The existence of a 30‐nm fiber as a basic folding unit for DNA packaging has remained a topic of active discussion. Here, we characterize the supramolecular structures formed by reversible Mg2+‐dependent self‐association of linear 12‐mer nucleosomal arrays using microscopy and physicochemical approaches. These reconstituted chromatin structures, which we call “oligomers”, are globular throughout all stages of cooperative assembly and range in size from ~50 nm to a maximum diameter of ~1,000 nm. The nucleosomal arrays were packaged within the oligomers as interdigitated 10‐nm fibers, rather than folded 30‐nm structures. Linker DNA was freely accessible to micrococcal nuclease, although the oligomers remained partially intact after linker DNA digestion. The organization of chromosomal fibers in human nuclei in situ was stabilized by 1 mM MgCl2, but became disrupted in the absence of MgCl2, conditions that also dissociated the oligomers in vitro. These results indicate that a 10‐nm array of nucleosomes has the intrinsic ability to self‐assemble into large chromatin globules stabilized by nucleosome–nucleosome interactions, and suggest that the oligomers are a good in vitro model for investigating the structure and organization of interphase chromosomes.
An in vitro system for chromatin packaging shows that short array of nucleosomes has the intrinsic ability to self‐assemble into large chromatin globules devoid of folded 30‐nm fibers.
Nucleosomal arrays self‐associate into large globular structures in a Mg2+‐dependent manner.
The globular structures range in size from ˜50 to 1,000 nm in diameter, sediment between ˜5,000–350,000 S, and contain ˜1–400 Mb DNA/structure.
The packaged nucleosomal arrays adopt extended 10‐nm fibers, not folded 30‐nm fibers.
Nucleosomal and H1‐arrays can fold into 30‐nm fibers in vitro, but only under very specific ionic conditions.
Both linker DNA and attractive nucleosome–nucleosome interactions contribute to the formation and stability of the globular structures.
In a typical human nucleus, about two meters of DNA is packaged into nucleoprotein structures termed chromatin and then into chromosomes. At its core, a chromosome consists of a single ~50‐ to 250‐Mb DNA molecule assembled into a chain of ~105–106 nucleosomes. The nucleosome is composed of ~147 bp of DNA bound to an octamer of core histone proteins (H2A, H2B, H3, H4) (Luger et al, 1997). Nucleosomes repetitively spaced along DNA at ~160‐ to 210‐bp intervals and connected by stretches of free linker DNA are called nucleosomal arrays (Hansen, 2002). Chromatin refers to nucleosomal arrays bound to linker histone H1 and/or other chromosome‐associated proteins. The long linear chromatin molecule is condensed extensively within an interphase chromosome, such that chromosomal DNA can fit inside the nucleus, and during mitosis, the long chromatin chain is further packaged into a mitotic chromosome (Ohta et al, 2010; Maeshima et al, 2014b; Hirano, 2015).
Physicochemical studies of short nucleosomal arrays, typically 12–60 nucleosomes in length, have shown that chromatin condensation in vitro is salt dependent and driven by both intra‐fiber and interfiber nucleosome–nucleosome interactions (Hansen, 2002; Pepenella et al, 2014). At very low salt concentrations (e.g. < 0.5 mM Mg2+), nucleosomal arrays have an extended beads‐on‐a‐string conformation termed the 10‐nm fiber (Hansen, 2002). As salt initially is titrated into solution (e.g. 0.5–2 mM Mg2+), nucleosomal arrays fold into helical structures that are ~30–40 nm in diameter, generically referred to as the “30‐nm fiber”. Folding is mediated by intra‐fiber interactions involving the H4 N‐terminal tail domains of one nucleosome with the surface acidic patch domains of neighboring nucleosomes (Luger et al, 1997; Kalashnikova et al, 2013). Folded 30‐nm fibers are stabilized by the H1 linker histones (Hansen, 2002). The structure of the 30‐nm fiber has been proposed to be a one‐start solenoid, a two‐start zig‐zag, or a heteromorphic combination of the two (Robinson & Rhodes, 2006; Grigoryev et al, 2009). At higher divalent cation concentrations (e.g. ≥ 3 mM Mg2+), short nucleosomal arrays self‐associate to form large “oligomers” that pellet immediately in a microfuge (Hansen, 2002). While self‐association is mediated by interfiber nucleosome–nucleosome interactions distinct from those involved in folding (Hansen, 2002), nothing is known about the structure, subunit organization, and assembly of the chromatin oligomers due to their extreme size and the lack of available quantitative physicochemical assays.
The widely held paradigm for chromosome structure and assembly holds that the chromosomal fiber first forms a helical 30‐nm chromatin structure (Finch & Klug, 1976; Langmore & Paulson, 1983; Woodcock et al, 1984; Widom & Klug, 1985; Dorigo et al, 2004; Gilbert et al, 2004; Schalch et al, 2005; Robinson et al, 2006; Song et al, 2014), mimicking the folding of a nucleosomal array as salt is added into solution. A central premise of this paradigm is that the 30‐nm fiber is a requisite folding intermediate in the assembly and maintenance of condensed interphase and mitotic chromosomes. However, small‐angle X‐ray scattering (SAXS) experiments indicated that no repetitive structures beyond the 10‐nm fiber were present in the chromatin of isolated nuclei (Joti et al, 2012) or mitotic chromosomes (Nishino et al, 2012). Similarly, cryo‐electron microscopy (EM) studies of interphase (Bouchet‐Marquis et al, 2006; Gan et al, 2013) and mitotic chromosomes (Eltsov et al, 2008), and electron spectroscopic imaging studies of mouse cells (Fussner et al, 2012), visualized packed 10‐nm fibers, but no folded 30‐nm fibers, even in the highly condensed heterochromatin regions. More recent super‐resolution imaging also showed heterogeneous groups of nucleosomes called “clutches” (Ricci et al, 2015). Based on these results, an alternative model has been proposed in which chromosomes are assembled through long‐range interactions of extended 10‐nm fibers to form an interdigitated polymer melt‐like structure (Maeshima et al, 2010, 2014b). In the established paradigm, formation of condensed domains beyond the 30‐nm fiber occurs through continuous twisting and coiling of the chromosomal chain of nucleosomes (Alberts et al, 2007). Conversely, chromosome conformation capture experiments (e.g. 3C, HiC) suggest that interphase chromosomes are organized into 0.1‐ to 10‐Mb‐sized globular structures such as “topologically associating domains” (TADs) (Dixon et al, 2012; Nora et al, 2012; Sexton et al, 2012; Dekker et al, 2013; Rao et al, 2014; Eagen et al, 2015), which further self‐associate into discrete chromosomal territories (Cremer & Cremer, 2010). Similarly, globular chromatin domains of ~1 Mb in size have been observed using fluorescence microscopy imaging, as foci of DNA replication via pulse labeling (Albiez et al, 2006). Altogether, the new data support a view of chromosome structure and assembly that fundamentally differs from the textbook model. This in turn requires a reexamination of the relationships between chromatin folding and oligomerization in vitro and chromosome assembly in vivo.
