Direct visualization and tracing of chromatin folding in the Drosophila embryo

TL;DR

This study uses cryo-electron tomography to directly visualize how chromatin folds in Drosophila embryos, revealing an irregular zig-zag pattern and diverse nucleosome conformations.

Contribution

The study provides the first direct in situ visualization of chromatin folding and nucleosome conformations in a living organism using cryo-electron tomography.

Findings

Chromatin folds in an irregular zig-zag pattern with low linker DNA bending.

Nucleosomes show conformational variability, including open, closed, and gaping states.

Non-octameric nucleosome-like particles with one or three DNA gyres were observed.

Abstract

Chromatin organization, through the assembly of DNA with histones and the folding of nucleosome chains, regulates DNA accessibility for transcription, DNA replication and repair. Although models derived from in vitro studies have proposed distinct nucleosome chain geometries, the organization of chromatin within the crowded cell nucleus remains elusive. Using cryo-electron tomography of thin vitreous sections, we directly observed the path of nucleosomal and linker DNA in situ from a flash-frozen organism - Drosophila embryos. We quantified linker length and curvature, characterizing an irregular zig-zag chromatin-folding motif, with a low degree of linker bending. Nucleosome conformations could be identified on individual particles in favorable orientations without structure averaging. Additionally, we observed particles that accommodate a number of DNA gyres ranging from less than one to up to three, which resemble previously proposed non-octameric nucleosomal particles with variable DNA wrapping.

DNA is organized in quasiperiodic arrays of nucleosomes connected by a DNA linker, but how these arrays fold in cell remains unclear. This study uses cryo-electron tomography of Drosophila embryos to directly visualize linker DNA, revealing an irregular zig-zag chromatin fold.

Cryo-ET visualizes chromatin in its native cellular and organismal context.Individual DNA linkers were traced between nucleosomes enabling direct measurement of their length and curvature.An irregular zig-zag chromatin geometry was revealed upon tracing nucleosome arrays.Nucleosomes exhibit rich conformational variability, including open, closed, and gaping states.Nucleosome-like particles containing one or three DNA gyres were observed, consistent with the presence of tetrasomes, hemisomes, and overlapping dinucleosomes in situ.

Cryo-ET visualizes chromatin in its native cellular and organismal context.

Individual DNA linkers were traced between nucleosomes enabling direct measurement of their length and curvature.

An irregular zig-zag chromatin geometry was revealed upon tracing nucleosome arrays.

Nucleosomes exhibit rich conformational variability, including open, closed, and gaping states.

Nucleosome-like particles containing one or three DNA gyres were observed, consistent with the presence of tetrasomes, hemisomes, and overlapping dinucleosomes in situ.

Cryo-electron tomography allows the direct observation of linker DNA geometry and nucleosome conformational variability in a near-native cellular context.

Figures

Chromatin visualization enhanced by VPP imaging and computational denoising.(A) A section of freeze-substituted embryonic CNS nucleus shows a constitutive heterochromatin domain (cHC), nucleolus (NO), and dispersed chromatin domains (arrows) containing ECfHC. (B, C) One-voxel (4.25 Å) thick tomographic slice of a cryo-tomogram containing cHC (B) or ECfHC (C) domains after Warp denoising. (B’, C’) Enlargements of regions squared in (B, C). The putative chromatin domain boundaries are outlined with white dashed lines in (B, B’, C, C’). (D) Magnified area from (C’) showing nucleosomes in top and

DNA linker tracing and WLC fitting.(A) Examples of linker DNA traced between two successive nucleosomes (2N class, A) or from one nucleosome only (1N, B). Each linker is shown first in one-voxel (4.25 Å) tomographic slices (left column), then with tracing points indicated as thin-lined magenta circles when located in the same slice, or as magenta thick-lined circles or disks when located in adjacent slices (central column). The right column shows the corresponding models, where two STA-derived nucleosomes are fitted into the nucleosome densities visible in the subvolume and connected by WLCs (

Analysis of DNA linkers demonstrates disordered zig-zag chromatin folding in situ.(A) Linker length distribution for the 2N class of linkers traced in ECfHC (*n* = 66), cHC (*n* = 85) and all linkers combined (*n* = 151). (B) Curvature distributions of experimental data plotted separately for ECfHC 1N (*n* = 85), cHC 1N (*n* = 52), ECfHC 2N (*n* = 66), and cHC 2N (*n* = 85) linkers, as well as for all linkers combined (all; *n* = 288), presented together with curvature distributions calculated for the zig-zag (green) and the solenoid (red) models computed from the same number of linkers (*n* =

Evidence for unusual nucleosome-related structures in ECfHC domains.(A) Atomic models of the complete nucleosome (octasome, pdb: 2PYO) and sub-nucleosomal particles (tetrasome and hemisome). Corresponding simulated cryo-EM densities are shown below. The simulated density of the octasome, previously shown in Fig. [1G’](#Fig1), is reused here as a reference for comparison with sub-nucleosomal particles. Contrary to hemisome, the H3–H4 tetramer in the tetrasome keeps the dyad axis symmetry. Blue arrows indicate the initial dyad axis direction of the nucleosome and tetrasome. In the hemisome, the

Full text

Introduction

DNA association with histone proteins organizes eukaryotic genomes into quasiperiodic arrays of nucleosomes connected by a DNA linker (Bilokapic et al, 2018; Olins and Olins 1978). Nucleosome arrays behave as flexible heteropolymers capable of folding/unfolding upon interactions between the negatively charged DNA and cations and histone tails enriched in positively charged amino acids. The structural changes of nucleosome arrays influence the local chromatin environment and DNA accessibility and thus play a key role in genome-related processes. However, the precise mechanisms underlying these transitions remain an open question in cell biology (Kornberg and Lorch, 2020). The canonical nucleosome consists of 145 to 147 DNA base pairs wrapped into a 1.7 turn of a left-handed superhelix around an octamer of core histones. Yet nucleosomes are expected to be pleomorphic, with considerable conformational and chemical variability related to intrinsic dynamics, incorporation of histone variants and post-translational modifications, variations of DNA sequence and binding of additional histone and non-histone proteins (Zhou et al, 2019; Zlatanova and Victor, 2009). In vitro, nucleosome arrays can fold into regular helical superstructures known as 30 nm fibers, of which two families of models exist: solenoids implying linker bending (Robinson et al, 2006) and zig-zags with straight linkers (Schalch et al, 2005), with dependence on nucleosome repeat length (NRL (Routh et al, 2008)), nucleosome structure (Takizawa et al, 2020), and presence/absence of linker histones (Routh et al, 2008). It remains unclear to what extent these models are relevant in the native genome context characterized by variable NRL and DNA sequence, non-uniform binding of linker histones and regulatory proteins, and a highly dynamic nucleosome landscape (Baldi et al, 2020). There is no experimental evidence of 30 nm fibers in native chromatin in situ, except in a few highly specialized cell systems such as rodent rod receptors (Kizilyaprak et al, 2010), granulocytic differentiation (Xu et al, 2021), or fully inactive chromatin of nucleated erythrocytes (Scheffer et al, 2011) and echinoderm spermatozoa (Woodcock, 1994). High-resolution Hi-C experiments and hybrid approaches have suggested that local zig-zag and solenoidal folds could exist on a short range (Ohno et al, 2019; Risca et al, 2017). However, recent live imaging studies demonstrate that nucleosomes exhibit a high local mobility in open and compact chromatin states, evidencing a locally disordered, liquid-like structure (Lerner et al, 2020; Maeshima, 2025; Minami et al, 2025; Nozaki et al, 2023).

Nucleosomes and DNA filaments were imaged in situ by transmission electron microscopy (EM) of dehydrated, resin-embedded samples (Kizilyaprak et al, 2010; Ou et al, 2017; Rapkin et al, 2012). But nucleosome conformation and linker DNA geometry depend on electrostatic contacts that need to be preserved, which is achieved by cryo-immobilization of macromolecules in their native hydrous and ionic environment, followed by cryo-electron tomography (Cryo-ET).

A major obstacle in preparing chromatin samples for in situ cryo-ET is that conventional plunge freezing methods do not allow vitrification of the thick nucleus in its native state for most higher eukaryotic cell types. This has been circumvented by nucleus or chromosome isolation (Beel et al, 2021; Li et al, 2023), providing ex situ information, with modifications of the osmotic and ionic environment, which can affect chromatin structure. The addition of glycerol or DMSO has also been used (Chen et al, 2025; Hou et al, 2023b), but is known to alter solvation and electrostatics, crucial in biomolecular interactions, especially in the case of chromatin (Bendandi et al, 2020; Diaz et al, 2022; Liang et al, 2001). The vitrification difficulties also limited the choice of the samples accessible for chromatin analysis to “unicellular” systems such as cell cultures, yeasts and Chlamydomonas, with results which might not be fully generalized to differentiated tissues of multicellular organisms. Other limitations are the low signal-to-noise ratio and the anisotropic resolution due to the missing wedge, especially challenging for small and pleomorphic objects such as nucleosomes and DNA filaments. The conventional solution, known as subtomogram averaging (STA), has revealed nucleosome structure in situ (Cai et al, 2018a, Cai et al, 2018b, Chen et al, 2025, Eltsov et al, 2018, Hou et al, 2023b; Kelley et al, 2024; Kreysing et al, 2025; Wang et al, 2024; Zhou et al, 2025). Classification of nucleosome subtomograms suggested the existence of two major open and closed states (Chen et al, 2025; Hou et al, 2023b), and the presence of non-canonical structures (Tan et al, 2023). While STA provides information on populations of macromolecular complexes, it lacks precision for analyzing individual structures. This limitation is particularly relevant for DNA linkers, whose path has not been directly resolved to date. The available interpretations were inferred from the identified angular distribution of nucleosomes (Cai et al, 2018a; Hou et al, 2023b; Kreysing et al, 2025).

