Polymer modelling unveils the roles of heterochromatin and nucleolar organizing regions in shaping 3D genome organization in Arabidopsis thaliana

Epigenomic states analyses

ChIP-seq epigenomic data at 400 bp of resolution for 4 histone marks: H3K4me2, H3K4me3 (signatures of active genes), H3K27me3 (signature of facultative, polycomb-like heterochromatin) and H3K9me2 (specific to constitutive heterochromatin) were collected from published works (44,45). To each 3 kb-genomic region of the genome, an average epigenomic signal was assigned for each of the four marks. A K-means algorithm (Euclidean distance, k = 4) allowed clustering the 3 kb-regions into four groups: active chromatin (AC) enriched in H3K4me2/3, facultative heterochromatin (FH) enriched in H3K27me3, constitutive heterochromatin (CH) enriched in H3K9me2 and undetermined (UND) depleted in all these four marks. The lengths and the genomic localization of the domains assigned to each of the four chromatin states were used to generate the plots in Figures 1B and C and in Supplementary Figure S1.

Genome-wide chromosome simulations

Analysis of the polymer models

Epigenomics-driven folding of A. thaliana chromosomes using polymer models

In this study, we tested the hypothesis that specific interactions mediated by epigenomics are driving forces of the genome structural organization in A. thaliana. To this end, we applied to a plant species a modeling method that has been previously applied to the fly (33,37) and human (34–36,72–75) genomes and that posits that epigenomics-driven interactions partition the genome into spatial compartments. Here, we built polymer models of the chromosomes using beads of 30 nm hosting each 3 of chromatin (Figure 1A). We used short-range attractive and repulsive interactions between 3 kb-regions defined by their epigenomic state in conditions of density and confinement mimicking the nuclear environment.

Based on the enrichment in epigenomic marks (44,45), we assigned to each 3 kb-region one of four chromatin states (33) (Materials and Methods). A total of 52% of the genome was assigned to active chromatin (AC) enriched in H3K4me2 and H3K4me3, 14% to facultative, polycomb-like heterochromatin (FH) decorated with H3K27me3, 14% to constitutive heterochromatin (CH) enriched in H3K9me2 and 12% to undetermined (UND) regions that were depleted in all the considered epigenomic marks (Figure 1B and C, and Supplementary Figure S1).

Extending previous modeling approaches, the remaining parts of the A. thaliana genome were assigned to two other genomic categories that we used as complementary to the epigenomic states. The nucleolar organizing regions (NORs), that are the constitutive sequences of the nucleolus (41,49,50), account for 6% of the genome and are localized in the small arms of chromosomes 2 (NOR2) and 4 (NOR4). The telomeres, that account for about 1% of the genome, are the ∼150 kb regions at the ends of each chromosome (Figure 1C, Supplementary Figure S1, and Supplementary Table S1). To account for the high concentrations of RNA and proteins within the nucleolus (41,49,50) and for the typically increased stiffness of the telomeres (76), NORs and telomeric 3 kb-regions were modelled as thicker beads (Figure 1A) of diameter 132 nm allowing to mimic the formation of a spherical nucleolus of radius about 1.4 μm as typically observed in A. thaliana nuclei (50,77) (Supplementary Methods). Excluding the NORs, the more extended epigenomic domains of ∼400 kb were assigned to constitutive heterochromatin (CH) (Figure 1B) and, consistently with previous analysis (78,79), were localized at the chromocenter (centromeric and pericentromeric region) of each chromosome (Figure 1C and Supplementary Figure S1A–E). In our analysis, chromocenters are interspersed with short sequences hosting active chromatin (maximum size 54 kb) and facultative heterochromatin (maximum size 18 kb), which is consistent with the presence of ‘punctual’ active genes like the 5S rRNA gene clusters in the peri-centromeres of chromosomes 4 and 5 (80). Overall, the genomic regions occupied by active chromatin and facultative heterochromatin were organized into many interspersed domains of shorter lengths (maximum 93 kb for AC and 84 kb for FH, and median 6 kb for AC and 3 kb for FH).

Single-chromosome analysis allows parameterizing the epigenomics-driven interactions

To find the optimal epigenomics-driven model, we designed a strategy to minimize the amount of calculations needed and yet get a good understanding of how the different parameters affect the final compliance with the experiments. We focussed initially on the folding of chromosome 4 as it is the shortest in A. thaliana (Supplementary Table S1) and neglected for simplicity the nucleolar organizing region (NOR4). We simulated a toy-model with five copies of chromosome 4 with random initial placements and orientations in a cubic box with periodic boundary conditions at the typical DNA density (ρ = 0.004 bp/nm³) of the A. thaliana nuclear environment. In the initial conformation, the five model chromosomes were prepared as linear rod-like objects to mimic elongated mitotic states (29) (Material and Methods).

As illustrated in Figures 2A–E, we tested different types of short-range interactions involving the epigenomic chromatin regions defined above: self-attraction (full circles) and repulsion (dashed lines). Unless specified, the model beads interact with an excluded volume potential that allows the fibre to maintain a thickness of 30 nm and to avoid chain crossing (Supplementary Methods). Specifically, we started exploring three distinct scenarios for the interactions involving the constitutive heterochromatin (CH) regions (Figure 2): repulsions between CH beads and the other epigenomic states (Figure 2A), self-attraction between CH beads (Figure 2B), and a combination of the two (Figure 2C). These cases aimed to describe interactions driven by heterochromatin protein 1 (HP1) both in vitro and in vivo. Recent papers showed that HP1 (or its counterparts in plants LHP1 and ADCP1) can promote liquid-liquid phase separation (LLPS) mediated by intrinsically disordered regions (IDR) in vitro (81,82), can favour the formation of heterochromatin compartments in vivo (81,83,84), and generate a phase from which some proteins may be excluded (81,82). Overall, the collected evidence is yet not conclusive on whether the in vivo formation of HP1 phases is mainly driven by attraction between HP1 or by repulsion of HP1 with other chromatin states or with other chromatin-binding proteins. LLPS, in general terms, can be triggered via both self-attraction of a compound (in this case HP1) or via a repulsive interaction of a compound with the others present in the system, as it occurs for hydrophobic phases (85). On top of the CH-driven interactions, we tested separately the self-attraction of the active-chromatin (AC) regions (Figure 2D and Supplementary Figures S2–S4) and of the facultative heterochromatin (FH) beads (Figure 2E and Supplementary Figures S2–S4). The latter interactions are based on the observations that the binding of RNA PolII to active genes can prime micro-phase separation (86,87) and polycomb-mediated interactions can form local domains hosting H3K27me3-enriched gene-clusters (56,88,89).

In total, we tested 50 distinct scenarios with strengths of interaction ranging from 10⁻⁶ to 1.00 k_BT for repulsions and 0.025–1.00 k_BT for attractions (Supplementary Figures S2–S4). One k_BT typically represents an energy of the order of the thermal noise. The selected values of interaction strength allowed sampling distinct scenarios in which each of the imposed interactions varied between a small fraction to the same order (1.00 k_BT) of the thermal noise. For each of the 50 distinct scenarios, we simulated 10 independent trajectories of a few hours (30,62) using Langevin dynamics (Material and Methods) and obtained an ensemble of ∼400 conformations per parameter set (Figures 2F–J for illustrative snapshots at the end of the simulations).

To select the optimal interaction model, we computed predicted contact maps at 30 kbp resolution (Figures 2K–O and Materials and Methods) on the generated 3D models and compared them with the experimental Hi-C maps (44,45). The comparisons included the Spearman correlation coefficient (SCC) (90,91), which captures the overall similarity between model and experiment, and the compartment strength (CS) (71) for each epigenomic state (CH, AC, and FH), that quantifies the degree of compartmentalization of a given state by measuring the contact enrichment within versus between chromatin domains (Figures 2P–T, Supplementary Figures S2–S4, and Materials and Methods).

