprintsandpermissions/ 1. VanHolde, K.E. Chromatin (Springer-Verlag, New York, 1988). 2. Luger, K., Mader, A.W., Richmond, R.K., Sargent, D.F. & Richmond, T.J. Crystal structure of the nucleosome core particle at 2.8 A resolution. Nature 389, 251–260 (1997). 3. Germond, J.E., Hirt, B., Oudet, P., Gross-Bellark, M. & Chambon, P. Folding of the DNA double helix in chromatin-like structures from simian virus 40. Proc. Natl. Acad. Sci. USA 72, 1843–1847 (1975). 4. Wolffe, A. Chromatin (Academic Press, London, 1998). 5. Cui, Y. & Bustamante, C. Pulling a single chromatin fiber reveals the forces that maintain its higher-order structure. Proc. Natl. Acad. Sci. USA 97, 127–132 (2000). 6. Brower-Toland, B.D. et al. Mechanical disruption of individual nucleosomes reveals a reversible multistage release of DNA. Proc. Natl. Acad. Sci. USA 99, 1960–1965 (2002). 7. Hayes, J.J. & Hansen, J.C. New insights into unwrapping DNA from the nucleosome from a single-molecule optical tweezers method. Proc. Natl. Acad. Sci. USA 99, 1752– 1754 (2002). 8. Strick, T.R., Allemand, J.F., Bensimon, D., Bensimon, A. & Croquette, V. The elasticity of a single supercoiled DNA molecule. Science 271, 1835–1837 (1996). 9. Simpson, R.T., Thoma, F. & Brubaker, J.M. Chromatin reconstituted from tandemly repeated cloned DNA fragments and core histones: a model system for study of higher order structure. Cell 42, 799–808 (1985). 10. Prunell, A. & Sivolob, A. Paradox lost: nucleosome structure and dynamics by the DNA minicircle approach. in Chromatin Structure and Dynamics: State-of-the-Art Vol. 39 (eds. Zlatanova, J. & Leuba, S.H.) 45–73 (Elsevier, London, 2004). 11. Catez, F. et al. Network of dynamic interactions between histone H1 and high-mobilitygroup proteins in chromatin. Mol. Cell. Biol. 24, 4321–4328 (2004). 12. Phair, R.D. et al. Global nature of dynamic protein-chromatin interactions in vivo: three-dimensional genome scanning and dynamic interaction networks of chromatin proteins. Mol. Cell. Biol. 24, 6393–6402 (2004). 13. McBryant, S.J. et al. Preferential binding of the histone (H3–H4)2 tetramer by NAP1 is mediated by the amino-terminal histone tails. J. Biol. Chem. 278, 44574–44583 (2003). 14. Leuba, S.H. et al. Three-dimensional structure of extended chromatin fibers as revealed by tapping-mode scanning force microscopy. Proc. Natl. Acad. Sci. USA 91, 11621–11625 (1994).

