Euchromatin forms condensed domains with short active regions on the surface

Euchromatin forms condensed domains with short active regions on the surface | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Euchromatin forms condensed domains with short active regions on the surface View ORCID Profile Joseph M. Paggi , View ORCID Profile Bin Zhang doi: https://doi.org/10.1101/2025.08.05.668703 Joseph M. Paggi 1 Department of Chemistry, Massachusetts Institute of Technology , Cambridge, MA, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Joseph M. Paggi Bin Zhang 1 Department of Chemistry, Massachusetts Institute of Technology , Cambridge, MA, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Bin Zhang Abstract Full Text Info/History Metrics Supplementary material Data/Code Preview PDF Abstract Technological advances in chromatin structure characterization have continually refined our understanding of transcriptional regulation in eukaryotic systems. Despite these developments, achieving nucleosome-resolution structural characterization remains a significant challenge. As a result, it remains unclear what structural features distinguish active enhancers and promoters and how these elements are organized. To address this, we developed a simulation framework that leverages high-resolution Region-Capture Micro-C (RCMC) contact maps to infer conformational ensembles of megabase-scale chromatin segments at nucleosome resolution. A key component of this framework is a balancing strategy tailored for Micro-C data, which identifies per-nucleosome variation in contact density, in contrast to existing methods that assume uniform contact density. Our model accurately reproduces contact frequencies observed in RCMC data, pairwise spatial distances measured via chromatin tracing, and local structural motifs observed in imaging studies. The high spatial and genomic resolution of the inferred structures reveal a striking departure from the classical view of euchromatin as uniformly open. Instead, euchromatin generally folds into compact domains, consistent with the “packing domains” observed in imaging studies. These domains are further organized into disordered, insulated clusters of approximately 50 nucleosomes, resembling nucleosome clutches. Notably, kilobase-scale regions surrounding active promoters and enhancers often protrude from these condensed domains, becoming highly accessible. This spatial arrangement effectively compartmentalizes regulatory elements from the surrounding chromatin, facilitating protein binding and promoting enhancer–promoter communication. The distinct structural features of euchromatin revealed here offer new insights into enhancer regulation and may help explain their enigmatic behavior. Introduction The textbook view of genome organization posits that transcriptionally inactive heterochromatin adopts closed conformations, whereas active euchromatin adopts open ones. In this model, transcriptional machinery can access only euchromatin, leading to selective gene expression. However, recent evidence challenges this dichotomy, suggesting that euchromatin also contains largely condensed domains [ 1 – 4 ]. Accurately quantifying the compactness of euchromatin and resolving its three-dimensional (3D) organization—particularly at the nucleosome level near promoters—could yield critical insights into the mechanisms of transcriptional regulation. Achieving this, however, demands both high spatial and genomic resolution—an ongoing technological challenge. Advances in imaging have substantially deepened our understanding of chromatin organization. Techniques such as super-resolution microscopy [ 5 ] and electron microscopy [ 1 , 6 – 10 ] have reached single-nucleosome resolution and uncovered structural features ranging from packing domains [ 1 , 11 , 12 ] to nanodomains [ 13 ] and clutches [ 5 , 14 ]. However, these methods generally have limited ability to identify the specific genomic loci being imaged and to trace the chain of nucleosomes, leaving critical questions unanswered. In particular, the hierarchical relationships among structural motifs—e.g., how clutches (tens of nucleosomes) aggregate into packing domains (thousands of nucleosomes)—and how these features depend on genomic context remain elusive. It also remains unclear whether condensed domains identified through imaging correspond to active or inactive chromatin states. Chromatin tracing methods [ 12 , 15 , 16 ] can target specific genomic segments, but lack the resolution required to resolve single-nucleosome features and address these questions. Chromatin conformation capture and related methods offer complementary advantages by capturing spatial proximity between DNA segments in situ [ 17 – 21 ]. Micro-C, in particular, can achieve high genomic resolution [ 22 – 25 ]. Nonetheless, interpreting contact maps remains challenging due to the confounding effects of population averaging and the inherently indirect relationship between contact frequency and 3D structure. Computational approaches [ 26 – 42 ], such as maximum entropy inversion (MEI) [ 43 – 47 ], have made progress in addressing these challenges by reconstructing 3D conformational ensembles consistent with average contact maps. However, the limited sequencing depth typical of standard Micro-C experiments continues to constrain the resolution of the inferred structures. Region-capture Micro-C (RCMC) mitigates this limitation by concentrating sequencing depth on selected genomic regions [ 48 – 50 ]. This approach dramatically enhances resolution and has enabled the generation of high-quality, nucleosome-resolution contact maps. These maps have already revealed previously unknown structural motifs, such as micro-compartments, and support modeling efforts aimed at reconstructing nucleosome-resolution 3D structures. In this study, we apply MEI to RCMC data to reconstruct nucleosome-resolution conformational ensembles. To enable this, we developed a balancing strategy, “neighbor balancing,” which recovers variations in contact density. Our simulations accurately reproduces both RCMC contact maps and pairwise distances from chromatin tracing. The simulated conformations contain structural motifs consistent with packing domains (or TAD-like domains) [ 1 , 12 ] and clutches [ 5 ]. In this way, our results provide a coherent, multiscale view of chromatin architecture—from single nucleosomes to megabase domains—bridging structural motifs observed across diverse techniques. Notably, our analysis reveals a surprising similarity in the overall compaction of euchromatin and heterochromatin. At the same time, we identify euchromatin-specific structural features, including an organization in which compact chromatin domains