In this study, we explored the chromatin landscape in intact multicellular organisms, Drosophila embryos vitrified at the late development stage (13–15) when the epigenetic landscapes have been established (Walther et al, 2020). High-pressure freezing (HPF) enabled complete vitrification of embryos without cryo-protectants, keeping chromatin in situ in its native state and cellular and organismal context (Bouchet-Marquis and Fakan, 2009; Eltsov et al, 2018). We focused on interphase nuclei of Drosophila embryonic brain, and imaged ultrathin cryo-sections by cryo-ET using contrast enhancement by Volta Phase Plates (VPP) (Danev et al, 2017), well adapted for DNA visualization and nucleosome analysis (Chua et al, 2016), followed by deep learning-based denoising independent of structure averaging (Lehtinen et al, 2018). We were thus able to visualize and analyze the DNA filament and quantify the length and curvature of linker DNA between nucleosome particles. Taking advantage of the distinctive organization of embryonic Drosophila chromosomes, with segregation of constitutive heterochromatin (cHC) into large compact domains, as shown by freeze-substitution analysis of a GFP-labeled heterochromatin protein 1a (HP1a) Drosophila line (James and Elgin, 1986; Vermaak and Malik, 2009), we were able to distinguish constitutive heterochromatin (cHC) domains from euchromatin and/or facultative heterochromatin (ECfCH) ones dispersed in the nucleoplasm. This lets us compare linker length and curvature between these two types of chromatin domains. We also detected individually a variety of nucleosome conformations, among which particles accommodating different DNA amounts wrapped around, from less than one to three gyres, localized in ECfHC nanodomains.

Results

Drosophila embryo as a model system for cryo-ET chromatin analyses

We chose the central nervous system (CNS) of Drosophila embryos at late developmental stages (13–15) as a model system because of its many practical advantages. Entire embryos can be vitrified by high-pressure freezing (Eltsov et al, 2018; Eltsov et al, 2015), and the CNS can be reproducibly found in the interval 70–100 µm from the embryo’s anterior tip (Fig. EV1A,B), thus enabling targeted trimming for cryo-sections (Appendix Fig. S1A,B). A large relative area is occupied by diploid nuclei that accounts for ~50% of the total tissue section area (Figs. 1A and EV1C), thus ideally supporting the targeting of chromatin domains in vitreous sections and facilitating tomographic data collection. Additionally, freeze-substitution of embryos expressing fluorescent (GFP) HP1a reveal the stereotypical organization of Drosophila embryo chromatin domains in CNS nuclei (see Materials and methods for details; Fig. EV1D,E): a large compact constitutive heterochromatin (cHC) domain is attached to the nuclear envelope and associated with the nucleolus (NO), while more dispersed domains of euchromatin and/or facultative heterochromatin (ECfHC) are distributed within the nucleosplasm, letting us distinguish and target cHC compartments in cryo-tomograms (Fig. 1B; Appendix Fig. S1C,D). This is fully compatible with the fact that the ribosome gene cluster in Drosophila is located in the pericentric heterochromatin region within the X chromosome (Hilliker et al, 1980). Accordingly, the small (≤300 nm) dispersed domains observed in the nucleoplasm correspond to euchromatin and facultative chromatin (ECfCH) (Figs. 1A,C and EV1D,E; Appendix Fig. S1). In the absence of specific labeling, domains of euchromatin were not distinguished here from facultative heterochromatin. This chromatin organization is invariably present in CNS nuclei and is also found in the majority of Drosophila embryonic tissues.Figure 1. Chromatin visualization enhanced by VPP imaging and computational denoising.(A) A section of freeze-substituted embryonic CNS nucleus shows a constitutive heterochromatin domain (cHC), nucleolus (NO), and dispersed chromatin domains (arrows) containing ECfHC. (B,** C**) One-voxel (4.25 Å) thick tomographic slice of a cryo-tomogram containing cHC (B) or ECfHC (C) domains after Warp denoising. (B’,** C**’) Enlargements of regions squared in (B,** C**). The putative chromatin domain boundaries are outlined with white dashed lines in (B,** B**’,** C**,** C**’). (D) Magnified area from (C’) showing nucleosomes in top and side views and linker DNA (magenta arrowhead). The pseudo-dyad axes of the top-view nucleosome is indicated by the blue arrow. (E) Different side view nucleosomes. The two DNA gyres characteristic of side views are indicated by magenta arrows in (D,** E**). (F) Visualization of the complete wrapping of DNA around the histone core in an individual particle, with fitted crystallographic model of the nucleosome (pdb:2PYO). This nucleosome shows a larger lateral spacing between DNA entry and exit sites (dotted double arrow). (G–I) Individual top-view nucleosomes. A representative top view (G) displays an internal density pattern similar to the simulated cryo-EM density of the nucleosome model (G’). (G,** G’) A nearby linker DNA seen in cross-section is indicated by the magenta arrowhead. A closed and an open conformation are shown side by side with corresponding models in (H) and (I), respectively. Blue arrows indicate the direction of the nucleosome dyad axis in (G, G’, H**, I). (J) Side views of two neighboring nucleosomes, N1 and N2, showing a difference in their intergyral distances (P) are represented (gaping). P_N1_ is very close to that of the canonical nucleosome (~2.7 nm), whereas P_N2_ is larger (~4.0 nm); the crystallographic model (pdb:2PYO) fits poorly in N2 (arrow in isosurface). (K) An example of a partially unwrapped nucleosome shown as side and top views, and the corresponding isosurface views with fitted model of hexasome (Bilokapic et al, 2018). Source data are available online for this figure.

Visualization of the DNA filament around and between nucleosomes

We recorded VPP cryo-tomograms on either 50 or 75 nm thick vitreous sections. Denoising of tomograms was performed with a nonlinear anisotropic diffusion (NAD) filter (Frangakis and Hegerl, 2001) or deep learning networks based on the Noise2Noise principle (Lehtinen et al, 2018), in Warp (Tegunov and Cramer, 2019) and Topaz (Bepler et al, 2020) (Appendix Fig. S2). In all cases, tomogram reconstructions present a disordered granular aspect typical of chromatin (Fig. 1B,C). Zooming in reveals nucleosomes (Fig. 1B’,C’), barely visible in raw reconstructions, but unambiguously identified after denoising (Appendix Fig. S2A,B) with their typical contrasted side views dominated by the two DNA gyres drawing characteristic V-, X-, or stripped patterns (Fig. 1D,E,J), and circular top views, 11 nm in diameter (Fig. 1D). In addition, the density pattern visible in many top-view particles is very similar to that would be formed by the core histone octamer, simulated with resolution of 20–25 Å, and clear identification of the dyad axis, which is confirmed by the path of the DNA (Fig. 1G,G’). In the best cases, the complete path of DNA wrapped around the histone octamer may be followed around individual nucleosomes (Fig. 1F; Movie EV1).

Importantly, this also reveals DNA linkers connecting nucleosomes (Fig. 1D,G, purple arrowheads; Appendix Fig. S2B). The best visibility is obtained by the deep-learning network Warp (Tegunov and Cramer, 2019), but linkers are also revealed by Topaz (Bepler et al, 2020), and a nonlinear anisotropic diffusion (NAD) filter (Frangakis and Hegerl, 2001) (Appendix Fig. S2AB), supporting that these linear densities are bona fide DNA linkers, not deep-learning artefacts.

Conformational variability of individual nucleosomes

We performed gold-standard (GS) STA of all manually picked particles from two ECfHC reconstructions (ECfHC1, 549 particles; ECfHC2, 552 particles) and one cHC reconstruction (860 particles), resulting in a 3D nucleosome structure at 20 Å resolution (Fig. EV2). Fitting the X-ray atomic model of the Drosophila nucleosome core particle (pdb:2PYO) shows that the subtomogram average is very similar to the canonical nucleosome conformation (Fig. EV2). Subtomogram averages show that the structure of nucleosomes is not affected by compression during cryo-sectioning, which confirms previous findings (Cai et al, 2018b; Harastani et al, 2021; Harastani et al, 2022).

The analysis of individual nucleosomes reveals rich conformational variability. Disk-like top views of nucleosomes (Fig. 1D,G) demonstrate “open” and “closed” conformations (Fig. 1H,I). Closed conformations show DNA crossing at the nucleosome entry/exit site (Fig. 1I, closed). Open conformations show DNA entry and exit points at a distance larger than in canonical X-ray models, revealing partial DNA unwrapping, also called nucleosome breathing (Bilokapic et al, 2018; Buning and van Noort, 2010) (Fig. 1H, open). This unwrapping could go to a large degree resulting in detaching more than 40 DNA bp (Fig. 1K, unwrapped) as we can estimate from the fitting of an atomic model. Such unwrapping is characteristic of the hexasome formation via the loss of a histone H2A-H2B dimer demonstrated by single particle cryo-EM in vitro (Bilokapic et al, 2018; Zhang et al, 2023), in good agreement with fitting of an atomic model of the hexasome (Fig. 1K). Inter-gyre breathing out of the nucleosome plane predicted by simulations (Huertas and Cojocaru, 2021) is also observed at DNA entry and exit sites (Fig. 1F, dotted double arrow). Furthermore, some nucleosome side views show inter-gyre distance variation, compatible with gaping (Fig. 1J, “gaping”), i.e., edge-opening, in agreement with FRET experiments in vitro (Ngo and Ha, 2015) and our previous findings in vitro and in situ (Eltsov et al, 2018; Harastani et al, 2021).