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15. Bouchiat, C. & Mezard, M. Elasticity model of a supercoiled DNA molecule. Phys. Rev. Lett. 80, 1556–1559 (1998). 16. Ben-Haim, E., Lesne, A. & Victor, J.M. Chromatin: a tunable spring at work inside chromosomes. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64, 051921 (2001). 17. Schiessel, H., Gelbart, W.M. & Bruinsma, R. DNA folding: structural and mechanical properties of the two-angle model for chromatin. Biophys. J. 80, 1940–1956 (2001). 18. Woodcock, C.L., Grigoriev, S.A., Horowitz, R.A. & Whitaker, N. A chromatin folding model that incorporates linker variability generates fibers resembling native structures. Proc. Natl. Acad. Sci. USA 90, 9021–9025 (1993). 19. Barbi, M., Mozziconacci, J. & Victor, J.M. How the chromatin fiber deals with topological constraints? Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 031910 (2005). 20. Schalch, T., Duda, S., Sargent, D.F. & Richmond, T.J. X-ray structure of a tetranucleosome and its implications for the chromatin fiber. Nature 436, 138–141 (2005). 21. De Lucia, F., Alilat, M., Sivolob, A. & Prunell, A. Nucleosome dynamics. III. Histone tail-dependent fluctuation of nucleosomes between open and closed DNA conformations. Implications for chromatin dynamics and the linking number paradox. A relaxation study of mononucleosomes on DNA minicircles. J. Mol. Biol. 285, 1101–1119 (1999). 22. Bednar, J. et al. Nucleosomes, linker DNA, and linker histone form a unique structural motif that directs the higher order folding and compaction of chromatin. Proc. Natl. Acad. Sci. USA 95, 14173–14178 (1998). 23. Goulet, I., Zivanovic, Y., Prunell, A. & Revet, B. Chromatin reconstitution on small DNA rings. I. J. Mol. Biol. 200, 253–266 (1988). 24. Luger, K. & Richmond, T.J. DNA binding within the nucleosome core. Curr. Opin. Struct. Biol. 8, 33–40 (1998). 25. Sivolob, A., De Lucia, F., Revet, B. & Prunell, A. Nucleosome dynamics. II. High flexibility of nucleosome entering and exiting DNAs to positive crossing. An ethidium bromide fluorescence study of mononucleosomes on DNA minicircles. J. Mol. Biol. 285, 1081–1099 (1999). 26. Sivolob, A., Lavelle, C. & Prunell, A. Sequence-dependent nucleosome structural and dynamic polymorphism. Potential involvement of histone H2B N-terminal tail proximal domain. J. Mol. Biol. 326, 49–63 (2003). 27. Sivolob, A. & Prunell, A. Linker histone-dependent organization and dynamics of nucleome entry/exit DNAs. J. Mol. Biol. 331, 1025–1040 (2003). 28. Harada, Y. et al. Direct observation of DNA rotation during transcription by Escherichia coli RNA polymerase. Nature 409, 113–115 (2001). 29. Sarkar, A. & Marko, J.F. Removal of DNA-bound proteins by DNA twisting. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64, 061909 (2001). 30. Shaw, S.Y. & Wang, J.C. Knotting of a DNA chain during ring closure. Science 260, 533–536 (1993). 31. Angelov, D., Vitolo, J.M., Mutskov, V., Dimitrov, S. & Hayes, J.J. Preferential interreaction of the core histone tail domains with linker DNA. Proc. Natl. Acad. Sci. USA 98, 6599–6604 (2001). 32. Klug, A. & Lutter, L.C. The helical periodicity of DNA on the nucleosome. Nucleic Acids Res. 9, 4267–4283 (1981). 33. Prunell, A. A topological approach to nucleosome structure and dynamics: the linking number paradox and other issues. Biophys. J. 74, 2531–2544 (1998). 34. Norton, V.G., Imai, B.S., Yau, P. & Bradbury, E.M. Histone acetylation reduces nucleosome core particle linking number change. Cell 57, 449–457 (1989). 35. Garner, M.M., Felsenfeld, G., O’Dea, M.H. & Gellert, M. Effects of DNA supercoiling on the topological properties of nucleosomes. Proc. Natl. Acad. Sci. USA 84, 2620–2623 (1987). 36. Clark, D.J., Ghirlando, R., Felsenfeld, G. & Eisenberg, H. Effect of positive supercoiling on DNA compaction by nucleosome cores. J. Mol. Biol. 234, 297–301 (1993). 37. Misteli, T., Gunjan, A., Hock, R., Bustin, M. & Brown, D.T. Dynamic binding of histone H1 to chromatin in live cells. Nature 408, 877–881 (2000). 38. Liu, L.F. & Wang, J.C. Supercoiling of the DNA template during transcription. Proc. Natl. Acad. Sci. USA 84, 7024–7027 (1987). 39. Bustin, M., Catez, F. & Lim, J.H. The dynamics of histone H1 function in chromatin. Mol. Cell 17, 617–620 (2005). 40. Hansen, J.C. & Lohr, D. Assembly and structural properties of subsaturated chromatin arrays. J. Biol. Chem. 268, 5840–5848 (1993). 41. Fulconis, R. et al. Twisting and untwisting a single DNA molecule covered by RecA protein. Biophys. J. 87, 2552–2563 (2004). 42. Meersseman, G., Pennings, S. & Bradbury, E.M. Mobile nucleosomes–a general behavior. EMBO J. 11, 2951–2959 (1992). 43. Mangenot, S., Leforestier, A., Durand, D. & Livolant, F. X-ray diffraction characterization of the dense phases formed by nucleosome core particles. Biophys. J. 84, 2570–2584 (2003).