The obtained SCC values were larger than 0.70 for all the tested interaction models (Figures 2P–T and Supplementary Figures S2–S4) indicating that the explored models allow capturing the overall arrangement of chromosome 4. These high correlations are mainly due to the formation of a segregated domain (Figures 2K–O) at the chromocenter, that, in the models, is favoured by the CH-driven interactions. In fact, the addition of self-attraction within AC or FH improves marginally the SCC only by 1%. The difference between CH-scenarios (Figures 2P–R) is also weak (at most 0.05) with the CH repulsion scenario overall leading to higher similarity between models and experiments.

As expected, as the strengths of epigenomic interaction are increased, the CS augments (Figures 2P–T and Supplementary Figures S2–S4). Interestingly, we found that optimal parameters for CS are also close to optimal for SCC, with weak or intermediate values for interaction strengths. For example, in the simulations where the optimal CH self-attraction (E_CH = 0.30 k_BT) is combined with increasing AC self-attraction (Supplementary Figures S3 and S5), we observed that the intra-arm contact pattern of chromosome 4, that was made of strips (∼100 kb thick), was well captured only for mild interaction strength. As the AC interaction strength was increased, the separation between enriched and depleted strips became sharper with the effect of degrading the similarity of the CS with the Hi-C map.

The highest SCC value of 0.83 and the optimal similarity with the Hi-C compartment strength values were obtained for the CH-repulsive scenario (E_CH-* ∼ 0.0004 k_BT) together with self-attraction within active chromatin and facultative heterochromatin (E_AC–AC = 0.20 k_BT and E_FH-FH = 0.50 k_BT) regions (Figures 2S–T). Hence, this set of interactions was used to generate genome-wide models.

Genome-wide models reveal an overall preferential V-shape for A. thaliana chromosomes

To generate genome-wide models, we prepared each of the 10 model chromosomes (chromosomes 1 to 5 in two copies each, Supplementary Table S1) as rod-like objects made of stacked rosettes along the main axis (29,62), each mimicking a simplified shape of elongated mitotic chromosomes (Supplementary Videos S2 and Supplementary Figure S6A). The positions and orientations of each chromosome were chosen randomly inside a sphere of diameter 5.0 micrometres (μm), that is the typical A. thaliana nuclear size (77).

From 50 independent replicates of these initial chromosome conformations (Figure 3B), we simulated a few hours of the full genome dynamics (62) applying the optimal set of parameters inferred from the single-chromosomes simulations (Figure 3A). To characterize the contact patterns of the obtained models (representative snapshot in Figure 3C), we computed the genome-wide contact map (Figure 3D) and the average probability of contact P as a function of the genomic distance s between genomic regions on a set of ∼2000 conformations and compared them with the genome-wide interaction map and the P(s) obtained from Hi-C experiments (44,45) (Figure 3E and Material and Methods).

From the models, we recovered the contact patterns of the Hi-C at the genome-wide scale. Cis-chromosome areas of the contact map (see black dashed squares in Figure 3D) had much more contacts than the trans-chromosome ones. This feature indicates that the models well captured the organization of the nucleus into distinct chromosome territories (41–44). The epigenomics-driven models also recapitulated the contact enrichment between chromocenters of different chromosomes (see brown squares in Figure 3D) indicating that the effective repulsions between CH and the other chromatin states recover both the segregation of chromocenters at the cis-chromosome scale and the effective trans-chromosome attraction between chromocenters (41–46,52). To quantify the similarities of the models with experiments, we computed the CS for each epigenomic state and the SCC between the genome-wide maps, the 5 cis-chromosome maps (Figure 3F) in Hi-C and in our predictions. The comparisons between contact maps resulted in similar CS distributions (Supplementary Figure S8A) and significant SCC values. We found that the minimal SCC of 0.44 was obtained for the genome-wide contact maps, where the size of the compared samples is ∼7 000 000, and that in the per-chromosome comparisons the SCCs were always larger than 0.70 (sample-size > 180,000).

Interestingly, we found a discrepancy between the experimental and the predicted contact probabilities P(s) (Figure 3E). The experimental P(s) exhibits two regimes: at short and intermediate genomic distances (100 kb < s < 10 Mb) P(s) decays as s^−0.84, which is very well captured by the models. But, at larger genomic distances (s > 10 Mbp), corresponding to the typical range of inter-arm contacts, the observed increase of P(s) in Hi-C is missing in our prediction. Confirming the visual impression, we found a weak SCC value ( = 0.22 for sample-size = 1,014) when comparing the predicted and observed P(s) (Figure 3F).

To account for the inter-arm increase of contacts in the Hi-C maps, we designed a novel strategy to precondition the chromosome models as V-shaped arrangements (Figure 3G). The preconditioning attempted to incorporate an effective memory of chromosome structure throughout the cell cycle, which was suggested by Carl Rabl already in 1885 (92) based on microscopy observations of dividing cells in salamanders. Additional elements in favour of a persistent V-shape organization of interphase chromosomes were provided by modelling studies in several species, including yeast (93–96), drosophila (97), and human (98). In A. thaliana, during anaphase chromosomes are pulled, centromeres first, towards opposite poles of the mother cell (52,99). This results in a V-shape organization for metacentric chromosomes 1, 3 and 5 and in hook-like structures for acrocentric chromosomes 2 and 4. Assuming that chromosomes exhibit inherent properties of long-polymers in dense or semi-dilute solutions (31,32,100), we hypothesize that chromosomes will maintain an effective memory of these V-like shapes during interphase.

Accordingly, we initially arranged each chromosome in a linear (rod-like) shape (Supplementary Figure S6A) and then pulled it by the kinetochore (centromere) with harmonic forces along parallel directions (Supplementary Video S3 and Supplementary Figure S6B). To allow for the dragging of the entire chromosome structure, during the pulling process we pinned the chromosomes in a looped conformation using harmonic bonds bridging regions at a typical separation of ∼40 kb (14 model beads) (Supplementary Methods).

We simulated 50 replicates of the system with V-shaped chromosomes using the optimal epigenomics-driven interactions and characterized quantitatively the obtained conformations (representative snapshots in Figures 3G–H) computing the genome-wide contact map and the P(s) (Figures 3I and J). Applying the SCC analysis to compare with Hi-C, we observed that preconditioning the chromosomes in V-shaped conformations allowed capturing qualitatively and quantitatively the behaviour of the P(s), whose model versus Hi-C SCC increased dramatically from 0.22 to 0.88 (Figures 3J and K). The comparison of the contact maps (Figure 3K) were slightly improved (between 4 and 6% in SCC) for the genome-wide and the cis-chromosome cases of the acrocentric chromosomes 2 and 4, and the metacentric chromosome 3. SCC of the other metacentric chromosomes (chromosomes 1 and 5) were only marginally degraded (3 and 2% in SCC respectively). The distributions of compartment strength (Supplementary Figure S8) were shifted towards larger values in the V-shaped chromosomes, but yet they were largely consistent with the Hi-C ones. The overall improvement of the results with V-shaped chromosomes prompted us to use this chromosome shape for the rest of the genome-wide simulations.

Interestingly, we also tested the possible formation of V-shaped chromosomes from a radial chromosome pulling which is less biologically-founded (Figures 3L–P, Supplementary Video S4, Supplementary Figure S6C, and Materials and Methods). We found overall lower correlations with the Hi-C (Figure 3P). In particular, the SCC of the P(s) dropped from 0.88 for the parallel pulling case to 0.78 for the radial one.