Besides nucleosomes, other molecular complexes such as chaperonins and proteasomes are readily recognized in the nucleoplasm (Appendix Fig. S2C).

Linker DNA analysis reveals an irregular zig-zag chromatin folding

Visualization of DNA linkers allows us to trace their trajectories and explore their geometry. Linker paths were traced following the procedure described for cryo-tomograms of isolated mitotic chromosomes (Beel et al, 2021) (Fig. EV3). Linkers were identified as fibrillar structures with a diameter of approximately 2 nm in the xy plane, slightly elongated in the z direction due to missing wedge effects. Linkers were observed to be associated with at least one recognizable nucleosome and, under optimal conditions, could be visualized bridging two identifiable nucleosomes, allowing for the reconstruction of the complete linker path (Fig. 2A). This class of linkers is hereafter named 2N. In 46% of the traced linkers (Appendix Table S1A), only one linked nucleosome can be identified. The linker may end within or close to a density that cannot be assigned to a recognizable nucleosome (Figs. 2B and EV3) and could be another unknown macromolecular complex interacting with chromatin, or correspond to an artefactual density overlap of the tomographic reconstruction (Turonova et al, 2016). The linker may also turn abruptly untraceable (Fig. 2B). We combined all cases where the complete linker length was not defined into class 1N. We also observed situations where the DNA linker was too short to be traced: successive nucleosomes are then in contact, and DNA can be followed passing from one histone core to the other (Fig. 2C, linker-less). Altogether, traceable linkers correspond to about 13% of the amount expected from the number of manually picked nucleosomes (Appendix Table S1A). Simulated tomograms of synthetic chromatin (Appendix Fig. S3) demonstrate a local variability in the linker path restoration upon reconstruction and denoising, depending on the signal-to-noise ratio and on chromatin crowding, with partial or even complete loss of the signal in crowded regions (Appendix Fig. S3BC), in good agreement with the situation observed in real data (untraceable linkers or partial linker segments). In addition, to test for a possible bias of the denoising algorithm towards preferential recovery of low-curvature straight linkers versus high-curvature linkers, we simulated noisy tomograms containing crowded dinucleosomes with straight and bent linkers (Appendix Fig. S3, bent linker). We found that both situations have the same signal-to-noise ratio threshold for signal recovery and traceability (0.25; Appendix Fig. S3B). Lastly, we checked that the distribution of the linker “end-to-end” vector directions within the section’s volume shows no statistically significant difference from an isotropic distribution (Appendix Fig. S4), indicating the absence of substantial cutting-induced deformations at the scale of the DNA linker.Figure 2DNA linker tracing and WLC fitting.(A) Examples of linker DNA traced between two successive nucleosomes (2N class, A) or from one nucleosome only (1N, B). Each linker is shown first in one-voxel (4.25 Å) tomographic slices (left column), then with tracing points indicated as thin-lined magenta circles when located in the same slice, or as magenta thick-lined circles or disks when located in adjacent slices (central column). The right column shows the corresponding models, where two STA-derived nucleosomes are fitted into the nucleosome densities visible in the subvolume and connected by WLCs (pink) fitted to the manually traced points (magenta spheres). Note that the 1 N example shown as two tomographic slices through the central plane of a subvolume is rotated 90° to display a linker that turns abruptly untraceable. (C) Example of a linker-less dinucleosome (arrows) shown in side (XY) and top (XZ) views. (D) Example of an optimal WLC trajectory (pink) fitted to manually traced points (purple). L_pixel_ represents the length of the polyline connecting tracing points (in nanometers and in base pairs); L_bp_ is the length of the best-fitted WLC in base pairs (see Materials and methods for details). Source data are available online for this figure.

In order to quantify linker length and curvature, worm-like chain (WLC) models (Doi and Edwards, 1988) with a chain unit of 1 bp and a persistence length of 50 nm were fitted into the traced linkers (Fig. 2D). Best fits were processed to calculate linker length and curvature for the 2 N class, curvature only for the 1 N class. Interestingly, the Kolmogorov–Smirnov (KS) test showed no significant difference between linker length and curvature found in ECfHC and cHC (Appendix Table S1CD). Distributions for the different chromatin compartments are shown in Fig. 3A. The mean linker length is 32 bp in ECfHC and 29 bp in cHC (SD 14 bp in both cases, Fig. 3A; Appendix Table S1B), in agreement with previous measurements of 25–40 bp obtained using micrococcal nuclease digestion followed by gel migration and/or sequencing in Drosophila cells and larvae (Baldi et al, 2018; Lu et al, 2009). Nevertheless, linker lengths up to 76 bp and down to a few bp (Fig. 3A) are observed, revealing a large local variability. Linker curvature is generally low (mean ~0.10 nm^–1^, SD 0.01 nm^–1^, Fig. 3B). No statistically significant differences in linker length and curvature were revealed between ECfHC and cHC (Appendix Table S1CD).Figure 3. Analysis of DNA linkers demonstrates disordered zig-zag chromatin folding in situ.(A) Linker length distribution for the 2N class of linkers traced in ECfHC (n = 66), cHC (n = 85) and all linkers combined (n = 151). (B) Curvature distributions of experimental data plotted separately for ECfHC 1N (n = 85), cHC 1N (n = 52), ECfHC 2N (n = 66), and cHC 2N (n = 85) linkers, as well as for all linkers combined (all; n = 288), presented together with curvature distributions calculated for the zig-zag (green) and the solenoid (red) models computed from the same number of linkers (n = 288). Schematic views of the minimal structural dinucleosomes motif of the zig-zag and solenoid models calculated for a linker length of 30 bp (equal to the mean value of experimental data) are shown on the right. Violin plots (A,** B**) show symmetric kernel density estimates of the data distributions. The central line indicates the median, box limits represent the first and third quartiles (25th and 75th percentiles), whiskers extend to data points within 1.5× the interquartile range, and the violin shapes were truncated at the minimal and maximal data points. (C,** D**) The average curvatures per linker (y-axis) plotted versus its length (x-axis) for the zig-zag and solenoid models (C) and the experimental data (D). The correlation lines based on the Spearman correlation coefficient show a high significance correlation only for the solenoid model (D, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{{{\mathrm{Spearman}}}}=-0.4$$\end{document} , p = 7.7⋅10^−13^, see Appendix Table S1E for details), a low significance correlation for cHC (C, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{{{\mathrm{Spearman}}}}=-0.27$$\end{document} , p = 0.01), and the absence of correlation between linker curvature and length in ECfHC and the zig-zag model (C,** D**). (E) Representative 4.25 Å thick tomographic slices illustrating the variety of zig-zag motifs drawn by three successive nucleosomes. The right example in (F) shows the same closed nucleosome as in Fig. 1I, together with its linked neighboring nucleosomes. (F) Molecular models showing our interpretations of views in (E). (G) Snapshot of a coarse-grained simulation incorporating the measured distributions of linker length and curvature. Source data are available online for this figure.

To compare our measurements in situ with classical zig-zag and solenoid models, we simulated their minimal structural motif as dinucleosomes, with stacking interaction for solenoids (high linker curvature) and non-interacting nucleosomes for zig-zags (Fig. 3B, “zig-zag” and “solenoid”). We plotted experimental linker curvature distributions and compared them to simulated distributions for zig-zag and solenoid fibers. We observed an agreement between the curvature distribution of our experimental data and that of zig-zag models (Fig. 3B). In addition to a higher linker curvature, the solenoid model is characterized by a significant negative correlation (−0.40, p = 7.7⋅10^−13^; Fig. 3D; Appendix Table S1E) between curvature and linker length ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{{{\mathrm{Spearman}}}}$$\end{document} ) because of a higher degree of bending required for shorter linkers to stack consecutive nucleosomes. Interestingly, while linkers of ECfHC domains, as well as of all linkers taken together, show an absence of correlation between linker length and curvature, characteristic of a zig-zag folding, a weak increase of linker curvature with decrease of linker length is indicated in the cHC compartment (Fig. 3C,D; Appendix Table S1E).

Taken together, our results argue against a widespread solenoidal fold and suggest a predominance of zig-zag chromatin geometry, both in ECfHC and cHC, despite indications of increased curvature in short-length linkers of cHC. In line with this, wherever two or more consecutive linkers are visualized in the analysed data, they show zig-zag motifs (Fig. 3E,F). Possible chromatin folds can be obtained by simulations based on experimental values of linker length and curvature, as shown in Movie EV2. A snapshot is shown in Fig. 3G.

