Optical tweezers use a focused laser beam to physically hold and move microscopic dielectric beads. Ashkin and colleagues reported the first use of what is now commonly referred to as an optical trap: a tightly focused beam of light capable of holding microscopic particles stable in three dimensions [19]; see [20] for a recent overview of the physical principles behind optical tweezers. In the late 1980s, Ashkin and colleagues first applied the technology to the biological sciences, using it to trap individual tobacco mosaic virus particles, Escherichia coli bacteria and various eukaryotic cells [21,22]. Throughout the 1990s and afterwards, researchers like Carlos Bustamante and Steven Block pioneered the use of optical trap force spectroscopy to characterize molecular-scale biological motors [23]. The first application to chromatin fibers appeared in 2000 [24] and other insightful experiments rapidly followed (reviewed in [25,26]). “Chromatin optical tweezers” in PubMed now retrieves 20 references, only half of which are primary experimental papers actually dealing with nucleosomes or chromatin fibers.

Magnetic tweezers use external magnets to physically pull/rotate microscopic paramagnetic beads to which one attaches DNA molecules or chromatin fibers. Typical applications are single-molecule micromanipulation and studies of force/torque-regulated processes. Forces are typically on the order of a few piconewtons. Due to their simple architecture, magnetic tweezers are one of the most popular and widespread biophysical techniques [27]. They were first used to handle a single DNA molecule and measure its elasticity [28] and response to torsion [29], before being applied to study single nucleosomal arrays [30,31]. “Chromatin magnetic tweezers” in PubMed now retrieves 15 references, of which a third are primary experimental papers actually dealing with chromatin fibers.

The first single-molecule study of chromatin assembly was carried out by Viovy's group [33]. They used real-time video-microscopy to follow the shortening (as a consequence of DNA wrapping around the histone core that occurs during nucleosome formation) of a single λ-DNA molecule attached at one end to a glass surface, the other end being stretched by the flow of cell-free extracts in the chamber. Other approaches to address chromatin assembly have been setup by Bennink et al. [36] (Figure 2e) and Leuba et al. [30] (Figure 2d) by attaching a bead to the free extremity of the DNA/chromatin fragment for subsequent manipulation of the assembled fibers. These studies showed that the kinetics of assembly is dependent on the applied force; nucleosome formation is inhibited at forces >10 pN.

Recently, nucleosome assembly has been studied on topologically-constrained DNA to more closely mimic the in vivo situation, where chromatin fibers are topologically constrained in loops [57]. Assembly was achieved using chicken erythrocyte core histones and histone chaperone Nap1. Only partial assembly was observed on the topologically-constrained DNA tethers, with much more complete assembly on unconstrained (nicked) DNA. To verify the hypothesis that the lack of full nucleosome assembly was due to compensatory accumulation of positive supercoiling in the rest of the template, experiments were performed in which the positive stress was mechanically relieved by rotating the external magnetic field; indeed, such rotation led to resumption of assembly. The positive supercoiling density that led to stalling of assembly was estimated to be in the range of 0.025–0.051.

Chromatin disassembly under applied force has been mostly studied using optical tweezers [24,35,37,40,41] (Figure 2a,b) and only more recently with magnetic tweezers [31] (Figure 2c). Note that the first pulling studies on single chromatin fibers were done by AFM [58,59], but it turned out to be quite tricky to interpret due to interactions of the nucleosomes with the glass surface [4]. Indeed, saw-tooth patterns were observed in force-distance curves, similar to those expected from unravelling of individual nucleosomes (and later seen in OT experiments, see below). Careful analysis of the data, however, revealed that the drops in force observed were simply due to detachment of individual nucleosomes from the surface of the AFM cells [4]. Note that getting rid of such surface interaction artefacts is also one of the major issues in OT and MT experiments, particularly when playing with histones, which are highly positively charged, and thus very sticky to surfaces. One should be careful to check that discrete signals such as saw-tooth patterns or steps are not due to nucleosome desorption from the surface of the beads; this can usually be done by repeating the experiments at various forces and in various salt conditions, and also by adding naked DNA spacer at each end of the reconstituted nucleosome array (to prevent histone sticking to surfaces; see below). Finally, correspondence between the number of steps and the number of nucleosomes on one hand, and the step size and the nucleosomal DNA length on the other hand, is a good indication of the relevance of the experiment [31,35,37].

Force measurements in OT setups have revealed the existence of internucleosomal attraction that maintains the compacted chromatin structure under physiological condition [24]. These studies showed that, in the absence of any chromatin remodeling factors, the fibers undergo reversible stretching at forces <∼20 pN and irreversible unfolding at forces >∼20 pN [35,37,40]. A step-wise release of the DNA/histone interactions was observed by Wang and colleagues [37] (Figure 3) and recently confirmed on single mononucleosomes [44]. Various chromatin remodelers use the energy of ATP hydrolysis to facilitate the process in vivo, lowering the unfolding energy barriers [31,41]. Finally, it was recently possible to measure, in DNA unzipping experiments, the relative strengths of the histone/DNA interactions along the length of nucleosomal DNA [47].

