<figure><img src="image_75.png" /></figure>

<figure><img src="image_76.png" /><figcaption>**Figure 1** Schematic of the experiment. A single nucleosome array (~7.5 kbp), sandwiched between two naked DNA spacers (~600 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.</figcaption></figure>

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 single-duplex DNA⁸. Compared to naked DNA, chromatin is shorter by ~1.35 µm, and its center of rotation is shifted by -24 ± 2 turns. This corresponds to a shortening of ~-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 vitro*¹³ 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

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 ~700 nm and -13 ± 1.5 turns, or ~54 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 = -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.

## Stretching

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

**Figure 2** Micromanipulation of single chromatin fibers. (a) Extension-versus-rotation 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.

<figure><img src="image_77.png" /></figure>
<figure><img src="image_78.png" /></figure>

<figure><img src="image_79.png" /></figure>

**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 **Figure 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.

(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 ~15% in the first condition and ~30% 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 ~2–3 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).

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 ~−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 (~5 nm, compared to ~80 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

**Figure 4** Salt-dependence of the fiber's mechanical behavior. (a) Extension-versus-rotation behavior of a fiber in B₀ (black) and in B₀ plus 25 mM NaCl (blue crosses; blue line shows filtered average) at 0.35 pN. (b) Extension-versus-rotation behavior of a fiber in B₀ (black) and in B₀ plus 40 mM NaCl and 2 mM MgCl₂ (blue crosses; blue line shows 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 ~5 pN is reached, the process is reversed, and the force is progressively lowered to its initial value (~0.05 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.

<figure><img src="image_80.png" /></figure>
<figure><img src="image_81.png" /></figure>

**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 $\Delta L_{k_o}$ ~ -0.7 (open, no crossing), $\Delta L_{k_n}$ ~ -1.4 (closed negative, negative crossing) and $\Delta L_{k_p}$ ~ -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 loop<sup>10,21</sup>. Notably, cryo-EM visualization of reconstituted fibers in low-salt conditions has also suggested the occurrence of such states<sup>22</sup>. In contrast, they do not appear in the tetranucleosome crystal structure<sup>20</sup>, presumably because the high-salt conditions used for crystallization and the crystal packing energies favor closed conformations<sup>10</sup>.

The existence of the open state was first documented in mini-circles<sup>23</sup>, but it was only after the core particle crystal structure was disclosed<sup>2</sup> 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 ~10 bp and are defined by their super-helix location (SHL) relative to the dyad<sup>2</sup>. The SHL ± 6.5 sites are located at the nucleosome entry/exit and have the weakest binding energy<sup>24</sup>. 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 titration<sup>25</sup> and relaxation<sup>21,26,27</sup>. 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 DNA<sup>2</sup>, equally affects the energies of the closed negative and closed positive states (N.C.eS. & A.P., unpublished data).

**Figure 5** Three-state model of the chromatin fiber. (a) Diagrams of individual nucleosomes in the negative ($\alpha$ ~ 54°; blue), open ($\alpha$ ~ -30°; yellow) and positive ($\alpha$ ~ 30°; 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.

## 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 length-versus-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 ($U_n$ = +0.4 kcal mol<sup>-1</sup>, that is +0.7 $k_B T$ per molecule, where $k_B T$ is the thermal energy), and between the positive and open states ($U_p$ = +1.2 kcal mol<sup>-1</sup>, that is +2 $k_B T$) 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

<figure><img src="image_82.png" /></figure>

**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 $B_o$ 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 ($U_n$ = +0.4 kcal mol<sup>-1</sup>) and the positive versus open state ($U_p$ = +1.2 kcal mol<sup>-1</sup>) and adjusts the number of nucleosomes only; upper left key gives best-fit number of nucleosomes.

<figure><img src="image_83.png" /></figure>
<figure><img src="image_84.png" /></figure>

**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).

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 ~30 turns around the center of rotation, that is, substantially smaller than that exerted by polymerases (>5 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 ($U_n$ = +0.4 kcal mol⁻¹ and $U_p$ = +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 ($U_n$ = +0.5 kcal mol⁻¹ and $U_p$ = +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 ~-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 ~-20 turns, associated with a constant slope of ~-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

'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 ~25 nm per turn occurs at ~+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 ~3 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 nanMANipulation 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 ΔLk 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

<figure><img src="image_85.png" /></figure>
<figure><img src="image_86.png" /></figure>

in the open state. The same occurred in our experiment (Fig. 4b): $\Delta$Lk ~ -1 was obtained in higher salt, compared to $\Delta$Lk ~ -0.8 in $B_0$ (also favoring entry/exit DNA repulsion). Notably, a similar ~ +0.2 shift in $\Delta$Lk 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 ($\sigma$ ~ -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 ~10 positive turns on the right part of the fiber and ~10 negative turns on the left side. The Lk difference between a relaxed and an 'all-negative' or a 'most-positive' fiber is ~-0.5 or ~+0.4 per nucleosome, respectively (see Fig. 5b and Supplementary Fig. 4). For these two constrained states of the fiber, the torque is ~3 pN nm rad⁻¹. Hence, the total torque is ~6 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 ~50 nucleosomes (equivalent to a topological buffer of ~25 × 0.4 = 10 turns) can sustain

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 plctoneme 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 regularity 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 °C after a two-fold dilution with 100% (v/v) glycerol.

**Magnetic tweezers apparatus.** A poly-di-methylsiloxane (PDMS; Dow-Corning) flow cell with a 2-mm-wide and 80-µm-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 °C, 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 ~5 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 µl with TE, was mixed with 100 µg of 2.8-µm-diameter streptavidin-coated magnetic beads (Dynal). After 1 min of
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.

*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/Ministère de l'Éducation 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.

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**Bancaud et al. : Structural plasticity of single chromatin fibers**
**revealed by torsional manipulation**

**SUPPLEMENTARY MATERIAL**

**1- Fiber-to-fiber variability in the torsional response: clusters of close-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** (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 regularly spaced and close-packed regions (the latter with an 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 nucleosome/nucleosome attractive, tail-mediated, interactions². These interactions 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 access the closed states. Thus, those close-packed nucleosomes should not accommodate rotational constraints as efficiently as regularly positioned ones, explaining how they could confer a larger torsional rigidity to their fibers. In order to further support that conclusion, we tried to adjust their extension-vs.-rotation
<figure><img src="image_87.png" /></figure>

<figure><img src="image_88.png" /></figure>

<figure><img src="image_89.png" /><figcaption>**Supplementary figure 1.** Regular and irregular fibers. Theory-vs.-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).</figcaption></figure>
response using our molecular model (see main text, "modelling" 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
favored position before being frozen into place. The corresponding population of
fibers, which 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).

**2- Modeling**

"One state" The fiber was first modeled as a regular sequence of nucleosomes locked in their negative conformation (Supplementary Fig. 2a), as inferred from the core particle⁵ and tetranucleosome crystal⁶ structures. Nucleosomes were connected by straight linkers, according to the two-angle model⁷. The first angle, α, is between the nucleosome entry-exit linkers, and the second, β, between successive nucleosomes. α was set to 54°, the angle between entry-exit DNAs in the crystal structure⁵, whereas β = 115° depends on the DNA periodicity, both in the linkers (10.5 bp/turn) and on the histone surface (~145 bp with a local periodicity of 10.15 bp/turn, to account for the ΔTw = 0.3-turn overtwisting observed in the minicircle system with 5S mononucleosomes⁸). The fiber architecture could then be modeled using a computer algebra system (Maple 9 software) (Supplementary Fig. 2b). The incremental length per nucleosome along the nucleosome array axis (Δl), as well as the linking number change per nucleosome⁹ (ΔLkᵣ) were computed (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
<figure><img src="image_90.png" /></figure>

<figure><img src="image_91.png" /><figcaption>**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 I 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).</figcaption></figure>
assumed that the fibers' extension ($z_{tot}$) and topology relative to DNA ($\Delta L k_{tot}$) 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**, $z_{DNA}$ is the extension of the fraction of naked DNA, and $z_{chromatin}$ the extension of a nucleosome array containing $n$ nucleosomes. The dependence of these extensions on $f$ and $C$ was explicitly evaluated using the analytical expression proposed in<sup>12</sup>, where the bending (resp. twist) persistence length of naked DNA was set to 60 nm (resp. 80 nm) (see Fig. 2d in main text), and that of chromatin computed as in<sup>10</sup>. In the topological equation of **Supplementary Equation 1**, the first term corresponds to the linking number change of $n$ nucleosomes, relative to the corresponding free DNA; the third term is for the effect of the external constraints on the DNA linking number, according to the corresponding expression derived in<sup>12</sup>, and the second one for the contribution of external constraints on the fiber itself, whose persistence length is calculated according to<sup>10</sup>. Note that **Supplementary Equation 1** are valid to describe the mechanical response of the fiber close to the apex only, because they rely on the perturbative approach followed in<sup>12</sup>.

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 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 paradox<sup>13-15</sup>. 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 model<sup>16</sup> on the predicted rotational response, a torsional persistence length of 35 nm is deduced (data not shown). This is smaller than the value for
$$z_{tot}(C, f) = z_{DNA}(C, f) + z_{chromatin}(C, f)$$

$$\Delta L k_{tot}(C, f) = n \cdot \Delta L k^R + \Delta L k_{chromatin}(C, f) + \Delta L k_{DNA}(C, f)$$

**Supplementary Equation 1** Length and topology. The length and the topology of the fiber ($z_{tot}$ and $\Delta L k_{tot}$, 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 $\Delta L k_R$). The dependence of the DNA or chromatin extension-topology on the external force *f* and torque *C* are described in **Supplementary section 2**.

<figure><img src="image_92.png" /><figcaption>b</figcaption></figure>

<table><thead><tr><th>NS state</th><th>Open</th><th>Positive</th></tr></thead><tbody><tr><td>α</td><td>- 30°</td><td>30°</td></tr><tr><td>β</td><td>90°</td><td>115°</td></tr><tr><td>Δl (nm)</td><td>8.3</td><td>2.8</td></tr><tr><td>ΔLk<sub>t</sub> (turn)</td><td>- 0.5</td><td>- 0.4</td></tr><tr><td>ΔLk<sub>m</sub> (turn)</td><td>- 0.7</td><td>- 0.4</td></tr></tbody></table>

**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).
naked DNA (80 nm), but still much larger than the experimental value for the real fibers (5 nm; see main text).

**"Three states"** In contrast with the previous one-state model, we allow the nucleosomes to fluctuate between three topologically discrete conformations referred to as "negative", "open" and "positive"⁸ (see main text). The *negative* state has been described above. In the open conformation, we imposed $\alpha$=-30° and a nucleosomal DNA length of 125 bp as a consequence of the breaking of the most distal histone-DNA binding sites at SHL±6.5, as observed in¹⁷,¹⁸. In the positive state, a minimal kink was introduced in the nucleosome entry-exit region to make the positive crossing possible. $\alpha$ was then taken equal to +30° and the nucleosomal DNA length to 145 bp. Subsequently, $\beta$, $\Delta Lk_t$ and $\Delta l$ could be evaluated, and the corresponding fibers constructed (**Supplementary Fig. 3a-b**).

Assuming these states are in thermodynamic equilibrium, the Gibbs free energy can be calculated (**Supplementary Equation 2**). In this equation, *C* is the torque, $\theta$ the angular rotation with respect to the relaxed situation for the fiber, and $n_n$ (resp. $n_o$, $n_p$ and $n$) the number of nucleosomes in the negative state (resp. open, positive and total number). Finally, $U_n$ (resp. $U_p$) are the energy differences between the negative (resp. positive) conformation and the open one. Because the Gibbs free energy is minimal at thermodynamic equilibrium, we could derive the proportion of nucleosomes in each state as a function of the torque *C*. For instance, the expression for the number of nucleosomes in the negative conformation is computed in **Supplementary Equation 3**.

To describe the fiber mechanics, we followed the same approach as above, and hypothesized that the global response in torsion resulted from the additive contribution of the naked DNA portions and of the "open" (resp. "negative" and "positive") nucleosome array containing $n_o(C)$ (resp. $n_n(C)$ and $n_p(C)$) nucleosomes. This amounts, in particular, to neglect nucleosome/nucleosome interactions, and distortions associated with the boundaries between series of nucleosomes in different states. Within this approximation, **Supplementary Equation 1** could be used, introducing three terms to describe the chromatin contribution instead of one in the "single state" approach. Finally, by reversing the topological equation in
$$G = kT \{ n \ln(n) - n_n \ln(n_n) - n_p \ln(n_p) - n_o \ln(n_o) - n_n U_n - n_p U_p \} - C\theta$$

**Supplementary Equation 2** Gibbs free energy of a fiber containing nucleosomes fluctuating between 3 states (open, negative and positive). $n, n_n, n_o$ and $n_p$ 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; $U_n$ and $U_p$ correspond to the difference in energy of the negative or positive states relative to the open one, respectively. C is the torque and $\theta$ the angular deformation relative to the relaxed state.

$$n_n(C) = n \times \frac{\exp\left\{-\frac{U_n - 2\pi C \times (\Delta L k_n - \Delta L k_o)}{k_B T}\right\}}{1 + \exp\left\{-\frac{U_n - 2\pi C \times (\Delta L k_n - \Delta L k_o)}{k_B T}\right\} + \exp\left\{-\frac{U_p - 2\pi C \times (\Delta L k_p - \Delta L k_o)}{k_B T}\right\}}$$

**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 ($\Delta L k_n, \Delta L k_o, \Delta L k_p$) are described in **Supplementary Figs. 2-3**. The other parameters are defined in **Supplementary Equation 2**.
**Supplementary Equation 1**, the torque can be expressed as a function of the topological deformation applied to the fiber ($\Delta Lk_{tot}$), and **Supplementary Equation 3** becomes a function of supercoiling with three adjustable parameters, namely $n$, $U_n$ and $U_p$.