Evidence of sub-nucleosomal particles

Besides nucleosomes captured in different conformations and linker DNA, we detected structures displaying nucleosome-like features. These structures are connected by DNA linkers to normal nucleosomes and/or each other and visually resemble nucleosomes, but with a key difference: the number of DNA gyre when observed in their side views (Figs. 4 and EV4), either one (Figs. 4A–D and EV4; Appendix Fig. S5–7; Movie EV3) or three (Fig. 4E; Movie EV4). They can be unambiguously distinguished from non-nucleosomal bent DNA segments, on account of (i) the presence of an internal cryo-EM density indicating proteinaceous core showing—in some cases—a characteristic histone pattern; (ii) their DNA curvature (mean ~0.185 nm^–1^, SD 0.015 nm^–1^, measured on six particles), similar to that of the nucleosome (mean ~0.192 nm^–1^, SD 0.017 nm^–1^, measured on five particles), and very different from other forms of highly curved DNA such as hairpins (see Appendix Fig. S7). This suggests that 1-gyre particles are indicative of sub-nucleosomes, such as tetrasomes and hemisomes, previously documented in vitro and in silico (Bancaud et al, 2007; Zlatanova et al, 2009). Both maintain only a single gyre of DNA, while their histone contents are different: the tetrasome contains the complete tetramer of H3/H4 histones, while the hemisome maintains a single copy of each histone. Observed in top view, the tetrasome, with its H3–H4 tetramer, presents a density indentation, along its dyad symmetry axis (Fig. EV4A). This indentation remains discernable on cryo-EM projection patterns simulated at the resolution of our data from an atomic tetrasome model (Fig. 4A). The internal density of some of the 1-gyre particles in top views indeed presents symmetric patterns with an indentation oriented towards DNA entry/exit place (Figs. 4B,C and EV4; Appendix Fig. S6) that enables their identification as possible tetrasomes. In contrast, the modeling of hemisomes predicts their internal density to be asymmetric (Zlatanova and Victor, 2009) (Fig. 4A). In addition, the histone pattern alone is not the only distinguishing feature between hemisomes and tetrasomes. Hemisomes are predicted to form from nucleosome splitting, as proposed by Zlatanova and colleagues (2009), and are therefore expected to appear in pairs, separated by a short linker (typically less than 50 bp (Zlatanova and Victor, 2009). In contrast, tetrasomes result from the unbinding of 39 bp at both the entry and exit regions of a nucleosome, meaning that two consecutive tetrasomes should be separated by a linker of at least 78 bp. Both scenarios were observed in our data (Fig. 4C,D). In Fig. 4D (see also Movie EV3), the two 1-gyre particles not only lack symmetric histone patterns but are also connected by a DNA segment of ~25–28 bp—consistent with a pair of hemisomes and incompatible with a pair of tetrasomes. Conversely, in Fig. 4C, the histone patterns is more symmetric, and the linker length is around 75 bp—too long for hemisomes but consistent with a pair of tetrasomes.Figure 4. Evidence for unusual nucleosome-related structures in ECfHC domains.(A) Atomic models of the complete nucleosome (octasome, pdb: 2PYO) and sub-nucleosomal particles (tetrasome and hemisome). Corresponding simulated cryo-EM densities are shown below. The simulated density of the octasome, previously shown in Fig. 1G’, is reused here as a reference for comparison with sub-nucleosomal particles. Contrary to hemisome, the H3–H4 tetramer in the tetrasome keeps the dyad axis symmetry. Blue arrows indicate the initial dyad axis direction of the nucleosome and tetrasome. In the hemisome, the brown arrow marks the dyad axis orientation of the original octasome before splitting into two halves. (B) An example of a putative tetrasome particle showing a symmetry in histone density, shown as a tomographic slice (left) and an isosurface with fitted model (right). (C) Zig-zag fold formed by two successive tetrasome-like particles (core marked by blue spheres) and a canonical nucleosome (green arrow), shown as a tomographic slice and isosurfaces with fitted models. The transverse tomographic section (inset) corresponding to the blue plane demonstrates that the particle is formed by a single DNA loop. This particle shows an additional density attached to DNA oriented perpendicular to the plane of the DNA loop (pale purple arrow). (D) A pair of putative hemisomes, likely corresponding to a split nucleosome with its two halves, is represented as a tomographic slice and isosurface with fitted nucleosome and DNA models. The blue spheres indicate the same particle in the tomographic slice and models (see also Movie EV3). (E) Three-gyre particle shown as tomographic slices of side (squared in black) and top (in blue) views, and as isosurface views with the fitted model of the overlapping nucleosome (pdb:5GSE). The third DNA gyre of the model does not fully fit the density, indicating conformational differences in situ (see also Movie EV4). An oblique virtual section (in yellow) shows its connection to a tetrasome-like particle (blue sphere). Source data are available online for this figure.

Interestingly, we also observed a three-gyre or super-nucleosomal particle, which may correspond to an overlapping dinucleosome (Kato et al, 2017), as supported by the fitting of its crystallographic structure (pdb: 5GSE, Fig. 4E; Movie EV4).

All these putative nucleosome-related structures were only found in ECfHC nanodomains. In two of our ECfHC tomograms, we manually picked 549 and 552 nucleosomes (used for STA), and identified 8 and 13 1-gyre particles respectively, which corresponds to 1.5–2.4% of the nucleosome population. They appear dispersed within or at the periphery of ECfHC domains, in some cases as pairs of particles. Appendix Fig. S8 shows their repartitions within the two ECfHC tomograms used for STA. In this work, we additionally explored four ECfHC tomograms, and a few (5 to 10) 1-gyre particles were found in each of them. Note that the number of both picked nucleosomes and putative sub-nucleosomes per tomogram is underestimated, as only unambiguously recognized particles were considered. Their small number, combined with their structural diversity, prevents subtomogram averaging approaches. A few of them also present additional densities that can be attributed to bound (unknown) proteins (Fig. 4C, purple arrow), which, together with their localization in ECfHC domains, suggest that these particles are related to active chromatin regions.

Discussion

Nucleosome and chromatin structural analysis in situ is challenging. With the progresses of cryo-ET, a few recent studies have been able to image chromatin either in situ (Cai et al, 2018a, Cai et al, 2018b, Eltsov et al, 2018, Hou et al, 2023b; Tang et al, 2007; Wang et al, 2024; Zhou et al, 2025), of after chromosome or nucleus isolation (Beel et al, 2021; Li et al, 2023). Subtomogram averaging has revealed a nucleosome average conformation close to the canonical crystallographic one (Chen et al, 2025; Harastani et al, 2021; Harastani et al, 2022; Kelley et al, 2024; Kreysing et al, 2025; Tan et al, 2023).

The use of VPP cryo-ET coupled to deep-learning-based denoising makes it possible to visualize the DNA filament in cryo-tomograms, as already shown ex situ, by cryo-ET of isolated chromosomes and nuclei (Beel et al, 2021; Hou et al, 2023b). We were thus able to follow DNA trajectories in situ within the native Drosophila embryo. The DNA path can be visualized, wrapped around and between nucleosome particles, revealing both local chromatin fold and nucleosome conformations at the individual level. The observation of individual nucleosomes not only confirms previous findings of gaping particles (Eltsov et al, 2018; Harastani et al, 2021), but let us to describe various DNA opening angles in and out of the nucleosome plane (Fig. 1F,H,I,K), and provides direct evidence that nucleosomes accommodate variable DNA length. Between particles, beyond the simple visualization of DNA linkers, we were able to trace the DNA filament. Only 10–15% of the linker paths were determined, due to a combination of crowding (Appendix Fig. S3), presence of a number of proteins bound to DNA and missing wedge effects in tomographic reconstructions. Figure EV5; Appendix Fig. S9; and Movie EV5 summarize our findings, with picked nucleosomes mapped back into the tomogram together with the subset of traced linker that connects to them. Although our analysis describes but a subset of all linkers, a bias toward under- or overestimation of either length or curvature is unlikely because of the detection of very diverse linker lengths and the finding of both strongly curved or nearly straight ones (see Fig. 3B). In addition, we were able to visualize directly and trace the zig-zag folding path over three to four successive nucleosomes.

Altogether, our data reveal a disordered zig-zag folding (Fig. 3E–G; Movie EV2), evocative of the conformations found by Bednar et al in their seminal observations of oligonucleosome solutions (Bednar et al, 1995). Zig-zag paths were also traced in isolated mitotic chromosomes (Beel et al, 2021) or observed in inactive erythrocyte nuclei (Li et al, 2023), as well as inferred from nucleosome relative positions and orientations at the nuclear envelope periphery of human interphase nuclei (Cai et al, 2028a; Hou et al, 2023a; Kreysing et al, 2025). A disordered zig-zag fold, with variable linker length and lack of extensive order, is therefore a reasonable model of chromatin folding in interphase nuclei in situ. Here, the large variation of DNA linker length (from nearly zero to about 80 base pairs) results in an especially irregular fold, which accounts for the lack of a regular fiber coiling motif (Bascom et al, 2017; Collepardo-Guevara and Schlick, 2014; Maeshima et al, 2019). In ECfHC, we found no correlation between linker length and curvature, indicating a freely-fluctuating DNA and an absence of geometric constraints, for example, stacking of consecutive nucleosomes along the DNA strand, like in a solenoid type of compaction (Fig. 3C,D; Appendix Table S1E). The zig-zag fold minimizes energy penalties for linker bending (Brouwer et al, 2021); it is compatible with the high dynamics of nucleosomes at the local scale and interdigitation of neighboring fibers leading to molten globule-like domains (Maeshima et al, 2019). The low significant correlation between linker length and curvature revealed in cHC data might indicate the accidental presence of stacking interaction between consecutive nucleosomes resulting in linker bending, that might be associated with the formation of internucleosome bridges by HP1 (Machida et al, 2018).

Liquid-like behavior has been described in both EC and HC (Minami et al, 2025; Nozaki et al, 2023). In line with this dynamics and a fluctuating chromatin fold, we observe multiple nucleosome conformations. In particular, closed conformations with DNA crossing at nucleosome entry/exit sites coexist with open ones showing variable DNA wrapping/unwrapping. This can occur due to chromatin folding fluctuations and/or the presence of other molecular players, for example, linker histones that have been shown to transiently bind chromatin (Shimazoe et al, 2025), and result in the closed conformation of a chromatosome (Hayes et al, 1994); or chromatin remodeling complexes leading to open reaction intermediates (Dodonova et al, 2020; Farnung et al, 2017; Willhoft et al, 2018). Interestingly, STA obtained by (Cai et al, 2018a, Chen et al, 2025, Hou et al, 2023b; Kreysing et al, 2025), have also revealed closed average conformations, consistent with the presence of H1 in a chromatosome. Our results indicate that the in situ structural fluctuation of nucleosomes goes beyond the conformational changes of canonical nucleosomes, revealing a distinct set of single-gyre particles. While our resolution does not allow precise identification of their protein components, their DNA curvature and protein density patterns suggest they include tetrasomes and hemisomes (Zlatanova et al, 2009). Additionally, we obtained initial evidence for the presence of triple-gyres particles that might correspond to the overlapping dinucleosome reconstituted in vitro (Kato et al, 2017), in which an octasome contacts a hexasome (nucleosome lacking one histone dimer).

