Giovanni B BrandanipersName, Chenyang GupersName, Soundhararajan GopipersName, Shoji TakadapersName (2024date). “Multiscale Bayesian simulations reveal functional chromatin condensation of gene loci.” PNAS Nexustitle·j.
Object of study — 3D chromatinterm·dom organization of the Sox2, Pou5f1 and Nanogterm·key loci of mouse embryonic stem cells
Research question — what physical principles govern chromatinterm·dom organization across the scales of a gene and link its structure to function
Contribution — Hi-C metainferenceterm·mth, a Bayesian method that adds contact data to physics-based chromatinterm·dom priors, and what it reveals about gene loci
phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | transient chromatin condensation bringing enhancers and promoters into contact — “At the larger scale, we find that enhancer–promoter contacts are driven by the transient condensation of chromatin into compact domains stabilized by extensive internucleosome interactions.” | |
| claim-type | mechanism — “At the larger scale, we find that enhancer–promoter contacts are driven by the transient condensation of chromatin into compact domains stabilized by extensive internucleosome interactions.” | |
| method — evidence | — “This approach combines both bottom-up (the physics-based prior) and top-down (the data-driven posterior) strategies to characterize the 3D organization of a target genomic locus.” | |
| object of study — evidence | — “We observe that the studied loci are conformationally heterogeneous and organized as crumpled globules, favoring contacts between distant enhancers and promoters.” | |
| research question — evidence | — “Despite substantial progress in recent years, our understanding of the physical principles governing chromatin organization across different scales of genes remains limited, which hinders further exploration of the interplay between genomic structure and function.” | |
| contribution — evidence | — “To aid our understanding of the principles underlying chromatin organization, we introduce Hi-C metainference, a Bayesian approach that integrates Hi-C contact frequencies into multiscale prior models of chromatin.” | |
| mechanism | internucleosome interactions Internucleosome interactions alone suffice to explain the dynamic condensation of the Nanog locus. — “Based on this similarity, we suggest that internucleosome interactions alone are sufficient to explain the observed dynamic condensation of the 10 kb Nanog locus.” | mechanisms[0] |
| mechanism | separation of timescales CRE contacts form and break in under a second, far faster than gene activation, which hides structure-expression correlations. — “This separation of timescales helps explain difficulties in the experimental detection of correlations between 3D genome structure and gene expression ( 56 , 57 ).” | mechanisms[1] |
| sense | bottom-up and top-down - a physics-based prior refined by a data-driven posterior — “This approach combines both bottom-up (the physics-based prior) and top-down (the data-driven posterior) strategies to characterize the 3D organization of a target genomic locus.” | senses[0] |
| sense | the Bayesian bias as a stand-in for missing in vivo forces - epigenetics, transcription-factor binding and loop extrusion absent from the physics model — “This bias introduced by the Bayesian inference can be regarded as representing in vivo effects originating from epigenetics ( 25 , 32 , 49 ), TF binding ( 31 , 41 ), and cohesin loop extrusion ( 30 ), which are not explicitly included into the physics-based model.” | senses[1] |
| relation | TADs —same-as→ topologically associated domains — (TADs) — “Chromatin fibers further fold into topologically associated domains (TADs), contiguous regions with enriched physical contacts separated by insulator elements ( 14 ).” | concept_edges[0] |
| weight | TADs —same-as→ topologically associated domains — 0.95 — “Chromatin fibers further fold into topologically associated domains (TADs), contiguous regions with enriched physical contacts separated by insulator elements ( 14 ).” | concept_edges[0] |
| relation | CREs —same-as→ cis-regulatory elements — (CREs) — “The pattern of TADs and compartments along the genome influences the communication between cis-regulatory elements (CREs), such as enhancers and promoters ( 16 , 19 , 20 ).” | concept_edges[1] |
| weight | CREs —same-as→ cis-regulatory elements — 0.95 — “The pattern of TADs and compartments along the genome influences the communication between cis-regulatory elements (CREs), such as enhancers and promoters ( 16 , 19 , 20 ).” | concept_edges[1] |