The present studies aim to improve our understanding of chromatin oligomerization and its relevance to chromosome structure and organization. We hypothesize that the fiber–fiber interactions that mediate the oligomerization of short nucleosomal arrays in vitro are equivalent to the long‐range fiber–fiber interactions that help assemble and organize higher‐order chromatin domains within the nucleus. A direct prediction of this hypothesis is that the chromatin oligomers will possess many of the same structural features as an intact interphase chromosome. To test our hypothesis and its predictions, we have used fluorescence light (FM) and transmission electron (TEM) microscopy, sedimentation velocity analytical ultracentrifugation (SV‐AUC), and SAXS to quantitatively characterize the structure of the oligomers formed by salt‐dependent self‐association of 12‐mer nucleosomal arrays, and micrococcal nuclease to determine the role of linker DNA in oligomer stability. We also examined the salt dependence of chromatin organization and compaction in situ. The in vitro studies have yielded novel information regarding the size, morphology, subunit packaging, and mechanism of assembly of the nucleosome oligomers and have revealed the effects of linker histones on the oligomerization transition. The in vitro data indicate that the ability to self‐assemble through interdigitated packaging of 10‐nm fibers into globular structures with diameters of ~50–1,000 nm is an intrinsic property of an array of nucleosomes. In the case of the in situ experiments, low salt conditions that disassemble oligomers in vitro disrupt heterochromatin and euchromatin compartments and cause extensive chromatin decondensation in isolated nuclei. Collectively, our data support a new paradigm in which long‐range interactions of the 10‐nm chromatin fiber are important determinants of the structure and organization of interphase chromosomes. Our results further suggest that the chromatin oligomers provide a good in vitro model system for investigating eukaryotic chromosome structure and function.
Nucleosomal arrays self‐associate into large globular oligomers
The standard assay for nucleosomal array oligomerization is differential centrifugation (Schwarz & Hansen, 1994; Tse & Hansen, 1997). This assay determines the fraction of the chromatin sample that pellets after a short microfuge spin. Figure EV1A shows a control differential centrifugation experiment performed with linear 12‐mer 601 (Lowary & Widom, 1998) and 5S (Simpson et al, 1985) nucleosomal arrays reconstituted to an average of 11–12 nucleosomes per DNA template. In both cases, all of the nucleosomal arrays in 0–2 mM MgCl2 remained in the supernatant, indicating that no oligomerization had occurred under these conditions. About 10% of the samples pelleted in 3 mM MgCl2, 30% in 4 mM MgCl2, 60% in 4.5 mM, and 90% by 6 mM MgCl2. Altogether, the pelleting curves for the 601 and 5S nucleosomal arrays were superimposable. While these data indicate that both the 601 and 5S nucleosomal arrays formed rapidly sedimenting oligomers in ≥ 3 mM MgCl2, this assay yields no structure‐based information.
To determine oligomer size and morphology, samples were analyzed by FM and TEM. Representative FM images of the 601 oligomers obtained in 4.5 and 10 mM MgCl2 are shown in Fig 1A. In both salt conditions, the oligomers were globular and had diameters ranging from several hundred to ~1,000 nm. Moreover, the ~1,000‐nm particles were the largest oligomers present in 4.5 and 10 mM MgCl2, suggesting that there is an upper size limit to the self‐association process. No particles were observed in control images taken at 0–2.5 mM MgCl2 (Fig 1B), consistent with the lack of oligomerization seen by the differential centrifugation assay (Fig EV1A). Of note, the size and morphology of the 5S oligomers assembled in 5 and 10 mM MgCl2 (Fig EV1B) were similar to those of the 601 oligomers in Fig 1A. Thus, the formation of large globular oligomers was not critically dependent on the nearly perfect nucleosome positioning of the 601 nucleosomal arrays. The 601 oligomers next were characterized by TEM as described by Woodcock et al (1991). This protocol involves glutaraldehyde fixation to preserve macromolecular interactions and gross structure, adsorption to a carbon grid, negative staining, and dehydration. Figure 1C shows representative images of the oligomers visualized in 4.5 and 10 mM MgCl2. In both salt conditions, the predominant oligomers observed were globular and ~400 nm in diameter (Fig 1C, left panels), in agreement with the FM results. Darker regions in the TEM images result from pooling of the negative stain, indicating that the surfaces of the oligomers were uneven and textured (Fig 1C, left panels). The edges of the oligomers were irregular, and in some cases, smaller globules could be seen at the periphery of the larger particles (Fig 1C, left panels). At higher magnification, individual nucleosomes could be seen in the interior of the oligomers as bright 10‐nm‐diameter particles that were closely packed and in physical contact (Fig 1C, right panels). No regular repetitive folded structures such as the 30‐nm fiber could be identified at the higher magnifications.
The FM studies (Fig 1) suggest that a population of oligomers exists in solution at any given salt concentration and that the oligomers reach a maximum size of about 1,000 nm in ≥ 4.5 mM MgCl2. An ideal complementary technique to address these questions under native solution conditions and quantitatively characterize macromolecular self‐association is SV‐AUC (Schuck, 2013). However, in the past, it has not been possible to study oligomerization using SV‐AUC and the standard absorption optical system because the oligomers pellet before data can be collected. To overcome this hurdle, we employed the interference optical system, which measures concentration based on refractive properties of the sample and collects a complete concentration versus radial distance dataset in ~2–3 s (compared to about ~90 s for the absorbance optics) (Rogge & Hansen, 2015). The scans obtained from a typical interference SV‐AUC experiment in 10 mM MgCl2 are shown in Appendix Fig S1. Under these conditions, the samples formed broad but discrete boundaries during sedimentation, qualitatively indicating that there was a heterogeneous population of oligomers with upper and lower size limits.