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Bancaud et al. : Structural plasticity of single chromatin fibers

nucleosome/nucleosome attractive, tail-mediated, interactions2. These interactions

revealed by torsional manipulation

compete with the small gain in energy to position a nucleosome specifically on the 5S sequence (~1 kT)3. For reasons of steric hindrance, close-packed nucleosomes are very probably unable to rotate around their dyad relative to each other, and to

SUPPLEMENTARY MATERIAL

access the closed states. Thus, those close-packed nucleosomes should not accommodate rotational constraints as efficiently as regularly positioned ones,

1- Fiber-to-fiber variability in the torsional response: clusters of close-

further support that conclusion, we tried to adjust their extension-vs.-rotation

packed nucleosomes As shown in Fig. 2c (main text), and again in Supplementary Fig. 1a, the maximal length of regular chromatin fibers at their center of rotation essentially varies linearly with their topological shift relative to the naked DNA, i.e. with the number of NSs, with the exception of some fibers which deviate from that behavior. These irregular fibers show a relatively smaller rotational shift, suggesting they contain a higher proportion of nucleosomes in the open (or closed positive) state. Interestingly, these irregular nucleosome arrays also appear to be more rigid in torsion than regular fibers: the width of their torsional responses was narrower at a similar compaction level (compare curves Supplementary Figs. 1b (blue) and 1c

response using our molecular model (see main text, “modeling” section and below), assuming that the fibers contained nucleosomes either close-packed or regularly positioned every 208 bp. For the data in Supplementary Fig. 1c, for instance, a satisfactory fit was obtained with 10 regularly spaced nucleosomes, and 21 in contact. Next, we purposely favored the formation of close-packed nucleosomes through the shortening of some critical dialysis steps in the protocol, so that the reconstitution lasted ~8 hours instead of the usual 24 hours4. Under these conditions, histone-DNA and histone-histone attractions occur more abruptly, and most histone octamers cannot slide along the DNA and “find” their energetically most

(green)). We considered these data in the light of scanning force microscopy (SFM) studies that systematically investigated nucleosome spacing in 5S tandemly repeated arrays1. A significant heterogeneity was observed, with a bimodal distribution involving

explaining how they could confer a larger torsional rigidity to their fibers. In order to

regularly

spaced

and

close-packed

regions

(the

latter

with

an

favored position before being frozen into place. The corresponding population of fibers mostly consisted in close-packed nucleosomes, as confirmed by the microccocal nuclease assay, and showed a narrow width when tested for their extension-vs.-torsion response (not shown).

internucleosome distance smaller than 20 bp). The close-packed configuration seems to correspond to a local minimum in free energy, attributed to the existence of

1

2- Modeling 2

“One state” The fiber was first modeled as a regular sequence of nucleosomes locked

explicitly evaluated using the analytical expression proposed in12, where the bending

in their negative conformation (Supplementarty Fig. 2a), as inferred from the core

(resp. twist) persistence length of naked DNA was set to 60 nm (resp. 80 nm) (see

particle5 and tetranucleosome crystal6 structures. Nucleosomes were connected by

Fig. 2d in main text), and that of chromatin computed as in10. In the topological

straight linkers, according to the two-angle model7. The first angle, D, is between the

equation of Supplementary Equation 1, the first term corresponds to the linking

nucleosome entry-exit linkers, and the second, E, between successive nucleosomes.