| relation | MD —same-as→ molecular dynamics — (MD) — “Metainference is one such Bayesian approach, originally developed to integrate NMR data into all-atom force fields for protein molecular dynamics (MD) simulations ( 44 ).” | concept_edges[2] |
| weight | MD —same-as→ molecular dynamics — 0.95 — “Metainference is one such Bayesian approach, originally developed to integrate NMR data into all-atom force fields for protein molecular dynamics (MD) simulations ( 44 ).” | concept_edges[2] |
| relation | Metainference —contrasted-with→ maximum entropy principle — Compared with the maximum entropy principle — “Compared with the maximum entropy principle ( 25 ), metainference does not require iterative optimization and can consistently account for both random and systematic errors within a Bayesian framework, although the two approaches are expected to give identical results in the limit of low errors and strong bias ( 44 , 67 , 68 ).” | concept_edges[3] |
| weight | Metainference —contrasted-with→ maximum entropy principle — 0.8 — “Compared with the maximum entropy principle ( 25 ), metainference does not require iterative optimization and can consistently account for both random and systematic errors within a Bayesian framework, although the two approaches are expected to give identical results in the limit of low errors and strong bias ( 44 , 67 , 68 ).” | concept_edges[3] |
| evidential status | mechanism — we suggest — “Based on this similarity, we suggest that internucleosome interactions alone are sufficient to explain the observed dynamic condensation of the 10 kb Nanog locus.” | mechanisms[0] |
| replication | original | |
| no type for this | nucleosome → Chromatin — the nucleosome is the fundamental unit of chromatin - a unit-of relation the vocabulary's part-of cue list does not carry — “The fundamental unit of chromatin is the nucleosome, an assembly comprising about 150 bp of DNA wrapped around a histone octamer ( 4 ).” | unhoused_relations[0] |
| limitation | As an equilibrium method it may distort the kinetics of nonequilibrium processes such as loop extrusion. — “However, being an approach based on thermodynamic equilibrium, the kinetics of nonequilibrium processes such as cohesin loop extrusion ( 30 ) could be potentially affected.” | limitations[0] |
| limitation | Simulations are too short to see exchanges between the four clusters in one trajectory. — “While the timescale of our metainference simulation is not sufficient to observe dynamic exchanges between these four clusters in the same trajectory, the absence of high barriers in the free energy landscape (Fig. S6A ) suggests that such transitions should be diffusion limited and relatively rapid.” | limitations[1] |
| limitation | The prior is uniform and represents no epigenetic marks or transcription-factor binding. — “We note that our metainference simulations were performed using a uniform prior model lacking any representation of epigenetic modifications and TF binding that could be physically responsible for differences in chromatin compaction, indicating that the bias employed within our Bayesian framework can be interpreted as an effective representation of forces acting differentially along the genome.” | limitations[2] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | The loci are heterogeneous and organized as crumpled globules favouring distant enhancer-promoter contacts. — “We observe that the studied loci are conformationally heterogeneous and organized as crumpled globules, favoring contacts between distant enhancers and promoters.” | content_tags.findings[0] |
| finding | Agreement with target contact maps improves as replicas rise from 4 to 128. — “The correlation between the contact probabilities increases, as the number of replicas increases from 4 to 128 (Fig. 2 B).” | content_tags.findings[1] |
| finding | Metainference also recovers the dynamics of the target copolymer. — “Finally, we confirmed that metainference can also recover the dynamics of the target copolymer system, as shown by the good correlation between the cluster transition probabilities estimated by Markov state modeling ( 53 ) of the metainference and target copolymer simulations (Fig. 2 G, see SI for details of the Markov state modeling).” | content_tags.findings[2] |
| finding | Loci switch between small and large enhancer-promoter distances in under a second. — “As indicated by the rapid decay of the EP distance autocorrelation functions (Fig. S3A ), these loci typically undergo fast transitions between conformations with small (<50 nm) and large (>300 nm) EP distances (Fig. 3 G), over a timescale of less than a second, much faster than the typical timescales of gene bursting dynamics ( 58 ).” | content_tags.findings[3] |