are folded internally, exposing regulatory regions on the surface. We discuss the functional implications of this architecture in the context of enhancer–promoter communication and transcriptional regulation. Results Neighbor balancing recovers biological variation in contact density Iterative correction (ICE) is a widely used balancing technique for Hi-C and micro-C data [ 51 ]. The role of balancing is to account for biases in read coverage in different genomic windows, including digestibility by restriction enzymes or MNase and PCR amplification biases. Without balancing, genomic regions with intrinsically higher coverage would have inflated contact frequencies. ICE balancing and other popular approaches [ 52 ] remove variations in coverage by enforcing that each genomic window is assigned the same contact density: the sum of its contact frequencies with all other windows. There is a natural relationship between the contact density and the physical density of the system ( Figure 1a ). If we assume a model in which a micro-C contact is likely if two nucleosomes are within some “capture radius” of each other and unlikely otherwise [ 53 ], then the ensemble average physical density is equal to the contact density divided by the volume enclosed by the capture radius. In this way, the assumption of constant contact density is equivalent to an assumption of constant average physical density. Download figure Open in new tab Figure 1: Neighbor balancing recovers variation in contact density. (a) Illustration of the relationship between contact maps and the underlying conformational ensemble. (b) Contact maps for a synthetic test system composed of two densely packed regions connected by an extended linker. The left panel shows the true contact map on the upper-triangle and the true contact map corrupted by multiplicative biases drawn from a log-normal distribution in the lower-triangle. The per-nucleosome contact density and neighbor contacts for the true map are shown at the bottom. The center and right panels show the ICE and neighbor balanced maps, respectively, computed starting from the corrupted contact map. (c) Comparison of contact densities inferred using neighbor balancing for RCMC data from Goel et al. [ 48 ] to condensability scores [ 54 ], ATAC-seq coverage, and several active histone marks. The sources for all epigenetics data are provided in Supplementary Table 2. (d) Enrichment of contact probabilities for windows in the top 5% of the indicated epigenetic feature over windows in the bottom 50%. (e) Comparison of ICE balanced and neighbor balanced contact maps for the interaction between the Sox2 promoter and one of its enhancers. (f) Comparison of contact densities for the entirety of chr5 computed using genome-wide micro-C data from Hsieh et al. [ 25 ] to A and B compartment scores and RNA-seq coverage (log10(1 + reads per genomic content)). All genome-wide data are at 25.6 kb resolution (see Supplementary Information). When applied to systems that do not have a uniform physical density, ICE balancing erases the differences, artificially inflating contact frequencies for low density regions and decreasing them for high density regions. This likely results in problems in real systems because some regions of the genome, like acetylated regions, are believed to be more open than others [ 54 , 55 ]. We demonstrate this effect using a synthetic system consisting of two dense domains separated by an extended linker ( Figure 1b ). After simulating this system and producing an ICE balanced contact map, the contact frequencies inside the dense domains are too low while those for the linker regions are too high, relative to the ground truth. We propose “neighbor balancing” to recover variation in contact density. Unlike ICE, which assumes uniform contact density across all nucleosomes, our approach is based on the assumption that neighboring nucleosomes are consistently in contact. The intuition behind our approach is that, if neighboring nucleosomes are generally close enough that they have a high probability of being ligated in micro-C, then the contact frequencies between neighbors should all be the same. This assumption is supported by our analysis in the next section. To enforce uniform contact frequency between neighboring nucleosomes, we re-balance the ICE-balanced contact map based on local interaction patterns. Specifically, for each nucleosome, we compute the average of its interaction frequency with its two neighbors then divide each row and column by the square root of this average (see Methods). In our synthetic example, we observe that in the ICE balanced contact map the neighbor contact frequencies are not constant and instead are inversely proportional to the true contact density ( Figure 1b , blue lines). By normalizing against these neighbor interactions, our method effectively restores true variations in contact density. On the synthetic example system, neighbor balancing correctly reproduces the true contact densities. We applied neighbor balancing to RCMC data for five genomic regions in mouse embryonic stem cells (mESCs) at nucleosome resolution (200 bps) [ 48 ]. Most nucleosomes have approximately the same contact density, except for short regions with as little as half the average density ( Figure 1c , Fig. S3). These dilute positions are highly correlated with condensability scores [ 54 ], ATAC-seq, H3K27ac, H3K4me3, and other marks associated with active chromatin ( Figure 1c , Fig. S3). ICE balancing predicts that nucleosomes with active marks have high contact probabilities with nucleosomes within 1 kb, suggesting that they are locally compact, whereas neighbor balancing predicts that these regions are expanded at all scales ( Figure 1d ). The trend observed with neighbor balancing is in line with a variety of data suggesting that such regions are more extended and form fewer contacts [ 56 – 58 ]. Conversely, inactive marks, including H3K9me3, H3K27me3, and histone H1, are positively correlated with contact density although this trend is much weaker ( Figure 1d ). Since regions around promoters and enhancers tend to have lower contact density, the contact frequencies between enhancers and promoters are reduced, however, they remain visible in the contact map ( Figure 1e , Fig. S4). Neighbor balancing is not specific to RCMC and can be applied to typical, genome-wide micro-C (see Supplementary Information and Methods). We applied neighbor balancing to compute contact densities using genome wide micro-C in mESCs at a resolution of 25.6 kb [ 25 ]. The contact density is relatively consistent: nearly all positions fall within 50% of the average ( Figure 1f ). We observed similar correlations between contact densities