number change of n nucleosomes, relative to the corresponding free DNA; the third

D was set to 54°, the angle between entry-exit DNAs in the crystal structure5,

term is for the effect of the external constraints on the DNA linking number,

whereas E = 115° depends on the DNA periodicity, both in the linkers (10.5 bp/turn)

according to the corresponding expression derived in12, and the second one for the

and on the histone surface (~145 bp with a local periodicity of 10.15 bp/turn, to

contribution of external constraints on the fiber itself, whose persistence length is

account for the ¨Tw = 0.3-turn overtwisting observed in the minicircle system with

calculated according to10. Note that Supplementary Equations 1 are valid to

5S mononucleosomes8). The fiber architecture could then be modeled using a

describe the mechanical response of the fiber close to the apex only, because they

computer algebra system (Maple 9 software) (Supplementary Fig. 2b). The

rely on the perturbative approach followed in12.

incremental length per nucleosome along the nucleosome array axis ('l), as well as the

linking

number

change

per

9

nucleosome

('Lkt)

were

computed

When trying to fit our data, however, severe inconsistencies were encountered. As a typical example, let us reinvestigate the response of the fiber analyzed in Fig. 5b. The vertical position of the apex is compatible with the presence of 31+/-1

(Supplementary Fig. 2c). The chromatin mechanics is fully characterized by the intrinsic elasticity of the linkers10,11, and of the two flanking naked DNA spacers (see Fig. 1, main text). We assumed that the fibers’ extension (ztot) and topology relative to DNA ('Lktot) resulted from the additive contributions of naked DNA and chromatin. Notably, this approximation is supported by the linear relationship observed between the compaction and the topological shift (Fig. 2c, and Supplementary Fig. 1a). For a given torque C and force f, this leads to Supplementary Equation 1. In the extensional equation of Supplementary Equation 1, zDNA is the extension of the fraction of naked DNA, and zchromatin the extension of a nucleosome array containing n nucleosomes. The dependence of these extensions on f and C was

3

nucleosomes in the fiber. Using our topological predictions, this would imply a rotational shift of the apex (relative to naked DNA) of -1.4x30=-42 turns, far from the experimental results (-24 turns, Supplementary Fig. 2d, red curve). This discrepancy could be compensated by allowing the nucleosomal DNA to overtwist to a local periodicity of ~9.7 bp/turn, as initially proposed to solve the linking number paradox13-15. The resulting curve (black in Supplementary Fig. 2d) is then correctly centered but its breadth is much too small, reflecting a large rigidity: applying the worm-like rope model16 on the predicted rotational response, a torsional persistence length of 35 nm is deduced (data not shown). This is smaller than the value for naked DNA (80 nm), but still much larger than the experimental value for the real

4

contribution of the naked DNA portions and of the “open” (resp. “negative” and

fibers (5 nm; see main text).

“positive”) nucleosome array containing no(C) (resp. nn(C) and np(C)) nucleosomes. “Three states” In contrast with the previous one-state model, we now allow the

This amounts, in particular, to neglect nucleosome/nucleosome interactions, and

nucleosomes to fluctuate between three topologically discrete conformations referred

distortions associated with the boundaries between series of nucleosomes in different

to as “negative”, “open” and “positive”8 (see main text). The negative state has been

states. Within this approximation, Supplementary Equations 1 could be used,

described above. In the open conformation, we imposed D=-30° and a nucleosomal

introducing three terms to describe the chromatin contribution instead of one in the

DNA length of 125 bp as a consequence of the breaking of the most distal histone-

“single state” approach.

DNA binding sites at SHL±6.5, as observed in17,18. In the positive state, a minimal

Supplementary Equation 1, the torque can be expressed as a function of the

kink was introduced in the nucleosome entry-exit region to make the positive

topological deformation applied to the fiber ('Lktot), and Supplementary Equation

crossing possible. D was then taken equal to +30° and the nucleosomal DNA length

3 becomes a function of supercoiling with three adjustable parameters, namely n, Un

to 145 bp. Subsequently, E'Lkt and 'l could be evaluated, and the corresponding

and Up.

fibers constructed (Supplementary Fig. 3a-b).