Notably, whereas the theoretical linking number change $\Delta Lk_t$ for the two closed states was similar to those obtained with the minicircle approach ($\Delta Lk_m)^8$, $\Delta Lk_t$ for a “pure” chain of nucleosomes in the open state was significantly different (-0.5 against -0.7; see **Supplementary Fig. 3b**). We attribute this discrepancy to the 3-D architecture of the fiber: the geometrical organization of the nucleosomes (a collective effect) can affect the global topology of the fiber, with respect to a mere addition of nucleosomes individual deformations. However, due to nucleosome thermal fluctuations, this additional collective contribution is expected to vanish in real fibers. For that reason, the fitting used the minicircle $\Delta Lk_m$ values as fixed parameters. Interestingly, this discussion is reminiscent of the work of Woodcock & al⁷, who showed that a fiber constructed with identical and regularly repeated nucleosomes may adopt, depending on the linker length, widely different 3-D shapes, and that allowing for fluctuations in linker length within the same fiber leads to fibers closer to physiological ones, as appear in electron microscopy in isolated chromatin and nuclei. In our case, fluctuations concern the nucleosome conformational state rather than the linker length, but they should similarly disrupt the long-range correlations along the fiber.

Our topological and mechanical predictions were then again applied, as an example, to the data represented in **Fig. 5b**, main text. We deduced that the fiber contained $n=31$ nucleosomes, short of the theoretical maximum of 36. The fit (see **Fig. 5b**, main text) allowed us to access the energies $U_n$ and $U_p$ (resp. 0.7 kT and 2 kT, see main text). The relaxed state for the fiber at zero torque was obtained at -27 turns (relative to the naked DNA), with a number of nucleosomes in the different states $n_o=21$, $n_p=2$ and $n_n=8$. This makes ~68 % open, 26 % negative and 6% positive nucleosomes (**Supplementary Fig. 4a**), and gives a mean $\Delta Lk$ of $0.68x(-0.7)+0.26x(-1.4)+0.06x(-0.4)=-0.86$ per nucleosome. This value agrees well with the -0.8±0.1 figure obtained in this work after partial nucleosome disruption (**Figs. 2 a** and **b** in main text), and with the -0.8 value obtained with plasmids made of the
<figure><img src="image_93.png" /></figure>

<figure><img src="image_94.png" /></figure>

**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.
same tandemly repeated 5S-208 sequences reconstituted with hyperacetylated histones¹⁹ (the N-terminal tails of histones H3 interact less with nucleosome entry-exit DNAs, which increases their mutual electrostatic repulsion, and mimics our low ionic strength Bo 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)).

Using the model to fit other *regular* fibers (see **Supplementary Fig. 1a**; and **Fig. 6**, main text), similar values of the energy differences between the states were obtained, in spite of rather different numbers of nucleosomes. As a consequence, a satisfactory fit of the behavior of all regular fibers could be achieved with the above single set of energy values, leaving the number of nucleosomes as the single adjustable parameter. The experimental horizontal and vertical dependencies of the rotation curves on the number of nucleosomes (**Fig. 6** in main text) are thus well accounted for by the model, which was used to draw the straight line in **Fig. 2c**, main text, and **Supplementary Fig. 1a**.

**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
<figure><img src="image_95.png" /><figcaption>**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.</figcaption></figure>
along a first order transition line (i.e. at constant torque), and more specifically of
the formation of plectonemes on naked DNA<sup>20</sup>. This process, i.e. the conversion of
twist into writhe through the formation of “telephone chord” structures, corresponds
to a well-defined mechanical problem, thoroughly studied by physicists both
experimentally and theoretically<sup>16,20,21</sup>. Thus, rather general and model-independent
arguments enable us to deduce the torque exerted in this regime from the value of
the length-vs.-rotation decay<sup>16</sup>. For naked DNA in B<sub>0</sub>, this torque is typically ~6
pN•nm/rad at 0.3 pN (data not shown).

For chromatin fibers, plectonemes are also expected to form. This process is,
however, significantly more complex than for naked DNA, and we cannot capture the
behavior in a quantitative physical model. A few qualitative features are consistent
with this interpretation, however. According to the worm-like rope model<sup>16</sup>, for
instance, the lower slope should be associated with a smaller bending persistence
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
approach<sup>16,21</sup> to fit the chromatin length-vs.-rotation decay, we could deduce the
torque applied to the fiber in the plectoneme regime (~3-4 pN•nm/rad,
**Supplementary Fig. 4b** (Lower panel)). This indeed corresponds well to the value
of the torque predicted by the three states model, at the points associated with the
plectoneme transition (-40 and -10 turns, respectively: see **Supplementary Fig.
5b**, lower panel).

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
place in the nucleosome array. This process would be favored by the “kinking” effect
of nucleosomes which brings entry/exit DNAs close together, and also by the partial
screening of DNA/DNA electrostatic repulsions by histone tails, which should reduce
the effective diameter of the DNA and hence of the plectoneme. Interestingly, this
implies that the bulky nucleosomes do not play a significant adverse role of steric
hindrance, i.e. that they organize on the outer face of the plectonemes
(**Supplementary Fig. 5B**). This plectoneme formation may also be favored by the presence of naked DNA gaps with missing Nss, in our imperfect fibers.

Clearly, a more detailed study of the plectoneme formation process would better be achieved with perfectly regular and gap-free nucleosome arrays, which may soon be constructed on nucleosome "super-positioning" sequences³.

**Supplementary References:**

1. Yodh, J. G., Woodbury, N., Shlyakhtenko, L. S., Lyubchenko, Y. L. & Lohr, D. Mapping nucleosome locations on the 208-12 by AFM profiles clear evidence for cooperativity in array occupation. Biochemistry 41, 3535-3574 (2002).

2. Solis, F. J., Bash, R., Yodh, J., Lindsay, S. M. & Lohr, D. A statistical thermodynamic model applied to experimental AFM population and location data is able to quantify DNA-histone binding strength and internucleosomal interaction differences between acetylated and unacetylated nucleosomal 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).

4. Hansen, J. C., van Holde, K. E. & Lohr, D. The mechanism of nucleosome assembly onto oligomers of the sea urchin 5 S DNA positioning sequence. J Biol Chem 266, 4276-4282. (1991).

5. Luger, K., Mader, A. W., Richmond, R. K., Sargent, D. F. & Richmond, T. J. Crystal structure of the nucleosome core particle at 2.8 Å resolution. Nature 389, 251-260 (1997).

6. 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).

7. 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. Nat. Acad. Sci. USA 90, 9021-9025 (1993).

8. 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).

9. 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).

10. 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).
11. 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).

12. Moroz, J. D. & Nelson, P. Torsional directed walks, entropic elasticity, and DNA twist stiffness. Proc. Natl. Acad. Sci. USA 94, 14418-14422 (1997).

13. White, J. H. & Bauer, W. R. The helical repeat of nucleosome-wrapped DNA. Cell 56, 9-10 (1989).

14. Klug, A. & Travers, A. The helical repeat of nucleosome-wrapped DNA. Cell 56, 10-11 (1989).

15. Klug, A. & Lutter, L. C. The helical periodicity of DNA on the nucleosome. Nucleic Acids Res 9, 4267-83 (1981).

16. Bouchiat, C. & Mezard, M. Elasticity model of a supercoiled DNA molecule. Phys. Rev. Lett. 80, 1556-1559 (1998).

17. Prunell, A. & Sivolob, A. in Chromatin Structure and Dynamics: State-of-the-Art (eds. Zlatanova, J. & Leuba, S. H.) 45-73 (Elsevier, London, 2004).

18. 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).

19. Norton, V. G., Imai, B. S., Yau, P. & Bradbury, E. M. Histone acetylation reduces nucleosome core particle linking number change. Cell 57, 449-57 (1989).

20. Strick, T. R., Allemand, J. F., Bensimon, D. & Croquette, V. Behavior of supercoiled DNA. Biophys J 74, 2016-2028. (1998).

21. Neukirch, S. Extracting DNA twist rigidity from experimental supercoiling data. Phys Rev Lett 93, 198107 (2004).
## I.4 Résultats et discussion

<figure><img src="image_96.png" /><figcaption>Figure S6 : Le système des pinces magnétiques</figcaption></figure>

Les fibres de chromatine utilisent des fragments d'ADN constitués de 2x18 répétitions de la séquence 5S du gène d'oursin de mer. A chaque extrémité de la fibre est ajouté un fragment d'ADN modifié permettant de fixer la fibre à la cellule d'une part, et à une bille paramagnétique de l'autre. Une paire d'aimants permet alors de tirer la bille et de la faire tourner (figure S6). Sur un graphe représentant la longueur de la fibre en fonction de la rotation (figure 2a, dans l'article), la chromatine apparaît plus courte que l'ADN nu et le centre de rotation est décalé, par rapport à l'ADN nu, vers les rotations négatives. La réduction de longueur est de 55 nm (soit ~ 150 pb ; l'ADN enroulé sur le nucléosome) par tour négatif absorbé.

Malgré l'ADN construit à partir de séquences répétées ayant une certaine capacité à positionner les nucléosomes, l'espacement des nucléosomes n'est pas toujours parfaitement régulier. Certains se touchent : ils sont dépourvus d'ADN de liaison, on parle alors de nucléosomes compacts. Nous avons pu montrer grâce au modèle moléculaire (voir plus bas) que les nucléosomes compacts sont rigides et que seuls les nucléosomes régulièrement espacés contribuent à la largeur de la courbe. Lorsqu'on compare ces courbes à celle d'un ADN nu de même longueur, on observe qu'elles sont beaucoup plus larges. Ceci traduit le fait que la chromatine est beaucoup plus flexible : elle peut emmagasiner une large contrainte rotationnelle sans changement important de sa longueur.
Nous avons cherché à ajuster le “modèle du ver” (la fibre de nucléosomes est considérée comme une corde élastique isotrope) aux résultats expérimentaux : la longueur de persistance est alors de 28 nm et le module d’étirement de 8 pico-Newton, valeurs compatibles avec les estimations déterminées auparavant par simple étirement de la fibre de chromatine. En accord avec la largeur de la courbe, la longueur de persistance en rotation apparaît cependant remarquablement faible : 5 nm, contre 80 nm pour l’ADN nu.

Pour comprendre cette étonnante élasticité rotationnelle de la chromatine, nous avons d'abord modélisé la fibre en utilisant les paramètres cristallographiques, avec des ADNs entrant-sortant croisant négativement. La longueur de persistance en rotation est alors de 35 nm. Nous avons alors considéré des nucléosomes capables d'accéder aux trois états conformationnels mis précédemment en évidence par la "technique des minicercles". Ces trois états correspondent à des déformations topologiques différentes de l'ADN, et la torsion peut donc les influencer. La partie supérieure (le chapeau) des réponses expérimentales en longueur/torsion peut alors être décrite avec un seul paramètre ajustable : le nombre de nucléosomes régulièrement espacés. Les faibles différences d'énergie entre les trois conformations impliquent un équilibre dynamique des nucléosomes dans la fibre, qui va dépendre de la rotation appliquée. Au centre de rotation, la plupart des nucléosomes sont dans l'état ouvert (pas de croisement des ADNs entrant-sortant). Sur le bord négatif du chapeau, ils adoptent la conformation fermée négative, et sur le bord positif on trouve surtout la conformation fermée positive.

L'équilibre au centre de rotation peut être modifié en ajoutant du sel. Les cycles successifs de torsion-détorsion sont alors moins reproductibles, et pour obtenir la même longueur il faut exercer une force plus importante (ces effets sont le résultat de l'écrantage des charges et de la diminution la répulsion électrostatique entre les ADNs entrant-sortant et également entre les nucléosomes). Le centre de rotation est déplacé vers les valeurs négatives : la conformation fermée négative est favorisée. Au contraire, une augmentation de la force de traction avantage l'état ouvert et le centre de rotation est déplacé vers la droite.

Au-delà de la zone du chapeau, la longueur de la fibre diminue rapidement avec l'augmentation de la torsion (positive ou négative) : c'est le régime des plectonèmes. Ceux-ci se forment plus facilement que dans le cas de l'ADN nu : la pente est plus faible. Ceci traduit un rayon du plectonème plus petit, vraisemblablement un effet des queues des histones qui, en
interagissant avec les ADNs de liaison, diminuent leur répulsion, c'est-à-dire leur diamètre apparent.

Les plectonèmes ne sont pas amorcés à la même contrainte rotationnelle selon qu'elle est négative ou positive. Dans la branche gauche de la courbe, la formation des plectonèmes demande plus d'énergie que le croisement négatif des nucléosomes et elle ne "démarre" qu'après uniformisation des conformations. Du côté droit, par contre, les plectonèmes sont déclenchés avant que l'ensemble des nucléosomes ne soient fermés positifs.

On peut se poser la question de la fonction de cet équilibre dynamique des nucléosomes. L'ensemble des processus nucléaires implique des changements topologiques et notamment la transcription. Dans le modèle des "domaines complémentaires", l'ARN polymérase induit un surenroulement positif à l'avant et négatif à l'arrière. L'équilibre entre les trois états exerce une sorte d'effet tampon, permettant d'absorber au moins en partie les contraintes induites, sans intervention des topoisomérides.