| finding | Open tetranucleosomes sit at cis-regulatory elements; compact ones lie between them. — “We find that the open tetranucleosomes are prevalently observed at the CREs of the locus, as determined from the ChIP-seq profiles of RNAPII binding ( 61 ) and H3K27ac tail modification ( 62 ) (Fig. 5 B).” | content_tags.findings[4] |
| finding | Mean nearest-nucleosome distance is about 12 nm. — “The average nearest nucleosome distance throughout the locus is ∼12 nm, consistent with the value obtained in our prior 1CPN simulations and the experimental value obtained by in situ cryo-ET of human T-lymphoblast interphase chromatin ( 12 ).” | content_tags.findings[5] |
| finding | All three Nanog enhancers often cluster with the promoter into a single hub. — “Notably, all CREs often cluster together into a single hub (Fig. 4 B, bottom left snapshot, and Fig. S4B for the free energy landscape projected on a pair of EP distances), suggesting that the three enhancers may cooperatively activate their target ( 60 ), or compensate for each other's loss ( 55 ).” | content_tags.findings[6] |
| quantity | 21% — — “the EP domain cluster (21%) is characterized by a distinct compact domain bounded by the −5 kb enhancer and the Nanog promoter;” | content_tags.quantities[0] |
| quantity | N = 1/ P — — “This is to be expected, since reproducing the formation of a contact with probability P requires roughly N = 1/ P or more replicas, as the contact should appear at least once in the ensemble of replicas used to represent the true infinite ensemble during the MD simulation.” | content_tags.quantities[1] |
| variable | number of replicas — “The correlation between the contact probabilities increases, as the number of replicas increases from 4 to 128 (Fig. 2 B).” | content_tags.variables[0] |
| definition | nucleosome — “The fundamental unit of chromatin is the nucleosome, an assembly comprising about 150 bp of DNA wrapped around a histone octamer ( 4 ).” | content_tags.definitions[0] |
| definition | TADs — “Chromatin fibers further fold into topologically associated domains (TADs), contiguous regions with enriched physical contacts separated by insulator elements ( 14 ).” | content_tags.definitions[1] |
| definition | Hi-C metainference — “To aid our understanding of the principles underlying chromatin organization, we introduce Hi-C metainference, a Bayesian approach that integrates Hi-C contact frequencies into multiscale prior models of chromatin.” | content_tags.definitions[2] |
| key-terms | chromatin, Hi-C metainference, nucleosome, crumpled globule, enhancer–promoter contacts, Micro-C, molecular dynamics, tetranucleosome, Nanog |
| concept | Chromatin — the complex assembly of DNA and associated proteins — “Chromatin, the complex assembly of DNA and associated proteins, plays a pivotal role in orchestrating various genomic functions.” | concepts[0] |
| concept | Hi-C metainference — a Bayesian approach that integrates Hi-C contact frequencies into multiscale prior models of chromatin — “To aid our understanding of the principles underlying chromatin organization, we introduce Hi-C metainference, a Bayesian approach that integrates Hi-C contact frequencies into multiscale prior models of chromatin.” | concepts[1] |
| concept | Metainference — one such Bayesian approach, originally developed to integrate NMR data into all-atom force fields for protein molecular dynamics (MD) simulations — “Metainference is one such Bayesian approach, originally developed to integrate NMR data into all-atom force fields for protein molecular dynamics (MD) simulations ( 44 ).” | concepts[2] |
| concept | nucleosome — an assembly comprising about 150 bp of DNA wrapped around a histone octamer — “The fundamental unit of chromatin is the nucleosome, an assembly comprising about 150 bp of DNA wrapped around a histone octamer ( 4 ).” | concepts[3] |
| concept | topologically associated domains — contiguous regions with enriched physical contacts separated by insulator elements — “Chromatin fibers further fold into topologically associated domains (TADs), contiguous regions with enriched physical contacts separated by insulator elements ( 14 ).” | concepts[4] |
| concept | TADs — topologically associated domains — “Chromatin fibers further fold into topologically associated domains (TADs), contiguous regions with enriched physical contacts separated by insulator elements ( 14 ).” | concepts[5] |
| concept | cis-regulatory elements — not defined in this paper's own words; the paper names enhancers and promoters as examples — “The pattern of TADs and compartments along the genome influences the communication between cis-regulatory elements (CREs), such as enhancers and promoters ( 16 , 19 , 20 ).” | concepts[6] |