The epigenomics-driven models capture the nuclear organization in A. thaliana

To further characterise the models obtained from the optimal set of parameters, we looked at the preferential nuclear location of the regions assigned to each epigenomic state (Figures 4A–E) and computed the distribution of their radial positions (Figures 4F–J, Supplementary Figure S9, and Material and Methods). To disentangle which of the typical nuclear positioning was to attribute to the specific epigenomics-based interactions, we designed and performed a reference set of simulations in which the initial V-shaped chromosome positioning and the NORs and telomeres attractions were maintained, but the other interactions were removed (see networks in Supplementary Figures S7 and S8B). The results of this variant system are shown in the histograms in Figures 4F–J in white colour as a term of comparison with the optimal interaction model whose results are shown in the characteristic colour of the epigenomic state.

Interestingly, we found that the nucleolus typically assumed a round shape with a radius ∼1250 nm and occupied the centre of the model nucleus (Figures 4A and F). The telomeres tended to localize at the nucleolar periphery (Figures 4B and G). These features were consistent with the reference model in which NORs and telomeres were involved in the same interactions. Notably, the constitutive heterochromatin (CH) domains typically occupied the outermost shell of the nucleus in the optimal model but not in the reference one (Figures 4C and H), in which the CH repulsions were removed. The active-chromatin tended to a slightly less peripheral positioning than in the reference interaction model (Figures 4D and I). Overall, these results are consistent with experimental evidence on the typical positioning of the nucleolus at the nuclear centre (41,49,50), of telomeres at the nucleolar periphery (42–46), and of heterochromatic regions at the nuclear periphery (46,52).

Next, we tested whether the preferential locations of the nucleolus and heterochromatin are also consistent with the fact that the telomeres, and chromocenters of chromosomes 2 and 4 (which host the NORs) associate with the nucleolus forming the so-called nucleolar-associated domains (NADs) (50), which are stable landmarks of the A. thaliana genome organization and are maintained under heat stress conditions (101). In A. thaliana, NADs correspond to repetitive elements that are transcriptionally silenced by repressive histone modifications and DNA methylation. To identify the predicted NADs in the nuclear models, we computed per each 3 kb-region (one bead) in the models the number of contacts with the NORs particles within a distance cutoff of 200 nm (Materials and Methods). In agreement with the experiments (50), we found that the top 10% regions making contacts with the NORs particles are the telomeric regions of each chromosome and the short arms of chromosomes 2 and 4 (Figure 4K). As a consequence, also the chromocenters of chromosomes 2 and 4 are involved in many contacts with the nucleolus and are typically found in a perinucleolar location in agreement with the experimental data (46,52).

Next, we tested whether the typical location of the heterochromatic regions at the nuclear periphery is also consistent with the experimental evidence that groups of chromocenters coalesce together in 8.6 ± 0.2 distinct foci (46). Specifically, in each snapshot of the trajectories, we considered the regions composing each of the 10 centromeres (as a proxy of the chromocenters, Supplementary Table S1) and associated to each of them a sphere centred at the centre of mass of the beads with a radius equal to their radius of gyration (Figure 4L). Per each chromocenters pair, we computed the overlap volume between the two representative spheres. To compare with experiments (46), we selected the threshold of the significant overlap to 0.34 so that the average number of distinct chromocenters in the model nuclei over the 50 replicates simulations is 8.6 that matches the average number measured experimentally (8.6 ± 0.2). Overall, the distribution computed from the models is slightly skewed towards larger numbers of foci than the experimental one (Figure 4M). Yet, the corresponding distribution of chromocenters’ numbers resembles the experiments with all the predicted values per bin showing no significant differences with the experimental measures. The differences with the prediction might be also due to an underestimation of the linear size of the centromeric regions in the A. thaliana reference genome, which was used to define the length of the model chromosomes (102). Larger centromeric sequences would likely favour co-localisation in the models and skew the predicted distribution in Figure 4M closer to experimental data.

NORs and heterochromatin interactions shape the nuclear organization in A. thaliana

To test the role of each epigenomics-based interaction, we generated models for eight variant cases in which we modified the interactions involving one chromatin state at a time. Specifically, we perturbed the optimal interaction model (Figure 3A) by removing the self-attraction among NORs and telomeric regions (Figure 5A and Supplementary Figure S12), removing the repulsions between CH beads and the other epigenomic states (Figure 6A and Supplementary Figure S15), removing the self-attraction between AC regions (Supplementary Figure S10), and removing the self-attraction between FH beads (Supplementary Figure S11). To further test the role of the nucleolus and of the constitutive heterochromatin, we varied the size of the NORs particles (Figure 5B–C and Supplementary Figures S13–S14), and tested the alternative CH interactions schemes of Figures 2B and C, where the constitutive heterochromatin was self-attractive and self-attractive+repulsive respectively (Supplementary Figures S15 and S16).

Each of the variants was compared to the optimal model by considering the radial distributions of chromatin states and by performing a SCC analysis on the genome-wide contact maps.

We found that removing only the self-attraction of the NORs and the telomeric beads and maintaining the other epigenomic-driven interactions caused dramatic nuclear rearrangements involving all the chromosomes. As expected, the compact nucleolus was disrupted (Figure 5D, representative snapshot) and the NORs regions were spread over the entire nucleus, resulting in an enrichment of NORs beads at the nuclear periphery and a depletion at the centre with respect to the optimal interaction model (Figure 5G). Interestingly, these findings are qualitatively consistent with the imaging data in human Dnmt1-deficient cells where the nucleolus is disrupted and the nucleolar rRNA genes are scattered throughout the nucleus (103). The telomeres expectedly lost their preferential perinucleolar positioning and relocalized in more peripheral shells of the nucleus (Supplementary Figure 12B). The perturbation of NORs interactions also affected the nuclear positioning of the constitutive heterochromatin, active chromatin and facultative heterochromatin, that are found in more central nuclear positions despite the maintenance of the epigenomics-driven interactions (Figure 5J and Supplementary Figure S12C–E).

Varying the size of the self-attracting NORs particles had also large impacts on the nuclear positionings of all the chromatin states. Small NORs beads induced the formation of a smaller nucleolus of radius about 1 μm (Figures 5E and 5H) and allowed all the other chromatin states to occupy more central nuclear positions (Supplementary Figures S13C–E). In particular, the constitutive heterochromatin (which maintained its repulsive interactions) lost its preferential peripheral positioning (Figure 5K) indicating that, in our prediction, the nucleolar push is necessary to recapitulate the expected CH positioning at the nuclear periphery. This is confirmed by the simulations performed with larger NORs beads that lead to a nucleolus that occupies almost the entire nucleus (Figures 5F and I) and that pushes all the chromatin states towards the nuclear periphery with an enhanced effect for CH (Figure 5L and Supplementary Figures S14C–E).

Interestingly, the large changes in nuclear positioning induced by each of the NORs’ variant systems had a marginal effect on the respective contact patterns. The corresponding genome-wide contact maps, that did not include the NORs regions for consistency with the Hi-C interaction maps, appeared to be visually very similar to the one obtained for the optimal interaction model (Figures 5M–O) and quantitatively correlated equally well with the Hi-C interaction maps (Supplementary Figures S7C–E).

The removal of the repulsive interactions between CH beads and the other epigenomic states (Figure 6A) had the effect to push the heterochromatic regions towards the nuclear centre so that CH beads are less probably found in the outermost nuclear shell than in the optimal interaction model (Figures 6D and G). Notably, the CH neutrality also marginally affected the nuclear location of the other epigenomic (AC and FH) states by pushing them slightly towards the nuclear centre (Supplementary Figures S15D–E). Interestingly, the main reverberation of the CH perturbation appears in the genome-wide contact map. Specifically, the signatures of the segregation of the centromeric regions are visually lost, and the trans-chromosome sections of the map are different from the correspondent parts in the optimal interaction case (Figure 6J). Quantitatively, the similarity of the model and the Hi-C contacts map were degraded with respect to the optimal model both in terms of the Spearman correlation (SCC = 0.43 vs SCC = 0.49 for the optimal), and the CS distribution that was only marginally matching the Hi-C (Supplementary Figures S7F and 8F). Although the average contact probability as a function of the genomic separation, P(s), is captured accurately (SCC = 0.93) (Supplementary Figure S7F).