and epigenetic marks as in the RCMC data (Fig. S5e) and that contact densities are inversely correlated with A/B compartment scores and RNA-seq coverage ( Figure 1f ). Neighbor balancing suggests that B compartment regions are roughly 20% denser than A compartment regions [ 59 ]. Nucleosome-resolution chromatin modeling bridges contact maps with chromatin tracing While the RCMC contact maps and contact densities from neighbor balancing begin to suggest what distinguishes active from inactive chromatin, they do not provide the complete picture. We therefore used maximum entropy inversion (MEI) to recover a 3D conformational ensemble consistent with the contact maps ( Figure 2 ). In MEI, one begins with a baseline model and then adds auxiliary energy terms to make the system recapitulate experimental data (see Methods). Thereby, to apply MEI, we needed to define the baseline model and a way to compute a simulated micro-C contact map from a set of simulation frames. Download figure Open in new tab Figure 2: Data-driven modeling of chromatin at nucleosome resolution. In maximum entropy inversion (MEI), we begin with a base model of the system and an experimentally determined contact map. In the base model, all nucleosomes interact uniformly, and thereby the features in the contact map are not reproduced. MEI updates the nucleosome interaction potentials so that the simulations closely recapitulate the experimental contact map. This example uses RCMC data from the Nanog region [ 48 ]. Selecting a baseline model posed two competing requirements. Using a nucleosome resolution model appeared to be important to accurately capture the behavior of the short dilute regions detected by neighbor balancing ( Figure 1c ). The differences in contact density are diminished if viewed at coarser resolution (Fig. S5d), and we reasoned that the dilute regions could have different local structures. At the same time, it was essential to simulate at least megabase-scale systems to capture complete topologically associating domains (TADs). Relatively large genomic windows are required to include the majority of contacts; on average to include 75% of a nucleosome’s contacts requires simulating a 1 MB region (Fig. S5a,b). To meet these two criteria, we used a highly simplified nucleosome-level model, in which nucleosomes are positioned uniformly along the DNA and interact uniformly with an isotropic potential (see Methods). Computing a simulated contact map requires specifying the likelihood of two nucleosomes forming a micro-C contact as a function of their distance. We call this function the “contact indicator function” and it’s 50% point the “capture radius”. The choice of contact indicator function strongly influences the overall scale of the optimized system: smaller capture radii lead to more compact systems and larger capture radii lead to more extended systems. To choose a contact indicator function and generally validate our approach, we compare our simulations to chromatin conformations observed using Optical Reconstruction of Chromatin (ORCA) [ 12 ]. ORCA uses fluorescent probes to sequentially image regions along the chromatid, providing 3D coordinates of specific genomic regions in thousands cells. ORCA data is available for two of the regions for which we have RCMC data: Nanog and Sox2 [ 60 , 61 ]. The Nanog data has a 140 kb region tiled at 15 kb resolution and the Sox2 data has a 1.6 MB region tiled at 30 kb resolution. Using a capture radius of 42 nm (two bond lengths in our model), the overall scaling of pairwise distances as a function of genomic separation in our simulations closely matches the ORCA experiments, after accounting for measurement uncertainty ( Figure 3a,c , see Supplementary information). Moreover, the average pairwise distances between specific genomic regions are also well matched (r=0.89 for Nanog , r=0.92 for Sox2 , Figure 3b,d ). This correlation is greater than what is expected purely due to genomic separation, as illustrated by distance striated correlation coefficients ( Figure 3b,d ). The only substantial disagreement between our simulated ensemble and the chromatin tracing data is that the simulations underestimate median distances at short genomic separations ( Figure 3a ). We suspect this occurs because our simulations assume full nucleosome occupancy, whereas in reality at least some nucleosomes are missing, which would locally expand the system. Moreover, the full distributions of per-frame pairwise distances in simulation closely matches the per-cell distributions from ORCA ( Figure 3e , Fig. S7). Our simulation protocol contains no free parameters controlling the relative values of specific pairwise distances, so the close correspondence with ORCA is validation of the simulation approach. Download figure Open in new tab Figure 3: Simulations reproduce pairwise distance distributions from chromatin tracing. (a) Comparison of the median pairwise distances as a function of genomic separation from simulations of the Nanog locus to chromatin tracing data from Fujimori et al. [ 60 ]. The solid green line is the raw simulation output, and the dashed green line is the simulation output corrupted by measurement noise estimated using control experiments (see Supplementary Information). Importantly, the capture radius used in the simulations was selected to match this distance scaling trend, whereas the remaining results are validation. (b) Comparison of individual pairwise distances. Each point is colored by its genomic separation to highlight that the simulation predictions are better correlated with the chromatin tracing data than can be explained by only genomic separation. The distance striated correlation coefficient is the average of Pearson correlations computed separately for each genomic separation. (c, d) Equivalent to panels a and b but comparing simulations for the Sox2 locus to chromatin tracing data from Hafner et al. [ 61 ]. (e) Distributions of distances to the Nanog promoter from simulation and chromatin tracing. The solid lines show the median value, while the shaded region encloses the 20 to 80th percentile. (f) Comparison of median distances from simulation and ORCA for the Sox2 locus. Together, these results show that our simulations recapitulate state-of-the-art experimental measurements of contacts frequencies from RCMC (Fig. S6) and pairwise distance distributions from ORCA ( Figure 3 , Fig. S7). Both heterochromatin and euchromatin are largely comprised of condensed domains We ran simulations for five approximately 1 MB regions using RCMC data from Goel et al. [ 48 ]. The five regions mostly fall into the A-compartment based on eigenvector analysis of genome-wide micro-C data, except for Fbn2 , which