| concept | CREs — cis-regulatory elements — “The pattern of TADs and compartments along the genome influences the communication between cis-regulatory elements (CREs), such as enhancers and promoters ( 16 , 19 , 20 ).” | concepts[7] |
| concept | crumpled globule — not defined in this paper's own words; the paper gives its scaling: contact frequency ∼1/ L and end-to-end distance < R > ∼ L 1/3 — “Except for very small genomic distances L , we find that the studied genomic loci are spatially organized as a crumpled globule ( 47 ), with the frequency of contacts scaling as ∼1/ L (Fig. 3 E, as over very large distances ( 15 )) and the average end-to-end distances scaling as < R > ∼ L 1/3 (Fig. 3 F).” | concepts[8] |
| concept | 1CPN model — not defined in this paper's own words; one of two “bottom-up coarse-grained models of chromatin”, at nucleosome resolution — “As priors, we employ two distinct bottom-up coarse-grained models of chromatin: the 1CPN model ( 35 ) at nucleosome resolution, previously parametrized from near-atomistic nucleosome simulations ( 45 ), and a chromatin polymer model at 1 kb resolution newly parametrized from extensive 1CPN simulations.” | concepts[9] |
| concept | molecular dynamics — not defined in this paper's own words in this sentence — “Metainference is one such Bayesian approach, originally developed to integrate NMR data into all-atom force fields for protein molecular dynamics (MD) simulations ( 44 ).” | concepts[10] |
| concept | MD — molecular dynamics — “Metainference is one such Bayesian approach, originally developed to integrate NMR data into all-atom force fields for protein molecular dynamics (MD) simulations ( 44 ).” | concepts[11] |
| concept | TICA — time-structure based independent component analysis — “To provide a rigorous comparison of the ensemble statistics, we divided the conformations observed in the copolymer and metainference simulations into 50 clusters using k -means ( 51 ) after performing a time-structure based independent component analysis (TICA) dimensionality reduction ( 52 ) (see Supporting Information [SI] Methods).” | concepts[12] |
| concept | maximum entropy principle — not defined in this paper's own words in this sentence — “Compared with the maximum entropy principle ( 25 ), metainference does not require iterative optimization and can consistently account for both random and systematic errors within a Bayesian framework, although the two approaches are expected to give identical results in the limit of low errors and strong bias ( 44 , 67 , 68 ).” | concepts[13] |
Full text — tagged
Multiscale Bayesian simulationsterm·mth reveal functional chromatinterm·dom condensation of gene loci Abstract Chromatinterm·dom, the complex assembly of DNA and associated proteins, plays a pivotal role in orchestrating various genomic functions. To aid our understanding of the principles underlying chromatinterm·dom organization, we introduce Hi-C metainferenceterm·mth, a Bayesian approach that integrates Hi-C contact frequencies into multiscale prior models of chromatinterm·dom. This approach combines both bottom-up (the physics-based prior) and top-down (the data-driven posterior) strategies to characterize the 3D organization of a target genomic locus. We first demonstrate the capability of this method to accurately reconstruct the structural ensemble and the dynamics of a system from contact information. We then apply the approach to investigate the Sox2, Pou5f1, and Nanogterm·key loci of mouse embryonic stem cells using a bottom-up chromatinterm·dom model at 1 kb resolution. We observe that the studied loci are conformationally heterogeneous and organized as crumpled globulesterm·dom, favoring contacts between distant enhancers and promoters. Using nucleosome-resolution simulationsterm·mth, we then reveal how the Nanogterm·key gene is functionally organized across the multiple scales of chromatinterm·dom. At the local level, we identify diverse tetranucleosometerm·key folding motifs with a characteristic distribution along the genome, predominantly open at cis-regulatory elementsterm·dom and compact in between. At the larger scale, we find that enhancer–promoter contactsterm·key are driven by the transient condensation of chromatinterm·dom into compact domains stabilized by extensive internucleosome interactions. Overall, this work highlights the condensed, but dynamic nature of chromatinterm·dom in vivo, contributing to a deeper understanding of gene structure–function relationships.