The two variant simulations in which the constitutive heterochromatin (CH) was involved in purely self-attractive (Figure 6E) and in combined self-attractive and repulsive (Figure 6F) interactions also showed significant differences with the optimal model case. Neither of the two scenarios leaded to a significant peripheral localization of CH as the optimal case (Figures 6H and I) demonstrating that, although the overall compliance with the Hi-C data (Figures 6K and L) is similar with the optimal case both in terms of Spearman correlation (Supplementary Figures S7G–H) and compartment strength (Supplementary Figures 8G and H), the different types of CH-interactions had an impact on its recruitment at the nuclear periphery, that could in turn precondition CH to a tethering with the nuclear lamina. Similarly to CH, AC and FH were also significantly brought towards the nuclear center in the alternative scenarios (Supplementary Figures S15–S17).

The perturbations of the AC and FH interactions (Supplementary Figures S10–S11), that involved a sizeable fraction of the genome (52% and 14%, respectively) had only negligible effects on both the radial positioning of the corresponding chromosome regions and the genome-wide contact pattern.

The model plasticity allows accommodating fine-scale structural properties: the KNOT engaged elements (KEEs) and the local polycomb-like domains

To test whether adding specific sets of interactions (both epigenomics-driven or not) may help to recover structural properties at fine-scale without compromising the ones at large-scale, we studied more in detail the structural role of the KNOT engaged elements, KEEs (aka Interacting Heterochromatic Islands (IHIs)) (42,43) and of the facultative, polycomb-like (FH) heterochromatin (Figure 7 and Supplementary Figures S18 and S19). In particular, we tested whether we could recover the formation of long-range interactions between the 10 KNOT Engaged Elements (aka IHIs) that had been identified in Hi-C contact maps of A. thaliana (42,43). KEEs appear as strong cis- and trans-chromosome peaks in the Hi-C interaction maps. Notably, we found that the KEEs associated peaks were completely absent in the predictions of the optimal epigenomics-driven model (Supplementary Figure S19A) indicating that it is unlikely that such contacts are promoted by epigenomics-driven interactions alone. In fact, in our analysis the KEEs were not enriched in any of the four epigenomic states (Supplementary Figure S18), consistent with other ChIP-seq analysis that suggested that KEEs are not associated with a specific chromatin state (42,44,79).

Association rates of four KEEs’ pairs (KEE6–KEE1 20%, KEE5–KEE4 35%, KEE6–KEE3 66%, KEE5–KEE10 16% with an average of 34%) were previously measured by Fluorescent In Situ Hybridization (FISH) (43), which showed an average of 34% co-localization of KEEs pair. To enforce their mutual spatial proximity, we applied long-range harmonics (both cis- and trans-chromosomes) between the central beads of KEEs’ pairs (Materials and Methods). To use the minimal set of harmonics and the minimal possible forces, we computed the distances between all the pairs of KEEs central beads (both in cis- and trans-chromosome) in the 50 final snapshots obtained from the optimal model simulations and ranked the pairs for increasing mutual distance. On the same 50 snapshots (representative snapshot in Figure 3H), we applied harmonics (Material and Methods) between the closest 34% (or, when available, the specific FISH association rate (43)) of each KEEs pair to promote their spatial colocalization.

We found that the plasticity of the models allowed accommodating all the KEEs interactions and that the generated contact pattern around KEEs pairs was a cross appearing in the inter KEEs portions of the contact map (Figure 7A). This specific pattern was due to the applied constraints that bring into spatial proximity only the central beads. However, recovering the KEEs contacts largely affected the large-scale chromosome rearrangements as it is conveyed visually by the genome-wide contact map (Figure 7B) and quantitatively by the Spearman correlation with the Hi-C interaction map, that degrades both genome-wide and in each cis-chromosome parts with respect to the optimal interaction model (Supplementary Figure S19D).

Next, we focussed on local structural features involving the 162 gene clusters enriched in the H3K27me3 polycomb-related histone mark (median length 7.5 kb and maximum length 95 kb) which have been identified in the A. thaliana genome (56). In the Hi-C interaction map, these clusters form a local plaid pattern indicating the presence of interactions within and between them. We considered a 4 Mb region (chr4:6 700 000–10,700 000) (Figure 7C) centred at the longest gene cluster, the 95 kb-long cluster-100 of (56). Interestingly, we observed that the FH self-attraction already present in the optimal models (Figure 3A) were primed to capture the formation of these local contact domains between H3K27me3-enriched gene clusters (Figure 7E). These domains were not recapitulated in the perturbed system where the FH self-attraction is removed (Figure 7D–F). This finding suggests that we could recover structural features at the scale of a few hundreds of kilobases, that were close to the limit of the model coarse-graining (∼300 kb).