Three years after Leuba/Zlatanova's MT studies of chromatin assembly, Bancaud et al. succeeded in using MT to apply torsion to single chromatin fibers, showing that chromatin can accommodate surprisingly large amount of torsional stress, either negative or positive, without much change in its extension [31,53]. In these two studies, nucleosome arrays were reconstituted on 2 × 18 tandem repeats of the 208 bp 5S nucleosome positioning sequence. They were subsequently ligated at each end to a naked DNA spacer (introduced into the construct to prevent histone sticking to surfaces) followed by a DNA sticker labeled appropriately for attachment of one end of the construct to the coated bottom of the flow cell and of the other end to a paramagnetic bead (Figures 2c). The rotation of the magnets, hence of the paramagnetic bead, exerts torsion on the attached fiber. The fiber torsional behavior is described, at a given force, by its length-versus-rotation plot (Figure 4a).

The response of the corresponding naked DNA, obtained following salt dissociation of the histones, displays the signature of an intact (non-nicked) single duplex DNA. The central (plateau-like) part of the DNA response curve corresponds to the elastic regime, and the quasi-linear compactions on either side to the plectonemic regimes (formation of positive or negative plectonemes upon introduction of positive or negative rotations). The lower compaction on the negative side is due to a force-dependent DNA melting at high negative torsions, which prevents further increase of the torque on the molecule and prevents further plectoneme formation. Compared to DNA, chromatin is shorter and its center of rotation is shifted to negative values (see double arrow in Figure 4a). The shift is the expected consequence of the absorption of approximately one negative superhelical turn per nucleosome (actually ΔLk_p ≈ −0.8 ± 0.1; see below), the observed shortening (∼50 nm, i.e., 150 bp per nucleosome) resulting from DNA wrapping around the histone core. Therefore, compared to DNA of the same length, the fiber in the elastic regime appears to be extremely torsionally flexible, i.e., it can absorb large amounts of torsion without much shortening. This large torsional resilience was interpreted as a reflection of the nucleosome dynamic equilibrium between the three conformational states previously identified in minicircles studies [60–62] (Figure 4c). More surprisingly, these chromatin fibers, after extensive positive supercoiling, display no nucleosome loss but rather a hysteretic behavior in their mechanical response to torsion [53] (Figure 4b). This hysteresis was interpreted as a consequence of the trapping of positive turns in individual nucleosomes through their transition to an altered form, originally called reversome (for reverse nucleosome) and later termed R-octasome (for right-handed nucleosome containing the full complement– 8–of histones) [63]. This structure is reminiscent of the previously documented R-tetrasome (a right-handed sub-nucleosomal particle containing only the H3/H4 histone tetramer), which occurs as a result of a chiral transition of the tetrasome [64] (Figure 4d).

To better characterize how the chromatin fiber may respond to mechanical constraints, some elastic parameters have to be determined, including bending flexibility, torsional flexibility and stretching modulus. Micromanipulation approaches coupled with modeling have been crucial in estimating these parameters both for DNA and chromatin. However, one should keep in mind that, beside divergences arising from experimental and data analysis differences, DNA sequence effects [65] and geometrical variability [66,67] can greatly influence DNA and chromatin elastic parameters, respectively. Hence, the given values are mostly to be taken as orders of magnitude (Table 2). It is also worth noticing that, whereas forces are easily and precisely evaluated by OT as well as MT, torques remained more difficult to access [68,69]. The two devices can indeed be used to twist the molecule: in optical tweezers, light polarization is used to apply a torque, while in magnetic tweezers the magnetic field imposes the angular position of the molecule. In both cases, the torque in the range of pN.nm is far more difficult to measure than the stretching force. Remarkably, Sun and colleagues recently succeeded in measuring the torque exerted on a chromatin fiber by using a new MT setup that manipulates a ferromagnetic rod coupled to a magnetic bead in the field of a cylindrical magnet [70].

The persistence length of a polymer, A, a measure of bending flexibility (the smaller A, the more flexible), has been determined for DNA in various experiments, leading to a consensus value of ∼50 nm (150 bp) at physiological ionic strength [71,72]. The values for chromatin are more divergent, from ∼ 30–50 nm estimated from single-molecule stretching [24,31,35], recombination frequencies [73] or cross-linking probabilities [74] to more than 200 nm from recent in situ hybridization experiments [75]. Remarkably, such different values are all consistent with theoretical models and could be explained by polymorphic connection geometry between nucleosomes in the fiber [66,67].

The torsional persistence length C, a measure of twisting flexibility, has been estimated for naked DNA by various bulk experiments to be ∼70–100 nm (200–300 bp) [76,77]; this value is consistent with single-molecule data [29] analyzed through an elastic model [78]. The torsional persistence length of the chromatin fiber, measured only recently, has a surprisingly low value of 5 nm [31]; this is almost 20-times lower than that of naked DNA, and also lower than the value predicted from analytical models of chromatin fibers [66]. However, this unexpected experimental result is easily explained by the conformational nucleosome dynamics (see discussion above), and is fully consistent with new chromatin models that include this nucleosome property [31].