Finally, by reversing the topological equation in

Notably, whereas the theoretical linking number change 'Lkt for the two closed

Assuming these states are in thermodynamic equilibrium, the Gibbs free energy

states was similar to those obtained with the minicircle approach (¨Lkm)8, 'Lkt for a

can be calculated (Supplementary Equation 2). In this equation, C is the torque,

“pure” chain of nucleosomes in the open state was significantly different (-0.5

Tthe angular rotation with respect to the relaxed situation for the fiber, and nn (resp.

against -0.7; see Supplementary Fig. 3b). We attribute this discrepancy to the 3-D

no, np and n) the number of nucleosomes in the negative state (resp. open, positive

architecture of the fibers: the geometrical organization of the nucleosomes (a

and total number). Finally, Un (resp. Up) are the energy differences between the

collective effect) can affect the global topology of the fiber, with respect to a mere

negative (resp. positive) conformation and the open one. Because the Gibbs free

addition of nucleosomes individual deformations. However, due to nucleosome

energy is minimal at thermodynamic equilibrium, we could derive the proportion of

thermal fluctuations, this additional collective contribution is expected to vanish in

nucleosomes in each state as a function of the torque C. For instance, the expression

real fibers. For that reason, we used for the fitting the minicircle 'Lkm values as fixed

for the number of nucleosomes in the negative conformation is computed in

parameters. Interestingly, this discussion is reminiscent of the work of Woodcock &

Supplementary Equation 3.

al7, who showed that a fiber constructed with identical and regularly repeated

To describe the fiber mechanics, we followed the same approach as above, and

nucleosomes may adopt, depending on the linker length, widely different 3-D

hypothesized that the global response in torsion resulted from the additive

shapes, and that allowing for fluctuations in linker length within the same fiber leads

5

6

to fibers closer to physiological ones, as appear in electron microscopy of isolated chromatin

and

nuclei.

In

our

case, fluctuations

concern

the

Using the model to fit other regular fibers (see Supplementary Fig. 1a; and

nucleosome

Fig. 6, main text), similar values of the energy differences between the states were

conformational state rather than the linker length, but they should similarly disrupt

obtained, in spite of rather different numbers of nucleosomes. As a consequence, a

the long-range correlations along the fiber.

satisfactory fit of the behavior of all regular fibers could be achieved with the above

Our topological and mechanical predictions were then again applied, as an

single set of energy values, leaving the number of nucleosomes as the single

example, to the data represented in Fig. 5b, main text. We deduced that the fiber

adjustable parameter. The experimental horizontal and vertical dependencies of the

contained n=31 nucleosomes, short of the theoretical maximum of 36. The fit (see

rotation curves on the number of nucleosomes (Fig. 6 in main text) are thus well

Fig. 5b, main text) allowed us to access the energies Un and Up (resp. 0.7 kT and 2

accounted for by the model, which was used to draw the straight line in Fig. 2c,

kT, see main text). The relaxed state for the fiber at zero torque was obtained at -27

main text, and Supplementary Fig. 1a.

turns (relative to the naked DNA), with a number of nucleosomes in the different states no=21, np=2 and nn=8. This makes ~68 % open, 26 % negative and 6% positive nucleosomes (Supplementary Fig. 4a), and gives a mean 'Lk of 0.68x(0.7)+0.26x(-1.4)+0.06x(-0.4)=-0.86 per nucleosome. This value agrees well with the -0.8r0.1 figure obtained in this work after partial nucleosome disruption (Figs. 2a and b in main text), and with the -0.8 value obtained with plasmids made of the same tandemly repeated 5S-208 sequences reconstituted with hyperacetylated histones19 (the N-terminal tails of histones H3 interact less with nucleosome entryexit DNAs, which increases their mutual electrostatic repulsion, and mimics our low ionic strength B0 conditions). Notably, the average proportion of nucleosome in each state can be computed for any topological deformation using our model (Supplementary Fig. 4b (Upper panel)). Finally, it is noteworthy that the torque-

vs.-rotation response predicted by this model compares well with that deduced from the worm-like rope approach, despite the widely different concepts used (Supplementary Fig. 4b (Lower panel)).