is mostly B-compartment ( Figure 4a-c , Fig. S8). Visual analysis of our simulations reveals that the systems are comprised of condensed domains punctuated by kilobase-scale protrusions adopting extended structures ( Figure 4d-g ). Download figure Open in new tab Figure 4: Both heterochromatin and euchromatin are largely comprised of condensed domains. (a, b, c) Contact maps from RCMC used in MEI, the probability of each position forming a protrusion, i.e. not in a domain, ATAC-seq coverage, and A/B compartment profile computed using genome-wide micro-C data [ 25 ]. (d, f, g) Randomly selected simulation frames for each of the three regions. Packing domains are shown in rainbow colors and protrusions are shown in black. (h) Protrusions are generally about a kilobase long. (i) Packing domains most commonly contain about 10 kb of genomic content (left), however, some packing domains are closer to 1 MB in size. Plotting packing domain sizes weighted by size (right) reveals that most nucleosomes are positioned in large packing domains. To quantify these structures, we used density-based clustering with noise (DBSCAN) [ 62 ] (see Supplementary Information). DBSCAN groups densely packed points into clusters and assigns points in sparse regions as noise points. This leads to a natural interpretation of the clusters being “condensed domains” and the noise points being exposed “protrusions”. For both a heterochromatin region ( Fbn2 ) and largely euchromatin regions (e.g. Klf1 and Ppm1g ), the majority of nucleosomes occur in domains with only ∼ 5 % of the Fbn2, Sox2 , and Ppm1g regions and ∼ 15 % of the Klf1 and Nanog regions forming protrusions (Table S1). The domains identified by DBSCAN appear to correspond to experimentally observed packing (or TAD-like) domains [ 1 , 12 ]. Consistent with experimental observations, the domains contain between a few kilobases to a megabase of DNA content and have diameters ranging from tens to hundreds of nanometers ( Figure 4 ). Moreover, as has been observed in experiments [ 12 , 13 , 63 ] and previous simulation studies [ 64 ], the positioning of the domains in simulation varies greatly between single conformations. For example, the contact map for the Fbn2 region suggests the presence of three topologically associating domains (TADs) (Fig. S10). In some frames, the entire region forms a single domain, while in others a single TAD is split into multiple packing domains. The packing domains are generally but not always formed by contiguous regions, as observed in chromatin tracing experiments [ 12 ]. The packing domains have nucleosome concentrations of approximately 300 µM (Fig S18). However, the precise value ranges depending on the approach used, ranging from about 250 µM using probe excluded volume to nearly 500 µM using the maximum local concentration (see Supplementary Information). The nucleosome concentration, as well as the scaling of radius of gyration with size ( Figure 5c ), shows only minor variations between regions, despite their different epigenetic states (Fig. S9). We will discuss this perhaps unexpected result in more detail later. This concentration is largely consistent with in vitro [ 65 ] and in vivo [ 4 ] measurements. Additionally, this packing domain density would allow the whole genome to fit comfortably in the nucleus with over half of the volume mostly devoid of chromatin [ 1 ]: 6 GB of DNA in a nucleus of 10 µm nucleus would require a nucleosome concentration of about 100 µM if uniformly spaced. Download figure Open in new tab Figure 5: Packing domains are composed of clutches. (a) Illustration of the packing domains in a representative simulation frame. (b) Decomposition of the same simulation frame into clutches. (c) Zooming into the representative frame shows that clutches are generally unmixed, but contact each other on their surfaces to form packing domains. (d) A zoom-in highlighting the conformation of a 100 kb segment of the system. Modeling this region on its own would neglect a significant fraction of nucleosome interactions. (e) Relationship between the radius of gyration (Rg) and size of packing domains. Packing domains have similar Rg between regions, despite them having different epigenetic state. The scaling exponents are shown for domains smaller and larger than 50 KB. Small packing domains scale with a larger exponent because they are often formed by a single clutches and inherit their fiber-like character. (f) Clutches are about 10 kb in size, consistent with the peak in packing domain sizes. (g) Average segment lengths over each region. All regions initially display similar scaling, but at large separations gene rich regions, e.g. Klf1 , are more extended. Packing domains are loose aggregations of clutches Various imaging experiments suggest that packing domains contain internal structure. For instance, Szabo et al. [ 13 ] observed “chromatin nanodomains” corresponding to dense blobs inside of packing domains and Ricci et al. [ 5 ] observed “clutches” corresponding to clustered groups of tens of nucleosomes. Additionally, heterogeneous fiber-like structures have been observed in vitro [ 66 ] and in vivo using cryo-ET [ 7 – 9 ]. However, without the ability to trace the chromatin strand, it has proven hard to precisely characterize these structures and relate them to higher-order chromatin structure. Indeed, packing domains in our simulations are far from homogeneous droplets. Especially for domains larger than 10 kb, packing domains contain dense regions interspersed with unfilled cavities ( Figure 5a ). Visual inspection shows that the dense regions largely correspond to contiguous chromatin segments ( Figure 5b ). This suggests that the chromatin chain decomposes into compact, contiguous segments, which then loosely aggregate to form packing domains. We refer to these contiguous segments as “contiguous nucleosome clutches” (or “clutches” for short) because they appear to correspond roughly to the small, dense structures observed in super-resolution images by Ricci et al. [ 5 ]. We define clutches using insulation scores calculated from single-frame contact maps. Positions with fewer than half the median number of cross contacts are defined as clutch boundaries, and the segments between such boundaries are defined as clutches (Supplementary Information). By construction clutches are insulated from flanking regions, however, we find that the clutches are also generally not mixed with other regions ( Figure 5c , Fig. S14c). This definition differs from the original definition of nucleosome clutches as clustered nucleosome localizations in super-resolution images [ 5 ]. Under our definition, the clutches are explicitly defined as contiguous segments, which is enabled