gkaa1275_Supplemental_Files

• 1. Misteli T. Beyond the sequence: cellular organization of genome function. Cell. 2007; 128:787–800. [DOI] [PubMed] [Google Scholar]
• 2. Gibcus J.H., Dekker J.. The hierarchy of the 3D genome. Mol. Cell. 2013; 49:773–782. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 3. Bonev B., Cavalli G.. Organization and function of the 3D genome. Nat. Rev. Genet. 2016; 17:661–678. [DOI] [PubMed] [Google Scholar]
• 4. Sexton T., Cavalli G.. The role of chromosome domains in shaping the functional genome. Cell. 2015; 160:1049–1059. [DOI] [PubMed] [Google Scholar]
• 5. Dekker J., Mirny L.. The 3D Genome as moderator of chromosomal communication. Cell. 2016; 164:1110–1121. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 6. Bonev B., Mendelson Cohen N., Szabo Q., Fritsch L., Papadopoulos G.L., Lubling Y., Xu X., Lv X., Hugnot J.-P., Tanay A.et al.. Multiscale 3D genome rewiring during mouse neural development. Cell. 2017; 171:557–572. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 7. Stadhouders R., Vidal E., Serra F., Di Stefano B., Le Dily F., Quilez J., Gomez A., Collombet S., Berenguer C., Cuartero Y.et al.. Transcription factors orchestrate dynamic interplay between genome topology and gene regulation during cell reprogramming. Nat. Genet. 2018; 50:238–249. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 8. Paulsen J., Liyakat Ali T.M., Nekrasov M., Delbarre E., Baudement M.-O., Kurscheid S., Tremethick D., Collas P.. Long-range interactions between topologically associating domains shape the four-dimensional genome during differentiation. Nat. Genet. 2019; 51:835–843. [DOI] [PubMed] [Google Scholar]
• 9. Dixon J.R., Jung I., Selvaraj S., Shen Y., Antosiewicz-Bourget J.E., Lee A.Y., Ye Z., Kim A., Rajagopal N., Xie W.et al.. Chromatin architecture reorganization during stem cell differentiation. Nature. 2015; 518:331–336. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 10. Zheng H., Xie W.. The role of 3D genome organization in development and cell differentiation. Nat. Rev. Mol. Cell Biol. 2019; 20:535–550. [DOI] [PubMed] [Google Scholar]
• 11. Dekker J., Rippe K., Dekker M., Kleckner N.. Capturing chromosome conformation. Science. 2002; 295:1306–1311. [DOI] [PubMed] [Google Scholar]
• 12. Cremer T., Cremer C.. Chromosome territories, nuclear architecture and gene regulation in mammalian cells. Nat. Rev. Genet. 2001; 2:292–301. [DOI] [PubMed] [Google Scholar]
• 13. Boyle S., Gilchrist S., Bridger J.M., Mahy N.L., Ellis J.A., Bickmore W.A.. The spatial organization of human chromosomes within the nuclei of normal and emerin-mutant cells. Hum. Mol. Genet. 2001; 10:211–219. [DOI] [PubMed] [Google Scholar]
• 14. Bolzer A., Kreth G., Solovei I., Koehler D., Saracoglu K., Fauth C., Müller S., Eils R., Cremer C., Speicher M.R.et al.. Three-dimensional maps of all chromosomes in human male fibroblast nuclei and prometaphase rosettes. PLoS Biol. 2005; 3:e157. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 15. Branco M.R., Pombo A.. Intermingling of chromosome territories in interphase suggests role in translocations and transcription-dependent associations. PLoS Biol. 2006; 4:e138. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 16. Lieberman-Aiden E., van Berkum N.L., Williams L., Imakaev M., Ragoczy T., Telling A., Amit I., Lajoie B.R., Sabo P.J., Dorschner M.O.et al.. Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science. 2009; 326:289–293. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 17. Sexton T., Yaffe E., Kenigsberg E., Bantignies F., Leblanc B., Hoichman M., Parrinello H., Tanay A., Cavalli G.. Three-dimensional folding and functional organization principles of the Drosophila genome. Cell. 2012; 148:458–472. [DOI] [PubMed] [Google Scholar]
• 18. Wang S., Su J.-H., Beliveau B.J., Bintu B., Moffitt J.R., Wu C.-T., Zhuang X.. Spatial organization of chromatin domains and compartments in single chromosomes. Science. 2016; 353:598–602. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 19. Imakaev M., Fudenberg G., McCord R.P., Naumova N., Goloborodko A., Lajoie B.R., Dekker J., Mirny L.A.. Iterative correction of Hi-C data reveals hallmarks of chromosome organization. Nat. Methods. 2012; 9:999–1003. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 20. Rao S.S.P., Huntley M.H., Durand N.C., Stamenova E.K., Bochkov I.D., Robinson J.T., Sanborn A.L., Machol I., Omer A.D., Lander E.S.et al.. A 3D map of the human genome at kilobase resolution reveals principles of chromatin looping. Cell. 2014; 159:1665–1680. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 21. Boettiger A.N., Bintu B., Moffitt J.R., Wang S., Beliveau B.J., Fudenberg G., Imakaev M., Mirny L.A., Wu C.-T., Zhuang X.. Super-resolution imaging reveals distinct chromatin folding for different epigenetic states. Nature. 2016; 529:418–422. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 22. Xu J., Ma H., Jin J., Uttam S., Fu R., Huang Y., Liu Y.. Super-resolution imaging of higher-order chromatin structures at different epigenetic states in single mammalian cells. Cell Rep. 2018; 24:873–882. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 23. Dixon J.R., Selvaraj S., Yue F., Kim A., Li Y., Shen Y., Hu M., Liu J.S., Ren B.. Topological domains in mammalian genomes identified by analysis of chromatin interactions. Nature. 2012; 485:376–380. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 24. Nora E.P., Lajoie B.R., Schulz E.G., Giorgetti L., Okamoto I., Servant N., Piolot T., van Berkum N.L., Meisig J., Sedat J.et al.. Spatial partitioning of the regulatory landscape of the X-inactivation centre. Nature. 2012; 485:381–385. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 25. Bintu B., Mateo L.J., Su J.-H., Sinnott-Armstrong N.A., Parker M., Kinrot S., Yamaya K., Boettiger A.N., Zhuang X.. Super-resolution chromatin tracing reveals domains and cooperative interactions in single cells. Science. 2018; 362:eaau1783. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 26. Szabo Q., Jost D., Chang J.-M., Cattoni D.I., Papadopoulos G.L., Bonev B., Sexton T., Gurgo J., Jacquier C., Nollmann M.et al.. TADs are 3D structural units of higher-order chromosome organization in. Sci Adv. 2018; 4:eaar8082. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 27. Le Dily F., Vidal E., Cuartero Y., Quilez J., Nacht A.S., Vicent G.P., Carbonell-Caballero J., Sharma P., Villanueva-Cañas J.L., Ferrari R.et al.. Hormone-control regions mediate steroid receptor-dependent genome organization. Genome Res. 2019; 29:29–39. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 28. Szabo Q., Bantignies F., Cavalli G.. Principles of genome folding into topologically associating domains. Sci. Adv. 2019; 5:eaaw1668. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 29. Rosa A., Everaers R.. Structure and dynamics of interphase chromosomes. PLoS Comput. Biol. 2008; 4:e1000153. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 30. Rosa A., Becker N.B., Everaers R.. Looping probabilities in model interphase chromosomes. Biophys. J. 2010; 98:2410–2419. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 31. Vettorel T., Grosberg A.Y., Kremer K.. Statistics of polymer rings in the melt: a numerical simulation study. Phys. Biol. 2009; 6:025013. [DOI] [PubMed] [Google Scholar]
• 32. Halverson J.D., Smrek J., Kremer K., Grosberg A.Y.. From a melt of rings to chromosome territories: the role of topological constraints in genome folding. Rep. Prog. Phys. 2014; 77:022601. [DOI] [PubMed] [Google Scholar]