7

3- Plectoneme formation at larger torsional constraints Close to the apex, torsion can be easily accommodated by nucleosome structural transitions. However, the energetic penalty associated with forcing all nucleosomes in a single state increases nonlinearly, and makes the torque necessary to twist the fiber further larger and larger (the onset of this torsional rigidification is apparent in Fig. 5c in main text and Supplementary Fig. 4b (Lower panel)). The fiber in Fig. 5b (main text) reaches the essentially all-negative (positive) state (i.e. fiber 2) at ~-40 (respectively -10 turns) turns, and, beyond these topological constraints, it can still accommodate ~15 turns with a nearly linear length decay of ~25 nm/turn. As noted in main text, this slope is weaker than that of naked DNA (~90 nm/turn (Fig. 2a, main text)). Thus, another mechanism must be considered to account for the behavior at high rotational deformations. The linear regime is reminiscent of a system evolving along a first order transition line (i.e. at constant torque), and more specifically of 8

the formation of plectonemes on naked DNA20. This process, i.e. the conversion of

place in the nucleosome array. This process would be favored by the “kinking” effect

twist into writhe through the formation of “telephone chord” structures, corresponds

of nucleosomes which brings entry/exit DNAs close together, and also by the partial

to a well-defined mechanical problem, thoroughly studied by physicists both

screening of DNA/DNA electrostatic repulsions by histone tails, which should reduce

16,20,21

. Thus, rather general and model-independent

the effective diameter of the DNA and hence of the plectoneme. Interestingly, this

arguments enable us to deduce the torque exerted in this regime from the value of

implies that the bulky nucleosomes do not play a significant adverse role of steric

the length-vs.-rotation decay16. For naked DNA in B0, this torque is typically ~6

hindrance, i.e. that they organize on the outer face of the plectonemes

pNxnm/rad at 0.3 pN (data not shown).

(Supplementary Fig. 5). This plectoneme formation may also be favored by the

experimentally and theoretically

For chromatin fibers, plectonemes are also expected to form. This process is,

presence of naked DNA gaps with missing NSs, in our imperfect fibers.

however, significantly more complex than for naked DNA, and we cannot capture the Clearly, a more detailed study of the plectoneme formation process would

behavior in a quantitative physical model. A few qualitative features are consistent 16

with this interpretation, however. According to the worm-like rope model , for

better be achieved with perfectly regular and gap-free nucleosome arrays, which

instance, the lower slope should be associated with a smaller bending persistence

may soon be constructed on nucleosome “super-positioning” sequences3.

length for the fiber, as compared to naked DNA. We already reached that conclusion when studying the fiber’s behavior at the apex (28 nm for chromatin vs. 60 nm for DNA, Fig. 3a in main text). Using the generalization of the worm-like rope approach16,21 to fit the chromatin length-vs.-rotation decay, we could deduce the

Supplementary References: 1.

Mapping nucleosome locations on the 208-12 by AFM profides clear evidence

torque applied to the fiber in the plectoneme regime (~3-4 pNxnm/rad, Supplementary Fig. 4b (Lower panel)). This indeed corresponds well to the value

Yodh, J.G., Woodbury, N., Shlyakhtenko, L.S., Lyubchenko, Y.L. & Lohr, D.

for cooperativity in array occupation. Biochemistry 41, 3535-3574 (2002). 2.

of the torque predicted by the three states model, at the points associated with the

Solis, F.J., Bash, R., Yodh, J., Lindsay, S.M. & Lohr, D. A statistical thermodynamic model applied to experimental AFM population and location

plectoneme transition (-40 and -10 turns, respectively: see Supplementary Fig.

data is able to quantify DNA-histone binding strength and internucleosomal

5b, lower panel).

interaction differences between acetylated and unacetylated nucleosomal

Because this torque is significantly smaller than that required to form plectonemes on naked DNA (6 pN.nm/rad), it is improbable that they form in the flanking DNA spacers (see Fig. 1, main text). We propose that they instead take

9

arrays. Biophys. J. 87, 3372-3387 (2004). 3.