by the ability to trace the chromatin chain in our simulations. There are likely cases where multiple contiguous clutches are pressed against each other and thereby appear as a single cluster in imaging. Conversely, large or irregularly shaped contiguous clutches may be separated into multiple clusters or not fit in the field of view when imaged. The precise choice of parameters used to define clutches, and thereby their precise sizes and boundary probabilities, is somewhat arbitrary, as hierarchically folded structure exists across a broad range of scales (Fig. S12). However, there are several factors supporting that clutches, as defined here, are an important layer of chromatin organization. First, these are the largest contiguous segments that are mostly unmixed (Fig. S14e). Second, their sizes coincide with a change in the end-to-end distance scaling exponent from to ( Figure 5g ). Finally, their size distribution overlaps the distribution of packing domain sizes, suggesting that clutches represent an underlying feature that can either occur alone as small packing domains or group together into large packing domains ( Figure 5f , Figure 6a ). Download figure Open in new tab Figure 6: Protrusions, clutch boundaries, contact density, and ATAC-seq coverage are closely related. (a) Cartoon depicting the relationship between enhancers and promoters, clutches, and packing domains. (b) The probability of a boundary between clutches is correlated with ATAC-seq coverage. (c) The probability of a position occurring as a protrusion explains much of the variation in average local nucleosome concentration, defined as the concentration within a 40 nm sphere of each nucleosome. (d) Contact density, protrusion probability, clutch boundary probability, domain sizes, and ATAC-seq coverage for the Ppm1g region. For the domain size traces, the solid line shows the median value and the shaded region encloses the 25th to 75th percentile. The reference contact density is shown in red and the simulated contact frequency is shown in gray. Clutches on average contain about 10 KB (50 nucleosomes) of genomic content ( Figure 5d ). This makes them similar in size to the experimentally observed clutches [ 5 , 14 ]. The clutches are smaller in the vicinity of active regulatory elements and larger elsewhere ( Figure 6d , Fig. S15a), consistent with experimentally observed changes in clutch size upon hyper-acetylation [ 67 ] and the preferential association of small clutches with nascent RNA [ 68 ]. Meanwhile, the chromatin nanodomains observed by Szabo et al. [ 13 ] are generally larger and likely represent aggregations of clutches. Clutches have an elongated fiber-like character with their radius of gyration scaling with genomic content with an exponent of 0.46 (Fig. S15b), reminiscent of the heterogeneous fibers observed in cryo-ET [ 7 – 9 , 66 ]. In this way, packing domains can be viewed as a mosaic of fiber-like clutches ( Figure 6a ). This underlying structure is largely obscured without access to the chain index because clutches often press against each other on their surfaces, leading to continuously high density ( Figure 5b,c ). Clutch boundaries are enriched at ATAC-seq peaks ( Figure 6b , Fig. S13b). The most defined boundaries are present in over 75% of frames ( Figure 6d ). These well-phased boundaries result in clutches that appear in the population average contact map as small squares along the diagonal (Fig. S16) [ 25 ]. However, all positions, even those not associated with any clear features in the contact map, have a non-zero probability of forming a clutch boundary ( Figure 6d , Fig. S13). These stochastic boundaries do not appear in the contact map because they are positioned differently between frames. In this way, there is a similar relationship between these small squares along the diagonal and clutches as between TADs and packing domains [ 12 ]. Packing domains expose active enhancers and promoters at their periphery We now turn our attention to the short “protrusions” from packing domains, which by definition are highly accessible. The protrusions we observe are typically on the scale of a few kilobases, rarely exceeding 10 kb, and generally adopt extended conformations, consistent with a 10 nm fiber ( Figure 4h , Figure 5a ). The protrusions sometimes link two packing domains, but just as frequently exit from and return to the same packing domain. The probability of a nucleosome occurring in a protrusion is higher at active promoters and enhancers ( Figure 6d , Fig. S15a,d). The highest protrusion probabilities, e.g. at 85.4 MB in the Klf1 region, are ∼ 50% but probabilities of ∼ 25% are more typical. The probability of forming a protrusion is enriched specifically in short regions with active epigenetics marks, not the A compartment generally. For example, using the typical eigenvector analysis (at 12 kb resolution), the entirety of the simulated Ppm1g region is identified as A compartment. However, the region from 31.8–32.2 mb has few ATAC peaks and has a low probability of forming a protrusion ( Figure 4b ). Conversely, the Fbn2 region is largely called as B compartment, but nonetheless there is an increase in protrusion probability at the few ATAC-seq peaks present ( Figure 4a ). Without neighbor balancing, we see little enrichment for protrusion formation at active promoters and enhancers (Fig. S11). There is a close connection between protrusions and the boundaries between clutches ( Figure 6a ). Clutch boundaries are a local property and are formed when a few kilobases of chromatin adopt an extended conformation. Meanwhile, protrusions are a global property, and their formation requires a nucleosome not to be crowded by local interactions and to extend out from packing domains. In this way, a protrusion will generally be a clutch boundary, but a clutch boundary can be buried inside of a packing domain and thereby not a protrusion. The probabilities of a position forming a protrusion or clutch boundary are strongly correlated ( Figure 6d , Fig. S15a,c), suggesting that local extension generally emerges as global accessibility independent of context. However, the correlation is not perfect, and it is possible that in some cases local and global compaction are modulated separately to control gene expression. Discussion We introduced a protocol to generate nucleosome-resolution conformational ensembles that reproduce contact frequencies from RCMC and pairwise distance distributions from chromatin tracing. Our approach simultaneously provides high spatial and genomic resolution, allowing us to observe the connection between genomic features and structural motifs. Packing domains with regulatory protrusions Our simulations suggest that