Les différentes conformations peuvent être impliquées dans des interactions spécifiques. Par exemple, les histones de liaison sont en compétition avec les HMGN (*High Mobility Group N*) pour les nucléosomes fermés. La dynamique de la chromatine peut ainsi être couplée à des processus nucléaires. De plus, les informations pourraient se propager par le surenroulement, à longue distance, plus rapidement que par la simple diffusion des protéines. Un tel mécanisme pourrait apporter une réponse rapide à des stimuli de régulation.
**<u>ARTICLE III</u> : Fibres de chromatine sous contrainte rotationnelle**
**positive : une transition chirale possible du nucléosome.**

**I.1 Résumé**

Lorsqu'on leur impose une forte contrainte rotationnelle positive, les fibres de nucléosomes ont un comportement hystérétique. Les fibres restent plus longues lors du relâchement de la torsion et ne retrouvent leur longueur initiale qu'au centre de rotation. Cette hystérésis dépend strictement de la présence des dimères H2A-H2B, et son amplitude, du nombre de nucléosomes régulièrement espacés. Nous proposons qu'un réarrangement des dimères H2A-H2B se produit, couplé à la transition chirale du tétrasome, pour former un nucléosome de chiralité inversée. La faible énergie nécessaire au processus (6 kT) suggère un rôle *in vivo* pour la forme altérée. L'ARN polymérase II qui, seule, ne peut pas traverser un nucléosome sur un substrat linéaire (sauf à augmenter la force ionique à des valeurs non physiologiques), pourrait utiliser cette transition chirale comme levier pour rompre les interactions dimères-tétramère.

**I.2 Article**
Single Chromatin Fibers under Positive Torsional Stress.
A Potential Chiral Transition of the Whole Nucleosome

Aurélien BANCAUD¹£, Gaudeline Wagner¹£, Natalia Conde e Silva², Julien Mozziconacci³,
Hua Wong³, Christophe Lavelle²,³,⁵, Andrei Sivolob⁴, Eric Le Cam⁵, Liliane Mouawad⁶,
Jean-Louis Viovy¹, Jean-Marc Victor³*

and Ariel Prunell²*

¹ Institut Curie (CNRS-UMR 168), 75231 Paris, France
Present address : LAAS-CNRS, 7 avenue du Colonel Roche 31077 Toulouse, France

² Institut Jacques Monod (CNRS-UMR 7592), 2 place Jussieu 75251 Paris, France

³ Laboratoire de Physique Théorique de la Matière Condensée (CNRS-UMR 7600),
Place Jussieu, 75252 Paris, France

⁴ Department of General and Molecular Genetics, Taras Shevchenko National
University, 64 Vladimirskaya street, 01033 Kiev, Ukraine

⁵ Laboratoire de Microscopie Moléculaire et Cellulaire (CNRS-UMR 8126), Institut
Gustave Roussy, 39 rue Camille Desmoulins, 94805 Villejuif, France

⁶ Integrative Imaging Unit (INSERM U759), Institut Curie-Recherche, Centre
Universitaire Paris-Sud, Bâtiment 112, 91405 Orsay, France

Running title: Single chromatin fibers under positive torsion

£ These authors, in alphabetical order, contributed equally to the work

*Correspondence to [prunell@ccr.jussieu.fr](mailto:prunell@ccr.jussieu.fr), or [victor@lptl.jussieu.fr](mailto:victor@lptl.jussieu.fr)
## Summary

Using magnetic tweezers, we show that chromatin fibers subjected to large positive supercoiling display hysteretic behavior in their mechanical response to torsion. Fibers remain more extended than before, and the hysteretic behavior ends when they are returned to the torsionally relaxed state. The hysteresis strictly depends on the presence of H2A-H2B dimers, and its amplitude, proportional to the number of regularly-spaced nucleosomes, indicates the trapping of one positive turn per such nucleosome. The results suggest a rearrangement of the dimers, coupled with the previously documented chiral transition of the tetrasome (the (H3-H4)₂ tetramer with its bound DNA), to give a chirally-reverse nucleosome. The low energy of the altered form, ~6 kT, suggests its physiological relevance. We propose it facilitates transcription elongation by providing the main RNA polymerase with a lever to break dimer docking on the tetramer.

## Introduction

The genome of higher eukaryotes is folded into chromatin, whose repetitive motif - the nucleosome - is a nucleoprotein complex with ~160 bp of DNA wrapped around a (H2A, H2B, H3, H4)₂ histone octamer (van Holde, 1988). Chromatin structure is dynamic, and this property is essential for DNA transactions such as transcription, which correlates with decompaction of the fiber and alterations at the nucleosome level. In particular, core particles prepared from transcribed chromatin display a deficit of H2A-H2B dimers (Baer and Rhodes, 1983), and a selective dimer exchange with the histone pool was observed in actively transcribed regions (Louters and Chalkley 1985; Schwager et al., 1985; Pfaffle et al., 1990; Kimura and Cook, 2001). These alterations could be due to the transcription process itself, as observed with RNA polymerase II which displaces one dimer in vitro (Kireeva et al., 2002), in contrast to prokaryotic RNA polymerases and polymerase III which translocate the octamer (Studitsky et al., 1997). Nucleosome alterations might also be driven by the wave of positive supercoiling generated in front of the polymerase (Liu and Wang, 1987). This was previously inferred from in vivo experiments with yeast
minichromosomes using a conditional topoisomerase mutant to convert DNA supercoiling from negative to positive (Lee and Garrard, 1991). *In vitro*, chromatin reconstitutions on positively supercoiled plasmids showed particles containing their normal histone complement but unable to store negative supercoiling (Jackson, 1993).

Here, we further investigate the influence of positive supercoiling on nucleosome structure through torsional manipulation of single chromatin fibers with magnetic tweezers. After application of a large positive torsion in low-salt, their extension-vs.-torsion response becomes hysteretic. The hysteresis reflects a nucleosome transition to an altered state and is strictly dependent on the presence of the H2A-H2B dimers. This transition is slow under low salt conditions, which accounts for the fibers hysteretic behavior, but it gathers pace under more physiological conditions, showing its intrinsic dynamic character. We propose that the transition involves a rearrangement of the H2A-H2B dimers, coupled with a switching of the (H3-H4)₂ tetramer from its left-handed to its right-handed chiral conformation (Hamiche et al., 1996), to give a chirally-reverse nucleosome, or reversome. These findings are discussed in the context of transcription.

# Results

## The standard torsional response

Nucleosome fibers were reconstituted on a template consisting of 2x18 tandemly repeated 190 or 208 bp 5S nucleosome positioning sequences, and nan-manipulated using magnetic tweezers (Strick et al., 1996; Bancaud et al., 2006; Figure 1A). Typical fibers in Figure 1B show more or less regularly-spaced nucleosomes with occasional gaps and clusters of two or three close-packed nucleosomes lacking linker DNA (arrowheads). These fibers resemble those observed on the same template with atomic force microscopy, for which a detailed study of nucleosome distribution showed the positioning ability of the sequence together with a similar cooperativity in nucleosome location (Yodh et al., 2002). Typical extension-vs.-torsion responses of fibers in low salt (blue curves in Figure 2A) show a broad apex, previously accounted for by a molecular model involving a dynamic equilibrium between three nucleosome conformations of distinct topologies, depending on the
<figure><img src="image_97.png" /><figcaption>**Figure 1.** The set-up and the fibers</figcaption></figure>

(A) Scheme of the set-up (Strick et al., 1996; Bancaud et al., 2006).

(B) Electron microscopic visualization of typical "190-bp" fibers before their attachment to the bead and into the flow cell. Arrowheads indicate clusters of close-packed nucleosomes. Nucleosome-free DNA spacers and stickers (~1100 bp total; see (A)) flanking the arrays are well visible.

crossing status of entry/exit DNAs, negative, null or positive (Bancaud et al., 2006).

Regularly-spaced nucleosomes can undergo these transitions, but close-packed nucleosomes could not. Once all regularly-spaced nucleosomes are in the negative or positive state, further torsions result in quasi-linear regimes in which the fiber compacts rapidly. This shortening is associated with the formation of plectoneme-like structures (Bancaud et al., 2006) that accumulate until the fiber end-to-end distance is close to zero for positive torsions or the backbone DNA starts to denature for negative torsions (e. g. Figure 2A, panel 4). The forward (*loading*) and backward (*releasing*) curves, obtained upon increase or decrease of the torsion, respectively, coincide as long as the positive torsion is not increased much beyond the zero-length limit (Bancaud et al., 2006).
<figure><img src="image_98.png" /><figcaption>Figure 2. The hysteretic response</figcaption></figure>

(A) Extension-vs.-rotation responses in B₀ (TE plus 0.1 mg/mL BSA) of four "208-bp" fibers at ~0.3 pN. The 0-turn rotation reference corresponds to the relaxed state of the corresponding DNAs obtained after histone removal (black dashed curves; Bancaud et al., 2006). After acquisition of the loading curves (blue), the releasing curves (green) obtained when returning from high torsions reveal an hysteresis. Panel 1: vertical and horizontal arrows correspond to shifts in lengths or rotations, respectively (see text). Panel 4: straight lines are drawn on the linear pletonemic regimes.

(B) Hysteresis amplitudes measured by the shifts along the abscissa (e.g. horizontal arrow in (A)) are plotted versus total (left panel) or regularly-spaced (right panel) nucleosome numbers (see Equations (1) and (2)) for 28 "190-" (blue) and "208-bp" (red) fibers. The slope of the linear fit is 1.3±0.1 turn per regularly-spaced nucleosome. Black arrowheads correspond to fibers 1-4 in (A).

## The hysteresis

Beyond this limit, i. e. upon the application of typically +70 turns, the releasing curves depart from the loading curves (blue and green in Figure 2A) and the torsional response becomes hysteretic. This hysteresis is reproducible over many
cycles of torsion/detorsion and is observed with the two repeat lengths of the 5S sequence, and with a poly 601 (200 bp) sequence (Huynh et al., 2005; P. Recouvreux and N. C. e S., unpublished results). This behaviour is unlikely related to long-range nucleosome-nucleosome attraction within the fiber, potentially favored by the torsion-induced compaction. Indeed such long-range interactions would cause the fiber to be shorter, pulling the releasing curve below the loading curve. The hysteresis thus more likely reflects a structural alteration of the nucleosomes, which switch back to normal near zero rotation, where the green curves converge onto the blue ones (Figure 2A).

Formally, the hysteresis could signal an increase in the nucleosome length along the fiber axis due to DNA unwrapping (vertical arrow in Figure 2A, panel 1), a trapping of positive turns (horizontal arrow), or a combination of the two. The first possibility is energetically disfavored: unfolding of positively-crossed nucleosomes present in the positive plectonemic regime (see above) requires removal of the positive crossing at their entry/exit, which can only increase the applied positive torsion. On the contrary, a trapping of positive turns is favored because it relaxes the applied constraint. Such trapping would result in a displacement of the torsional response parallel to the abscissa, which seems to be the case: note the parallelism between plectonemic regimes in the blue and green curves (straight red lines in panel 4). Finally, a compelling evidence for trapping of positive turns in the altered nucleosome comes from the observation that fibers in releasing curves start to decompact at higher positive torsions than does naked DNA (compare black dotted and green curves in Figure 2A), in contradiction with the notion that DNA in chromatin should always be negatively wrapped around the histones.

The hysteresis amplitude, i. e. the shift along the abscissa, is not correlated with the total number of nucleosomes (Figure 2B, left panel), but is directly proportional to the number of regularly-spaced nucleosomes (see Experimental Procedures), with a rate of 1.3 (±0.1) turns per such nucleosome (right panel). This suggests that close-packed nucleosomes, which contribute little to the breadth of the torsional response (see above), do not participate in its hysteresis either, and further argues for the involvement of individual nucleosomes in the hysteresis. With ΔLk_p ~ -0.4 (±0.1) (Lk is the DNA linking number) being the topological deformation of
positively-crossed nucleosomes (Bancaud et al., 2006), the topological deformation
associated with the altered form relative to unconstrained DNA is ΔLk<sub>a</sub> ~ ΔLk<sub>p</sub> +1.3 ~
+0.9 (±0.2).

The H2A-H2B dimers

Dimers removal by heparin. In order to test the altered form for the presence of dimers, we removed them and checked the consequence on the torsional response. We first used heparin, a strong polyanion which releases dimers in a sequential way from mononucleosomes reconstituted on DNA minicircles (Figure 3A and legend). The flow-cell was flushed with heparin at concentrations ranging from 0.01 to 100 µg/mL. The fiber length was not much affected up to 2 µg/mL, but increased above 5 µg/mL (not shown), and nucleosomes were destroyed at 100 µg/mL (Bancaud et al., 2006). We tentatively chose the milder treatment at 1 µg/mL and obtained the red curve in Figure 3B, panel 2, not much different from the initial loading curve (blue). A departure from the heparin-free behavior was observed only following the excursion at large positive torsion, which led to a reproducible curve (purple in panel 2) very similar to the initial green curve. Canonical nucleosomes reform at negative torsions, as suggested by the merging of purple and blue curves, but they switch to the altered form as soon as the constraint becomes positive, presumably as a result of a heparin-facilitated transition. Nucleosome core particles were subsequently added as histone acceptors (Voordouw and Eisenberg, 1978), leading to a ~650 nm extension of the fiber (purple curve in panel 3), i. e. ~24 nm per total nucleosome. This suggests that all nucleosomes in the fiber have been unwrapped by ~1 turn of DNA each, arguing for the release of the dimers.
<figure><img src="image_99.png" /><figcaption>Figure 3. H2A-H2B release with heparin</figcaption></figure>

(A) Mononucleosomes were reconstituted using the salt-jump method and pUC18 plasmid DNA as a carrier on a ΔLk ~-1 topoisomer of a DNA minicircle formed by circularization of a ³²P-end-labelled 357 bp fragment containing the 5S 190/208-bp repeat unit of the present arrays (Duband-Goulet et al., 1992). Reconstitution products were incubated with 0, 0.4, 0.8, 1.8 and 3.9 µg/mL heparin (Sigma) in B₀ at 37°C for 10 min, and electrophoresed in a 4 % (w/v) polyacrylamide gel in TE, along with starting mononucleosomes (Cₙ) and (H3-H4)₂ tetrasomes (Cₜ) similarly reconstituted on the same topoisomer. Nucleosomes (nucl) progressively vanish upon increase in the heparin concentration, to the benefit of hexasomes (hex: a single turn of DNA around the (H3-H4)₂ tetramer plus one H2A-H2B dimer) and tetrasomes (tet). Note the broad band of nucleosomes resulting from the fractionation of subsets of their ~15 distinct positions relative to the DNA sequence (Duband-Goulet et al., 1992). "-1": residual unreconstituted topoisomer.