Keywords: chromatinterm·dom structure, nucleosomesterm·dom, enhancer–promoter communication, Hi-C contact maps, molecular dynamicsterm·mth simulationterm·mth Eukaryotic genomes are organized into a complex of DNA and proteins called chromatinterm·dom. The structure and dynamics of chromatinterm·dom are intimately linked to key genomic functions such as gene regulation, but the physical mechanisms underlying such interplay remain unclear. By combining molecular models of chromatinterm·dom with experimental data on mouse genome organization, we show how the 3D organization of chromatinterm·dom over multiple length scales is ideally suited to support the function of several genes. At the small scale, the plasticity of chromatinterm·dom allows for the formation of easily accessible conformations at gene regulatory elements, and compact ones elsewhere. At the scale of entire gene loci, the dynamic condensation of chromatinterm·dom brings together distant gene regulatory elements, supporting their communication.
Introduction Chromatinterm·dom, the complex of DNA and proteins organizing the Eukaryotic genome, plays a pivotal role in orchestrating a multitude of genomic functions, including DNA replication ( 1 ) and the precise regulation of gene activity ( 2 ). Its structure exhibits a hierarchical organization, with biological function affected by structural changes across all levels of the hierarchy ( 3 ). The fundamental unit of chromatinterm·dom is the nucleosometerm·dom, an assembly comprising about 150 bp of DNA wrapped around a histone octamer ( 4 ). Nucleosomesterm·dom are not simply barriers preventing access to genomic DNA; rather, they can be better understood as flexible platforms on top of which key biological processes can be organized ( 5 ). For example, nucleosomal DNA sliding and unwrapping from histones modulate transcription factor (TF) binding ( 6–8 ), with downstream effects on gene expression. At a higher hierarchical level, these nucleosomesterm·dom interact together to form chromatinterm·dom fibers exhibiting remarkable structural polymorphism ( 9–11 ). In vivo, these fibers are predominantly disordered ( 12 ), but specific chromatinterm·dom motifs are associated with distinct genomic regions, such as gene promoters or gene bodies ( 13 ). Chromatinterm·dom fibers further fold into topologically associated domainsterm·dom (TADsterm·dom), contiguous regions with enriched physical contacts separated by insulator elements ( 14 ). At the same time, phase separation drives the condensation of chromatinterm·dom into large-scale compartments enriched in specific epigenetic modifications ( 15–18 ). The pattern of TADsterm·dom and compartments along the genome influences the communication between cis-regulatory elementsterm·dom (CREsterm·dom), such as enhancers and promoters ( 16 , 19 , 20 ). Pointing to the intimate link between genome structure and function, genetic engineering has shown a correlation between the probability of enhancer–promoter (EP) contacts and gene expression levels ( 21 ), while transcription bursting dynamics was found to be linked with EP looping over time ( 22 ).
Despite substantial progress in recent years, our understanding of the physical principles governing chromatinterm·dom organization across different scales of genes remains limited, which hinders further exploration of the interplay between genomic structure and function. In this work, we integrate in vivo experimental genomic contact frequency data into polymer models to explore the 3D structure of mammalian genes from the local chromatinterm·dom fiber level to long-distance interactions between CREsterm·dom. Our findings shed light on how this organization can contribute to gene regulatory functions.
Theoretical approaches rooted in polymer physics have become increasingly important for complementing experiments and uncovering genomic structure–function relationships ( 23 ). Some of these approaches are data driven ( 24–29 ), with interactions between genomic sites optimized to match the experimental Hi-C contact frequencies ( 15 ). Others are centered around a key mechanism responsible for 3D genome organization, such as cohesin loop extrusion ( 30 ), bridging mediated by proteins ( 31 ), or phase separation dependent on specific epigenetic modifications ( 18 , 32 , 33 ). Furthermore, advances in the development of bottom-up molecular models of chromatinterm·dom ( 34–37 ), parametrized based on the physics of its biomolecular components, now offer a viable route to provide a mechanistic understanding of genes based on first principles ( 38 ). Such models have revealed some of the molecular determinants of chromatinterm·dom organization, including the role of nucleosometerm·dom plasticity in mediating liquid–liquid phase separation ( 39 ). Notably, Bascom et al. utilized a nucleosome-resolution model to explore the structure of the HOXC gene locus in mouse embryonic stem cells (mESCs) ( 40 ), identifying the spontaneous formation of loops linking gene promoters with other regions of the locus. However, such physics-based chromatinterm·dom models typically do not capture the effects of all the factors constituting the complex cellular environment, such as potential effects originating from TF binding ( 31 , 41 ). Due to the practical consideration in modeling the behavior of several contributing molecular factors, physics-based models may not always accurately reproduce the experimental organization of chromatinterm·dom in vivo, as determined from Hi-C or Micro-Cterm·key contact frequencies ( 15 , 42 ).