euchromatin is generally comprised of condensed domains, but short regions at active promoters and enhancers sometimes form extended, highly exposed protrusions ( Figure 6a ). This view is consistent with a variety of experimental data suggesting that euchromatin is generally compact [ 2 ], while providing an explanation as to how enhancers and promoters are nonetheless accessible. The tendency for active promoters and enhancers to form exposed protrusions leaves them accessible to transcription factors, the transcriptional machinery, and each other. Compared to a case where the entirety of euchromatin exists as a 10 nm fiber, the arrangement of the majority of euchromatin into domains lowers the entropic penalty for enhancer–promoter contacts by effectively shortening the tether between them. Moreover, non-active regions being less accessible limits the search space of transcription factors, potentially introduces a means to repress nearby genes, and allows compaction of the genome into the nucleus. Together, this arrangement naturally brings enhancers and promoters together, as they tend to be positioned on the exterior of packing domains, facilitating the formation of microcompartments [ 48 ] and fine-scale A-compartments [ 69 ]. Packing domain density is independent of chromatin state In our simulations, the density inside of packing domains is largely consistent between regions, despite differences in epigenetic state. This perhaps surprising result requires three clarifications. First, short regions near promoters and enhancers are more likely to exist as protrusions, which are substantially less dense and more extended. In this way, euchromatin defined narrowly as active promoters and enhancers is indeed on average less dense ( Figure 6c,d ). Second, gene-rich regions are broken into more, smaller packing domains ( Figure 4i ) and overall adopt more extended conformations on large length scales ( Figure 5e ). As a result, while the packing domains are of approximately the same density, the overall system is in some sense less dense [ 70 , 71 ]. Moreover, since the surface-area-to-volume ratio of smaller domains is higher, these gene rich regions are generally more exposed. The fraction of time a nucleosome spends on the surface, which includes both time spent as a protrusion and time on the surface of a packing domain, explains much of the variation in local density (Fig. S9e). Third, here we only considered data for embryonic stem cells, which are believed to have an overall more open chromatin structure to support pluripotency [ 72 ]. Future work is needed to assess if heterochromatin regions in differentiated cells are more dense. Several experimental observations support that most nucleosomes are compacted into domains with a similar density and only short regions around promoters and enhancers are highly exposed [ 2 ]. Imaging studies reveal that the chromatin is arranged heterogeneously with much of the genome grouped into dense domains and a small fraction partitioned into a substantially more dilute phase [ 1 , 4 , 73 ]. Tagging of specific regions [ 74 ] or histone marks [ 55 ] show that active regulatory elements are enriched in these dilute regions. Probing chromatin compaction by measuring sedimentation velocities [ 56 ] and digesting DNA with varying concentrations of MNase [ 57 ] both show that there are minimal large-scale differences in compaction but short regions around active promoters and enhancers are disproportionately open. Mechanisms of packing and clutch formation Our simulations provide a unified account of sub-packing-domain-scale chromatin organization. Previous studies have reported dense nucleosome clusters inside of packing domains of different sizes [ 5 , 13 , 75 ]. Additionally, short sections of native chromatin have been observed to form heterogeneous fiber-like structures in vitro [ 66 ] and fiber-like structures have been observed in vivo [ 8 , 9 ]. Our simulations suggest that contiguous sections of chromatin collapse along the chain to form clutches with heterogeneous fiber-like structures. These clutches aggregate hierarchically to form dense nucleosome clusters at a variety of scales, as well as packing domains themselves ( Figure 5 , Fig. S12). The boundaries between clutches, which are comprised of locally extended chromatin segments, often propagate up to emerge as protrusions, which are globally exposed. Different experimental techniques and data analysis pipelines likely produce different views of this underlying hierarchical structure. The ability to trace the chromatin strand in our simulations allowed us to define clutches explicitly as contiguous chromatin segments. This is important because it highlights the mechanisms driving their formation and regulation. Clutches appear to be held together particularly tightly by the physical tethers between nucleosomes, corresponding to “correlation blobs” in polymer physics [ 76 ]. The boundaries between clutches are highly enriched at ATAC-seq peaks ( Figure 6b ). This likely stems from the presence of nucleosome-free regions at ATAC-seq peaks, which have been shown to induce domain boundaries in both experimental and computational studies [ 77 – 79 ]. Additionally, the boundaries are correlated with low condensability scores [ 54 ], suggesting that decompaction could be mediated by decreased nucleosome interaction energies ( Figure 1c ). Simulations using RCMC data from cohesin-depleted cells [ 48 ] suggest that clutch formation is largely independent of loop extrusion. At large genomic separations, contact frequencies decrease, segment end-to-end distances increase, and the size of packing domains decreases substantially but they remain present (Fig. S17). This increase in segment end-to-end distances and the continued presence of packing domains is consistent with chromatin tracing data [ 12 , 61 ]. Meanwhile, for separations less than 10 kb, there are only minor changes to contact frequencies, segment end-to-end distances, and clutch sizes. Cohesin depletion having only a minor change on 10 kb end-to-end distances is consistent with chromatin tracing data [ 80 ]. These findings suggest that, while cohesin-mediated loop extrusion plays a significant role in forming packing domains and large-scale structure generally, clutches are mostly shaped by other factors. This is also supported by the near 1/2 scaling of segment distances on short length scales ( Figure 5g ). Theoretical models of loop extrusion suggest this regime occurs because on short scales the chromatin chain has time to fully relax between cohesin looping events [ 81 ]. These models also predict the decay to scaling exponents less than 1/3 at above 30 kb observed in our simulations. Methods