(B) Extension-vs.-rotation behaviour of a "190-bp" fiber at 0.35 pN through the successive steps of the heparin assay (see text). (1): Loading and releasing curves of the initial fiber in B₀. (2): First loading curve in the presence of B₀+1 µg/mL heparin (red). Following the application of a large positive torsion, the response stabilizes on the purple curve. (3): Response (purple) obtained after flushing the flow-cell with 1 µg/mL nucleosome core particles (reconstituted on chicken ~146 bp DNA originating from native core particles with purified octamers from the same source) in B₀ plus 50 mM NaCl, and rinsing with B₀ after 5 min (4): Corresponding DNA response (black).
<figure><img src="image_100.png" /><figcaption>**Figure 4.** H2A-H2B release with yNAP-1 under traction, and reincorporation
(A) Same as Figure 3A, except that mononucleosomes were incubated with 0, 2.5, 7 and 20 NAP-1 per octamer (n/n) for 1h at 37°C in B₀ plus 100 mM NaCl. The first dimer is removed, as observed with heparin in Figure 3A, but not the second.</figcaption></figure>

(B) Torsional behaviour of a "190-bp" fiber at 0.2 pN through the successive steps of the *force* assay. (1): Fiber initial response in B₀. (2): The force was increased to 3.5 pN at the fiber center of rotation in B₀ plus 50 mM NaCl and 250 nM yNAP-1, and maintained until the first ~25 nm steps, which signal the removal of tetramers (Brower-Toland et al., 2002; Claudet et al., 2005), were observed (data not shown). The force was then decreased to its original value and the flow-cell rinsed with B₀. The loading curve shows an extension of the fiber (red) and the residual hysteresis disappears following excursion at high torsion (purple). (3): The fiber initial hysteretic response is rescued when the flow cell is filled with 40 nM H2A-H2B chaperoned with 40 nM yNAP-1 in B₀ plus 50 mM NaCl, and flushed with B₀ after 5 min (bold curves). (4): Corresponding naked DNA (black). Note that the hysteresis amplitude, i.e. the number of regularly-spaced nucleosomes, is significantly smaller than in Figure 3B.
**Dimers removal by NAP-1 under traction.** NAP-1 (Nucleosome Assembly Protein-1; Ishimi and Kikuchi, 1991) also removes one dimer from mononucleosomes in bulk experiments, but is less efficient to remove the second (Figure 4A; Kepert et al., 2005). For this reason, we combined NAP-1 treatment with traction, which was shown alone to destabilize dimers in single molecule experiments (Claudet et al., 2005; Mihardja et al., 2006). After rinsing NAP-1 out, the first torsion/detorsion cycle revealed a fiber lengthened by ~420 nm or ~19 nm/nucleosome (red in Figure 4B, panel 2), which loses its hysteresis in the second cycle (purple), and much resembles that obtained above after treatment with heparin and core particles. Dimers chaperoned with NAP-1 were then flowed back into the cell and rinsed out after a 5 min incubation. The rescue of the fiber initial hysteresis (bold curves in Figure 4B, panel 3) indicates a successful reincorporation of the dimers, confirming that they were released at the previous step (purple curve in panel 2). We conclude that the hysteresis strictly depends on the presence of dimers, and that the altered nucleosome form contains them.

**The tetrasome fiber**

**General features.** The torsional response of a tetrasome fiber reveals: i) an extended structure; ii) no hysteresis; and iii) a striking similarity with the nucleosome releasing curve in both its breath and its center of rotation which approximates that of naked DNA (compare purple and green curves in Figure 3, panel 3). The first feature is consistent with DNA unwrapping in tetrasomes relative to nucleosomes, the second with the strict dimer-requirement of the hysteresis, and the third with tetrasomes known ability to fluctuate between "pseudo-mirror-symmetrical" left- and right-handed chiral conformations of nearly equal and opposite $\Delta L_k$ [$\Delta L_k$ = -0.7 and +0.6 (±0.05) for 5S DNA; Sivolob and Prunell, 2004; see Discussion]. This last feature suggests that the whole nucleosome could, like the tetrasome, switch from a left- to a right-handed conformation, this switching being opposed by an energetic barrier in the nucleosome (but not in the tetrasome), due to the presence of dimers, thus the hysteresis.
**Structural dynamics of the tetrasome.** A number of experimental evidences exist for the tetrasome chiral transition (see Discussion). Here we detail the first Normal Modes analysis (NMA; Wilson et al., 1955; Mouawad and Perahia, 2006) of the tetrasome, to identify structure-based cooperative atomic motions within it. The more atoms involved, the more collective the motion, the lower its frequency, and the more useful that motion could potentially be for the dynamics of the complex. The three lowest-frequency modes essentially correspond to movements of the two H3-H4 dimers relative to one another, the rotation components of which are shown in Figure 5A. The first mode is linked to a wing-like motion of the tetrasome, and the third mode to its lateral opening. The second mode is directly relevant to the chiral transition. The tetrasome was perturbed along the direction of mode 2 toward positive handedness, and then allowed to relax free of any constraint to a local minimum of energy. Figure 5B, right, shows the DNA superhelix of the resulting tetrasome (red) superimposed on the nucleosomal DNA superhelix (green). Clearly, this local minimum corresponds to a right-handed, although relatively flat, superhelix. Next, the tetrasome was perturbed in the opposite direction, i. e. toward a more left-handed superhelix, and again let relax. No local energy minimum was now observed, and the structure went back to its initial conformation (yellow superhelix in Figure 5B, right panel). We conclude that intrinsic tetrasome structural dynamics encompass its switching to a right-handed conformation.
<figure><img src="image_101.png" /><figcaption>Figure 5. Normal Mode analysis of the tetrasome</figcaption></figure>

(A) The axes of the rotation components of the three main vibrational modes are shown for each mode, superimposed on the tetrasome DNA superhelix viewed along the dyad (blue dots and blue arrows) or the superhelix axis. The axis of mode 1 runs close to the dyad, and the axis of mode 3 is approximately parallel to the superhelix axis. Mode 2 axis is approximately perpendicular to both dyad and superhelix axes. All three axes traverse the cysteines 110 (green balls in middle superhelix).

(B) The tetrasome was perturbed along the direction of mode 2 in (A) toward right-handedness (Right), and let relax without constraint until its energy reaches a local minimum. The resulting tetrasome DNA superhelix (red) is shown superimposed onto one side of the nucleosomal superhelix (green) viewed perpendicular to both dyad and superhelix axes. A perturbation along mode 2 toward a more left-handed superhelix (Left) does not lead to a local energy minimum, and the tetrasome goes back to its initial conformation (yellow).
## Energetics

The metastability of the altered nucleosome that we putatively attributed to an energetic barrier against the transition was confirmed by monitoring the extension of a fiber at constant force in the releasing curve (dot 1 in Figure 6A, left panel). The fiber relaxes within ~30 min (green recording in Figure 6A, right panel) towards an equilibrium length close to the loading curve (dot 2), showing that the altered structure switches back to the canonical state when given enough time. The proportions of each state can be obtained as a function of time (inset in Figure 6A, right panel; and Figure S1 in Supplemental Data available with this article online), and used to estimate the energy parameters of the transition (see Experimental Procedures, and Supplemental Data). We obtained an equilibrium energy difference of 10 (±2) kT relative to the ground state of the nucleosome (the open state), and an energy barrier of ~30 (±5) kT. This barrier is high enough to transiently freeze the altered form, thus explaining the hysteresis.

### Figure 6. The transition in real time

(A) Left: Torsional response of a "208-bp" fiber in $B_0$ at 0.4 pN. Right: The "all-altered-nucleosome" fiber at +25 turns (point 1 on the red vertical line) was allowed to relax in $B_0$ at the same force down to the equilibrium (point 2; green recording). Inset: proportion of nucleosomes during the relaxation time course measured as shown in Supplemental Figure S1 available with this article online, and fit with a monomolecular reaction scheme (Eqation 5 in Experimental Procedures; smooth curve).

(B) Left: Same as (A) at 0.25 pN. Right: The force applied on the "all-nucleosome" fiber at +18 turns (point 1 on the red vertical line in (A)) is increased step-wise (blue recordings in right panel). A relaxation to a more extended fiber is observed when the force is raised to 3.4 pN. Upon decrease of the force back to 0.25 pN, a residual extension of ~150 nm is observed relative to point 1, corresponding to ~30% of the particles being in the altered state (measured as in (A)).

(C) Torsional responses of two fibers at 0.3 pN in $B_0$ (dashed) and $B_0 + 10$ mM NaCl or 25 mM NaCl (continuous). Three successive torsional cycles are shown in right panel.

(D) Left: Same as (A). Right: The flow-cell was flushed with $B_0+50$ mM NaCl, while the fiber was kept at a negative torsional constraint and at ~0.1 pN. A torsion of +12 turns was applied in ~5 sec (reaching point 1 on the red vertical line), and the length of the fiber was recorded in real time at 0.4 pN until a plateau is reached (point 2; blue tracing). Inset: fraction of nucleosomes measured as in (A) from the torsional response in $B_0$ (left), and fit (smooth curve).
<figure><img src="image_102.png" /></figure>

<figure><img src="image_103.png" /></figure>

<figure><img src="image_104.png" /></figure>

<figure><img src="image_105.png" /></figure>

<figure><img src="image_106.png" /></figure>

<figure><img src="image_107.png" /></figure>

<figure><img src="image_108.png" /></figure>

<figure><img src="image_109.png" /></figure>
Next, we started from the loading curve, i. e. a fiber containing only canonical, positively-crossed nucleosomes (dot 1 in Figure 6B, left panel). The fiber length, monitored for 30 min, showed no significant increase above the back-ground thermal fluctuations (not shown), as expected from the steady-state equilibrium containing mostly canonical nucleosomes (88 %, as obtained from the fit of the inset plot in Figure 6A, right panel, through Equation (5) in Experimental procedures). This suggests that a shift of the equilibrium toward the altered state, through a reduction of the free energy difference between the two states, is required for the transition to be observed in real time from the loading curve. This was done by raising the force step-wise until a large extension occurred at 3.4 pN (blue recording in Figure 6B, right panel). The force was then decreased to its initial value, leaving a residual extension as a tribute to the formation of the altered form upon mechanical constraint. Note that the requirement for a high tension to trigger the transition is an additional argument to exclude the contribution of collective effects in the hysteresis.

## Effect of salt

As described in our previous study (Bancaud et al., 2006), fibers in higher salt tend to compact from one rotation cycle to the next (blue curves in Figure 6C, right panel). This compaction appears to originate from the occurrence of tails-mediated attractive interactions between nucleosomes (Bertin et al., 2004; Korolev et al., 2006). Interestingly, these interactions break under a force of a few pN applied at the center of rotation, as shown by the rescue of the initial rotational response. This reinitialized response is close to that obtained in low salt (Bancaud et al., 2006). At the same time, the hysteresis tends to disappear in higher salt, to become hardly visible in 25 mM NaCl (Figure 6C).

A fiber in the loading curve (Figure 6D, left panel) was found to relax to an equilibrium length in ~1 min in 50 mM NaCl (right panel), as compared to ~30 min in low salt (see above). This results in a lower energy difference, 6 (±2) kT, and energy barrier, ~25 (±5) kT (see details in Supplemental Data). Because the transition rate depends exponentially on the energy barrier, the equilibrium between the two states becomes more dynamic in comparison to the time-scale of data acquisition, and loading and releasing curves tend to merge toward a unique curve corresponding to an intermediate equilibrium.
# Discussion

## The tetrasome chiral transition

Experimental evidences for that transition have accumulated since the initial observation that tetramer affinity increases almost equally with negative and positive supercoilings in DNA minicircles. Upon electron microscopic examination, tetrasomes assembled on DNA minicircles of $\Delta L_k = -1$ or +1, both ~0.7-turn particles, were undistinguishable from each other. The involvement of the protein in the transition was demonstrated through the oxydation of the two H3 cysteines 110 at the H3/H3 interface, which prevented reconstitution on either topoisomer +1 or -1, depending on the thiol reagent used. Moreover, the formation of a disulfide bridge between these two cysteines did not affect the transition. This latter observation, together with such an ability of a steric hindrance at the dyad to block the tetramer left- or right-handed, suggested that the transition occurred through a rotation of the two H3-H4 dimers relative to one another around the disulfide bridge (Hamiche et al., 1996; Alilat et al., 1999). An additional piece of evidence was obtained by neutron scattering, which showed that the pattern of tailless octamers exactly matches that predicted from the core particle crystal structure (Luger et al., 1997), in contrast to the pattern of tailless tetramers which substantially differed (Baneres et al., 2001). The discrepancy appeared to be related to an average flattening of the tetramer protein superhelix as a consequence of its chiral flexibility (J. Parello, personal communication).

The observation that the center of rotation of the tetrasome fiber approximates that of DNA (Figures 3 and 4), and thus must be associated with particles equally distributed between left- and right-handed conformations, provides another experimental evidence for the chiral transition. Note that the zero torque position does not necessarily coincide with the rotation center (Bancaud et al., 2006). Because the tetrasome right-handed conformation is energetically less favorable than the left-handed conformation (by ~2 kT under physiological conditions; Sivolob et al 2000), we anticipate that the torque is positive at the center.