Interestingly, all these putative nucleosome-related structures were found in ECfHC nanodomains. Although we cannot discriminate between EC and fHC, this finding suggests active structural transitions with nucleosome assembly-disassembly and sliding occurring during remodeling and transcription (Bruno et al, 2003; Kobayashi and Kurumizaka, 2019; Kornberg and Lorch, 2020; Petesch and Lis, 2008; Ulyanova and Schnitzler, 2005; Zlatanova and Victor, 2009). Indeed, sub-nucleosomal structures were detected in the dynamic chromatin of the yeast interphase nucleus (Rhee et al, 2014). Among these, nucleosomes split into pairs of hemisomes were recently detected bound by the transcription factor Oct4 (Nocente et al, 2024), and overlapping dinucleosomes may be present downstream of transcription start sites (Kato et al, 2017). The observation of these labile states in situ highlights the potential of denoising-enhanced cryo-ET to address functionally relevant chromatin reorganization directly in the context of the cell nucleus.

Methods

Reagents and tools tableReagent/resourceReference or sourceIdentifier or catalog number Experimental models

Drosophila melanogaster stocks D. melanogaster wild-type fliesBloomington Stock, Dept Biology, Indiana University, Bloomington, USA30564D. melanogaster expressing heterochromatin protein 1a fused with green fluorescence protein (HP1a-GFP)Bloomington Stock, Dept Biology, Indiana University, Bloomington, USA30561 Chemicals, enzymes and other reagents BleachSigma-AldrichCAS# 7681-52-9PBSSigma-AldrichP4417Dextran 40 kDaSigma-Aldrich31389NP-40Thermo Fisher Scientific85124Uranyl acetateElectron Microscopy SciencesCAS #541-09-3Dry acetoneThermo Fisher ScientificAC326801000Lowicryl HM 20Electron Microscopy SciencesSKU: 14340Reynolds lead citrateDelta microscopiesREF: 11300MethanolSigma-AldrichCAS# 67-56-1 Software Imodhttps://bio3d.colorado.edu/imod/ (Kremer et al, 1996; 10.1006/jsbi.1996.0013)Nonlinear anisotropic diffusion filter (nad_eed_3d)https://bio3d.colorado.edu/imod/doc/man/nad_eed_3d.html#TOP (Frangakis and Hegerl, 2001; 10.1006/jsbi.2001.4406)Topaz-Denoise, CNN denoising modelhttps://github.com/tbepler/topaz/ (Bepler et al, 2020; 10.1038/s41467-020-18952-1)Warp, CNN denoising modelhttps://github.com/warpem/warp/tree/main/Noise2Tomo (Tegunov and Cramer, 2019; 10.1038/s41592-019-0580-y) Other 200-mesh, gold R2/1 Quantifoil gridsElectron Microscopy SciencesQ2100AR1Carriers for high-pressure freezing A and B typesEngineering Office M. Wohlwend GmbHStereomicroscope M165 FCLeica MicrosystemsHigh-pressure freezing machine HPM 010ABRA Fluid AGCryo-microtome FC6/UC6Leica MicrosystemsDiamond trimmers and knivesDiatomeTransmission cryo-electron microscope Titan Krios G2Thermo Fisher Scientific

Reagents and tools

All reagents and commercial instruments are listed in the Reagents and Tools table.

Biological resources

Drosophila melanogaster wild-type flies (Bloomington Stock number 30564; Dept Biology, Indiana University, Bloomington, USA) and flies expressing heterochromatin protein 1a fused with green fluorescence protein (HP1a-GFP; Bloomington Stock number 30561) were maintained in a standard Bloomington medium.

Statistical analyses

Two-sample Kolmogorov–Smirnov (Hodges, 1958) test and Mann–Whitney U-test (Fay and Proschan, 2010) were used. Details and the null hypothesis are described in the corresponding sections of Methods, and legends of Appendix Fig. S4; Appendix Table S1.

Drosophila embryos preparation and vitrification

Drosophila embryo collection and vitrification were performed as described in Eltsov et al (Eltsov et al., 2018; Eltsov et al, 2015). Embryos were collected on apple agar plates, dechorionated in 50% (v:v) bleach (Sigma-Aldrich, St. Louis, USA), washed with PBS and sorted under a stereomicroscope (M165 FC; Leica Microsystems, Wetzlar, Germany). Embryos of developmental stages 14–15 (Campos-Ortega and Hartenstein, 1985) were selected and transferred into a drop of the PBS solution containing 25% dextran (40 kDa, Sigma-Aldrich) and 0.25% of NP-40 (Sigma-Aldrich). After <30 s incubation, the embryos were transferred into a 0.1 mm indentation of 3 mm Type A gold-plated copper carriers (Engineering Office M. Wohlwend GmbH). The anterior pole of the embryo head was oriented towards the periphery of the carrier (Appendix Fig. S1A), the carrier was filled with the PBS/Dextran/NP-40 solution and covered by the flat side of the Type B carrier (Engineering Office M. Wohlwend GmbH). This sandwich was processed for high-pressure freezing with an HPM 010 machine (ABRA Fluid AG, Widnau, Switzerland). The addition of NP-40 surfactant was necessary for compensation of the hydrophobic properties of the embryonic vitelline membrane, thus enabling embryos to be fully surrounded by the Dextran/PBS/NP solution. The wax layer of the vitelline membrane of embryos is not liquid permeable (Rand et al, 2010), therefore the Dextran/PBS/NP-40 solution cannot penetrate into the perivitelline liquid and cause any osmotic effect on embryos, whose development occurs normally with larvae hatching.

Freeze-substitution and conventional TEM analysis

Freeze-substitution was performed as described in Eltsov et al (Eltsov et al, 2015). The high-pressure frozen embryos were transferred into the chamber of a Leica EM FC6/UC6 cryo-microtome (Leica Microsystems) precooled to –145 °C, and were punctured with a fine needle (precooled in liquid nitrogen) outside the head area to pierce the vitelline membrane, improving the permeability of the freeze-substitution and embedding media into the embryo tissues. Embryos were then transferred into the AFS-2 apparatus equipped freeze-substitution processor unit (Leica Microsystems) precooled to −90 °C. Freeze-substitution began with incubation in glass-distilled acetone (Electron Microscopy Sciences, Hatfield, PA, USA) in the presence of 0.5% uranyl acetate (Electron Microscopy Sciences). After 48 h, the temperature was raised to −45 °C at a rate of 2 °C/h. After 16 h at −45 °C, the samples were washed three times with dry acetone and sequentially infiltrated with Lowicryl HM 20 (10, 25, 50, and 75%, 4 h for each concentration; Electron Microscopy Sciences). Then three incubations with 100% Lowicryl (10 h each) were carried out, followed by ultraviolet polymerization at −45 °C for 48 h, followed by warming to 20 °C and an additional 48 h of polymerization.

Embedded embryos were sectioned, perpendicular to the anterior–posterior axis, with diamond knives (ultra 35°; Diatome, Nidau, Switzerland) on a Leica Ultracut E microtome (Leica Microsystems). To explore the general anatomy of an embryo head, serial sections of 200 nm were cut starting from the anterior tip of the embryo and collected on microscopy glass slides, stained with toluidine blue; they were observed under a Zeiss Axiovert light microscope (Carl Zeiss, Oberkochen, Germany) using a x100 objective with oil immersion. After this initial analysis, new serial sections from freeze-substituted embryos were collected on slot grids for electron microscopy (Plano, Wetzlar, Germany) coated with Formvar film (Sigma-Aldrich). Sections were contrasted with 2% uranyl acetate in 70% methanol, followed by Reynolds lead citrate. The sections were examined with a Tecnai F30 electron microscope (Thermo Fisher Scientific, Waltham, USA) at magnification ×2300 corresponding to 5.3 nm/pixel and images were acquired with a 4k × 4k CCD (charge-coupled device) US4000 camera (Gatan, Pleasanton, USA) controlled by Serial EM software (Mastronarde, 2005). A higher resolution nuclear structure mapping was done using 200 nm thick embedded sections (Fig. 1A) acquired at magnification x12000.

Mapping of chromatin domain types and their distribution in the nucleus by correlative light and electron microscopy (CLEM)

Preparation, vitrification, and freeze-substitution of embryos expressing HP1a‑GFP were carried out following the same protocol used for wild-type embryos, with the sole modification that the freeze-substitution medium consisted of glass-distilled acetone without the addition of uranyl acetate or any other fixative. This adjustment was made to optimize the preservation of GFP fluorescence. Notably, even in the absence of fixatives, the freeze-substituted samples exhibited sufficient structural preservation to enable reliable assessment of nuclear architecture and mapping of chromatin domain organization (Fig. EV1D).

About 200-nm-thick sections containing embryonic brain were collected on hexagonal 100 mesh gold grids (Plano, Wetzlar, Germany) coated with Formvar film (Sigma-Aldrich). The sections were at first imaged with a laser scanning confocal microscope Zeiss LSM700 Imager M1 (Carl Zeiss, Oberkochen, Germany) using a W Plan-Apochromat 40×/1.0 objective and a pinhole size set to 1 Airy unit. GFP fluorescence image stacks were acquired, each comprising 10 frames, with a pixel size of 62 nm in the XY plane and the Z-axis step of 100 nm. The maximal intensity projections of stacks were obtained using FIJI and used for overlay with EM images (Schindelin et al, 2012).