Neighbor balancing The neighbor balanced contact frequencies C (neighbor) are computed from the ICE balanced contact frequencies C as The ICE balanced contact frequencies are smoothed using a Gaussian filter with a standard deviation of 1 bin when computing the denominator of this expression. First applying ICE balancing and then applying neighbor balancing gives more robust results then applying neighbor balancing to the raw read counts. This procedure is akin to the “square root vanilla coverage” balancing rule [ 82 ]. Note that if ICE balanced neighbor contacts were constant over a region, then this procedure would exactly update the neighbor contact frequencies to be one. In practice, the neighbor contacts are not constant and this procedure does not perfectly set the neighbor contact frequencies to one, but it does move them closer to one. While an analog of iterative correction could be used to bring the neighbor contact frequencies closer to 1, in practice, the simpler update rule is more robust. We processed the RCMC data largely following the procedure from the original study. However, we found that several changes were necessary to facilitate using the data as nucleosome-level contact probabilities. These changes include: (1) using an estimated nucleosome center position, instead of the 5’ read end position when determining contact coordinates, (2) accounting for an overabundance of short range inward oriented junctions, which appear to be unligated artifacts, and (3) developing an augmented ICE balancing procedure that accounts for missing data due to low read coverage or low capture probe coverage. A complete description of the processing pipeline and motivation for modifications is available in the Supplementary Information. We offer two guidelines for the practical application of neighbor balancing. First, applying neighbor balancing at a higher resolution than is supported by the sequencing depth results in noisy contact densities and should be avoided. As described in Supplementary Information, neighbor contact frequencies can be aggregated over larger windows and used to produce neighbor balanced contact maps at lower resolution. Second, contact densities should not be directly compared for micro-C datasets produced with different protocols. The micro-C procedure, especially the cross-linking profile, seems to influence the overall scale of the contact densities determined by neighbor balancing. In particular, stronger cross-linking yields lower contact densities, presumably mediated through a concomitant decrease in the capture radius. Consistent with this, Oksuz et al. [ 83 ] observed that using stronger crosslinking yields a higher fraction of short range cis contacts, consistent with a shorter capture radius. Maximum entropy inversion Maximum entropy inversion is a strategy for parameterizing data-driven simulations. That is to determine the value of parameters in a system’s energy function that result in the system reproducing experimental observables. This is a good match for our problem, where the experimental data are the probabilities of each pair of nucleosomes being in contact. Maximum entropy inversion has been used previously to model chromatin conformations, but these studies have generally focused on modeling larger genomic regions at lower resolution [ 43 , 84 , 85 ]. Say we have experimental observations T = [ t 1 , …, t n ] where each observation corresponds to the average of some property of the system, e.g. t i = ⟨f i ( X ) ⟩ where X are the conformations of the system, ⟨·⟩ denotes the ensemble average, and f i is a function mapping conformations of the system to a scalar. It can be shown that the least biased way to augment the system to i =1 match the experimental observations is to introduce auxiliary energy terms . The energy coefficients α are derived using an iterative procedure wherein the system is simulated with the current coefficients, the observables are estimated from the simulated ensemble, and then the coefficients are updated by comparing the simulated and experimental values [ 43 , 86 ]. In our work, the observables are the contact probabilities from micro-C, the functions f i of interest are “contact indicator” functions modeling the probability of two nucleosomes forming a micro-C contact given their distance, and the coefficients α i can be viewed as nucleosome-nucleosome interaction energies. Importantly, these interaction energies represent not just the intrinsic interaction energy between the two nucleosomes but also implicitly account for external factors, such as cohesinmediated looping and interactions mediated by auxiliary proteins. In this way, the optimized system abstracts the molecular mechanisms into an information-theoretic energy landscape. To initiate MEI, we must define a baseline model of the system and the contact indicator function, which we describe in detail below. For full details of the MEI procedure, see the Supplementary Information. Base nucleosome-level model Nucleosomes are modeled as hard spheres with a diameter of d = 11 nm. This diameter was chosen to match the major axis of nucleosomes. We use the Lenard-Jones potential cut off at 2 1/6 d to only include the repulsive regime. We set ϵ = 1. Consecutive nucleosomes are connected by “class2” bonds with an equilibrium distance b 0 = 21 nm fit to match the nucleosome-nucleosome distance observed in a cryo-EM structure of nucleosomes with a nucleosome repeat length of 197 bps plus 1 nm for the 3 additional base pairs [ 87 ]. The bond stiffness was set to , which allows fluctuations from approximately 10 to 30 nm, reflecting cases where neighboring nucleosomes are completely collapsed together to cases where nucleosomes are partially unraveled. The class2 potential was chosen to resist large deviations and favor collapse of nucleosomes together compared to large extensions. The geometry of nucleosomes results in a preference for acute angles between three consecutive nucleosomes. It is hard to set the strength of this potential from first principles because the angle preference likely depends heavily on epigenetic modifications to the nucleosomes and the DNA-sequence. Therefore to set this parameter we used a top-down approach where we match the distribution of angles observed in cryo-ET structures of isolated chromatin [ 66 ]. We were not able to recapitulate the distribution exactly because our nucleosomes are too large to allow for very acute angles. Nucleosomes form attractive interactions so we added short-range favorable nucleosome-nucleosome interactions [ 88 , 89 ]. As for the angle energy coefficient, the nucleosome-nucleosome binding energy is perturbed by epigenetic modifications as well as salt