Normal Modes analysis (NMA) has proved useful to identify near-equilibrium functional conformational changes within proteins and protein complexes (see Bahar
and Rader, 2005, for a review). Here NMA was applied to the tetrasome using the all-atom method (see Experimental Procedures). The three lowest-frequency, i. e. most cooperative, vibrational modes correspond to movements of the whole H3-H4 dimers about each other. Strikingly, the axes of their rotation components (Figure 5A) are approximately orthogonal to each other and all pass through the cysteines 110 (green balls in Figure 5A, middle). These features make the cysteines a pivot for H3-H4 dimers relative movements, as originally proposed (see above). Mode 2 appears most relevant to the transition, while mode 3 mediates tetrasome lateral opening (Figure 5A). A combination of modes 2 and 3 was not explored as an attempt to increase the superhelix right-handedness of the mode-2-minimized form (red in Figure 5B), although mode 3 may also be relevant. Topological data indeed suggested that the tetrasome was ~20 % more opened laterally in the right- than in the left-handed conformation (Sivolob et al., 2000).

## The nucleosome-reversome transition

**General features.** The topological deformation of the altered nucleosome form is close to that of the right-handed tetrasome (+0.9 against +0.6; see Results). The nucleosome releasing curve is also strikingly similar to the tetrasome torsional response (Figure 3, panel 3, and Results). This strongly suggests that the transition processes have a common basis in the two particles, at least in the *reverse* direction. The difference observed in the *direct* transitions (the hysteresis of nucleosomes) may then solely reflect their higher energy barrier, resulting in particular from the presence of H2A-H2B dimers (see below). We thus propose that the altered nucleosome is made of the right-handed tetrasome, with flanking H2A-H2B dimers arranged on each side.

**The final product.** A shift along the abscissa of the releasing curves *versus* the loading curves in the hysteresis (see Results; Figure 2A) implies that the lengths of canonical and altered nucleosomes along the fiber axis are similar. For this to occur, and taking into account that the tetrasome fiber is more extended than the nucleosome fiber (Figures 3 and 4), the dimers may simply continue the DNA wrapping beyond the ~0.7 turn of the tetrasome. This can be achieved if the dimers prolong the tetramer right-handed superhelical ramp on each side, leading to a chirally *reverse nucleosome*, or reversome.
**The transition steps.** In the first step, dimers are expected to break their docking on the tetramer (Figure 7). Clearly, dimers need to remain attached to their nucleosome during that process, otherwise they would diffuse into the cell and be lost. Dimers may remain tethered to the DNA through interactions of H2A and H2B N-terminal tails, and/or through their histone fold binding sites at superhelix locations (SHL) ±5.5, ±4.5 and ±3.5 (Luger et al., 1997). The H2B/H4 interface may also contribute. Although these contacts, taken individually, may be relatively weak (Li et al., 2005; Tomschik et al., 2005), their cumulative effects should be sufficient to hold the dimers in place. Older experiments support that possibility. Nucleosomes exposed to salt concentrations <0.2 mM were found to elongate, which was interpreted as an unfolding, driven by the repulsion between the DNA gyres, of nucleosomes considered as a sequential arrangement of the histones on the DNA (van Holde, 1988 and references therein). Once the docking is broken, the tetramer may undergo the chiral transition with the dimers still attached (Figure 7).

Bound dimers will facilitate the extension of the tetramer positive superhelical spool in the refolding step. The degree of compaction of the reversome will depend on the energy recovered upon formation of the new dimers/tetramer interface (compare histones arrows orientations in Figure 7). Clearly, the location of H3 αN helices and tails (dark blue) on the outer faces of the new particle, rather than in between the two DNA gyres, prevents them from clamping entry/exit DNAs (Figure 7) and assisting dimers refolding, as they do in nucleosomes. These features in turn explain why entry/exit DNAs do not cross (ΔLk~+1, instead of +2; see above). We infer from these results that dimers in the reversome are relatively unstable, consistent with reversome higher equilibrium energy relative to the canonical nucleosome.

**The energetic barrier.** The requirement to break dimers docking on the tetramer is expected to be a major contributor to the energy barrier (25-30 kT; see Results). This view is in keeping with microcaloric studies of octamer assembly in 2 M NaCl that gave an estimate of ~17 kT for the binding energy of one dimer onto the tetramer (Benedict et al., 1984). A mechanical (or elastic) barrier may also exist
<figure><img src="image_110.png" /><figcaption>**Figure 7.** Scenario for the transition</figcaption></figure>

Scheme of main steps of the transition for a nucleosome viewed as a sequential arrangement of the histones on the DNA. H2As and H2Bs in nucleosome upper and lower faces were differentiated by light and dark colors, and for H2As also by arrows. Note that H3 αN and N-terminal tails are in between the two DNA gyres in the nucleosome, but move to the outer faces in the reversome. The DNA diameter was made smaller compared to the overall particle dimensions in order to better show the histones. Nucleosome and reversome were enlarged relative to the intermediate structures.

beyond the point of dimers undocking. Twist may accumulate at the expense of writhe, and be suddenly released, generating an instability similar to that predicted for twisted rods (Neukirch et al., 2002). This writhing instability is expected to be enhanced by the histone-imposed DNA curvature, in conjunction with the extra lateral opening of the structure required at mid-transition to relieve the clash between entry/exit DNA arms (Figure 7; Sivolob et al., 2000).

**Modelling.** The transition scenario in Figure 7 was validated by a multiscale molecular dynamics approach (not shown), involving a substructuring of the nucleosome into 14 rigid ensembles of atoms (one every 10 bp), themselves articulated into a skeleton. The flexibility of the links separating each ensemble in the skeleton was defined by the results of the tetrasome Normal Modes analysis in Figure 5A. A robotic procedure, joined to inverse kinematics, was then used to move the skeleton. A realistic path of the nucleosome-reversome transition could be constructed in silico, with low deformations of the histones within the complex (H. Wong et al., unpublished data).

**Physiological relevance**

RNA polymerases exert a positive torque >1.25 kT/rad, and hence can generate an energy >8 kT over one turn (Harada et al., 2001). This energy should be sufficient to trigger the nucleosome/reversome transition (~6kT/turn in 50 mM salt) at a distance.
A nucleosome on a linear fragment presents an almost absolute block to *in vitro* transcription by RNA polymerase II at physiological ionic strength. Transcription can occur only at elevated ionic strength (>0.3 M KCl; Kireeva et al, 2002) when histone/DNA interactions, and possibly the strength of dimers docking on the tetramer, are weakened. The observation that FACT, an H2A-H2B chaperone, helps RNA polymerase II to traverse nucleosomes *in vitro* and *in vivo* by removing one dimer (Reinberg and Sims, 2006), suggests the barrier to transcription is due to dimers docking. It is interesting that blocks have also been identified within the tetrasome, which are not relieved by FACT, but this situation seems restricted to nucleosomes on strong positioning sequences such as the 601 (Bondarenko et al., 2006). Bearing in mind that torsional constraints cannot develop in the linear mononucleosome templates used by Kireeva et al. (2002), we propose that reversomes act as torsion-driven "activated" nucleosomes poised for polymerase passage. The ability of the tetramer to switch its chirality may then be the lever used by the main polymerase to break dimer docking. The activity of FACT or other intervening elongation factors may then be dispensable, but nature provides many examples of biological redundancy, in which distinct mechanisms were devised to the same end.

# Experimental Procedures

## Magnetic tweezers, nucleosome arrays and electron microscopy

Magnetic tweezers manipulation and nucleosome array preparation were done as described (Bancaud et al., 2006). For electron microscopy, 5 µl of reconstituted nucleosome arrays at 1-5 nM in TE (10 mM Tris-HCl [pH 7.5], 1 mM EDTA) were deposited onto a 600-mesh copper grid covered with a thin carbon film activated by glow-discharge in the presence of pentylamine. Grids were washed with aqueous 2% (w/v) uranyl acetate, dried and observed in the annular darkfield mode using a Zeiss 902 electron microscope. Images were captured with a MegaviewIII camera CCD.

### Regularly-spaced and close-packed nucleosomes

Regularly-spaced and close-packed (linker-free) nucleosomes assemble in variable proportions from one fiber to the next within the same preparation (Figure 1B). The
former nucleosomes fluctuate between the three conformations (open, negative and positive, of respective topology $\Delta Lk \sim -0.8, -1.4$ and $-0.4$), while the latter are frozen in the open state. Modelling showed that the proportion of each state at the apex of the extension-vs.-rotation curve of an all-regularly-spaced fiber is respectively 65 %, 20 % and 15 % (Bancaud et al., 2006). This leads to a mean topological deformation of $-0.85$ turn and to an effective extension of 6.5 nm per nucleosome, against $\sim -0.5$ turn and $\sim 4$ nm, respectively, for an all-close-packed fiber (156-bp repeat length). These figures lead to accurate fits of experimental extension-vs.-rotation data, via the number of regularly-spaced and close-packed nucleosomes (Bancaud et al., 2006).

These numbers can more simply be estimated from the length of the fiber ($L_{fiber}$) compared to that of the corresponding naked DNA at the same force ($L_{DNA}$). Measurements are made at the centres of rotation, which are shifted relative to one another by $\Delta Lk_{fiber}$. Fibers contain 8680 bp total: 36 208-bp nucleosome positioning sequences and two DNA spacers of $\sim 600$ bp (Figure 1A). One can write:

$$ \Delta Lk_{fiber} = -0.85n_{reg} - 0.5(n_{total} - n_{reg}) \quad (1) $$

$$ \begin{aligned} L_{fiber} = L_{DNA} \frac{1200}{8680} + 6.5n_{reg} + L_{DNA} \frac{208}{8680}(36 - n_{total}) & \\ +4(n_{total} - n_{reg}) + L_{DNA} \frac{50}{8680}(n_{total} - n_{reg} - 1) & \end{aligned} \quad (2) $$

with $n_{reg}$ the number of regularly-spaced nucleosomes, $n_{total}$ the number of all nucleosomes, and 50 bp the addition to the naked DNA length made by each close-packed nucleosome. Inversion of these equations gives $n_{total}$ and $n_{reg}$. Errors in $n_{total}$ and $n_{reg}$ are estimated to be $\pm 1$ and $\pm 2$ nucleosomes, respectively.

## Normal Mode analysis (NMA) of the tetrasome

The tetrasome ($\sim 50$ bp wrapped around the $(H3-H4)_2$ tetramer) was extracted from the nucleosome crystal structure (1KX5 in the protein data bank). The all-atom force field CHARMM27 (McKerell et al., 1998a) was then applied to it. The energy was minimized using the CHARMM program (McKerell et al., 1998b; Brooks et al., 1983) until it reached a root-mean-square gradient less than $10^{-5}$ kcal/mol.Å, necessary for
NMA, then 100 lowest-frequency NM were calculated using the DIMB method (Mouawad and Perahia, 1993 and 2006). The rotation components of the first three were calculated using Hingefind (Wriggers and Schulten, 1997; Figure 5A).

## Kinetic modelling of the transition

We consider a monomolecular reaction scheme for the structural transition with

$$ \text{Nucleosomes} \overset{k_1}{\rightleftharpoons} \text{Reversomes} \quad (3) $$

Calling f and 1-f the fractions of nucleosomes and reversomes in a fiber, respectively, transition reactions are governed by the following kinetics:

$$ \frac{df}{dt} = k_{-1}(1-f) - k_{1}f \quad (4) $$

If the fiber initially contains only reversomes, Equation (4) can be integrated into:

$$ f(t) = \frac{k_{-1}}{k_1 + k_{-1}} \left(1 - \exp\left[-(k_1 + k_{-1})t\right]\right) \quad (5) $$

k₁ and k-₁ can then be fitted and used to derive the energetical parameters of the reaction (see Supplemental Data).

## Supplemental Data

Supplemental Data include a discussion and one figure, and can be found with this article online at http://

## Acknowledgments

AB, GW, NCeS, HW and JM thank the French ministry of research, and NCeS the Foundation for medical research (FRM) and the Association for cancer research (ARC), for fellowships. AP is grateful to S. Leuba (University of Pittsburg, USA) for the gift of NAP-1, and to T. Strick (Institut J. Monod, Paris) for a critical reading of the manuscript, and CL and ELC to A. Justome and S. Baconnais for technical assistance. This work was supported by grants from the CNRS/MENRT programs "DRAB" and Institut Curie cooperative program "Physics of the cell" (JLV lab) and by CNRS (AP and JMV labs).
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# Single chromatin fibers under positive torsional stress. A potential chiral transition of the whole nucleosome

Mail to: [prunell@ccr.jussieu.fr](mailto:prunell@ccr.jussieu.fr), or [victor@lptl.jussieu.fr](mailto:victor@lptl.jussieu.fr)

## Supplemental Data

This supplement contains:

* Discussion

* Figure S1

* References

## Energy landscape of the transition

### a) Theory

Loading and releasing curves of the torsional responses correspond to limits at which all regularly-spaced particles were assumed to be either nucleosomes or reversomes (see model in main text, Figure 7). In a steady-state equilibrium, in contrast, the two states must coexist, and the fiber length must lie in between the two curves.

If the topological contribution of the linkers, i.e. of nucleosome arrangement in the fiber, is neglected, the fiber topology ($\Delta Lk_{fiber}$) can be expressed as:

$$ \Delta Lk_{fiber} = N_{nucl} \Delta Lk_{nucl} + N_{rev} \Delta Lk_{rev} \quad (S1) $$

where $\Delta Lk_{nucl} \sim -0.4$ and $\Delta Lk_{rev} \sim +0.9$ are the individual DNA topological deformations of positively-crossed nucleosomes in the positive pleconemic regime of the torsional response and of reversomes, respectively (see main text), and $N_{nucl}$ and $N_{rev}$ their numbers. The length of the fiber and its rotation status, $\Delta Lk_{fiber}$, at steady state define one point, $t_{fiber}$, in between the blue and green curves of the torsion plot (scheme in Figure S1). The horizontal line going through $t_{fiber}$ intersects the curves at
positions $t_{nucl}$ and $t_{rev}$, the abscissa of which correspond to the topology of an all-nucleosome or all-reversome fiber, respectively. Equation S1 can be solved graphically, and one gets

$$N_{rev}/N_{nucl} = [t_{nucl}t_{fiber}]/[t_{rev}t_{fiber}] \quad (S2)$$

with $[t_{nucl}t_{fiber}]$ and $[t_{rev}t_{fiber}]$ being the lengths of the corresponding segments measured on the abscissa (Figure S1).