To quantitatively analyze the boundaries, we first calculated the weight‐averaged second moment sedimentation coefficient (ssm) of the 601 oligomers as a function of MgCl2 (Fig 2A). In 4.0 mM MgCl2 (~30% oligomerized), the ssm was ~30,000S (S, a unit of time equal to 10−13 s). The ssm increased to ~100,000S in 4.5 mM MgCl2 (~60% oligomeric) before plateauing at ~200,000S in 5–10 mM MgCl2 (75–100% oligomeric). By comparison, bacteriophage T7 (875S) (Dubin et al, 1970) and amyloid fibrils (3,000S) (MacRaild et al, 2003) are the largest biological assemblages previously characterized by SV‐AUC. Thus, our studies have substantially increased the size threshold for SV‐AUC experiments. The plateau in the ssm at ≥ 5 mM MgCl2 was reproducible (Fig 2A, inset). In 4 mM MgCl2, the ~70% of the sample that did not pellet during centrifugation sedimented as monomeric folded 35–45S nucleosomal arrays (Appendix Fig S2). The existence of only nucleosomal array monomers and large oligomers at intermediate extents of self‐association demonstrates that oligomerization is highly cooperative. The boundaries of the experiment shown in Fig 2A next were analyzed by time‐derivative method to obtain the distribution of sedimentation coefficient g(s*) (Stafford, 1992). In this analysis, the subsequent scan in a pair of scans is subtracted from the previous scan to determine the change in sample concentration over time. Because the oligomers were extremely large and the sedimentation times very short, the sedimentation coefficient distributions were not expected to be affected by diffusion. In 4.0 mM MgCl2, the sedimentation coefficient distribution of the 601 oligomers ranged from ~5,000 to 60,000S, with a peak in the plot at ~25,000S (Fig 2B). In 4.5 mM MgCl2, the distribution of sedimentation coefficients was shifted to ~25,000–130,000S, and the peak in the g(s*) plot increased to ~70,000S. In 5 mM MgCl2, the 601 oligomers sedimented from ~40,000 to 250,000S, with a peak in the g(s*) plot at ~110,000S. In 8 and 10 mM MgCl2, the g(s*) plots were very similar and yielded sedimentation coefficient distributions from ~40,000 to 350,000S and a peak at ~130,000–140,000S. The overlapping g(s*) plots in 8 and 10 mM MgCl2 (Fig 2B) are consistent with the plateau observed in the ssm versus MgCl2 plot (Fig 2A) and indicate that the 601 oligomers reach a maximum average size of ~140,000S and a maximum absolute size of ~350,000S under ionic conditions that promote self‐association of 100% of the sample. When the 601 nucleosomal arrays were exposed to 8 mM MgCl2 and the sample returned to TE buffer, the oligomers dissociated into a homogeneous population of unfolded ~27–29S monomers (Fig EV2), demonstrating that all steps in Mg2+‐induced assembly of the oligomers are reversible (also see Schwarz et al, 1996).
The microscopy studies indicate that the oligomers are globular throughout the assembly process. Consequently, a number of physical properties of the oligomers can be calculated from the measured sedimentation coefficients assuming a spherical structure (Table 1). The smallest oligomers detected during the early stages of self‐association in 4 mM MgCl2 sedimented at ~5,000S, while the largest oligomers observed in 8 and 10 mM MgCl2 sedimented at ~350,000S. The 5,000S oligomers were estimated to consist of 4.5 × 103 nucleosomes and have a mass of 1 × 109 Da. The Stokes radius, equivalent to the radius of a sphere calculated from the frictional coefficient, was 65 nm and the 5,000S oligomers contained ~1‐Mb DNA/oligomer. At the other extreme, the 350,000S oligomers were estimated to have 2 × 106 nucleosomes and a mass of 5 × 1011 Da. The Stokes radius was ~500 nm and the 350,000S particles contained ~450‐Mb DNA/oligomer. The estimated Stokes radii are in the range determined by FM and TEM under the same ionic conditions (Fig 1). The calculated mass and Mb DNA/oligomer indicate that the globular oligomers assembled in vitro as a function of increasing salt spanned the size range of the chromatin domains found in interphase nuclei (Dixon et al, 2012; Nora et al, 2012; Sexton et al, 2012; Dekker et al, 2013; Rao et al, 2014; Eagen et al, 2015).
Nucleosomal array monomers are packaged as extended 10‐nm fibers, not folded 30‐nm fibers
An important question is whether the nucleosomal array subunits are packaged within the oligomers as 10‐ or 30‐nm fibers. The subunit structure of the oligomers was determined by SAXS, which is able to detect periodic structures in non‐crystalline biological materials in solution (Roe, 2000; Maeshima et al, 2014a) and, in particular, has proven useful for determining the repetitive structures within the bulk chromatin of both mitotic chromosomes (Nishino et al, 2012) and intact nuclei (Joti et al, 2012). As in the pioneering work of Langmore and co‐workers (Langmore & Paulson, 1983), scattering data are presented as plots of log(I × S2) versus 1/S) [I, intensity; S, scattering vector (1/nm)]. A peak in the curve is indicative of a periodic structure in the sample with a diameter of inverse of S (1/S nm) (Roe, 2000; Maeshima et al, 2014a). We first analyzed the structure of 601 nucleosomal arrays in 0–2.5 mM MgCl2. In TE buffer without MgCl2, the nucleosomal arrays sedimented at ~27S (Fig EV3), indicating that they were monomeric and in the extended 10‐nm beads‐on‐a‐string conformation (Hansen, 2002). The scattering curve of the nucleosomal arrays in 0 mM MgCl2 (Fig 3A) had a broad peak between 1/S = 10–20 nm resulting from the distances between the nucleosomes in the extended conformation, and a minor peak at ~6 nm corresponding to the width of the nucleosome disk (face‐to‐face positioning) (see also Fig 3C). No peak at ~30–40 nm due to folded nucleosomal arrays (i.e. 30‐nm fibers) was present under these low salt conditions, consistent with the SV‐AUC data. Of note, the experimental scattering curve is very similar to the modeled scattering profile for an extended dinucleosome (Fig 3D). Addition of salt to the solution causes the nucleosomal arrays to rapidly equilibrate between 10‐nm and 30‐nm conformations (Hansen, 2002), resulting in a progressively increased integral distribution of sedimentation coefficients in 1 and 2.5 mM MgCl2 (Fig EV3). Importantly, a small peak at ~40 nm corresponding to folded nucleosomal arrays appeared in the scattering curves in 1 and 2.5 mM MgCl2 (arrow in Fig 3A), in addition to the 10‐ to 20‐nm and 6‐nm peaks that were seen for the extended 10‐nm fiber. A prominent ~40‐nm peak was also present in the calculated scattering profile when either solenoid or zigzag 30‐nm structures made from the 12‐mer nucleosomal arrays were modeled (Fig 3E and F). The experimental (Fig 3A) and modeling (Fig 3E and F) data provide important controls showing that SAXS is a valid assay for nucleosomal array folding, including being able to detect even small amounts of folded 30‐nm structures when they are present.