Thastrom, A., Lowary, P. & Widom, J. Measurement of histone-DNA interaction free energy in nucleosomes. Methods 33, 33-44 (2004). 10

4.

Hansen, J.C., van Holde, K.E. & Lohr, D. The mechanism of nucleosome

12.

assembly onto oligomers of the sea urchin 5 S DNA positioning sequence. J

Biol Chem 266, 4276-4282. (1991). 5.

twist stiffness. Proc. Natl. Acad. Sci. USA 94, 14418-14422 (1997). 13.

14.

389, 251-260 (1997). 6.

Schalch, T., Duda, S., Sargent, D.F. & Richmond, T.J. X-ray structure of a

141 (2005).

15.

17.

the DNA minicircle approach. in Chromatin Structure and Dynamics: State-of-

Sivolob, A., Lavelle, C. & Prunell, A. Sequence-dependent nucleosome

the-Art, Vol. 39 (eds. Zlatanova, J. & Leuba, S.H.) 45-73 (Elsevier, London,

structural and dynamic polymorphism. Potential involvement of histone H2B

2004). 18.

Bednar, J. et al. Nucleosomes, linker DNA, and linker histone form a unique

Barbi, M., Mozziconacci, J. & Victor, J.M. How the chromatin fiber deals with

structural motif that directs the higher order folding and compaction of

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1940-1956 (2001).

11

12

Maximum length (µm)

a

a

1.2 1.0 0.8

b

0.6 0.4

- 30 - 28 - 26 - 24 - 22 - 20 - 18 - 16 Topological shift (turns) 1.0

Fiber length (µm)

b

c

0.8

0.6

0.4

30

d

115°

∆l (nm)

4.1

∆Lkt (turn)

-1.4 -1.4

0.7

Fibre length (µm)

- 30 - 20 - 10 0 10 20 Rotation (turns) 0.8

Fiber length(µm)

54°

β

∆Lkm (turn) 0.2

c

α

0.6 0.4

0.6

0.5

0.4

0.3

0.2 0.2

- 60

0.0

- 40 - 30 - 20 - 10 0 Rotation (turns)

10

Supplementary figure 1. Regular and irregular fibers.Theoryvs.-experimental data. (a) Same plot as in Fig. 2c (see legend in main text). Aligned data points correspond to regular fibers, whereas data points off the straight line correspond to irregular fibers.The three arrowheads refer to fibers at similar level of compactions whose torsional responses (same colors) are shown in b and c. (b) The rotational width of regular fibers (black) appears systematically larger than that of irregular fibers (blue) (for clarity, their centers of rotation are superimposed in b). (c) Extension-vs.rotation curve (blue) corresponding to the green arrowhead in a, and predictions assuming that this fiber contains 31 nucleosomes, 10 regularly spaced, and 21 close-packed (i.e. sterically blocked in the open state, separated by a DNA linker of 10 bp, and inducing a topological deformation (∆Lko) of -0.5 turn) (black).