To address this limitation, Bayesian methods offer a framework to incorporate experimental observations into an existing physical model ( 43 , 44 ). Metainferenceterm·mth is one such Bayesian approach, originally developed to integrate NMR data into all-atom force fields for protein molecular dynamicsterm·mth (MDterm·mth) simulationsterm·mth ( 44 ). We introduce and validate Hi-C metainferenceterm·mth, an extension of the original approach to augment an existing prior model of chromatinterm·dom to account for the observed in vivo contact frequencies of a target locus (from Hi-C ( 15 ), Micro-Cterm·key ( 42 ), or other related approaches ( 13 )), allowing one to characterize its 3D organization by MDterm·mth simulationsterm·mth. As priors, we employ two distinct bottom-up coarse-grained models of chromatinterm·dom: the 1CPN modelterm·mth ( 35 ) at nucleosometerm·dom resolution, previously parametrized from near-atomistic nucleosometerm·dom simulationsterm·mth ( 45 ), and a chromatinterm·dom polymer model at 1 kb resolution newly parametrized from extensive 1CPN simulationsterm·mth. Therefore, our exploration of the 3D genome organization can be regarded as a two-way process where the bottom-up prior is adjusted in a top-down fashion by integrating the experimental contact frequencies, retaining the advantages of both physics-based and data-driven approaches.
In this study, we integrate Micro-Cterm·key data ( 46 ) into our chromatinterm·dom models and investigate the organization of the Sox2, Pou5f1, and Nanogterm·key genomic loci in mESCs. First, our simulationsterm·mth show that in vivo genes adopt relatively compact conformations, with the same size scaling of a crumpled globuleterm·dom ( 47 ), while at the same time, displaying significant structural heterogeneity and fast dynamics. Using the nucleosome-resolution prior chromatinterm·dom model for a section of the Nanogterm·key locus, we find that the local organization of the chromatinterm·dom fiber is highly dependent on the underlying epigenetic marks, being open at CREsterm·dom and more compact elsewhere. Finally, we demonstrate that transient, direct contacts between the Nanogterm·key promoter and its nearest enhancer are driven by the condensation of the chromatinterm·dom fiber into a compact domain through extensive nucleosometerm·dom–nucleosometerm·dom interactions. Our simulationsterm·mth suggest that chromatinterm·dom plasticity over multiple length scales provides a physical basis for essential gene regulatory functions.
Results Bayesian integration of Hi-C data into prior physics-based chromatinterm·dom models We introduce Hi-C metainferenceterm·mth to update an existing prior model of chromatinterm·dom (Fig. 1 A, e.g. nucleosome-resolution 1CPN ( 35 ) or coarser 1 kb resolution model) using in vivo genomic contact frequencies from experiments, such as Hi-C ( 15 ) and Micro-Cterm·key ( 42 ). Within this framework, MDterm·mth simulationsterm·mth are used to sample the conformational ensemble of the target system from the posterior probability distribution according to the Bayes’ theorem ( 44 ). The infinite ensemble is represented using a finite number N of replicas of the same chromatinterm·dom system—for example, a polymer made of L beads, each representing a certain number of base pairs of genomic DNA (Fig. 1 B, top left panel, for N = 4 conformations of an L = 200 polymer made of 1 kb beads). The use of replicas makes metainferenceterm·mth ideally suited to model ensemble-averaged experimental data produced by highly heterogeneous systems, such as chromatinterm·dom ( 48 ). Given a chromatinterm·dom structure, we use a forward model that computes the L × L contact map of each replica (Fig. 1 B, bottom left panel). We then average the contact maps over the N replicas to compute a map of contact probabilities, which can be compared with the contact frequencies measured in experiments (Fig. 1 B, bottom right panel). The dynamics of the N replicas is then simulated in parallel using the interaction potential of the prior chromatinterm·dom model together with an additional Bayesian energy score accounting for the mismatch between experiments and predictions from the MDterm·mth ensemble. This bias introduced by the Bayesian inference can be regarded as representing in vivo effects originating from epigenetics ( 25 , 32 , 49 ), TF binding ( 31 , 41 ), and cohesin loop extrusion ( 30 ), which are not explicitly included into the physics-based model. These steps are repeated each MDterm·mth timestep until we obtain a converged conformational ensemble (see Materials and methods for more details). The final ensemble may be further validated by independent experiments probing chromatinterm·dom ensemble properties, for instance through microscopy ( 50 ).