The scattering curves obtained for the 601 oligomers assembled in 5 and 10 mM MgCl2 are shown in Fig 3B. In the range of 1/S > 20 nm, the slope of the curve was sharply downturned. This feature was observed in previous SAXS analyses of mitotic chromosomes (Nishino et al, 2012) and isolated nuclei (Joti et al, 2012), and results from the very large size of the oligomers. No ~40‐nm peak was observed in the oligomer samples, indicating that the nucleosomal array subunits were not in a folded 30‐nm conformation. The broad peaks at 1/S = 10–20 nm and 6 nm seen for the extended arrays (Fig 3A) were still present in the oligomeric samples, although between 1/S = 4–30 nm the slope of the curve was sharply positive (Fig 3B). For proteins, the upward slope is characteristic of a denatured polypeptide chain (Doniach, 2001), implying that the nucleosomal arrays remain somewhat mobile within the oligomers. Collectively, the SAXS analyses of monomeric and oligomeric nucleosomal arrays indicate that the oligomers consist of packaged 10‐nm fibers.
We next asked whether the packaged linker DNA within the oligomers could be completely digested by MNase and if so, whether the oligomers remained intact after digestion. Nucleosomal arrays were incubated in digestion buffer containing either 0.5 or 5 mM MgCl2. The arrays were ~100% monomeric in 0.5 mM MgCl2 and ~85% oligomeric in 5 mM MgCl2 as judged by the differential centrifugation assay (Fig 4A). For the oligomers in 5 mM MgCl2, the presence of only mononucleosomal DNA in the deproteinized MNase digest indicated that the linker DNA was completely accessible and digested to completion under the conditions used (Fig 4B). When the oligomers in 5 mM MgCl2 were digested to completion with MNase and examined by FM, we still observed oligomeric particles, but both the size (Fig 4C) and the number (Fig 4A) of the oligomers were reduced compared to the undigested control. Thus, both attractive nucleosome–nucleosome interactions (Liu et al, 2011) and linker DNA contribute to oligomer stability.
Linker histones modulate oligomer structure, assembly, and subunit packaging
Linker histones are the most abundant chromatin‐associated proteins in most eukaryotic cells (Woodcock et al, 2006) and promote chromatin condensation in vitro (Hansen, 2002) and in vivo (Fan et al, 2005; Hashimoto et al, 2010). We therefore determined how linker histones affected nucleosomal array oligomerization. When characterized by the differential centrifugation assay, the plot for the H1‐bound nucleosomal arrays was shifted to the left relative to that obtained for the nucleosomal arrays alone, although the shapes of the curves otherwise were very similar (Fig EV1A). While this indicates that linker histones in some way influence oligomerization, to more quantitatively address this question the H1‐bound nucleosomal arrays were characterized by microscopy, SV‐AUC, and SAXS as a function of salt.
Typical FM images obtained in 4 and 5 mM MgCl2 for the 601 H1‐oligomers are shown in Fig 5A. The H1‐oligomers visualized in 4 and 5 mM MgCl2 (~75% and 90% oligomerized, respectively) were globular and ~100–300 nm in size. Control FM images in 0, 1, and 3 mM MgCl2 are shown in Fig 5B. Very small particles were faintly visible in 1 and 3 mM MgCl2 but not at the lower salt concentration. In 4 mM MgCl2 the predominant oligomers observed by TEM were globular and had diameters of ~200–300 nm (Fig 5C, left), consistent with the diameters seen in the FM images under the same conditions (Fig 5A). As with the nucleosomal array oligomers (Fig 1C, right panels), at higher magnification one could see individual closely packed nucleosomes, but no regular repetitive folded structures such as the 30‐nm fiber (Fig 5C, right panel).
The ssm of the H1‐oligomers as a function of MgCl2 is shown in Fig 6A. The ssm in 3 mM MgCl2 was ~650S, which increased to ~13,000S in 4 mM MgCl2. While these sedimentation coefficients are very large, the ssm of the H1‐oligomers was smaller than the ssm of the nucleosomal array oligomers under equivalent extents of self‐association (Fig EV4A), consistent with the FM analysis (compare Figs 1A and 5A). Above 5 mM MgCl2, the oligomers pelleted immediately and the ssm was too large to measure, even with the interference optical system (Fig 6A). Analysis by the time‐derivative method yielded the distribution of H1‐oligomer sedimentation coefficients present at each salt concentration. In 3 mM MgCl2, the sedimentation coefficient distribution ranged from ~200 to 1,400S, with a peak in the plot at ~600S (Fig 6B and C). In 3.5 mM MgCl2, the distribution of observed sedimentation coefficients was shifted to ~600–3,000S, and the peak in the g(s) plot increased to ~1,100S (Fig 6C). In 4 mM MgCl2, the range of H1‐oligomer sedimentation coefficient increased significantly, extending from ~2,000 to 50,000S with a peak in the g(s) plot at ~12,000S (Fig 6B). To directly determine the effect of H1 on oligomer size, the oligomer sedimentation coefficient distributions determined in 4 mM MgCl2 in the absence and presence of H1 were converted to Mb DNA/oligomer (as in Table 1). In both cases, the DNA content of the H1‐oligomers ranged from < 1‐ to ~30 Mb/oligomer. However, the average for the H1‐oligomers was 4‐Mb DNA/oligomer compared to 12‐Mb DNA/oligomer for the nucleosomal array oligomers under these conditions (Fig EV4B).
Given that H1 stabilizes folded 30‐nm structures in vitro (Hansen, 2002; Robinson & Rhodes, 2006; Li & Zhu, 2015), we wanted to determine whether the subunit structure of the H1‐oligomers was the 30‐nm fiber. As a control, we first compared the results obtained by SV‐AUC and SAXS for H1‐bound nucleosomal arrays in 0–2.5 mM MgCl2. In 0 mM MgCl2, the H1‐arrays sedimented at ~32S (Fig EV5), indicating that they were monomeric and extended (Carruthers et al, 1998). The scattering curve of the H1‐arrays in 0 mM MgCl2 resembled that of parent nucleosomal arrays under the same conditions, with a broad peak at 10–20 nm, a minor peak at ~6 nm, but no peak at ~30–40 nm corresponding to folded fibers (Fig 7A). This indicates that the H1‐bound arrays in the absence of salt had an extended structure with 10‐ to 20‐nm internucleosomal distances in solution. In 1 mM MgCl2, the H1‐arrays began to form folded structures, as indicated by the increase in the maximum sedimentation coefficient to 45S (Fig EV5). Under these conditions, a significant peak at 30–40 nm appeared in the SAXS profile (arrow in Fig 7A), consistent with the similar peak seen for the modeled 30‐nm fibers (Fig 3E and F). SV‐AUC analysis of the H1‐array samples in 2.5 mM MgCl2 indicated two major populations of fibers; one sedimented at ~32–55S, while the other sedimented from ~90 to 130S. The former corresponds to a distribution of folded monomers, while the latter is indicative of small oligomers that do not pellet at 662 g. Importantly, the SAXS profile in 2.5 mM MgCl2 was dominated by a major peak at 30–40 nm. A comparison of the SAXS data for monomeric nucleosomal arrays (Fig 3A) and H1‐bound arrays (Fig 7A) demonstrates that H1 stabilizes folded 30‐nm fibers, as has been observed by SV‐AUC (Fig EV5) and other techniques (Robinson & Rhodes, 2006; Li & Zhu, 2015).