concentrations, so it is hard to assign a priori. For the potential, we assumed the tanh functional form with r c = 15 and σ = 8. We used an energy coefficient of -1 kT, which we justify below. In preliminary simulations, nearly all of the structures contained knots. This is in conflict with experimental data suggesting that interphase chromatin is largely free of knots [ 43 , 90 ], so we modified the system to prevent knotting. First, we introduced a string of spherical beads between each pair of bonded nucleosomes to prevent the strand from being able to cross itself. Second, we added a large bead to the end of each chain to prevent knots from entering the system through the ends. Buffer nucleosomes are added between these large beads and the core system to prevent this from biasing the ensemble. These additions leave the model kinetically trapped in an unknotted topology. We sample from this model with Langevin dynamics using OpenMM [ 91 ]. Each monomer is assigned a mass of 1. The Langevin middle integrator [ 92 ] is used with a timestep of 0.125 τ , a collision rate of 0.01 τ − 1, and a temperature of This choice of temperature results in kT being one, allowing us to easily specify our potential in reduced units. The simulations do not include periodic boundary conditions or any form of confinement potential. While this is not the most accurate nucleosome-level model available, it captures the basic properties of chromatin and allows for simulations of large genomic regions. Nucleosome-interactions impact the optimized ensemble Choosing the nucleosome interaction energy assumed by our base model from first principles is challenging because this quantity has proven hard to determine experimentally and depends on the conditions [ 88 ]. There is an argument that the interaction potential should be tuned to the theta condition. If we imagine the nucleus as a dense melt of chromatin, then we expect the chains to expand ideally as the interactions are effectively screened [ 76 ]. In this sense, tuning the interaction energy to the theta condition would implicitly account for the unmodeled remaining chromatin. However, imaging studies suggest the nucleus is not a dense melt of nucleosomes but separated into dense and dilute regions [ 1 , 4 ]. This motivates the choice of an interaction energy stronger than that corresponding to the theta condition to implicitly account for the seemingly poor solvent. To test the effects of this parameter, we performed MEI simulations on the Nanog region using base models with a range of interaction energies. We observed that stronger interactions yield systems that break into smaller, denser packing domains (Fig. S18b,f,h). However, this trend largely plateaus at or above the theta condition, which we found to be around 0.9 kT (Fig. S18a). In this regime, the conformations are visually similar (Fig. S18g) and protrusion probabilities show little change (Fig. S18i). In this way, our conclusions would not fundamentally change regardless of the specific value chosen. We selected an interaction energy of 1 kT for our production simulations. Computing simulated contact maps Given the output of a simulation, we wish to generate a simulated contact map comparable to contact maps from micro-C experiments. We assume the following model for how contact maps from micro-C arise. A large population of cells are provided as input to the micro-C experiment. In each cell, ligated junction reads are formed between nucleosomes (or other proteins) that are physically close to each other. We assume that the probability of a ligation is purely a function of the distance between nucleosomes, which we model using a “contact indicator” function f . The contact map is then produced by averaging the counts of junction reads across all the cells. This model leaves out details, such as that certain regions intrinsically produce more junction reads. We assume these complications are handled by ICE and neighbor balancing. A simulation (or set thereof) gives frames X = {X ( k ) ∈ R m× 3 , k = 1.. N} where N is the number of frames and m is the number of monomers. These simulation frames can be thought of as reflecting the chromatin conformations that might be present in a population of cells. Given a set of frames, we compute a simulated contact map S ∈ R m×m by computing instantaneous contact maps S ( k ) for each frame and then averaging them The instantaneous contact maps are computed as For the “contact indicator” function, which models the relative rate of observing a junction read between two nucleosomes as a function of distance, we use This function is one for short distances, reaches a value of 0.5 at the “capture radius” r c , and decays to zero for far distances. The parameter σ controls the rate of decay. When comparing to micro-C contact maps, we scale these probabilities by a constant such that the average contact frequency between neighboring nucleosomes is matched between the simulated and reference contact maps. The choice of contact indicator function has a major impact on the optimized ensemble. All else being equal, shorter capture radii result in dense, compact structures while longer capture radii result in dilute, extended conformations. This relationship is a complex function of the cross-linking, MNase digestion, and ligation protocol, and there does not appear to be a way to determine it from first principles. We set the contact indicator function to reproduce the average pairwise distances determined by chromatin tracing data for the Nanog locus [ 60 ]. This required repeated optimizations with different capture radii. A capture radius of 42 nm (two bond lengths in our base model) provided a reasonable match ( Figure 3a ). We note that while the overall magnitude of average distances was used to determine the model and thereby cannot be considered validation. No free parameters were available to fit the shape of the distance scaling curves, the individual pairwise distances, nor the full distributions of individual pairwise distances. Close agreement of these three quantities therefore validates of our model. Competing interests The authors declare that they have no competing interests. Data and materials availability The implementation for neighbor balancing is provided at: https://github.com/ZhangGroup-MITChemistry/neighbor-balance . Simulation trajectories and maximum entropy inversion code will be made available upon publication. Acknowledgements We are grateful to Advait Athreya, Anders Hansen, Alistair Boettiger, Lacramioara Bintu, and Taihei Fujimori for helpful discussions. This work was supported by the National Institutes of Health (Grant R35GM133580). 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