• 33. Jost D., Carrivain P., Cavalli G., Vaillant C.. Modeling epigenome folding: formation and dynamics of topologically associated chromatin domains. Nucleic Acids Res. 2014; 42:9553–9561. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 34. Brackley C.A., Johnson J., Kelly S., Cook P.R., Marenduzzo D. Simulated binding of transcription factors to active and inactive regions folds human chromosomes into loops, rosettes and topological domains. Nucleic Acids Res. 2016; 44:3503–3512. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 35. Di Pierro M., Zhang B., Aiden E.L., Wolynes P.G., Onuchic J.N.. Transferable model for chromosome architecture. Proc. Natl. Acad. Sci. U.S.A. 2016; 113:12168–12173. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 36. Di Pierro M., Cheng R.R., Lieberman Aiden E., Wolynes P.G., Onuchic J.N.. De novo prediction of human chromosome structures: Epigenetic marking patterns encode genome architecture. Proc. Natl. Acad. Sci. U.S.A. 2017; 114:12126–12131. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 37. Ghosh S.K., Jost D. How epigenome drives chromatin folding and dynamics, insights from efficient coarse-grained models of chromosomes. PLoS Comput. Biol. 2018; 14:e1006159. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 38. Sanborn A.L., Rao S.S.P., Huang S.-C., Durand N.C., Huntley M.H., Jewett A.I., Bochkov I.D., Chinnappan D., Cutkosky A., Li J.et al.. Chromatin extrusion explains key features of loop and domain formation in wild-type and engineered genomes. Proc. Natl. Acad. Sci. U.S.A. 2015; 112:E6456–E6465. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 39. Fudenberg G., Imakaev M., Lu C., Goloborodko A., Abdennur N., Mirny L.A.. Formation of chromosomal domains by loop extrusion. Cell Rep. 2016; 15:2038–2049. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 40. Brackley C.A., Johnson J., Michieletto D., Morozov A.N., Nicodemi M., Cook P.R., Marenduzzo D. Nonequilibrium chromosome looping via molecular slip links. Phys. Rev. Lett. 2017; 119:138101. [DOI] [PubMed] [Google Scholar]
• 41. Pecinka A., Schubert V., Meister A., Kreth G., Klatte M., Lysak M.A., Fuchs J., Schubert I.. Chromosome territory arrangement and homologous pairing in nuclei of Arabidopsis thaliana are predominantly random except for NOR-bearing chromosomes. Chromosoma. 2004; 113:258–269. [DOI] [PubMed] [Google Scholar]
• 42. Feng S., Cokus S.J., Schubert V., Zhai J., Pellegrini M., Jacobsen S.E.. Genome-wide Hi-C analyses in wild-type and mutants reveal high-resolution chromatin interactions in Arabidopsis. Mol. Cell. 2014; 55:694–707. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 43. Grob S., Schmid M.W., Grossniklaus U.. Hi-C analysis in Arabidopsis identifies the KNOT, a structure with similarities to the flamenco locus of Drosophila. Mol. Cell. 2014; 55:678–693. [DOI] [PubMed] [Google Scholar]
• 44. Wang C., Liu C., Roqueiro D., Grimm D., Schwab R., Becker C., Lanz C., Weigel D. Genome-wide analysis of local chromatin packing in Arabidopsis thaliana. Genome Res. 2015; 25:246–256. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 45. Liu C., Wang C., Wang G., Becker C., Zaidem M., Weigel D. Genome-wide analysis of chromatin packing in Arabidopsis thaliana at single-gene resolution. Genome Res. 2016; 26:1057–1068. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 46. Fransz P., De Jong J.H., Lysak M., Castiglione M.R., Schubert I.. Interphase chromosomes in Arabidopsis are organized as well defined chromocenters from which euchromatin loops emanate. Proc. Natl. Acad. Sci. U.S.A. 2002; 99:14584–14589. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 47. Schubert I., Shaw P.. Organization and dynamics of plant interphase chromosomes. Trends Plant Sci. 2011; 16:273–281. [DOI] [PubMed] [Google Scholar]
• 48. Armstrong S.J., Franklin F.C., Jones G.H.. Nucleolus-associated telomere clustering and pairing precede meiotic chromosome synapsis in Arabidopsis thaliana. J. Cell Sci. 2001; 114:4207–4217. [DOI] [PubMed] [Google Scholar]
• 49. Berr A., Schubert I.. Interphase chromosome arrangement in arabidopsis thaliana is similar in differentiated and meristematic tissues and shows a transient mirror symmetry after nuclear division. Genetics. 2007; 176:853–863. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 50. Pontvianne F., Carpentier M.-C., Durut N., Pavlištová V., Jaške K., Schořová Š., Parrinello H., Rohmer M., Pikaard C.S., Fojtová M.et al.. Identification of Nucleolus-Associated chromatin domains reveals a role for the nucleolus in 3D Organization of the A. thaliana genome. Cell Rep. 2016; 16:1574–1587. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 51. Sequeira-Mendes J., Gutierrez C.. Genome architecture: from linear organisation of chromatin to the 3D assembly in the nucleus. Chromosoma. 2016; 125:455–469. [DOI] [PubMed] [Google Scholar]
• 52. Fang Y., Spector D.L.. Centromere positioning and dynamics in living Arabidopsis plants. Mol. Biol. Cell. 2005; 16:5710–5718. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 53. Bi X., Cheng Y.-J., Hu B., Ma X., Wu R., Wang J.-W., Liu C.. Nonrandom domain organization of the genome at the nuclear periphery. Genome Res. 2017; 27:1162–1173. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 54. Zhou S., Jiang W., Zhao Y., Zhou D.-X.. Single-cell three-dimensional genome structures of rice gametes and unicellular zygotes. Nat Plants. 2019; 5:795–800. [DOI] [PubMed] [Google Scholar]
• 55. Liu C., Cheng Y.-J., Wang J.-W., Weigel D. Prominent topologically associated domains differentiate global chromatin packing in rice from Arabidopsis. Nat Plants. 2017; 3:742–748. [DOI] [PubMed] [Google Scholar]
• 56. Yu N., Nützmann H.-W., MacDonald J.T., Moore B., Field B., Berriri S., Trick M., Rosser S.J., Kumar S.V., Freemont P.S.et al.. Delineation of metabolic gene clusters in plant genomes by chromatin signatures. Nucleic Acids Res. 2016; 44:2255–2265. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 57. Nützmann H.-W., Doerr D., Ramírez-Colmenero A., Sotelo-Fonseca J.E., Wegel E., Di Stefano M., Wingett S.W., Fraser P., Hurst L., Fernandez-Valverde S.L.et al.. Active and repressed biosynthetic gene clusters have spatially distinct chromosome states. Proc. Natl. Acad. Sci. U.S.A. 2020; 117:13800–13809. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 58. de Nooijer S., Wellink J., Mulder B., Bisseling T.. Non-specific interactions are sufficient to explain the position of heterochromatic chromocenters and nucleoli in interphase nuclei. Nucleic Acids Res. 2009; 37:3558–3568. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 59. Simon L., Voisin M., Tatout C., Probst A.V.. Structure and Function of Centromeric and Pericentromeric Heterochromatin in Arabidopsis thaliana. Front. Plant Sci. 2015; 6:1049. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 60. Finch J.T., Klug A.. Solenoidal model for superstructure in chromatin. Proc. Natl. Acad. Sci. U.S.A. 1976; 73:1897–1901. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 61. Kremer K., Grest G.S.. Dynamics of entangled linear polymer melts: a molecular-dynamics simulation. J. Chem. Phys. 1990; 92:5057–5086. [Google Scholar]
• 62. Di Stefano M., Paulsen J., Lien T.G., Hovig E., Micheletti C.. Hi-C-constrained physical models of human chromosomes recover functionally-related properties of genome organization. Sci. Rep. 2016; 6:35985. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 63. Bystricky K., Heun P., Gehlen L., Langowski J., Gasser S.M.. Long-range compaction and flexibility of interphase chromatin in budding yeast analyzed by high-resolution imaging techniques. Proc. Natl. Acad. Sci. U.S.A. 2004; 101:16495–16500. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 64. Plimpton S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comp. Phys. 1995; 117:1–19. [Google Scholar]
• 65. Serra F., Baù D., Goodstadt M., Castillo D., Filion G.J., Marti-Renom M.A.. Automatic analysis and 3D-modelling of Hi-C data using TADbit reveals structural features of the fly chromatin colors. PLoS Comput. Biol. 2017; 13:e1005665. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 66. Marco-Sola S., Ribeca P.. Efficient alignment of illumina-like high-throughput sequencing reads with the GEnomic Multi-tool (GEM) mapper. Curr. Protoc. Bioinformatics. 2015; 50:11.13.1–11.13.20. [DOI] [PubMed] [Google Scholar]