Following the kinetic modelling (see Experimental Procedures in main text), we can compute the equilibrium constant $K= k_1/k_{-1}$, and derive the free energy difference, $\Delta G$, between nucleosome and reversome:

$$\Delta G = -k_B T \ln(K) = U - F[l_{rev} - l_{nucl}] - \Gamma[\theta_{rev} - \theta_{nucl}] \quad (S3)$$

where $U$ is the difference in energy, $F$ the force, $G$ the torque, $l_{rev}$ and $l_{nucl}$ are the particles respective lengths projected on the direction of the force, and $\theta_{rev}$ and $\theta_{nucl}$ their rotational deformations perpendicular to it.

<figure><img src="image_111.png" /><figcaption>Figure S1. Schematics of the hysteretic torsion cycle.</figcaption></figure>

At a given rotation $\Delta L k_{fiber}$, the steady-state extension of the fiber define one point ($t_{fiber}$) located in the region delimited by the loading curve (the "all-nucleosome" fiber; blue) and the releasing curve (the "all-reversome" fiber; green). The reversome or nucleosome proportions are equal to the length of the segments $[t_{nucl}t_{fiber}]$ or $[t_{rev}t_{fiber}]$, respectively (see Equation S2).

As assumed in Results of main text, $\Delta l = l_{rev} - l_{nucl}$ is small. In contrast, $\Delta \theta = \theta_{rev} - \theta_{nucl}$, i.e. the hysteresis amplitude, 1.3 (±0.1) turns (Figure 2B in main text), is comparatively large. Because the typical torque at 0.3 pN is ~3 pN.nm/rad (see below), $F\Delta l$ can be neglected relative to $G\Delta\theta$ in Equation S3. One finally obtains:

$$U = \Gamma[\theta_{rev} - \theta_{nucl}] - k_B T \ln K \quad (S4)$$
The torque cannot be measured experimentally, but it can be estimated from a fitting of the torsional curve with the worm-like rope model (Bouchiat and Mezard, 1998). In this model, the main determinant of the torque is the slope in the linear plectonemic regime reached after ~10 turns of positive torsion are applied to the fiber (Bancaud et al., 2006). The similar slopes of loading (blue) and releasing (green) curves in this regime (Figure S1) imply that the torques exerted on the all-positively-crossed-nucleosome or all-reversome fibers are about the same. We thus assume that the torque keeps the same value when the fiber relaxes at constant force to its steady state (see below).

In addition, the rate constants provide an estimate for the energetic barrier. We have:

$$k_1 = k_T \exp\left(-\frac{G^*}{k_B T}\right) \quad (S5)$$

where $k_T$ is the spontaneous fluctuation rate of dimers in a positively-crossed nucleosome (assuming the breakage of dimers docking on the tetramer is the rate-limiting step; Figure 7 in main text), and $G^*$ the activation free energy relative to the positively-crossed nucleosome. For chemical bond disruption, $k_T$ is usually estimated to be $10^8-10^9$ s⁻¹ (Brower-Toland et al., 2002; Pope et al., 2005). Fluctuations occurring at the nucleosome level should be much slower, and, taking the nucleosome as a sphere of volume V~500 nm³, one obtains $k_T \sim 3\eta V/k_B T \sim 3*10^6$ s⁻¹ with η the viscosity of water. Because we consider fluctuations of dimers within a nucleosome, we expect this fluctuation rate to be on the order of $10^7$ s⁻¹.

By analogy with Equation S4, and assuming the transition is driven by the external torque, one can write:

$$G^* = U^* - \Gamma(\theta^* - \theta_{nucl}) \quad (S6)$$

with $U^*$ being the activation energy relative to the positively-crossed nucleosome, and $\theta^*$ the rotational deformation of the reaction intermediate. $\theta^*$ should be ~0 according to our scenario (Figure 7 in main text), i.e. a tetrasome transiting from its left-handed to its right-handed conformation.
b) *Measurements*

i) **In lower salt.** Using Equation (S2), the proportion of nucleosomes during the relaxation time course can be estimated, and the kinetics can be fitted with Equation (5) in main text (Fig. 6A, insert in right panel). It comes $k_1=0.8*10^{-4} \sec^{-1}$ and $k_2=5.5*10^{-4} \sec^{-1}$. The torque was calculated (see above) to be ~3 (±1) pN.nm/rad, and Equation (S4) leads to $U = 8 (±2) \text{ kT}$. In low salt conditions ($B_0$: 10 mM Tris-HCl [pH 7.5], 1 mM EDTA, 0.1 mg/mL BSA) and in the absence of torsional stress, the ground state in energy is the open nucleosome, and the positive conformation is then characterized by an energy difference of ~2 kT (Bancaud et al., 2006). Consequently, the energy of reversomes relative to the ground state is 10 (±2) kT. Moreover, according to Equation (S6), $G^*$ is on the order of 26 (±3) kT. Thus, the energy difference between the reaction intermediate and the ground state is ~30 (±5) kT.

ii) **In higher salt.** Figure 6D in main text shows the transition observed at 0.4 pN in $B_0$+50 mM NaCl. Assuming a salt-independent topology of the reversome, and a reinitialized response in salt virtually identical to that obtained at the same force in $B_0$ (see Results in main text), the proportion of nucleosomes in the fiber during the relaxation time course can be deduced from the torsional response of the same fiber in $B_0$. The curve (inset in Figure 6D, right panel, in main text) appears to be sigmoidal rather than exponential, suggesting that some breakage of nucleosome-nucleosome interactions occurs at early stages (Cui and Bustamante, 2000). Fitting with Equation (5) (Experimental Procedures in main text) resulted in $k_1=5.0*10^{-3} \sec^{-1}$ and $k_2=6.0*10^{-4} \sec^{-1}$, showing that the forward reaction is ~50 times faster than in $B_0$, whereas the rate of the backward reaction is similar. For a torque of 3 (±1) pN.nm/rad, we obtain $U=4 (±2) \text{ kT}$, a value lower than the 8 kT obtained in $B_0$. Assuming the positively-crossed nucleosome remains unfavourable by ~2 kT relative to the open state in physiological conditions (Sivolob and Prunell, 2004), one finally obtains $U \sim 6 (±2) \text{ kT}$. Based on Equation (S6), the barrier free energy $G^*$ is 21 (±3) kT, and the energy difference of the reaction intermediate relative to the ground state is ~25 (±5) kT.
References

Bancaud, A. , Conde e Silva, N., Barbi, M., Wagner, G., Allemand, J.-F., Mozziconacci, J., Lavelle, C., Croquette, V., Victor, J.-M., Prunell, A. and Viovy, J.-L. (2006). Structural plasticity of single chromatin fibers revealed by torsional manipulation. *Nat. Struct. Mol. Biol.* **13**, 444-450.

Bouchiat, C. and Mezard, M. (1998). Elasticity model of a Supercoiled DNA Molecule. Phys. Rev. Lett. **80**, 1556-1559.

Brower-Toland, B. D., Smith, C. L., Yeh, R. C., Lis, J. T., Peterson, C. L. and Wang, M. D. (2002). Mechanical disruption of individual nucleosomes reveals a reversible multistage release of DNA. Proc. Natl. Acad. Sci. USA **99**, 1960-1965.

Cui, Y. and Bustamante, C. (2000). Pulling a single chromatin fiber reveals the forces that maintain its higher-order structure. Proc. Natl. Acad. Sci. USA **97**, 127-132.

Pope, L. H. , Bennink, M. L., van Leijenhorst-Groener, K. A., Nikova, D., Greve, J. and Marko, J. F. (2005). Single chromatin fiber streching reveals physically distinct populations of disassembly events. Biophys. J. **88**, 3572-3573.

Sivolob, A. and Prunell, A. (2004). Nucleosome conformational flexibility and implications for chromatin dynamics. Philos. Transact. A Math. Phys. Eng. Sci. **362**, 1519-1547.
## I.3 Résultats et discussion

L'hystérésis de la réponse rotationnelle (figure 2A, dans l'article) d'une fibre de chromatine soumise à une forte contrainte positive indique qu'une fraction de cette contrainte positive est piégée dans une forme altérée du nucléosome. De la même manière que pour la largeur de la courbe longueur/torsion, seuls les nucléosomes régulièrement espacés contribuent à l'hystérésis. La déformation topologique est d'environ un tour positif par particule altérée.

Pour examiner le rôle des dimères H2A-H2B dans l'hystérésis, nous les avons arrachés à l'aide de l'héparine. L'hystérésis disparaît, et les courbes allers-retours se superposent au tracé le plus large. La transition entre le nucléosome et sa forme altérée est donc facilitée en présence d'héparine. On a ensuite ajouté des particules-cœur du nucléosome pour piéger les dimères. La fibre s'allonge alors d'une valeur correspondant au déroulement d'un tour d'ADN par nucléosome et son centre de rotation se décale vers celui de l'ADN nu : c'est la fibre de tétrasomes.

Les dimères H2A-H2B ont aussi été enlevés à l'aide de la protéine chaperon NAP-1, après avoir augmenté la force de manière transitoire. On obtient finalement la même fibre de tétrasomes que précédemment. Les dimères sont alors réincorporés en présence de NAP-1. La fibre retrouve sa longueur initiale et son comportement hystérétique. On en déduit que les dimères sont indispensables à l'hystérésis et qu'ils sont présents dans la forme altérée.

Le centre de rotation de la fibre de tétrasomes, proche de celui de l'ADN nu, reflète la capacité des tétrasomes à fluctuer entre deux conformations symétriques de déformations topologiques presque opposées : la transition chirale. Celle-ci a déjà été mise en évidence par la "technique des minicercles", notamment au moyen du relâchement avec la topoisomérase et de la microscopie électronique. Dans ce travail, nous avons apporté en plus, et pour la première fois, un support théorique à la transition chirale, basé sur une analyse des modes normaux de vibration du tétrasome. Il s'agit de mouvements atomiques coordonnés qu'on peut prédire à partir des structures cristallographiques. Plus ces mouvements impliquent un grand nombre d'atomes plus ils sont révélateurs de la dynamique des complexes. Un des modes principaux est directement impliqué dans la transition chirale : un des deux dimères H3-H4 tourne par rapport à l'autre autour de leur interface H3/H3.
On peut concevoir la transition nucléosome-forme altérée de la manière suivante (figure 7 dans l'article). Les dimères H2A-H2B commencent par se désolidariser du tétramère (H3-H4)$_2$. Ils restent cependant en interaction avec l'ADN au niveau des sites d'interaction. Le tétrasome effectue alors la transition chirale avec les dimères sur ses bras. La transition effectuée, un repliement se produit et les dimères reviennent interagir avec le tétramère, prolongeant ainsi la superhélice formée par le tétramère en forme droite. On obtient alors un nucléosome de chiralité inversée : le réversome. Son degré de compaction dépend des interactions créées aux nouvelles interfaces dimères-tétramère. Les queues de H3 sont maintenant sur les faces externes du réversome et n'interagissent plus avec les ADNs entrant-sortant, expliquant que le réversome soit dans l'état ouvert (déformation topologique de + 1 et non + 2).

L'ARN polymérase II développe suffisamment d'énergie (> 8 kT / tour) pour pouvoir réaliser à distance la transition nucléosome-réversome (6 kT/ tour). Elle a cependant besoin de la protéine FACT (FAcilitates Chromatin Transcription), chaperon de H2A-H2B, pour déstabiliser des nucléosomes reconstitués sur un ADN linéaire, où la contrainte de torsion positive poussée par la polymérase s'évacue immédiatement par rotation de l'extrémité libre du substrat. Le détachement des dimères constitue en effet une barrière énergétique pratiquement infranchissable à force ionique physiologique. Nous proposons que le réversome une fois formé, la polymérase passe facilement grâce à la déstabilisation des dimères inhérente à cette forme altérée du nucléosome. Ainsi la flexibilité chirale du tétramère pourrait constituer le levier permettant à la polymérase de déstabiliser H2A-H2B. Des facteurs d'elongation, comme FACT, pourraient être alors considérés comme des systèmes redondants destinés à la même fin.
## CHAPITRE 4 :
CONCLUSIONS ET
PERSPECTIVES
## Le nucléosome centromérique

L'interaction de CENP-A avec le chaperon RbAp46/48, en dehors de tout complexe, laisse imaginer un dépôt passif de ce variant de H3 sur l'ensemble du génome. Un enlèvement des nucléosomes CENP-A, malencontreusement formés sur les bras des chromosomes, est possible grâce à la moindre stabilité des nucléosomes CENP-A par rapport aux nucléosomes H3, que notre travail démontre. Une fois désassemblés, les produits CENP-A, vraisemblablement sous forme de CENP-A/H4, peuvent être redirigés vers le centromère, ou bien dégradés par le protéasome, comme chez la levure ou la mouche du vinaigre.

Un tel schéma ne peut cependant fonctionner que s'il existe un mécanisme de protection des nucléosomes CENP-A dans le centromère. Nous proposons que l'impossibilité pour H1 de lier les nucléosomes CENP-A rompt localement la superstructure de la chromatine dans les bras des chromosomes. La condensation serait moindre au voisinage des nucléosomes CENP-A, les rendant accessibles aux facteurs de désassemblage (RbAp46/48 ?). Dans les centromères, au contraire, de nombreuses autres protéines sont présentes, recrutées après l'assemblage des nucléosomes CENP-A, qui assurent la cohésion de la chromatine centromérique et la rendent imperméable aux facteurs de désassemblage.