Fluorescence microscopy studies revealed that HP1a is enriched in domains of cHC of Drosophila cells, while also binding some euchromatic loci, leading to low-density diffuse distribution within the nucleus (James et al, 1989; Kellum et al, 1995; Strom et al, 2017; Swenson et al, 2016). Additionally, HP1a-positive heterochromatin domains were shown to be located at the periphery of Drosophila neurons and glial nuclei (Pindyurin et al, 2018). In agreement with these observations, we observed large bright domains of GFP fluorescence at the periphery of brain nuclei (Fig. EV1D, white arrows), together with a diffuse staining of the complete nuclei that enables them to roughly identify its borders in fluorescence microscopy.

After fluorescence imaging, the grids with sections were contrasted with 2% uranyl acetate in 70% methanol, followed by Reynolds lead citrate. The grids were inserted into a Tecnai F30 electron microscope operated at 300 kV, and two-dimensional montage images of the complete sections were acquired with a 4k × 4k CCD US4000 camera controlled by Serial EM software.

For correlation of fluorescence patterns (Fig. EV1D, FM) and structural features discernible in EM images (Expanded view EV1D, EM), the corresponding pair of images were resampled to 20 nm/pixel using FIJI and overlayed in Adobe Photoshop SC6 (Adobe Inc., San Jose, CA, USA). The diffuse component HP1 fluorescence enabled overlaying of the fluorescence images of nuclei visible in EM images.

The overlay demonstrated that the bright HP1-GFP fluorescence spots correspond to electron-dense domains (Fig. EV1D, overlay) located at the nuclear periphery. Representative examples of such domains are shown in the Expanded view EV1E. These domains are enclosed within the outer 500–700 nm layer of the nucleus and are elongated along the nuclear envelope. cHC domains are also located in the vicinity of the nucleolus (Fig. EV1E, example 3, NO). This observation agrees with the fact that the ribosome gene cluster in Drosophila is located within the pericentric heterochromatic region of X and Y chromosomes (Ritossa and Spiegelman, 1965). In vitreous cryo-sections, we identified cHC domains as large domains located at the nuclear envelope periphery, and ECfHC domains as those, always nano-sized, distributed within the nucleoplasm (Appendix Fig. S1CD). For our quantitative analysis, we selected the ECfHC domains located in the central region of nuclei, 700 nm away from the nuclear envelope.

Targeted cryo-trimming and vitreous cryo-sectioning

The carriers with high-pressure frozen wild-type embryos were transferred into a chamber of a Leica EM FC6/UC6 cryo-microtome precooled to −145 °C and mounted inside a flat sample holder so that the anterior tip of the embryo was oriented toward the knife (Appendix Fig. S1A). The flat-edge portion of trim 45° (Diatome) was used to remove the metal wall of the carrier, then the trimming continued, removing 70 µm of embryo material starting from its anterior tip (Appendix Fig. S1A), to gain access to the CNS. A 90° trimmer (trim 90°, Diatome) was then used to cut the edges off the sides, resulting in a 70 μm × 70 μm × 70 μm cubic block containing the brain tissue. The sections were cut with a nominal cutting feed of 50 or 75 nm using a cryo 25° diamond knife (Diatome) and collected and attached onto C-flat CF-2/1 or Quantifoil R2/1 grids (Electron Microscopy Sciences) with the Leica EM Crion operating in charge mode.

Tilt series acquisition, reconstruction, and denoising

For cryo-electron tomography, grids with sections were mounted into Autogrid rings (Thermo Fisher Scientific) and transferred into a Titan Krios (Thermo Fisher Scientific), operated at 300 kV, equipped with a Volta phase plate (VPP), a GATAN GIF Quantum SE post-column energy filter and a K2 Summit direct electron detector (Gatan). The section areas, optimally attached to supporting carbon film, were identified by tilting the grid with 10° steps at ×1400 magnification. The regions of the nuclei overlapping with the C-flat holes were then identified by brief screening at ×2300 (Appendix Fig. S1B–D), and automated tilt series recording was performed using Serial EM software (Mastronarde and Held, 2017). The dose-symmetric recording scheme (Hagen et al, 2017) was applied within an angular range from −60° to +60°, with a starting angle of 0° and 2° steps at a nominal magnification of ×64000 (2.12 Å/pixel). The data were collected with a Volta Phase Plate (VPP) in close to focus conditions (Mahamid et al, 2016). To avoid over-focusing parts of images at high tilts, −0.25 μm defocus was applied. The electron dose was set to 2.5 e^–^/Å^2^ for individual tilt images, corresponding to a total dose of 152 e^–^/A^2^ for the complete tilt series.

The denoising of the tomograms was performed with the nonlinear anisotropic diffusion (NAD) (Frangakis and Hegerl, 2001) filter of IMOD (Kremer et al, 1996) and deep learning networks based on the Noise2Noise principle (Lehtinen et al, 2018) available in the Warp (Tegunov and Cramer, 2019) and Topaz (Bepler et al, 2020) software packages. For training data preparation, dose-fractionation frames of the tilt series were aligned using the IMOD Alignframes tool, resulting in three tilt series: the complete one consisting of tilt images containing all frames for each tilt angle (complete); a tilt series consisting of tilt images containing only even frames for each tilt angle (even); and a tilt series consisting of tilt images containing only odd frames for each tilt angle (odd). Then, markerless tilt series alignment was performed on the complete series and used to align the odd tilt series and even tilt series. Tomograms were reconstructed using weighted back projection in the etomo program of IMOD with a pixel size of 4.25 Å (Kremer et al, 1996). A SIRT-like filter, equivalent to ten iterations, was applied to the reconstructions before applying the NAD filer. Reconstructions used for deep learning network training were done with the standard ramp filter. To provide a consistent input range for the network training, the reconstructions were normalized with EMAN2 (Tang et al, 2007) e2preproc.py to a mean density value of 0 and σ = 1.

Fifteen (15) iterations of the NAD filter, with the K value set to 1, were applied to the complete volumes. Noise2Map network of Warp was trained on the even and odd reconstructions, starting with the initial model noisenet3dmodel_256 using the following parameters: dont_augment, dont_flatten_spectrum, learningrate_start 1E-05, iterations 40000. The training and denoising was performed on a PC equipped with 2 NVIDIA Quadro RTX8000 GPUs. Note that network training was successful only for reconstructions with <0.6 nm of a mean residual error measured in etomo. Topaz denoise3d network was trained on even and odd reconstructions of each tomogram of 4.25 Å/px, without an initial model, using the following parameters: topaz denoise3d --optim adagrad --lr 0.0001 --criteria L2 --crop 96 --batch-size 10 --weight_decay 0 --momentum 0.8 --N-train 1000 --N-test 200 --num-epochs 50 --save-interval 10 --device -2 --num-workers 1. The training and denoising with Topaz were supported by the computational resources of a high-performance computing cluster of IGBMC.

Subtomogram averaging of manually picked nucleosomes and X-ray structure docking

Nucleosomes were manually picked from all reconstructions in IMOD after denoising, then the corresponding 64^3^ voxels (voxel size of 4.25 Å) were extracted from the original non-denoised volumes using AV3 toolbox (Forster and Hegerl, 2007). Subtomogram alignment and averaging were performed with the SubTomogramAveraging script (https://github.com/uermel/Artiatomi). The initial reference map was simulated from the crystal structure (pdb:2PYO (Clapier et al, 2008)) with 80 Å resolution using molmap command of UCSF ChimeraX (Pettersen et al, 2021); Resource for Biocomputing, Visualization, and Informatics at the University of California, San Francisco, USA. A Gaussian noise was added to the reference with a standard deviation of 1 using the AV3 toolbox. We performed alignment of the picked particles for each tomogram—for mapping them back in the corresponding reconstruction (Figs. EV2 and EV5), and alignment of all picked particles using a gold-standard approach for resolution assessment (Scheres, 2012) (Fig. EV2). In both cases, alignment of subtomograms was performed in ten iterations. A non-binary mask for subtomogram alignment was generated by applying a 3D Gaussian smoothing filter with a standard deviation of 0.5 to the reference map in MATLAB using the imgaussfilt3 command. A bandpass filter was applied with a low cutoff frequency of 5 reciprocal-space pixels (1/54.4 Å^–1^), a high cutoff frequency of 12 reciprocal-space pixels (1/22.6 Å^–1^), and a Gaussian edge smoothing with a standard deviation of three reciprocal-space pixels. Seven iterations of an unconstrained rotational search (three rotational degrees of freedom) were performed with an angular sampling step of 10°, followed by three iterations of rotational search constrained to 20° for three rotational degrees of freedom with an angular sampling step of 2°. We found that an increasing number of iterations does not result in further resolution improvement. For the gold-standard validation, all picked particles were divided into two independent subsets based on particle numbering (“even” and “odd”). Each subset was subjected to identical alignment and averaging procedures, using the same initial reference and mask. The gold-standard Fourier shell correlation (FSC) was computed using the PDBe FSC validation server (https://www.ebi.ac.uk/emdb/validation/fsc/). The resulting FSC curve indicated a resolution of 21.4 Å without masking and 18.9 Å after masking, based on the 0.143 criterion (Fig. EV2).