• 67. Vidal E., le Dily F., Quilez J., Stadhouders R., Cuartero Y., Graf T., Marti-Renom M.A., Beato M., Filion G.J.. OneD: increasing reproducibility of Hi-C samples with abnormal karyotypes. Nucleic Acids Res. 2018; 46:e49. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 68. Yan K.-K., Yardimci G.G., Yan C., Noble W.S., Gerstein M.. HiC-spector: a matrix library for spectral and reproducibility analysis of Hi-C contact maps. Bioinformatics. 2017; 33:2199–2201. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 69. Fudenberg G., Imakaev M.. FISH-ing for captured contacts: towards reconciling FISH and 3C. Nat. Methods. 2017; 14:673–678. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 70. Cattoni D.I., Cardozo Gizzi A.M., Georgieva M., Di Stefano M., Valeri A., Chamousset D., Houbron C., Déjardin S., Fiche J.-B., González I.et al.. Single-cell absolute contact probability detection reveals chromosomes are organized by multiple low-frequency yet specific interactions. Nat. Commun. 2017; 8:1753. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 71. Falk M., Feodorova Y., Naumova N., Imakaev M., Lajoie B.R., Leonhardt H., Joffe B., Dekker J., Fudenberg G., Solovei I.et al.. Heterochromatin drives organization of conventional and inverted nuclei. Nature. 2019; 570:395–399. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 72. MacPherson Q., Beltran B., Spakowitz A.J.. Bottom–up modeling of chromatin segregation due to epigenetic modifications. Proc. Natl. Acad. Sci. U.S.A. 2018; 115:12739–12744. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 73. Nuebler J., Fudenberg G., Imakaev M., Abdennur N., Mirny L.A.. Chromatin organization by an interplay of loop extrusion and compartmental segregation. Proc. Natl. Acad. Sci. U.S.A. 2018; 115:E6697–E6706. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 74. Brackley C.A., Brown J.M., Waithe D., Babbs C., Davies J., Hughes J.R., Buckle V.J., Marenduzzo D. Predicting the three-dimensional folding of cis-regulatory regions in mammalian genomes using bioinformatic data and polymer models. Genome Biol. 2016; 17:59. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 75. Buckle A., Brackley C.A., Boyle S., Marenduzzo D., Gilbert N.. Polymer simulations of heteromorphic chromatin predict the 3D folding of complex genomic loci. Mol. Cell. 2018; 72:786–797. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 76. Dekker J. Mapping in vivo chromatin interactions in yeast suggests an extended chromatin fiber with regional variation in compaction. J. Biol. Chem. 2008; 283:34532–34540. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 77. Dittmer T.A., Stacey N.J., Sugimoto-Shirasu K., Richards E.J.. LITTLE NUCLEI genes affecting nuclear morphology in Arabidopsis thaliana. Plant Cell. 2007; 19:2793–2803. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 78. Roudier F., Ahmed I., Bérard C., Sarazin A., Mary-Huard T., Cortijo S., Bouyer D., Caillieux E., Duvernois-Berthet E., Al-Shikhley L.et al.. Integrative epigenomic mapping defines four main chromatin states in Arabidopsis. EMBO J. 2011; 30:1928–1938. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 79. Sequeira-Mendes J., Aragüez I., Peiró R., Mendez-Giraldez R., Zhang X., Jacobsen S.E., Bastolla U., Gutierrez C.. The functional topography of the arabidopsis genome is organized in a reduced number of linear motifs of chromatin states. Plant Cell. 2014; 26:2351–2366. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 80. Cloix C., Tutois S., Yukawa Y., Mathieu O., Cuvillier C., Espagnol M.-C., Picard G., Tourmente S.. Analysis of the 5S RNA pool in Arabidopsis thaliana: RNAs are heterogeneous and only two of the genomic 5S loci produce mature 5S RNA. Genome Res. 2002; 12:132–144. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 81. Strom A.R., Emelyanov A.V., Mir M., Fyodorov D.V., Darzacq X., Karpen G.H.. Phase separation drives heterochromatin domain formation. Nature. 2017; 547:241–245. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 82. Larson A.G., Elnatan D., Keenen M.M., Trnka M.J., Johnston J.B., Burlingame A.L., Agard D.A., Redding S., Narlikar G.J.. Liquid droplet formation by HP1α suggests a role for phase separation in heterochromatin. Nature. 2017; 547:236–240. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 83. Zhao S., Cheng L., Gao Y., Zhang B., Zheng X., Wang L., Li P., Sun Q., Li H.. Plant HP1 protein ADCP1 links multivalent H3K9 methylation readout to heterochromatin formation. Cell Res. 2018; 29:54–66. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 84. Erdel F., Rademacher A., Vlijm R., Tünnermann J., Frank L., Weinmann R., Schweigert E., Yserentant K., Hummert J., Bauer C.et al.. Mouse Heterochromatin Adopts Digital Compaction States without Showing Hallmarks of HP1-Driven Liquid-Liquid Phase Separation. Mol. Cell. 2020; 78:236–249. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 85. Hyman A.A., Weber C.A., Jülicher F.. Liquid-liquid phase separation in biology. Annu. Rev. Cell Dev. Biol. 2014; 30:39–58. [DOI] [PubMed] [Google Scholar]
• 86. Sabari B.R., Dall’Agnese A., Boija A., Klein I.A., Coffey E.L., Shrinivas K., Abraham B.J., Hannett N.M., Zamudio A.V., Manteiga J.C.et al.. Coactivator condensation at super-enhancers links phase separation and gene control. Science. 2018; 361:eaar3958. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 87. Lu H., Yu D., Hansen A.S., Ganguly S., Liu R., Heckert A., Darzacq X., Zhou Q.. Phase-separation mechanism for C-terminal hyperphosphorylation of RNA polymerase II. Nature. 2018; 558:318–323. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 88. Veluchamy A., Jégu T., Ariel F., Latrasse D., Mariappan K.G., Kim S.-K., Crespi M., Hirt H., Bergounioux C., Raynaud C.et al.. LHP1 Regulates H3K27me3 Spreading and Shapes the Three-Dimensional Conformation of the Arabidopsis Genome. PLoS One. 2016; 11:e0158936. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 89. Plys A.J., Davis C.P., Kim J., Rizki G., Keenen M.M., Marr S.K., Kingston R.E.. Phase separation of Polycomb-repressive complex 1 is governed by a charged disordered region of CBX2. Genes Dev. 2019; 33:799–813. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 90. Trussart M., Serra F., Baù D., Junier I., Serrano L., Marti-Renom M.A.. Assessing the limits of restraint-based 3D modeling of genomes and genomic domains. Nucleic Acids Res. 2015; 43:3465–3477. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 91. Serra F., Di Stefano M., Spill Y.G., Cuartero Y., Goodstadt M., Baù D., Marti-Renom M.A.. Restraint-based three-dimensional modeling of genomes and genomic domains. FEBS Lett. 2015; 589:2987–2995. [DOI] [PubMed] [Google Scholar]
• 92. Rabl C. Uber Zelltheilung. Morphol. Jahrb. 1885; 10:214–330. [Google Scholar]
• 93. Duan Z., Andronescu M., Schutz K., McIlwain S., Kim Y.J., Lee C., Shendure J., Fields S., Blau C.A., Noble W.S.. A three-dimensional model of the yeast genome. Nature. 2010; 465:363–367. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 94. Wong H., Marie-Nelly H., Herbert S., Carrivain P., Blanc H., Koszul R., Fabre E., Zimmer C.. A predictive computational model of the dynamic 3D interphase yeast nucleus. Curr. Biol. 2012; 22:1881–1890. [DOI] [PubMed] [Google Scholar]