Dans le prolongement direct de notre travail, il nous semble intéressant d'étudier l'effet *in vivo* des nucléosomes contenant une histone CENP-A mutée, dans laquelle les résidus 83 et 49, engagés aux SHL ± 2,5 et ± 6,5, seraient remplacés par des arginines (comme dans H3). Ces nucléosomes seraient alors plus stables, sans être toutefois l'être autant que les nucléosomes H3. Il serait alors possible de relier la mitose et ses diverses manifestations à un paramètre : la stabilité relative des nucléosomes CENP-A.

Dans la majorité des cancers du côlon, CENP-A est surexprimée et est corrélée avec l'aneuploïdie par le biais de la formation de néocentromères (Tomonaga et coll., 2003). Dans ce cas, le système de désassemblage et de dégradation est probablement dépassé. Une suractivation de ces mécanismes régulateurs de la présence de CENP-A dans les bras des chromosomes pourrait alors constituer une voie thérapeutique possible.
La fibre de chromatine

Grâce aux pinces magnétiques, nous avons obtenu une confirmation des trois conformations du nucléosome mises en évidence à l'origine par le système des minicercles. Ceci n'est d'ailleurs pas surprenant, car le comportement de la fibre de chromatine n'est, au moins à basse force ionique, que la somme des comportements individuels des nucléosomes : en effet, nous n'avons pas mis en évidence d'interactions nucléosome-nucléosome. Nous avons également confirmé la transition chirale du tétrasome et montré qu'elle sert de base structurale au tétrasome. La fonction du réversome semble aller de soi : assurer la rupture des interactions dimères-tétramère pendant la transcription et la réplication.

Des travaux sont actuellement en cours pour progresser encore dans notre compréhension de la dynamique de la fibre de chromatine et de la transition nucléosome-réversome. Des histones dépourvues de queues vont, nous l'espérons, nous permettre de déterminer le rôle de ces queues, ainsi que leurs modifications, dans chacun de ces mécanismes.

Nous allons d'autre part ajouter l'histone de liaison H5 sur les nucléosomes de la fibre de chromatine. Comme indiqué par le système des minicercles, la flexibilité torsionnelle de la fibre devrait en être encore accrue.
ANNEXE
**<u>ARTICLE IV</u>**:Characterization of nucleosomes consisting of the human testis/sperm-specific histone H2B variant (hTSH2B).

Li A., Maffey A.H., Abbott W.D., Conde e Silva N., Prunell A., Siino J., Churikov D.,
Zalensky A.O. & Ausió J.

*Biochemistry* (2005) **44**, 2529-2535
Characterization of Nucleosomes Consisting of the Human Testis/Sperm-Specific Histone H2B Variant (hTSH2B)†

Andra Li,‡ Allison H. Maffey,‡ Wade D. Abbott,‡ Natalia Conde e Silva,§ Ariel Prunell,§ Joseph Siino,||
Dmitrii Churikov,⊥ Andrei O. Zalensky,⊥ and Juan Ausió*‡

Department of Biochemistry and Microbiology, University of Victoria, Victoria, British Columbia, Canada V8W 3P6,
Institut Jacques Monod, Centre National de la Recherche Scientifique, et Universite Denis Diderot Paris 7,
2 Place Jussieu, 75251 Paris Cedex 05, France, Jones Institute for Reproductive Medicine, East Virginia School of Medicine,
Norfolk, Virginia 23507, and Division of Biological Sciences, University of California, Davis, Davis, California 95616

Received September 8, 2004; Revised Manuscript Received November 2, 2004

ABSTRACT: We have reported earlier the occurrence of a specific histone H2B variant in human testis and sperm. Here we have structurally characterized this protein, its association with the rest of the histone octamer, and its effects on the nucleosome structure. We show that a reconstituted octamer consisting of hTSH2B and a stoichiometric complement of histones H2A, H3, and H4 exhibits a lower stability compared to the reconstituted native counterpart consisting of H2B. In contrast, the hTSH2B containing octamers are able to form nucleosome core particles which are structurally and dynamically indistinguishable from those reconstituted with octamers consisting of only native histones. Furthermore, the presence of hTSH2B in the nucleosome does not affect its ability to bind to linker histones.

Replacement histone variants are coming of age as the
functional and structural role of several replacement H2A
and H3 variants has only recently started being elucidated
(1, 2). Histone H2A.X has been the focus of recent attention
(3, 4). In its phosphorylated form, it has been shown to play
a critical role in DNA repair and in meiosis (5–7). The
functional relevance of histone H2A.Z is underscored by its
indispensability for survival in many organisms (8), and this
variant is currently at the center of controversial structural
and functional studies (9–14). The newest discovered
member of the H2A family of variants, macroH2A (15), has
also been the focus of attention of recent functional and
structural work (12, 16–18). In a similar fashion, the
physiological implications of histone H3.3 have started to
unravel in the past few years (1). As the functional role of
these variants is being clarified, their structural implications
still remain largely elusive (19).

The structural variation that differentiates replacement core
histone variants from their canonical counterparts can affect
different regions of the histone molecule to different extents
(2). For instance, in histone H2A.Z, the main sequence
departure takes place at the C-terminal end of the molecule
which is the part that has been shown to play a critical role
for its indispensability (8). MacroH2A contains a large non-
histone domain which extends from its C-teminal end (15).

Histone H3.3 is different from H3.1 and H3.2 in only a few
amino acids which mainly affect the histone fold domain of
the molecule. CENP-A,<fnref n="1" /> a histone variant related to H3
which is part of the centromeric chromatin, exhibits an
extensive amount of sequence variation at its N-terminal
domain and to a lesser extent throughout the rest of the
molecule (20). In contrast to H2A and H3, not many histone
variants have been characterized for either core histone H2B
or core histone H4.

In the course of vertebrate spermatogenesis, the somatic
histones which are present at the onset of the differentiation
process undergo several transitions. These transitions occur
in those organisms in which the main protein chromosomal
component consists of protamines in their mature sperma-
tozoa (21, 22). This involves the replacement by different
testis-specific histone variants (6, 23, 24) before they are
finally replaced by protamines at the end of spermatogenesis.
Human spermatogenesis is rather unique in that the sper-
matozoa, in addition to a massive protamine presence, retain
10–15% of specific core histone variants (25–27) with
unknown biological function. One such histone (hTSH2B)
has recently been characterized (28). The main sequence
difference between hTSH2B and human somatic H2B occurs
at the N-terminal end of the molecule where three of the
four proline amino acids that are present in the somatic
counterpart of this histone are replaced by phosphorylatable
(S/T) amino acids in hTSH2B (see Figure 1 and ref 28).

In this paper, we report the structural characterization of
hTSH2B and of the complexes resulting from its association

<footnote>†This work was supported by Canadian Institutes of Health Research (CIHR) Grant MOP-57718 to J.A. and by National Institutes of Health Grant HD 39830 to A.O.Z.</footnote>

<footnote>* To whom correspondence should be addressed. Phone: 250-721 8863. Fax: 250-721 8855. E-mail: jausio@uvic.ca.</footnote>

<footnote>‡ University of Victoria.</footnote>

<footnote>§ Centre National de la Recherche Scientifique and Universite Denis Diderot Paris 7.</footnote>

<footnote>|| University of California, Davis.</footnote>

<footnote>⊥ East Virginia School of Medicine.</footnote>

<footnote n="1">¹ Abbreviations: CD, circular dichroism; CENP-A, centromeric protein A; EDTA, ethylenediaminetetraacetic acid; HPLC, high-performance liquid chromatography; hTSH2B, human testis-specific histone H2B; nNCP, native nucleosome core particles; PAGE, polyacrylamide gel electrophoresis; SDS, sodium dodecyl sulfate.</footnote>
<figure><img src="image_112.png" /><figcaption>FIGURE 1: (A) Protein sequence comparison of somatic human histone H2B (59), chicken histone H2B (60), and the human hTSH2B sperm histone variant (28). (B) Schematic representation of the secondary structure of the human H2B histone variants. Shown in black are the α-helical regions of H2B determined from the crystallographic analysis of the histone octamer (61) and the nucleosome (52). Also shown are the α-helical (gray) and β-sheet (checkered pattern) regions predicted from the primary structure of the protein (36). The numbers indicate the amino acid location in the sequences shown in (A).</figcaption></figure>

with other core histones (histone octamer) and in the nucleosome.

## MATERIALS AND METHODS

*Protein Expression and Purification.* Recombinant hTSH2B was expressed in *Escherichia coli* and purified as described previously (28).

*Gel Electrophoresis.* Sodium dodecyl sulfate (SDS)-polyacrylamide gel electrophoresis (PAGE) was performed as described by Laemmli (29). Two-dimensional gel electrophoresis was carried out as described elsewhere (30). Native 4.5% PAGE in 20 mM sodium acetate, 1 mM EDTA, and 40 mM Tris-HCl (pH 7.2) buffer for the analysis of nucleosome core particles was carried out according to Yager and van Holde (31). In some instances the buffer was changed to 0.5× TBE [45 mM Tris-borate, 1 mM EDTA (pH 8.3)]. Analysis of the restriction fragments in the nucleosome positioning experiments was carried out in 8% PAGE (20:1 acrylamide:bisacrylamide) and 8.3 M urea in 1× TBE [90 mM Tris-borate, 2 mM EDTA (pH 8.3)] as described in ref 32. DNase I footprinting analysis was carried out in 8% PAGE (10:1 acrylamide:bisacrylamide) and 7 M urea in 1× TBE (33).

*Circular Dichroism.* Circular dichroism (CD) analysis of chicken histone H2B and hTSH2B in 100 mM NaCl and 10 mM Tris-HCl (pH 7.5) buffer was carried out at 20 °C. The spectra were recorded on a Jasco-J720 spectropolarimeter as previously described (34). The amount of α-helix was quantified as described in ref 35.

*Secondary Structure Prediction.* The secondary structure of histones was predicted by SOPM (self-optimized prediction method) (36) available at the ExPASy Molecular Biology Server (http://au.expasy.org/).

*Histone Octamer Reconstitution.* Histone octamers were reconstituted from native chicken erythrocyte histones and FPLC-purified (28) recombinant hTSH2B following the procedure described in ref 37. After reconstitution, the octamers were fractionated by gel filtration, in 2 M NaCl and 10 mM Tris-HCl (pH 7.5) buffer, using a 1.2 × 120 cm Sephacryl S-300-HR (see the Results section for more details).

*Nucleosome Reconstitution.* Recombinant human hTSH2B was mixed with chicken native H2A, H3, and H4 histones in stoichiometric amounts, and histone octamers were reconstituted onto either a random sequence 146 bp obtained from chicken erythrocyte nucleosome core particles (33) or onto a 196 bp fragment with defined sequence. The latter was obtained by EcoRI digestion of a 208–12 DNA construct consisting of 12 identical copies of a 196 bp fragment of the 5S rRNA gene from the sea urchin *Lytechinus variegatus* connected by a 12 bp DNA linker consisting of an EcoRI site at each end (38). After digestion with EcoRI, the 196 bp DNA was HPLC purified using a 75 × 7.5 mm Bio-Gel DEAE-5-PW (Bio-Rad, Hercules, CA). Reconstitution was carried out by a 2 to 0 M stepwise salt gradient dialysis (39) in 10 mM Tris-HCl (7.5) and 0.1 mM EDTA (8.0) as described elsewhere (37). The reconstituted chromatin particles thus obtained (at a concentration of ca. 40–50 µg/mL) were dialyzed against the appropriate buffers (33, 40) and used for subsequent analytical ultracentrifuge analysis (41, 42).

*Sucrose Gradient Purification.* Reconstituted hTSH2B nucleosome core particles in 10 mM Tris-HCl (pH 7.5) and 0.1 mM EDTA were loaded onto a 5–20% sucrose gradient in 25 mM NaCl, 10 mM Tris-HCl (pH 7.5), and 0.1 mM EDTA and centrifuged at 134400g for 19 h in a Beckman SW41 rotor at 4 °C. Fractions (0.5 mL) were collected and analyzed by SDS–PAGE.

*Analytical Ultracentrifuge.* Reconstituted hTSH2B nucleosomes were dialyzed against buffers of varying ionic strength as described in Ausió et al. (33). Sedimentation velocity runs were performed in a Beckman XL-A ultracentrifuge using an An-55 Al aluminum rotor. Samples were loaded in double-sector cells with aluminum-filled Epon centerpieces (40). UV scans were taken at 260 nm and analyzed by the van Holde and Weischet (43) method using the XL-A Ultra Scan version 4.1 sedimentation data software (Borries Demeler, Missoula, MT). A value of 0.650 cm³/g was used for the partial specific volume of the nucleosome (33).

*DNase I Footprinting.* DNase I footprinting of reconstituted nucleosomes was carried out at 0 °C (33). γ-³²P-labeled nucleosomes at a concentration of approximately 0.14 µg/µL were digested with 0.1 unit/µL DNase I (Invitrogen)
(800 units of DNase I/mg of DNA). The digestion was carried out for 0, 5, 10, and 20 min in 12.5 mM NaCl, 4.5 mM Tris-HCl (pH 7.5), and 1 mM MgCl₂. The reaction was stopped by addition of EDTA to a final 25 mM and boiling for 1 min. Proteinase K (1.2 ng/µL) was then added, and the solution was incubated for 60 min at 37 °C. After digestion the samples were mixed with an equal volume of 98% deionized formamide, 0.4% bromophenol blue, 0.4% xylene cyanol, and 10 mM EDTA and loaded on 8% polyacrylamide sequencing gel containing urea. The dried gel was exposed overnight.