3D subvolume visualization, atomic model docking, linker DNA modeling

The crystal structure of the Drosophila nucleosome pdb:2PYO was fitted automatically into the subtomogram average using the FitinMap tool from UCSF ChimeraX (Pettersen et al, 2021); Resource for Biocomputing, Visualization, and Informatics at the University of California, San Francisco, USA. For fitting, we set the simulated map resolution of pdb:2PYO to 20 Å according to the resolution of subtomogram averages assessed by FSC (Fig. EV2). The automated fitting gave cross-correlation coefficients of 0.6197, 0.6015, and 0.6183 for ECfHC1, ECfHC2, and cHC, respectively. The threshold level for the map isosurface was set to 2.86 according to the coverage of DNA gyres and histone octamer. The same threshold level was applied to all three averages.

To generate the chromatin models shown in Figs. 2 and 3, subvolumes of 100^3^ voxels (voxel size of 4.25 Å) containing two or three nucleosomes connected by visible linkers were extracted from denoised reconstructions by the boxing tool of EMAN2. The cryo-electron microscopy density map was simulated from the crystal structure (pdb:2pyo) with 18 Å resolution using EMAN2. This map was used for docking into the individual nucleosomes within extracted subvolumes, and then the atomic model of the nucleosome was fitted inside this map. This two-step docking procedure was used because an automated fitting of the atomic model of nucleosomes into tomogram subvolumes resulted in misorientations.

The accuracy of this docking depends on the orientation of the nucleosome relative to that of the missing wedge. The best results for the translational fitting and orientation were obtained for nucleosomes with the rotational axis perpendicular to the* z*-axis of the reconstruction. In this case, the rotational axis of the nucleosome could be defined automatically, and then the orientation of the dyad axis was manually tuned to fit the linker path. GraphiteLifeExplore (Life Explorer Initiative, https://www.lifeexplorer.info/) was used to model DNA linkers. Following guidance from Larivière et al (Lariviere et al, 2017), DNA linkers were placed following the isosurface extracted from the 3D subvolume using UCSF ChimeraX. For simulating crowding effects, the nucleosome-linker models were exported as .pdb files.

To generate the tetrasome model (Fig. 4A–C), we started by removing H2A/H2B dimers from the pdb:2PYO structure using UCSF Chimera, resulting in the H3/H4 tetramer and DNA. We then trimmed the DNA so that only the DNA region interacting with the H3/H4 tetramer remained. To generate the hemisome model (Fig. 4A,D), one of all four histones, and the corresponding gyre of DNA, were removed from pdb:2PYO. Next, the remaining DNA was trimmed, leaving only the part interacting with the remaining histones. The resulting tetrasome- and hemisome-like structures were manually fitted to the corresponding 3D subvolumes (Fig. 4B,D), then DNA entry/exit regions were modeled following the isosurface extracted from the 3D subvolume using GraphiteLifeExplore. Cryo-EM densities of the nucleosome, tetrasome, and hemisome shown in Fig. 4A were simulated in ChimeraX using the molmap command at a resolution of 25 Å and a voxel size of 4.25 Å. The missing wedge was then applied using custom MATLAB scripts based on functions provided by the AV3 toolbox.

Linker and nucleosomal DNA tracing

Using IMOD routines, DNA linkers were manually traced by three independent observers in two volumes containing eu/facultative chromatin domains (ECfHC1 and ECfHC2) and one volume of heterochromatin (cHC) denoised by Warp. Linkers were identified as the fibrillar objects found in tomograms, with a diameter of 2 nm, and with one or both ends coinciding with a recognizable nucleosome. To trace a linker, each observer chose a few voxels between which the linker appeared as a straight line (Fig. EV3). The centers of these voxels were then stored as the tracing points of the linker. In cases where linkers were identified by more than one observer, the tracings were found to be similar and a single consensus list of tracing points was stored. When only one nucleosome could be recognized, the tracing point numbering started from the nucleosome side. In total, 259 linkers were traced, with 140 double-ended linkers (2 N) having two nucleosomes identified, and 119 single-ended linkers having only one nucleosome (1 N)—see Appendix Table S1A.

The DNA path within round top views of nucleosomes, sub-nucleosomal particles, and sharply bent regions (hairpins) was traced by selecting points within the DNA density of the particle (see Appendix Fig. S7).

Visualizations of nucleosomes and linker DNA mapped back to tomographic data shown in Fig. EV5; Appendix Fig. S9; Movie EV5 were performed using ArtiaX plugin for ChimeraX (Ermel et al, 2022).

Analysis of linker DNA length and curvature

Theoretical background

Linkers were modeled as worm-like chains (WLCs). A WLC is a semi-flexible chain that we describe (as usual) as a curve, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r\left(s\right)$$\end{document} , parametrized by its arc length, s, and we denote the tangent vector as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t\left(s\right)=\frac{{dr}\left(s\right)}{{ds}}$$\end{document} . The modulus of the vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{dt}\left(s\right)}{{ds}}$$\end{document} is the curvature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa \left(s\right)$$\end{document} at point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r\left(s\right)$$\end{document} . The elastic energy of the WLC is equal to its bending energy

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{b}=\frac{{k}_{B}T}{2}{l}_{p} \int^{L}_{0}{\kappa }^{2}\left(s\right){ds}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{p}$$\end{document} is the persistence length of the chain, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{B}$$\end{document} is the Boltzmann constant and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=300K$$\end{document} is the temperature of the system (before freezing). L is the contour length of the chain.

To perform numerical simulations of WLCs, we used a discretized version of the WLC model with segments of 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mbox{bp}}$$\end{document} . In this model, the curvature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa \left(s\right)$$\end{document} is replaced by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{\varDelta {\theta }_{i}}{\varDelta s}$$\end{document} , where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta {\theta }_{i}$$\end{document} is the absolute value of the bending angle between segments i and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i+1$$\end{document} . This discretized version of the curvature requires \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta {\theta }_{i}\ll 1$$\end{document} which is fulfilled whenever \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta s\ll {l}_{p}$$\end{document} . The 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mbox{bp}}$$\end{document} discretization more than satisfies this condition. The bending energy of segment \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i+1$$\end{document} with respect to segment i is:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{b,i}=\frac{{k}_{B}T}{2}{l}_{p}{\frac{\varDelta {\theta }_{i}}{\varDelta s}}^{2}$$\end{document}

The Boltzmann distribution of the curvature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa \left(s\right)$$\end{document} at any point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r\left(s\right)$$\end{document} is (following (Rappaport et al, 2008)):

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\left(\kappa \right)d\kappa ={l}_{p}\varDelta s{e}^{-\tfrac{1}{2}{l}_{p}\varDelta s{\kappa }^{2}}\kappa d\kappa$$\end{document}

When the linker DNA has an intrinsic curvature, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{0}\left(s\right)$$\end{document} , the above equations need to be generalized. This is the case when the linker is subjected to a given bending torque Γ exerted by its flanking nucleosomes. Then the energy of the corresponding WLC model at mechanical equilibrium is given as a function of the geometric curvature, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{0}\left(s\right)$$\end{document} :

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{{WLC}}=\frac{{k}_{B}T}{2}{l}_{p}\int^{L}_{0}{\kappa }_{0}^{2}\left(s\right){ds}$$\end{document}

Now, at mechanical equilibrium, the torque Γ is constant along the linker. Since \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varGamma ={k}_{B}T{{l}_{p}\kappa }_{0}\left(s\right)$$\end{document} , it arises that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{0}$$\end{document} does not depend on s: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{0}=\frac{C}{{l}_{p}{k}_{B}T}$$\end{document} . However, thermal fluctuations induce some additional curvature: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa -{\kappa }_{0}$$\end{document} . The resulting Boltzmann distribution of the curvature is then:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\left(\kappa \right)d\kappa ={{A}^{-1}l}_{p}\varDelta s{e}^{-\tfrac{1}{2}{l}_{p}\varDelta s{\left(\kappa -{\kappa }_{0}\right)}^{2}}\kappa d\kappa$$\end{document}

where A is a numerical normalization factor:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A = \int^{\infty }_{0}{e}^{\frac{-1}{2}{\left(x-{\tilde{\kappa }}_{0}\right)}^{2}}{xdx}$$\end{document}

with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\widetilde{\kappa }}_{0}=\sqrt{{l}_{p}\varDelta s}{\kappa }_{0}$$\end{document} .

In this case, the validity of the discretization is subject to the condition: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{0}\varDelta s\ll 1$$\end{document} , which means that the segment length must be much smaller than the intrinsic radius of curvature of the linker DNA. Again, the 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mbox{bp}}$$\end{document} discretization still satisfies this condition, even in the most stringent case of the solenoid fiber where the intrinsic curvature is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{0}={{\mathrm{0,18}}}\,{{nm}}^{-1}$$\end{document} , i.e., a radius of curvature of ~5 nm.

Computing the actual trajectory of the linkers

The trajectory of any linker between two consecutive tracing points is almost straight, hence the sum of the distances between consecutive tracing points is a proxy of the actual contour length of the linker, either single- or double-ended. This sum, expressed in nanometers, is denoted \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{nm}}$$\end{document} . Then the integer part of the ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{L}_{{nm}}}{{{\mathrm{0,34}}}}$$\end{document} , here denoted \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{\mathrm{int}}}} (\frac{{L}_{{nm}}}{{{\mathrm{0,34}}}})$$\end{document} , is also a proxy of (and always smaller than) the actual number of base pairs in the linker DNA.