The stretching modulus σ, a measure of stretching elasticity (i.e., the propensity of a polymer to reversibly extend under a given tension - the smaller σ, the more extensible), is ∼1100 pN for naked DNA, as estimated from single-molecule experiments [79–81]. For the chromatin fiber, a much lower value of ∼ 5–8 pN has been derived from the same kind of experiments [24,31]; such value is close to the predicted one [66] and probably reflects the flexibility of the linkers as well as the weak internucleosomal interactions disrupted during the mechanical extension of the fiber at low ionic strength. Confirming this view, the stretching modulus is indeed greatly enhanced in high salt conditions where the fiber adopts a more compacted state [35,82].

Whereas MT and OT provide a unique tool for probing the mechanical properties of DNA-protein complexes, in particular those of nucleosomes, they remain of little help in characterizing chromatin fiber structure. As a matter of fact, force-extension diagrams require an underlying model for their interpretation. Of note, the Hookian behavior of regular arrays of nucleosomes, recently evidenced by van Noort and colleagues, has been claimed by this group to match a solenoid structure for a 197-bp repeat length array structure but a zig-zag structure for 167-bp fiber [55]. In their model, they assumed a priori a solenoid structure for the 197-bp repeat length array from which they deduced a nucleosome-nucleosome stacking energy as large as ∼14 kT, despite the fact that nucleosomes are loosely stacked in their solenoid structure. This stacking energy is obtained by fitting the force-extension plots with a mechanical model involving eight parameters, five of which are free. In this model, the Hookian behavior is related to the elasticity of the disordered histone tails which are assumed to bridge the stacked nucleosomes, until they eventually break at forces >3 pN in absence of linker histone.

At odds with this modeling, an alternative interpretation has been proposed (Victor et al, submitted) that assumes a zig-zag structure for both 167-bp and 197-bp fibers [83,84]. In this model, the Hookian behavior is related to a gradual unwrapping of the nucleosomal DNA, by consecutively breaking the histone/DNA contacts at the Super Helix Locations: SHL ± 6.5, then SHL ± 5.5, and eventually SHL ± 4.5. Note that the Hookian behavior as well as the corresponding spring stiffness of the fibers, either 167-bp or 197-bp, are well fitted with the so-called “tunable spring” model [66], in which the fiber stiffness is completely determined by the fiber geometry and the linker DNA persistence length. There is only one free parameter, namely the free energy of the SHL ± 5.5.

Remodeling has been also addressed using MT [46] and OT [43,45] (see [85] for a recent review). To date, only one family of remodelers has been studied by single-molecule manipulations, specifically the S. cerevisiae RSC and SWI/SNF complexes of the Swi2/Snf2 family. These remodelers are ATP-dependent DNA translocases. They contain two DNA-binding domains: one stationary tracking domain which remains in a fixed position relative to the histone octamer, and the other alternating between one of two conformations. The two domains bind the DNA at two different sites on the duplex, stabilizing a transient DNA loop, resulting in a temporary shortening of the molecule. Note that this shortening is what is monitored by MT. The inchworm-like action of both domains imparts DNA translocation.

The first single-molecule observation of DNA translocation by a remodeler has been performed in the group of Vincent Croquette and David Bensimon in collaboration with Tom Owen-Hughes [46]. Using MT with naked DNA, they observed at forces <1 pN that a single RSC complex causes transient shortening of the DNA, which results from the formation of a negatively supercoiled loop. At the same time, Bustamante's group used OT to monitor the action of both RSC and SWI/SNF complexes on single nucleosomes in real time [45]. This group worked at forces >3 pN in order to avoid loop formation within bare DNA; in this way they could study the translocase activity specifically related to nucleosome remodeling in isolation. Their setup gives access to the physical parameters associated with translocation except for the twist, namely speed, force and processivity. Importantly, DNA translocation has been observed to occur at constant speed under varying forces, suggesting that remodelers function as motors rather than as ratchets [76].

Wang's group recently used a sophisticated “unzipping” technique to analyse single nucleosome products after remodeling by SWI/SNF [43] (see Figure 5 for details). The general mechanism that emerges from these single-molecule studies is a “DNA inchworm” model involving both twist and loop propagation (∼1 bp of twist for 10 bp of translocation) [85]. This model explains why the displacements after remodeling that are measured by Wang's group are much smaller than the loop sizes measured by the other two groups. Indeed, the inchworm-like action of both DNA-binding domains generates large loops that are likely to be resorbed substantially before imparting DNA translocation. As a result, the displacements are expected to be much smaller than the loop sizes. Single-molecule studies with the three other families–Iswi, Nurd/Mi-2/Chd and Ino/Swr1–are anticipated, with a special attention to the ISWI complexes.