Schematics of Hi-C metainferenceterm·mth approach. A) Representations of the nucleosome-resolution 1CPN and 1 kb prior chromatinterm·dom models, indicating the 1 kb model bond distances ( d ) and angles ( θ ) whose potentials are parametrized based on the 1CPN simulationsterm·mth. In the 1CPN structure, nucleosomal DNA is represented as a tube, while the histone octamers are represented as spheres. In the 1 kb model, each coarse-grained bead represents five nucleosomesterm·dom. B) In Hi-C metainferenceterm·mth, we first simulate a target system using a conformational ensemble of N replicas based on the prior bottom-up model (e.g. N = 4, top panel, for a polymer of 200 1 kb beads). For each conformation, we generate a contact map using a forward model (bottom left). We average the contact maps over the replicas to generate a map of contact probabilities to be compared with the Hi-C data (bottom right). A top-down Bayesian energy score is added to the original interaction potential of the prior model to integrate the Hi-C data into the simulationterm·mth. The conformational ensemble is refined over the course of the hybrid bottom-up/top-down MDterm·mth simulationterm·mth, and it can then be validated against independent experimental data (for example, based on microscopy). C) Illustration of the bottom-up modeling approach showing the comparison of the probability distributions of the bond distances (left) and angles (right) between 1 kb coarse-grained particles from the 1 kb resolution and the 1CPN chromatinterm·dom models.
In principle, Hi-C metainferenceterm·mth can be applied using any prior MDterm·mth model of chromatinterm·dom, as different models cater to the needs of different applications. In this work, we use two chromatinterm·dom prior models at different resolution: the nucleosome-resolution 1CPN chromatinterm·dom model ( 35 ), and a coarse-grained 1 kb resolution model parametrized from 1CPN. The 1CPN modelterm·mth has been rigorously parametrized using a bottom-up procedure based on simulationsterm·mth of nucleosometerm·dom–nucleosometerm·dom interactions at near-atomic resolution ( 45 ), and validated against experimental chromatinterm·dom sedimentation coefficients. In the 1 kb model, chromatinterm·dom is represented as a polymer consisting of 1 kb beads (=5 nucleosomesterm·dom) connected by bond and angle potentials (Fig. 1 A, see Materials and methods for more details). The interaction parameters are optimized in a bottom-up way to match the distributions of bond distances and angles from long 1CPN simulationsterm·mth of 50-nucleosome fibers with a nucleosometerm·dom repeat length of 200 bp (Figs. 1 C and S1 ).
Validation by copolymer model In order to test the capability of metainferenceterm·mth to reconstruct a target polymer ensemble from its Hi-C map, we setup a test using a 200-kb copolymer made of ( L = 200) 1 kb beads modeled as the prior chromatinterm·dom model, except that three 10 kb regions (E1, E2, and E3) act as sticky CREsterm·dom with relatively strong interactions with each other and weaker interactions with the rest of the locus (gene bodies like). This model produces a complex copolymer ensemble with a variety of interactions between the CREsterm·dom, where these can be paired in the three possible combinations, or all be far away from each other, or all collapse into one single hub (Fig. 2 A, top panel). We tested whether metainferenceterm·mth using the noninformative prior chromatinterm·dom model and the copolymer contact map can reconstruct both the statistics and the dynamics of the target copolymer.