*Nucleosome Positioning.* The role of hTSH2B in the positioning of the nucleosome onto the 196 bp DNA fragment of the 5S rRNA gene of the sea urchin *L. variegatus* (38) was carried out as described elsewhere (44, 45).

*Histone H1 Binding.* γ-³²P-labeled 196 bp nucleosomes were titrated with increasing amounts of chicken erythrocyte histone H1 as described in ref 46. The electrophoretic mobility shift resulting from hisone H1 binding was analyzed by native 4.5% PAGE (see above).

*Relaxation of Nucleosomes on DNA Minicircles.* Nucleosome relaxation experiments were carried out as described previously using 351 and 356 bp pBR constructs (47).

## RESULTS AND DISCUSSION

*Histone hTSH2B Exhibits a Higher Helical Organization Than Histone H2B.* The sequence of histone hTSH2B is shown in comparison to human H2B and chicken H2B (see Figure 1). Chicken H2B has been used in the experimental part of this work as a nonvariant counterpart to hTSH2B.

As shown in Figure 1A, the most significant primary structure difference between the main human/chicken somatic H2B variants and hTSH2B occurs at the N-terminal domain of the molecule. It involves only a limited number (nine) of amino acids in the N-terminal domain in addition to several (four) amino acid replacements throughout the rest of molecule that involve G → S, N → S, and N → T transitions. The limited extent of this variation would allow the classification of hTSH2B as a homeomorphous replacement histone variant (48, 49).

The primary structure changes allow the prediction of a slight increase in the amount of secondary structure at the N-terminal end of hTSH2B (see Figure 1B). In fact, circular dichroism demonstrates a 6% increase in the α-helical content (Figure 2) as determined from the change in ellipticity at 222 nm (50). Careful inspection of the primary structure of hTSH2B (Figure 1A) shows that there is a replacement of two helix-breaker (proline) residues (present in both chicken and human somatic H2B) in the N-terminal domain of the hTSH2B. However, the predictive methods suggest that only an increase in β-turns occurs as a result of these substitutions (Figure 1B) and that the subtle increase in the α-helical content of this H2B variant may indeed occur in the histone fold.

*The hTSH2B Reconstituted Histone Octamer Exhibits a Lower Stability Than the Chicken H2B Reconstituted Histone Octamer.* Histone octamers were reconstituted using stoichiometric amounts of native chicken erythrocyte H2A, H3, and H4 and either native chicken H2B or hTSH2B, and the stability of the resulting complexes was assessed by gel filtration chromatography in 2 M NaCl (Figure 3) (51).

<figure><img src="image_113.png" /><figcaption>FIGURE 2: Circular dichroism spectra of histone H2B from chicken (line 2) in comparison to recombinant hTSH2B (line 1). The inset shows an SDS-PAGE of chicken hSTH2B (lane 1) in comparison to H2B (lane 2). CE is a chicken erythrocyte histone marker. Please note that hSTH2B comigrates with H2A on SDS-PAGE (28).</figcaption></figure>

<figure><img src="image_114.png" /><figcaption>FIGURE 3: (A) Gel filtration chromatography of reconstituted histone octamer complexes using a Sephacryl S-300-HR resin on a 1.2 × 120 cm column eluted at 4 °C at 5 mL per four fractions per hour with 2 M NaCl and 10 mM Tris-HCl (pH 7.5) buffer. The black circles correspond to complexes reconstituted with hSTH2B, and the open circles correspond to complexes reconstituted from native histones. (B) and (C) are the SDS-PAGE electrophoretic analyses of some of the fractions corresponding to the hTSH2B (B) and native histone (C) reconstituted complexes, respectively. The numbers under the lanes are those of the fractions analyzed.</figcaption></figure>

With the experimental protocol followed in this paper, histone octamers elute first, followed by H2A/H2B dimers and finally H3/H4 complexes (see Figure 3A,C). In 2 M NaCl, the native histone octamer [(H3–H4)₂ 2(H2A–H2B)] is in equilibrium with histone hexamers [(H3–H4)₂ (H2A–H2B)], tetramers [(H3–H4)₂], and dimers [(H2A–H2B)]. This equilibrium depends on the concentration of the starting sample, as well as on the pH and temperature (51).

As seen in Figure 3, while most of the complex reconstituted with native chicken histones elutes from the column as octamers, the histone complexes consisting of hTSH2B are eluted as a mixture in which the hTSH2B–H2A and H3–H4 complexes are the predominant forms. These results indicate that the hTSH2B-reconstituted histone complexes exhibit a reduced stability in 2 M NaCl at pH 7.5 and 4 °C
<figure><img src="image_115.png" /></figure>

FIGURE 4: (A) Native 4.5% PAGE analysis of nucleosomes reconstituted with native histone octamers (lane 2) or with hSTH2B (lane 3). Lane 1 is a CfoI cut pBR322 marker. The native gel was stained with ethidium bromide. (B) SDS-PAGE analysis of the histones from the reconstituted nucleosome core particles shown in (A). The assignment of lanes 2 and 3 is the same as in (A). Lane 1 is chicken erythrocyte histones used as a marker. The SDS-PAGE was stained with Coomassie blue.

when compared to the complexes consisting of the H2B counterpart. The interaction between the different histones is primarily determined by their histone fold domains. Within these regions, hTSH2B exhibits a sequence not unlike that for H2B (Figure 1). Therefore, in the absence of a crystallographic structure of the nucleosome (52, 53) for this variant, it is difficult to establish the reasons for the observed lower stability of the hTSH2B-containing octamer. However, the possibility that this is the result of yet unclear interactions between the various core histone tails cannot be disregarded (54).

Association of Stoichiometric Amounts of hTSH2B, H2A, H3, and H4 with 146 bp DNA Produces Stable Nucleosome Core Particles. In contrast to the results described above, when stoichiometric amounts of histones in 2 M NaCl were mixed with 146 base pair random sequence DNA in the same salt concentration and sequentially dialyzed down to low ionic strength (39), nucleoprotein complexes were obtained that exhibit the same electrophoretic mobility in native gels as nNCP (Figure 4A). Furthermore, the reconstituted nucleoprotein complexes sedimented in sucrose gradients as nNCP (Figure 5A,B) and exhibited a stoichiometric histone composition (Figures 4B and 5C).

Sedimentation velocity analysis in the analytical ultracentrifuge confirmed these results (Figure 6). As seen in this figure, the sedimentation coefficient of the nucleosome core particles reconstituted from hTSH2B exhibits an ionic strength dependence very similar to that of the nucleosomes reconstituted with the native H2B counterpart or with nNCP themselves (33). Furthermore, the DNase I footprinting analysis (Figure 7) shows that hTSH2B-containing nucleo-

<figure><img src="image_116.png" /></figure>

FIGURE 5: (A) Sucrose gradient fractionation of nucleosome core particles (NCPs). The solid line corresponds to hTSH2B-reconstituted NCPs, and the dashed line corresponds to chicken erythrocyte native NCPs. (B) Several fractions from the main peak were analyzed by native 4.5% PAGE and exhibited mobility identical to that of the *native* nucleosome core particles (nNCP) isolated from chicken erythrocyte chromatin. (C) Two-dimensional PAGE analysis of fractions 7 + 8. The first dimension was acetic acid-urea-PAGE (AU), and the second was SDS-PAGE (SDS).

<figure><img src="image_117.png" /></figure>

FIGURE 6: NaCl dependence of the sedimentation coefficient ($s_{20,w}$) of nucleosomes reconstituted with native histone octamers (open circles) or with hSTH2B (black circles). Sedimentation velocity experiments were carried out at 40000 rpm at 20 °C at different NaCl concentrations in 10 mM Tris-HCl and 0.1 mM EDTA (pH 7.5) buffer.

nucleosomes are structurally similar to nucleosomes reconstituted with the native H2B counterpart or nNCP.

Histone hTSH2B Does Not Affect the Mobility of the Histone Octamer in the Nucleosome and Does Not Change the Nucleosomal DNA Topology nor Affects the Binding of Histone H1 to the Nucleosome. It has recently been shown that the nucleosomes consisting of histones bearing *sin* mutations and H2A.Z histone variants affect the mobility of the histone octamer (55). It has also been shown that the N-terminal tail of histone H2B plays a role in the sliding of histone octamers reconstituted onto linear DNA templates (56) and in the structural and dynamic polymorphism of nucleosomes reconstituted onto circular DNA templates (47). As the largest extent of variation in hTSH2B occurs at the N-terminal end of the molecule (Figure 1), we therefore decided to check whether any of these parameters are affected by the presence of this H2B variant.
<figure><img src="image_118.png" /></figure>

FIGURE 7: DNase I footprinting analysis of nucleosomes reconstituted with native histone (H2B) or with hTSH2B (hSTH2B) octamers, in comparison to chicken erythrocyte native nucleosome core particles (nNCP). The open triangles indicate the increasing time of digestion. M = φX174 Hinfl digested marker. The numbers on the left-hand side represent the base pair numbers. The asterisk on the right-hand side points to an artifact band in nNCP resulting from the occurrence of partial (ca. 125 bp) subnucleosome core particle contamination resulting from overdigestion of DNA during the process of nucleosome core particle preparation.

To examine if nucleosome positioning was affected by the presence of the histone variant hSTH2B, nucleosomes were reconstituted onto a 196 bp DNA fragment of the 5S rRNA gene from the sea urchin *L. variegatus* (38). The nucleosome positioning was then compared to that of a nucleosome reconstituted on the same DNA template but consisting of native H2B. The results are shown in Figure 8. In native PAGE, both nucleosomes (see Figure 8A, lanes 3 and 4) appeared to consist of a major band and some minor bands with lower electrophoretic mobility (one for the native nucleosome and two for the variant nucleosome) corresponding to alternative positions. Incubation of these nucleosomes at different temperatures did not result in significant differences in this pattern (results not shown). A major and minor positioning was confirmed in both instances when the positioning was more accurately determined (Figure 8B; see also Figure 8C). The major position (approximately 90%) was found to be 5 ± 2 bp to 151 ± 2 bp, and the minor position (approximately 10%) was 47 ± 2 bp to 193 ± 2 bp (see Figure 8C) in agreement with previous results (45, 57).

To assess whether hTSH2B would modulate nucleosome dynamics, nucleosomes were reconstituted onto 351 and 356 bp pBR DNA minicircles, relaxed with topoisomerase I, and the equilibrium products analyzed. When performed on a 351–366 bp minicircle series, this analysis has allowed one to determine the relative accessibility of minicircle-borne nucleosomes to three distinct conformations, depending on the path of the entry/exit DNAs: negatively or positively

<figure><img src="image_119.png" /></figure>

FIGURE 8: (A) Native 4.5% PAGE (0.5× TBE) analysis of nucleosomes reconstituted onto a 196 bp fragment of the 5S rRNA sea urchin gene using native H2B (lane 3) or hSTH2B (lane 4) reconstituted histone octamers in comparison to nNCP (lane 2). Lane 1 is a CfoI cut pBR322 marker. The numbers on the left-hand side of the panel indicate the base pair size of the DNA fragments. The roman numerals point to different translational positions of the histone octamer. NP = nucleosome particle; D = free DNA. (B) Determination of the translational positioning of the native H2B and hSTH2B reconstituted nucleosomes on the 196 bp DNA fragment. The region of DNA directly associated with the histone octamer was determined by digestion of a gel-purified, end-labeled, deproteinized 146 bp micrococcal nuclease-resistant fragment with different restriction enzymes: DraI (lane 1); AluI (lane 2); MspI (lane 3); SauIII A1 (lane 4). Lane 5 is the 146 bp micrococcal nuclease resistant undigested fragment. M = φX174 Hinfl digested marker. The numbers indicate the base pair size of the DNA fragments. (C) Schematic representation of the main translational nucleosome positions on the reconstituted 196 bp DNA fragment. The ellipsoid black line represents the predominant position, and a weaker position is depicted by the gray line ellipsoid. The heavy line indicates the 5S rRNA coding sequence, and the open box indicates the intragenic TFIIIA binding site.

crossed and uncrossed (47). Data obtained with these two minicircle sizes were sufficient to conclude that hTSH2B- and regular H2B-containing nucleosomes were indistinguishable with respect to their respective conformational dynamics (results not shown).

Because of this lack of effect of the hTSH2B variant on the trajectory of the DNA entering and exiting the nucleosome, it was not surprising to find that binding of histone H1 (linker histones) to the nucleosome is not affected by the presence of hTSH2B. Gel shift analysis showed that H1 binds to the reconstituted nucleosomes with the same affinity and stoichiometry regardless of the presence or absence of hTSH2B (results not shown).

## CONCLUDING REMARKS

Our results indicate that the human sperm histone variant hTSH2B can be reconstituted to form nucleosomes that
exhibit an almost identical structural conformation with nNCP. Thus, it is very likely that this variant exists in a nucleosome organization in the selected chromatin loci with which it appears to be associated within the human sperm nuclei (28).

It may be proposed that most of the structural effects associated to the chromatin regions enriched with TSH2B could be the result of posttranslational modifications, most likely phosphorylation at several sites that are unique to this variant (28). These modifications may affect the physical parameters (stability, dynamics) of the chemically modified nucleosome or create an alternative histone code.

The lack of stability of the hTSH2B histone octamer in the absence of DNA contrasts with the otherwise indistinguishable properties of nucleosome core particles reconstituted with these octamers. While this observation is puzzling, it is interesting to note that two of the mutations in hTSH2B at position 77 (G → S) and 86 (N → S) are in the histone fold domain and remarkably close to the Y → G Sin mutation at position 86 of yeast histone H2B. Importantly, this mutation has been shown to bypass the requirement for Swi-Snf in yeast (58). Thus, it is possible that the transitions observed in the histone fold of the variant H2B histone have a similar behavior.

## ACKNOWLEDGMENT

We thank Ron M. Finn for skillful computer assistance in the preparation of the figures.

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