SAXS analyses of the H1‐oligomers assembled in 5 and 10 mM MgCl2 are shown in Fig 7B. In the range of 1/S > 20 nm, the slopes of the curves were sharply downturned due to the large size of the oligomers. The ~30‐ to 40‐nm peak seen in the 1 and 2.5 mM MgCl2 control samples was absent in the H1‐oligomers. Between 1/S = 4–10 nm, the slopes of the scattering curves were flat and prominent peaks at 6 and 11 nm were apparent (Fig 7B). The 6‐ and 11‐nm peaks have been proposed to come from edge‐to‐edge and face‐to‐face positioning of nucleosomes, respectively (Langmore & Paulson, 1983) (see Fig 3C). Several important conclusions can be drawn from these data. First, the 12‐mer nucleosomes within the H1‐oligomers were not folded into regular 30‐nm fibers. Second, H1 abolished the upward slope between 1/S = 4–10 nm seen in the plots of the nucleosomal array oligomers (Fig 3B), suggesting tighter subunit packing. Lastly, H1 sharpened the diffuse 6‐ and 11‐nm peaks present in the control H1 samples (Fig 7A) and the nucleosomal array oligomers (Fig 3B). The scattering curves for isolated native chicken chromatin fragments (which contain heterogeneous linker DNA lengths and near stoichiometric levels of H1) were similar to those obtained for the 601 H1‐arrays, but with lower concentration of MgCl2 (Fig 7C), indicating that SAXS results were not dependent on the regular positioning of the 601 arrays. We next modeled the SAXS curve for in silico oligomers composed of 100 randomly and tightly packed 12‐mer nucleosomal arrays in the 30‐nm conformation (Fig 7E and F). The nucleosome concentration of the in silico oligomers was about ~0.5 mM, comparable to that of mitotic chromosomes (Hihara et al, 2012). The scattering profile of the in silico oligomers closely resembled the experimental scattering profile for the H1‐oligomers, except for the presence of peaks at ~30–40 nm in the modeled curve (arrow in Fig 7F). The modeling results further support the conclusion that the subunit structure of the H1‐oligomers is not the folded 30‐nm fiber.
Low salt disassembles higher‐order chromatin structures in nuclei in situ
Our in vitro studies suggest that the oligomers formed by nucleosomal arrays in the absence and presence of histone H1 are good in vitro models for interphase chromosome structure in nuclei. Given that the oligomers are stable in 5 mM MgCl2, but not in < 1 mM MgCl2 (Fig EV1), we predicted that chromatin structure and organization in situ would appear normal in 5 mM MgCl2, but would be disrupted by exposure to EDTA, which reduces the MgCl2 concentration to essentially zero. To test our hypothesis, the effects of MgCl2 on the higher‐order chromatin structures present in situ in isolated HeLa nuclei were determined using FM and SAXS. To visualize nuclear structure, isolated nuclei were exposed to DAPI and analyzed by FM. In 1 and 5 mM MgCl2, all of the nuclei examined showed bright regions resulting from areas of intense DAPI staining (heterochromatin‐rich) interspersed with dark regions that were less concentrated with DAPI (euchromatin) (Fig 8A, center and right panels). The DAPI‐intense regions were especially prominent near the nuclear periphery and around nucleoli. These images show that canonical interphase chromatin organization is retained in 1 and 5 mM MgCl2. In distinct contrast, uniform DAPI staining was observed in nuclei exposed to EDTA (Fig 8A, left panel), demonstrating that higher‐order chromatin organization in situ was disrupted in the absence of cations. Quantitation of the nuclear sizes indicated that the nuclei in EDTA on the average were twice as large as those in 1 and 5 mM MgCl2 (Fig 8A), indicative of extensive chromatin decondensation. Independently, SAXS analysis of HeLa nuclei was used to examine bulk interphase chromatin as a function of salt. The scattering profiles in 1 and 5 mM MgCl2 (Fig 8B, center and right panels) closely resembled those observed previously for intact nuclei (Joti et al, 2012), and the H1‐oligomers (Fig 7B), with a prominent downturned slope in the range of 1/S > 15 nm and peaks at 6 and 11 nm. This indicates that the in vitro assembled oligomers and HeLa nuclear chromatin are packaged similarly in the presence of MgCl2. When the isolated HeLa nuclei were incubated in EDTA buffer, the scattering profile (Fig 8B, left panel) changed to one that more closely resembled those of the nucleosomal array and H1‐nucleosomal array monomers (Figs 3A and D, and 7A). It should be noted that 30‐ to 40‐nm peak seen in HeLa nuclei in EDTA buffer most likely results from the spatial constraint of the extensively decondensed chromatin present under these conditions, not from the presence of folded 30‐nm chromatin fibers (e.g. see Fig 4 in Eltsov et al, 2008). The FM and SAXS results together demonstrate that higher‐order chromatin structure in isolated nuclei in situ is disassembled in the absence of cations, conditions that also dissociate oligomeric nucleosomal arrays in vitro. These results further indicate that HeLa nuclear chromatin in situ is stabilized by lower MgCl2 concentration (~1 mM) than the nucleosomal array oligomers and H1‐oligomers, probably because the nuclear chromatin is at much higher concentration and complexed with more proteins than the model systems used in the in vitro experiments. The differential centrifugation assay of isolated HeLa chromatin is a good agreement with this finding, that is, the MgCl2 concentration at which 50% of the sample pellets (Mg50) for the oligomerization of the HeLa chromatin is ~1 mM MgCl2, compared to ~2.5 mM MgCl2 for H1‐nucleosomal arrays and ~4 mM MgCl2 for nucleosomal arrays (Appendix Fig S3 and Fig EV1).