• 95. Kalhor R., Tjong H., Jayathilaka N., Alber F., Chen L.. Genome architectures revealed by tethered chromosome conformation capture and population-based modeling. Nat. Biotechnol. 2011; 30:90–98. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 96. Di Stefano M., Di Giovanni F., Pozharskaia V., Gomar-Alba M., Baù D., Carey L.B., Marti-Renom M.A., Mendoza M.. Impact of chromosome fusions on 3D genome organization and gene expression in budding yeast. Genetics. 2020; 214:651–667. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 97. Li Q., Tjong H., Li X., Gong K., Zhou X.J., Chiolo I., Alber F.. The three-dimensional genome organization of Drosophila melanogaster through data integration. Genome Biol. 2017; 18:145. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 98. Tjong H., Li W., Kalhor R., Dai C., Hao S., Gong K., Zhou Y., Li H., Zhou X.J., Le Gros M.A.et al.. Population-based 3D genome structure analysis reveals driving forces in spatial genome organization. Proc. Natl. Acad. Sci. U.S.A. 2016; 113:E1663–E1672. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 99. Tiang C.-L., He Y., Pawlowski W.P.. Chromosome organization and dynamics during interphase, mitosis, and meiosis in plants. Plant Physiol. 2012; 158:26–34. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 100. Rosa A., Di Stefano M., Micheletti C.. Topological constraints in eukaryotic genomes and how they can be exploited to improve spatial models of chromosomes. Front. Mol. Biosci. 2019; 6:127–132. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 101. Picart-Picolo A., Picart C., Picault N., Pontvianne F.. Nucleolus-associated chromatin domains are maintained under heat stress, despite nucleolar reorganization in Arabidopsis thaliana. J. Plant Res. 2020; 133:463–470. [DOI] [PubMed] [Google Scholar]
• 102. Berardini T.Z., Reiser L., Li D., Mezheritsky Y., Muller R., Strait E., Huala E.. The arabidopsis information resource: Making and mining the ‘gold standard’ annotated reference plant genome. Genesis. 2015; 53:474–485. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 103. Espada J., Ballestar E., Santoro R., Fraga M.F., Villar-Garea A., Németh A., Lopez-Serra L., Ropero S., Aranda A., Orozco H.et al.. Epigenetic disruption of ribosomal RNA genes and nucleolar architecture in DNA methyltransferase 1 (Dnmt1) deficient cells. Nucleic Acids Res. 2007; 35:2191–2198. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 104. Andrey P., Kiêu K., Kress C., Lehmann G., Tirichine L., Liu Z., Biot E., Adenot P.-G., Hue-Beauvais C., Houba-Hérin N.et al.. Statistical analysis of 3D images detects regular spatial distributions of centromeres and chromocenters in animal and plant nuclei. PLoS Comput. Biol. 2010; 6:e1000853. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 105. Pawar V., Poulet A., Détourné G., Tatout C., Vanrobays E., Evans D.E., Graumann K.. A novel family of plant nuclear envelope-associated proteins. J. Exp. Bot. 2016; 67:5699–5710. [DOI] [PubMed] [Google Scholar]
• 106. Kind J., Pagie L., Ortabozkoyun H., Boyle S., de Vries S.S., Janssen H., Amendola M., Nolen L.D., Bickmore W.A., van Steensel B.. Single-cell dynamics of genome-nuclear lamina interactions. Cell. 2013; 153:178–192. [DOI] [PubMed] [Google Scholar]
• 107. Kind J., Pagie L., de Vries S.S., Nahidiazar L., Dey S.S., Bienko M., Zhan Y., Lajoie B., de Graaf C.A., Amendola M.et al.. Genome-wide maps of nuclear lamina interactions in single human cells. Cell. 2015; 163:134–147. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 108. Hu B., Wang N., Bi X., Karaaslan E.S., Weber A.-L., Zhu W., Berendzen K.W., Liu C.. Plant lamin-like proteins mediate chromatin tethering at the nuclear periphery. Genome Biol. 2019; 20:87. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 109. Paulsen J., Liyakat Ali T.M., Collas P.. Computational 3D genome modeling using Chrom3D. Nat. Protoc. 2018; 13:1137–1152. [DOI] [PubMed] [Google Scholar]
• 110. Sati S., Bonev B., Szabo Q., Jost D., Bensadoun P., Serra F., Loubiere V., Papadopoulos G.L., Rivera-Mulia J.-C., Fritsch L.et al.. 4D genome rewiring during Oncogene-Induced and replicative senescence. Mol. Cell. 2020; 78:522–538. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 111. Tavares-Cadete F., Norouzi D., Dekker B., Liu Y., Dekker J.. Multi-contact 3C reveal that the human genome is largely unentangled. Nat. Struct. Mol. Biol. 2020; 27:1105–1114. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 112. Dorier J., Stasiak A.. Topological origins of chromosomal territories. Nucleic Acids Res. 2009; 37:6316–6322. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 113. Mirny L.A. The fractal globule as a model of chromatin architecture in the cell. Chromosome Res. 2011; 19:37–51. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 114. Siebert J.T., Kivel A.N., Atkinson L.P., Stevens T.J., Laue E.D., Virnau P.. Are there knots in chromosomes. Polymers. 2017; 9:317–326. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 115. Zhang B., Wolynes P.G.. Topology, structures, and energy landscapes of human chromosomes. Proc. Natl. Acad. Sci. U.S.A. 2015; 112:6062–6067. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 116. Valdés A., Segura J., Dyson S., Martínez-García B., Roca J.. DNA knots occur in intracellular chromatin. Nucleic Acids Res. 2018; 46:650–660. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 117. Valdés A., Coronel L., Martínez-García B., Segura J., Dyson S., Díaz-Ingelmo O., Micheletti C., Roca J.. Transcriptional supercoiling boosts topoisomerase II-mediated knotting of intracellular DNA. Nucleic Acids Res. 2019; 47:6946–6955. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 118. Giorgetti L., Heard E.. Closing the loop: 3C versus DNA FISH. Genome Biol. 2016; 17:215. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 119. McStay B., Grummt I.. The epigenetics of rRNA genes: from molecular to chromosome biology. Annu. Rev. Cell Dev. Biol. 2008; 24:131–157. [DOI] [PubMed] [Google Scholar]
• 120. Grummt I., Längst G.. Epigenetic control of RNA polymerase I transcription in mammalian cells. Biochim. Biophys. Acta. 2013; 1829:393–404. [DOI] [PubMed] [Google Scholar]
• 121. Hult C., Adalsteinsson D., Vasquez P.A., Lawrimore J., Bennett M., York A., Cook D., Yeh E., Forest M.G., Bloom K.. Enrichment of dynamic chromosomal crosslinks drive phase separation of the nucleolus. Nucleic Acids Res. 2017; 45:11159–11173. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 122. Morf J., Wingett S.W., Farabella I., Cairns J., Furlan-Magaril M., Jiménez-García L.F., Liu X., Craig F.F., Walker S., Segonds-Pichon A.et al.. RNA proximity sequencing reveals the spatial organization of the transcriptome in the nucleus. Nat. Biotechnol. 2019; 37:793–802. [DOI] [PubMed] [Google Scholar]
• 123. Ho J.W.K., Jung Y.L., Liu T., Alver B.H., Lee S., Ikegami K., Sohn K.-A., Minoda A., Tolstorukov M.Y., Appert A.et al.. Comparative analysis of metazoan chromatin organization. Nature. 2014; 512:449–452. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 124. Haddad N., Vaillant C., Jost D. IC-Finder: inferring robustly the hierarchical organization of chromatin folding. Nucleic Acids Res. 2017; 45:e81. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 125. Chuang C.-H., Carpenter A.E., Fuchsova B., Johnson T., de Lanerolle P., Belmont A.S.. Long-range directional movement of an interphase chromosome site. Curr. Biol. 2006; 16:825–831. [DOI] [PubMed] [Google Scholar]
• 126. Mehta I.S., Amira M., Harvey A.J., Bridger J.M.. Rapid chromosome territory relocation by nuclear motor activity in response to serum removal in primary human fibroblasts. Genome Biol. 2010; 11:R5. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 127. Fili N., Toseland C.P.. Unconventional myosins: how regulation meets function. Int. J. Mol. Sci. 2019; 21:67–92. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 128. O’Toole E.T., Winey M., Richard McIntosh J.. High-Voltage electron tomography of spindle pole bodies and early mitotic spindles in the yeast saccharomyces cerevisiae. Mol. Biol. Cell. 1999; 10:2017–2031. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 129. Hintze J.L., Nelson R.D.. Violin plots: a box plot-density trace synergism. Am. Stat. 1998; 52:181. [Google Scholar]
• 130. Humphrey W., Dalke A., Schulten K.. VMD: visual molecular dynamics. J. Mol. Graph. 1996; 14:33–38. [DOI] [PubMed] [Google Scholar]

Supplementary Materials

Data Availability Statement

The Hi-C datasets analysed during the current study are available in the Sequence Read Archive (SRA) repository with accession numbers SRR1029605 from (44), SRR2626429, SRR2626163 from (45). Epigenomic data were extracted from the Supplementary Table 4 of (44). All scripts for simulations and data analysis used for this study are available on Github at https://github.com/MarcoDiS/Athaliana_simulations/.