- 40

- 20

0

Rotation (turns) Supplementary figure 2. The "single-state" fiber.Theory-vs.experimental data. (a) Outline of a nucleosome in its crystallographic configuration ( ~ 54°, blue core). (b) Modeling of a chromatin fiber with its nucleosomes locked in their crystallographic configuration.The repeat length is 208 bp. (c) Corresponding structural parameters: is the angle between the nucleosome entry-exit linkers is the phasing angle between successive nucleosomes l is the incremental length per nucleosome along the fiber axis, Lkt is the theoretical prediction for the linking number change per nucleosome (i.e. considering the nucleosome array geometry), and Lkm the measurements obtained from the minicircle approach8. (d) Length-vs.-rotation plots of the chromatin fiber in Fig. 5B (main text, blue squares), and predicted behavior of a single-state fiber containing 30 rigid nucleosomes locked in their crystallographic conformation (red curve).The same rigid fiber with a nucleosomal DNA overtwisted to 9.7 bp/turn is presented in black (see text). None of these curve fits the data, due to a narrow rotational breadth associated with this fiber (35 nm persistence length).

a

b

b NS state

Open

Positive

α

- 30°

30°

β

90°

115°

∆l (nm)

8.3

2.8

∆Lkt (turn)

- 0.5 - 0.7

- 0.4 - 0.4

∆Lkm (turn)

Supplementary figure 3. "Open-state" and "positive-state" ideal fibers. (a) Chromatin fibers with "open" nucleosomes (yellow cores) and "positive" nucleosomes (light blue cores), as computed from the model. (b) Corresponding fibers structural parameters (see legend of Supplementary Fig. 2c for details).

Torque (pN.nm/rad) Number of nucleosomes

a 30 25 20 15 10 5 0 6 4 2 0

-2 -4 -6

- 60

- 40 - 20 0 Rotation (turns)

20

Supplementary figure 4. The "three-state" fiber. (a) Modeling of the torsionally-relaxed (zero torque) fiber containing 60% "open" nucleosome (yellow) and 40% "negative" ones (dark blue). Note that the maximal-length fiber (state 1 in Fig. 5b; main text) is torsionally stressed by ~+5 turns relative to the relaxed fiber (Fig. 5c, main text), explaining the differences with the molecular models presented in Fig. 5b main text (state 1). (b) Top: Predictions for the number of nucleosomes in the negative (blue), open (black) and positive (green) states as a function of rotation.The fiber contains 31 nucleosomes, and the energy Un and Up are set to 0.7 kT and 2 kT, respectively.The red vertical line corresponds to the relaxed state.The two grey vertical lines give the positions of the onsets of plectonemes formation (see Supplementary section 3). Bottom: Torque-vs.-rotation as predicted by the worm-like rope model (light blue) and by the three-state model (black, same as Fig. 5c, main text).The two regions corresponding to the transitions between the regimes of nucleosome structural transition and plectoneme formation are circled.

a

b

Supplementary figure 5. Plectoneme structures. Modeling of the fiber architecture before (a) and after (b) plectoneme formation under negative torsional stress. Each of the two long DNA linkers corresponds to one missing nucleosome. Their length, 208+62=270 bp, or ~90 nm, is comparable to the DNA persistence length in low salt conditions (60 nm, see main text), hence their straight appearance.

Supplementary Equation 1 Length and topology.The length and the topology of the fiber (ztot and ∆Lktot, respectively) linearly depend on the contribution of the DNA spacers (Fig. 1, index DNA) and of the nucleosome array (index chromatin), which contains n nucleosomes (with a topological deformation at rest of ∆LkR). The dependance of the DNA or chromatin extension-topology on the external force f and torque C are described in Supplementary section 2.

Supplementary Equation 2 Gibbs free energy of a fiber containing nucleosomes fluctuating between 3 states (open, negative and positive). n, nn, no and np correspond to the total number of nucleosomes, and the number in the negative, open and positive states, respectively.The ground state in energy is the open one; Un and Up correspond to the difference in energy of the negative or positve states relative to the open one, respectively. C is the torque and θ the angular deformation relative to the relaxed state.

Supplementary Equation 3 Proportion of nucleosomes in the negative state as a function of the external torque C.The topology of the three nucleosome states (∆Lkn, ∆Lko, ∆Lkp) are described in Supplementary Figs. 2-3.The other parameters are defined in Supplementary Equation 2.