The oligomers characterized in our studies recapitulate key aspects of interphase chromosome structure and organization. Interphase chromosomes occupy discrete territories within the nucleus, and the territories appear globular when visualized by fluorescence in situ hybridization (Cremer & Cremer, 2010). Studies using chromosome conformation capture technology and its variants suggest that the long linear chromosomal chain of nucleosomes (Valouev et al, 2011) is assembled into arrays of higher‐order globular chromatin domains, often called topologically associating domains. Globular chromosomal domains also have been observed by fluorescence microscopy (Albiez et al, 2006). A typical chromatin domain contains ~0.1–10 Mb of DNA (Dekker et al, 2013; Rao et al, 2014; Eagen et al, 2015). In the case of in vitro oligomerization, the early stages of nucleosomal array self‐association produce globular particles containing ~1‐ to 10‐Mb DNA/oligomer (Fig 2, Table 1). At their maximum, the globular oligomers are the size of chromosomes. When H1 is bound to nucleosomal arrays in vitro, the early stages of self‐association produce globular oligomers consisting of ~0.5‐ to 1.0‐Mb DNA/oligomer, quite similar to the average size observed for the chromatin domains in nuclei (Dekker et al, 2013; Rao et al, 2014; Eagen et al, 2015). These observations indicate that the globular oligomers characterized in our studies span the size range of the chromatin domains present in nuclei, and suggest that the oligomers are good in vitro model systems for studying interphase chromosome structure and organization.
The single nucleosome fiber that makes up an interphase chromosome behaves as a flexible random coil polymer chain, for example (Barbieri et al, 2014). Thus, widely separated stretches of chromosomal nucleosomes will be able to interact over Mb distances, and the self‐association of 12‐mer nucleosomal arrays should be an in vitro reflection of the self‐interactions of a condensed chromosomal fiber. The biological relevance of nucleosome oligomerization was addressed experimentally by examining the effect of MgCl2 concentration on the structure of isolated human nuclei. In our hypothesis, the conditions that disassemble the oligomers in vitro should disrupt long‐range chromosomal fiber interactions and perturb higher‐order chromatin structure in the nucleus. Our FM and SAXS analyses of isolated nuclei demonstrate that the heterochromatin and euchromatin compartments present in ~1 mM MgCl2 in situ were abolished by exposure to EDTA, concomitant with extensive chromatin decondensation (Fig 8). In recent related studies, chromatin condensation within permeabilized cell nuclei increased dramatically as the divalent cation and polyamine concentration were increased from 0 mM into the physiological range (Visvanathan et al, 2013), and hypotonic treatment (low salt) in living mammalian cells caused extensive chromatin decondensation (Albiez et al, 2006). Collectively, the in situ results indicate that very low salt concentrations that destabilize nucleosome oligomers in vitro also destabilize the chromatin domains and higher‐order chromatin structures in isolated nuclei. This in turn suggests that core and linker histone‐mediated long‐range nucleosome–nucleosome interactions contribute significantly to interphase chromosome structure and organization. Of note, histone‐mediated long‐range nucleosome–nucleosome interactions also appear to be applicable to mitotic chromosome structure. Isolated mitotic chromosomes behave like interphase chromatin in the presence and absence of salt. Without MgCl2, the chromosomes are highly swollen and the chromosomal fibers are stretched into 10‐nm‐like fibers (Earnshaw & Laemmli, 1983; Eltsov et al, 2008; Takata et al, 2013), whereas in the presence of MgCl2, the chromosomes are highly condensed (Earnshaw & Laemmli, 1983; Eltsov et al, 2008; Takata et al, 2013). Mg2+‐dependent mitotic chromosome decondensation and condensation are highly reversible (Hudson et al, 2003).
The widely held paradigm for chromosomal DNA packaging in vivo maintains that helical 30‐nm chromatin structures are requisite folding intermediates in the establishment of higher‐order chromosomal domains, that is, the nucleosome chain must first fold into 30‐nm fibers before assembling into successively more condensed chromatin structures (for reviews, e.g. Hansen, 2002; Robinson & Rhodes, 2006; Grigoryev & Woodcock, 2012; Maeshima et al, 2014b; Li & Zhu, 2015). This view is based in large part on the fact that 10‐nm fibers initially fold into 30‐nm fibers when salt is titrated into solution in vitro. However, there is very little direct evidence for the existence of bulk 30‐nm fibers in chromosomes. Although a ~30‐ to 40‐nm peak was observed in SAXS studies of living cells, isolated nuclei, and mitotic chromosomes (Langmore & Paulson, 1983; Joti et al, 2012; Nishino et al, 2012), if the nuclei and mitotic chromosomes were first stripped of contaminating ribosomes, the ~30‐ to 40‐nm peak was absent (Joti et al, 2012; Nishino et al, 2012). Consistent with these results, cryo‐EM studies of interphase chromatin and mitotic chromosome (Bouchet‐Marquis et al, 2006; Eltsov et al, 2008; Gan et al, 2013) and electron spectroscopic imaging studies of mouse nuclei (Fussner et al, 2012) visualized packaged 10‐nm fibers, but no folded 30‐nm fibers, even in the heterochromatin regions. Recent studies using super‐resolution imaging also observed heterogeneous groups of nucleosomes (Ricci et al, 2015). Collectively, these studies argue for a new chromosome assembly paradigm that does not require folding into 30‐nm fibers. Our SAXS analysis of the packaging of nucleosomal array oligomers provides biochemical evidence in support of an alternative model. In our control SAXS experiments, folding of monomeric arrays into 30‐nm structures in 2.5 mM MgCl2 was indicated by the appearance of a peak in the scattering profile at ~30–40 nm (Figs 3A and 7A). However, this peak was noticeably absent in the SAXS profiles of both the H1‐bound and H1‐free oligomers, indicating that the subunit structure of the oligomers is not the 30‐nm fiber. Instead, the lack of observed repetitive structures above 20 nm indicates that the subunits adopt extended 10‐nm structures. We thus conclude that when studied in vitro nucleosomal arrays and H1‐chromatin only form 30‐nm fibers under very specific ionic conditions. In addition, given that the peaks at 6 and 11 nm arise from face‐to‐face and edge‐to‐edge nucleosome–nucleosome interactions, respectively (Fig 3C) (Langmore & Paulson, 1983), and the fact that linker DNA contributes to oligomer stability (Fig 4), we propose that the individual 10‐nm nucleosomal array subunits interdigitate to form a polymer melt‐like structure when packaged into the oligomers. Our studies ultimately provide a rigorous biochemical basis for how long‐range chromatin condensation can occur without first forming 30‐nm fibers.