To find the actual trajectory of each linker, we designed the following algorithm to find the WLC conformation(s) that cross(es) all its tracing pixels:

1. We start from a contour length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp}}={{\mathrm{int}}}\left(\frac{{L}_{{nm}}}{{{\mathrm{0,34}}}}\right)$$\end{document} .
2. We run a WLC simulation with contour length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp}}$$\end{document} , persistence length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{p}=50{nm}$$\end{document} and 1 bp discretization, and keep the optimal conformations, i.e., those that cross the largest number of tracing pixels.
3. We define the overlap σ as the fraction of tracing pixels that are crossed by the WLC (σ =  1 when the WLC crosses all tracing pixels). If the overlap \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma < 1$$\end{document} , we increment \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp}}$$\end{document} by 1 and we go back to step 2.
4. If the overlap \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma =1$$\end{document} , the algorithm stops and the corresponding value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp}}$$\end{document} is denoted \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp},{best}}$$\end{document} . This value \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp},{best}}$$\end{document} is the best estimate of the actual number of base pairs in the linker DNA.

Simulations were run for a given number of Monte-Carlo steps \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mbox{MCS}}$$\end{document}  = 10^8^ before stopping. For each of the three tomograms (ECfHC1, ECfHC2, and cHC), we ran the above algorithm for 1 N and 2 N linkers.

Computing the contour length of the linkers

We computed the distribution of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp},{best}}$$\end{document} for 2 N linkers in each of the three tomograms (ECfHC1, ECfHC2, and cHC) and we characterized each corresponding distribution with its two first moments (mean and standard deviation), as well as skewness and Fisher’s definition of the kurtosis (Appendix Table S1B). All distributions are clearly not normal. Skewness shows that the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp},{best}}$$\end{document} distributions are strongly asymmetric.

We then investigated whether these three histograms were significantly different or whether they could be put together into a common whole. We therefore applied a Kolmogorov–Smirnov (KS) two-sample test (Hodges, 1958) between any two of these three histograms to test the null hypothesis \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{0}$$\end{document} : “two experimental distributions are actually drawn from the same distribution”. We used the Scipy function (Jones et al, 2001) to run the KS test and compute the corresponding p values. The results of these tests are given in Appendix Table S1C. The null hypothesis \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{0}$$\end{document} “the two experimental distributions are drawn from the same distribution” cannot be rejected at the level of significance α = 0.1 neither for eu- nor heterochromatin histograms, therefore the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp},{best}}$$\end{document} distributions can be merged for analysis (see Fig. 3A).

Computing the curvature of the linker and nucleosomal DNA

The algorithm we described above gives access to the whole conformation of the WLC which has perfect overlap \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma =1$$\end{document} with a given linker. For this best-simulated WLC we computed the local curvature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left({\varDelta \theta }_{i}\right)/\varDelta s$$\end{document} , where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta {\theta }_{i}$$\end{document} is the absolute value of the bending angle between segments i and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i+1$$\end{document} . Curvature is expressed in nm^−1^. We could then compute the average curvature of the linker as the mean of the local curvature along the best-simulated WLC. The local curvature is the curvature between two consecutive base pairs. For example, a linker of length 10 bp has 10 – 1 = 9 local curvatures. The average curvature per linker is then the average over these nine local curvatures. The same approach was used to estimate the average DNA curvature within nucleosomes, sub-nucleosomal particles, and a sharply bent region (hairpin) (Appendix Fig. S7). To compare the curvature distributions between nucleosome and sub-nucleosomal particles, we used the Mann–Whitney U-test (Fay and Proschan, 2010).

To compute the linker curvature, we considered both 2 N and 1 N linkers from ECfHC1, ECfHC2, and cHC tomograms because curvature is a local feature, unlike the linker length, which is a global feature. We then ran a Kolmogorov–Smirnov two-sample test between any two of the six distributions of the average curvature per linker to test the null hypothesis \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{0}$$\end{document} : “are the values drawn from the same distribution?”. The results of these tests are given in Appendix Table S1D. The p values showed that we could not reject the null hypothesis \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{0}$$\end{document} . Consequently, we were allowed to combine the curvature distributions for further analysis (see Fig. 3B).

Coarse-grained model of zig-zag and solenoid fibers

To compare these experimental histograms with the classic zig-zag and solenoid models, we also computed the distribution of the average curvature per linker for these two models (see Fig. 3B). For each optimal linker length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp},{best}}$$\end{document} that was extracted from one of the three tomograms ECfHC1, ECfHC2, and cHC, we built both a zig-zag and a solenoid fiber, according to the following procedure:

• (i)A coarse-grained model of a rigid nucleosome is first built at the scale of 10.5  \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mbox{bp}}$$\end{document} . A frame is attached to each monomer of 10.5  \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mbox{bp}}$$\end{document} (corresponding to a length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l=3.57{{\mathrm{nm}}}$$\end{document} and a diameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=2{{\mathrm{nm}}}$$\end{document} ). The tangent follows the centerline of the DNA while the normal vector points towards the minor groove. A linker (with contour length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp},{best}}$$\end{document} ) exits the first nucleosome and connects to the second nucleosome. The orientation of the second nucleosome is given by the DNA (minor groove) rotational phase. The histone octamer is made of four capped-cylinders to avoid any nucleosome–nucleosome overlap. The system is coupled to a Langevin thermostat at the room temperature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=300K$$\end{document} (Carrivain et al, 2014). Bending torques (the persistence length we used is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{p}=50{{\mathrm{nm}}}$$\end{document} ) and twisting torques (with persistence length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{t}=85{{\mathrm{nm}}}$$\end{document} ) mimic the mechanical properties of DNA. Rigid bond constraints enforce DNA connectivity.
• (ii)We add stacking interaction between two consecutive nucleosome core particles to model a solenoid fiber (one start chromatin fiber, see Fig. 3B, solenoid). Although there is no stacking interaction for the disordered zig-zag model (see Fig. 3B, zig-zag), there is still excluded volume between nucleosomes. To minimize end effects, we extract one linker in the middle of the chromatin fiber to measure the average curvature per linker.

Of note, the local curvature density of the linkers in the zig-zag (resp. solenoid) model is in good agreement with the theoretical expression Equation [1] (resp. Equation [2]), as shown in Appendix Fig. S10. Therefore, we are confident that our simulations properly reproduced the curvature behavior of linker DNA in general.

Calculation of the correlation between linker length and average curvature

Spearman correlation coefficients ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{SPEARMAN}$$\end{document} ) between length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{{bp},{best}}$$\end{document} distributions of 2N linkers from ECfHC1, ECfHC2, and cHC, and their average curvature distributions were calculated using Scipy (seehttps://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.spearmanr.html for more details).

Simulation of chromatin fibers

Using the Open Dynamics Engine (https://gitlab.com/pcarrivain/fibre_ode), we simulated possible configurations of the chromatin filament entering our experimental measurements of linker length and curvature.

Simulation of crowding effects on DNA linker visibility after denoising

Tomographic volumes containing chromatin with bent and straight linkers were simulated with custom MATLAB scripts based on functions provided by the AV3 toolbox. Initially, atomic models containing two nucleosomes connected with a linker were built in GraphiteLifeExplore and saved as .pdb files. The model of the real volume two-nucleosome connected by the 50 bp linker shown in Fig. 2A (upper row) was used for simulation for the case of a straight linker. To simulate the bent linker situation, two nucleosomes were aligned along rotational axes and connected with 60 bp linker DNA (Appendix Fig. S3A). The intrinsic curvature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa }_{0}$$\end{document} of the straight and the bent linkers were 0 nm^−1^ and 0.13 nm^−1^, respectively. The density map was generated in UCSF ChimeraX using the molmap command with a resolution of 4.25 Å/px. The map was used without applied defocus, and placed into 1024^3^ voxels (435.2^3^ (nm)^3^) volumes, whilst being oriented randomly in all three rotational degrees of freedom. Each volume was filled separately with dinucleosome densities with either straight or bent linkers. We could achieve the density of 4.2 × 10^5^ nucleosome/(µm)^3^ corresponding to 0.69 mM both for low- and high-curvature linker dinucleosomes. This value is of the same order of magnitude as the density of compact chromatin in vivo measured by fluorescence-based techniques (0.25–0.5 mM) (3,4). To explore the visibility of linkers and nucleosomes at low crowding conditions, we generated a volume filled with the same randomly-oriented dinucleosome densities with the concentration of 5.5 × 10^3^ nucleosomes/µl (9 µM).

To mimic the sectioning process, we extracted the central slice of the simulated volumes measuring 435.2 × 435.2 × 75 nm. This slice was rotated and projected using the same angle range and increment as for the real tomograms, resulting in a series of tilt images. These images were normalized, and Gaussian noise was added to the tilt images with signal-to-noise ratios of 1, 0.5, 0.25, and 0.1. The tilt series were saved as MRC files, aligned, reconstructed, and denoised with the Warp model as was done for the real tomograms (see Tilt series acquisition, reconstruction, and denoising).

Influence of cutting on linker orientation and chromatin-folding path

The orientation of tomographic reconstructions of sections with respect to the cutting direction was determined from the orientation of the knife marks (Al-Amoudi et al, 2005). Two co-initial vectors were defined on the surface of the section containing knife marks: vector C is parallel to the cutting direction, and vector Nc is normal to the cutting direction. Then we defined the vector Ns that is normal to the section surface, and accordingly normal to C and Nc (see Appendix Fig. S4A).

The end-to-end vector of each linker was projected onto C, N_c_, and N_s_. The projection values were used to test the null hypothesis \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{0}$$\end{document} : “the projection follows a uniform distribution”. As the projection value of isotropic random vectors onto any direction is uniform, this test is equivalent to testing the isotropy of the distribution of the linker end-to-end vectors. Generating isotropic random vectors is equivalent to drawing random points on the unit sphere (https://mathworld.wolfram.com/SpherePointPicking.html).

Supplementary information

Appendix Peer Review File Movie EV1 Movie EV2 Movie EV3 Movie EV4 Movie EV5 Source data Fig. 1 Source data Fig. 2 Source data Fig. 3 Source data Fig. 4 Expanded View Figures