Oligomerization absolutely requires the core histone tail domains of the nucleosome. Tailless nucleosomal arrays do not self‐associate (Schwarz et al, 1996; Dorigo et al, 2003; Gordon et al, 2005), even in the presence of linker histones (Carruthers & Hansen, 2000). When the H2A, H2B, H3, and H4 tail domains are deleted individually, in each case the Mg50 is shifted toward higher MgCl2 concentrations (Dorigo et al, 2003; Gordon et al, 2005). Removal of the H4 tail has the largest effect on the Mg50 (Dorigo et al, 2003; Gordon et al, 2005), suggesting that it is a particularly important determinant. The need for more MgCl2 when the tails are deleted implies that they function through an electrostatic‐based mechanism. We speculate that the tails at least in part bind to linker DNA and screen negative charge, promoting interdigitated nucleosome–nucleosome interactions and oligomer assembly. In support of this hypothesis, the H4 and H3 tails can be cross‐linked in trans to the DNA of other arrays within the packaged oligomers (Zheng et al, 2005; Kan et al, 2009). Moreover, linker DNA contributes significantly to oligomer stability (Fig 4), as would be expected if it was the binding site for the tails. The H4 tail domain mediates 30‐nm fiber folding by binding the acidic patch present on the surface of neighboring nucleosomes (Kalashnikova et al, 2013). However, oligomerization and 30‐nm folding are mediated by distinct molecular mechanisms, and in particular, oligomerization does not require H2A/H2B (Schwarz et al, 1996). The involvement of the H4 tail in both folding and oligomerization, acting through different mechanisms, provides a potential explanation for why the subunits of the oligomers adopt the 10‐nm fiber structure. That is, under conditions where the H4 tails mediate oligomerization, they cannot simultaneously interact with the acidic patch of neighboring nucleosomes to promote 30‐nm folding. Certain tail post‐translational modifications affect the Mg50, including H4 acetylation (Shogren‐Knaak et al, 2006; Szerlong et al, 2010), H4 sumoylation (Dhall et al, 2014), and both H2A and H2B ubuiquitination (Jason et al, 2001; Fierz et al, 2011). Nucleosome‐depleted regions such as those found near promoters and enhancers, and the core histone variant H2A.Z (Fan et al, 2002), move the Mg50 toward higher MgCl2 concentrations relative to nucleosomal arrays alone. The macroH2A variant (Muthurajan et al, 2011) and chromatin architectural proteins such as MeCP2 (Nikitina et al, 2007) and Sir3p (McBryant et al, 2008) all lower the MgCl2 concentration at which oligomerization occurs. The large number of physiologically relevant determinants of oligomerization suggests that the equilibrium between local and global nucleosome–nucleosome interactions in any given region of a chromosomal fiber is a tightly regulated point of regulatory control.
Materials and Methods
Nucleosomal arrays were reconstituted from 12 × 207 bp 601 or 5S sequence DNA and purified chicken erythrocyte histone octamers using salt dialysis as described (Rogge et al, 2013). The DNA concentration was 0.5 mg/ml, and molar ratio of histone octamers to DNA repeats was 1.0–1.1. The extent of template saturation achieved after reconstitution was determined by sedimentation velocity in low salt (Hansen & Lohr, 1993). The nucleosomal arrays used in our studies sedimented between 26–29S in TE buffer (Figs EV2 and EV3), indicating that about half of the samples contained 11 nucleosomes per template and the other half contained 12 nucleosomes per template (Hansen & Lohr, 1993). H1‐nucleosomal arrays were assembled by mixing purified chicken H1.0 (Talbert et al, 2012) and reconstituted nucleosomal arrays at one H1 per DNA repeat in 50 mM NaCl, followed by dialysis against TE buffer overnight and sedimentation velocity in low salt to determine the extent of H1 binding (Lu et al, 2009).
Fluorescence light microscopy of nucleosomal arrays and isolated nuclei
Two micrograms of nucleosomal array and H1‐nucleosomal array samples was incubated with the desired concentration of MgCl2 for 15 min on ice and spun onto poly‐l‐lysine‐coated coverslips by centrifugation at 2,380 g for 15 min. The arrays were gently fixed with 2% formaldehyde (Wako, Japan) in the same buffer. After DNA staining with 4′,6‐diamidino‐2‐phenylindole (DAPI), the coverslips were sealed with a nail polish. Optical sectioning images with 200 nm thickness were recorded with DeltaVision microscope (Applied Precision) and deconvolved to remove out of focus information. Projected images with five sections were shown.
For nuclei imaging, HeLa nuclei isolation was performed as described previously (Takata et al, 2013). Isolated nuclei were suspended in H10Mg5 buffer (10 mM HEPES–KOH [pH 7.4] and 5 mM MgCl2) and attached to poly‐l‐lysine‐coated coverslips by centrifugation at 2,380 g for 15 min. The nuclei on the coverslips were gently placed in the following three buffers: H10Mg5, H10Mg1 [10 mM HEPES–KOH (pH 7.4) and 1 mM MgCl2], H10E [10 mM HEPES–KOH (pH 7.4) and 1 mM EDTA (pH 8.0)] buffers and then fixed with 2% formaldehyde in the same three buffers. After DNA staining with DAPI, the coverslips were sealed with a nail polish. Sectioning images were recorded and demonstrated as described above.
Transmission electron microscopy
Nucleosomal array or H1‐nucleosomal array samples were incubated with the desired concentration of 30X MgCl2 for 30 min at room temperature and fixed with 0.1% glutaraldehyde overnight on ice. The DNA concentration was 0.215 mg/ml. Samples (10 μl drops) were deposited on freshly glow‐discharged formvar‐ and carbon‐coated copper grids for 2 min, either with no dilution or at 1:20 and 1:40 dilutions. Excess sample was removed from the grids by blotting. The grids were successively stained for 2 min with 2% uranyl acetate, sample buffer, and 1.5% phosphotungstic acid, with blotting in between each. The grids were then examined and photographed using either a JEOL JEM‐2000 EX II transmission electron microscope operated at 100 kV and captured on film, or a JEOL JEM‐1400 transmission electron microscope equipped with an Orius model 832.J76VV0 (Gatan, Inc.) digital camera and operated at 100 kV. Images were collected at microscope magnifications from 30,000 to 300,000. Negatives were scanned at 1,200 dpi using an Epson Perfection V700 photo scanner and Adobe Photoshop. Images of the grids were processed using ImageJ for figures. Magnified images of the oligomer interiors were obtained by cropping and rescaling the initial images in order to make fine details more apparent.
Sedimentation velocity analyses were carried out in a Beckman XL‐A or XL‐I analytical ultracentrifuge. Experiments measuring the salt‐dependent folding of nucleosomal arrays and H1‐nucleosomal arrays were performed using the absorbance optical system as described (Lu et al, 2009). Absorbance sedimentation velocity data were analyzed by the method of Demeler and van Holde (2004) to yield the diffusion‐corrected integral distribution of sedimentation coefficients. Experiments characterizing nucleosomal array and H1‐nucleosomal array oligomers were performed using the interference optical system as described (Rogge & Hansen, 2015). The laser delay and duration for a sharp fringe pattern were determined using a sapphire window cell containing only buffer. The counterbalance was then used for radial calibration of the detector. For each interference sedimentation velocity run, a single nucleosomal array and H1‐arrays sample was prepared to a final concentration of 0.215 mg/ml DNA and the desired 30X MgCl2 concentration, loaded into a cell assembled with sapphire windows, and placed in an An60‐Ti rotor. The temperature of the run was 20°C. The speed of the runs initially was 662 g. After the collection of 20–60 interference scans at this speed, the oligomeric fraction of the sample had pelleted. The speed was then increased to 46,025 g to monitor sedimentation of the unassociated fraction of the sample. The interference sedimentation velocity data initially were analyzed using the second moment method to obtain the weight‐averaged sedimentation coefficient (ssm). The second moment analysis yields ssm for each scan, providing that the scan has a defined plateau and meniscus (Demeler, 2005). The ssm was plotted against the scan number and linear region of the plot extrapolated to the y‐axis to obtain the ssm values reported in Figs 3 and 6. The scans also were analyzed by the time‐derivative method to obtain the sedimentation coefficient distribution, g(s*) (Stafford, 1992). All sedimentation coefficients are expressed in Svedberg units (S); one Svedberg is equal to 10−13 s. All data editing and analyses were conducted using the UltraScanIII software (Demeler & Gorbet, in press).
SAXS experiments were performed at SPring‐8 using the BL45XU beamline. Following the approach of Langmore and Paulson (1983), the SAXS data in this paper are shown as plots of log(I × S2) versus 1/S, obtained after subtracting buffer scattering. Here, I and 1/S are the average intensity and inverse of the scattering vector, respectively. I × S2 gives the true relative strength (power) of the structural periodicities in the samples (Langmore & Paulson, 1983). A peak in the X‐ray scattering at a 1/S nm shows a periodicity of 1/S nm in the object. The data were averaged within concentric annuli of different radii about the experimental center to yield the average intensity I as a function of S.
BL45XU was set up for the SAXS experiment as follows (Fujisawa et al, 2000). The X‐ray wavelength and sample‐to‐detector distances were 1.0 Å (12.4 keV) and 3.5 m. While Nishino et al (2012) (Fig 3C) and Joti et al (2012) (Fig 3C) performed SAXS with a rather large angle setting, covering from ~2 to ~80 nm, in the present work we took a smaller angle setting from ~5 nm to > 100 nm to fully cover the 30‐ to 40‐nm range. The sample cell is made of stainless steel with 3 mm thickness sealed by 0.02‐mm‐thick synthetic quarts windows. The sample volume of it is 25 μl. The chromatin solutions and nuclei suspension were exposed to the X‐ray beam. Scattering data for the chromatin samples and buffer were collected at room temperature using an imaging plate system (R‐AXIS IV++; Rigaku) or 2D photon counting detector (PILATUS3X 2M; Dectris). Native chicken chromatin (Fig 7C and D) was purified as described in Ura and Kaneda (2001) with minor modifications. The HeLa nuclei used did not contain ribosomes.
Micrococcal nuclease digestion
Four micrograms of 601 nucleosome arrays was incubated in H10Mg5+Ca buffer [10 mM HEPES–KOH (pH 7.4), 0.15 mM CaCl2, 0.1 mM PMSF, and 5 mM MgCl2] to form the oligomers. For MNase digestion, the oligomers were digested for 5 min at 37°C using 1.6 U of MNase per μg of DNA. The reaction was stopped with 1 mM EGTA. The samples were subjected to fluorescence microscopy (FM) imaging or the differential centrifugation assay (9,100 g for 5 min). For FM imaging, the samples were spun onto BSA‐coated coverslips and processed as described for the nuclei imaging. For the verification of complete MNase digestion, DNA was purified, electrophoresed on 1.2% agarose gel, and visualized by staining with ethidium bromide.
We constructed model structures for a dinucleosome (PDB code: 1kx5), one‐start and two‐start 30‐nm chromatin fiber models with 12‐mer nucleosomes, and simulated oligomers containing tightly packed 30‐nm chromatin fiber models. The 12‐mer nucleosome models for the one‐start and the two‐start helixes were constructed based on the atomic coordinate models with 22‐mer nucleosomes, which were kindly provided by Dr. D. Rhodes, LMB, UK (Schalch et al, 2005; Robinson & Rhodes, 2006). The simulated oligomers were modeled as follows: (i) The position and orientation of the first 12‐mer (one‐start helix or two‐start helix) were generated randomly within a sphere with the radius R (Appendix Table S1). (ii) The position and orientation of the second 12‐mer were generated randomly within a sphere with the radius R (Appendix Table S1), so that the two 12‐mers have a contact. Here, two 12‐mers are defined to have a contact if the distance between closest nucleosomes of the two 12‐mers is < 12 nm. Selection of the model (one‐start or two‐start) was done using the random number. (iii) The position and orientation of the third and later 12‐mers were generated randomly within a sphere with the radius R (Appendix Table S1), so that the 12‐mer has at least two contacts with the previous 12‐mers.
In the computation of SAXS profiles for the simulated oligomers, we generated three kinds of simulated oligomers containing 13, 42, and 100 of the 12‐mer. SAXS profiles of 10 structures of each simulated oligomer were calculated and their average was obtained. Appendix Table S1 summarizes the parameters used in the modeling of the oligomeric structures.
SAXS profiles of the constructed model structures were calculated using the following equation: where and rij are the form factor of the i‐th atom and the distance between i‐th and j‐th atoms, respectively. Here, the summation is over non‐hydrogen atoms in each model. Software of our own making, which is parallelized using a message passing interface (MPI) library, was adopted to compute SAXS profiles for a few tens of millions of atoms efficiently. On request, the source file and model file are available.
KM and JCH designed the project; RR and ES synthesized the 12‐mer nucleosome arrays and oligomers; RR analyzed them by TEM and analytical ultracentrifugation; ST, KM, RR, and JH performed FM imaging of the oligomers and MNase digestion; KM, ST, CK, HS, and JD prepared human nuclei and chromatin and performed FM imaging; KM, TH, YJ, and TI performed SAXS analysis; JCH and KM wrote the manuscript with input from all other authors.
Conflict of interest
The authors declare that they have no conflict of interest.
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We thank Dr. S. Hihara for the technical assistance, Dr. J.J. Hayes for his critical reading of this manuscript, and Dr. M. Yamamoto for his support at SPring‐8 BL45XU. This work was supported by JST CREST Grant and MEXT Grant 23115005 (to K.M.) and NIH Grant GM045916 (to J.H.). Part of the computation was performed using the “Thin compute nodes” in the NIG supercomputer system. The synchrotron radiation experiments were performed at BL45XU in SPring‐8 with the approval of RIKEN (Proposal No. 20120023, 20130016, 20140025, 20150079).
FundingJapan Science and Technology Corporationhttp://dx.doi.org/10.13039/501100001695 CREST
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