Hi-C metainferenceterm·mth validation on complex copolymer ensemble. A) Target Hi-C map (right upper half in the bottom plot) generated by simulationsterm·mth of a 200-kb copolymer containing three sticky CREsterm·dom, vs. the Hi-C map generated from metainferenceterm·mth (left lower half) simulationsterm·mth using N = 128 replicas and the prior 1 kb chromatinterm·dom model. B) The comparison between the Hi-C contact probabilities computed from metainferenceterm·mth MDterm·mth ( y -axis) and from the original copolymer ensemble ( x -axis), for a different numbers of replicas. The inset shows the Pearson correlation coefficient ( r ) between the metainferenceterm·mth and target contact probabilities as a function of number of replicasterm·var. C) Comparison of the probability distributions of the distances between the CREsterm·dom E1 and E3 obtained from the target copolymer ensemble and metainferenceterm·mth MDterm·mth with N = 128 replicas. D) Free energy landscape of the N = 128 metainferenceterm·mth simulationsterm·mth projected on the first two TICAterm·mth coordinates, showing the locations of the 50 cluster centers. E) Kullback–Leibler (KL) divergence of the metainferenceterm·mth cluster probability distribution from the target copolymer distribution, as a function of the number of replicasterm·var. F and G) Comparison of the cluster equilibrium probabilities (F) and Markov state model–estimated transition rates (G) between the metainferenceterm·mth MDterm·mth ( y -axis) and the target copolymer system ( x -axis) for N = 16 and N = 128 replicas.
Figure 2 A shows the good agreement between the target contact map and the one generated from the metainferenceterm·mth simulationsterm·mth using N = 128 replicas. The correlation between the contact probabilities increases, as the number of replicasterm·var increases from 4 to 128 (Fig. 2 B). This is to be expected, since reproducing the formation of a contact with probability P requires roughly N = 1/ P or more replicas, as the contact should appear at least once in the ensemble of replicas used to represent the true infinite ensemble during the MDterm·mth simulationterm·mth. Hi-C metainferenceterm·mth can also recover properties not directly used as a bias, such as the distribution of distances between the different CREsterm·dom (Figs. 2 C, S2A and B ) and radius of gyration (Fig. S2C ). To provide a rigorous comparison of the ensemble statistics, we divided the conformations observed in the copolymer and metainferenceterm·mth simulationsterm·mth into 50 clusters using k -means ( 51 ) after performing a time-structure based independent component analysis (TICAterm·mth) dimensionality reduction ( 52 ) (see Supporting Information [SI] Methods). First, the free energy landscape of the N = 128 metainferenceterm·mth system projected on the first two TICAterm·mth coordinates (Fig. 2 D) is close to the one obtained from the target copolymer simulationsterm·mth (Fig. S2D ). The equilibrium probabilities of the different clusters are in good agreement (Fig. 2 F), and the agreement, as measured by the Kullback–Leibler divergence between the distributions, increases with the number of replicasterm·var used (Fig. 2 E). Finally, we confirmed that metainferenceterm·mth can also recover the dynamics of the target copolymer system, as shown by the good correlation between the cluster transition probabilities estimated by Markov state modeling ( 53 ) of the metainferenceterm·mth and target copolymer simulationsterm·mth (Fig. 2 G, see SI for details of the Markov state modeling).
mESC chromatinterm·dom has a compact but heterogeneous 3D organization We next applied Hi-C metainferenceterm·mth to explore the 3D organization of the 300 kb Pou5f1 and Sox2 genomic loci of mESCs by integrating the corresponding Micro-Cterm·key data ( 46 ) into our 1 kb chromatinterm·dom model. Together with Nanogterm·key, discussed next, the Pou5f1 and Sox2 genes express the core TFs maintaining pluripotency in embryonic stem cells ( 54 ). Their active state is maintained by distant enhancer elements ( 50 , 55 ), making these ideal systems to investigate the function of chromatinterm·dom spatial organization. Metainferenceterm·mth using 128 replicas produces contact maps in good agreement with the experiments (Fig. 3 A and B). In Fig. 3 C and D, we compared the distributions of the physical distances between the promoters and nearby genomic locations with single cell measurements made when the genes are actively expressed ( 50 ), finding that both averages and SDs are in good agreement with these experiments. These results suggest that the transcription status of the genes has a minor impact on the experimentally measured EP distances at these loci, consistent with recent data ( 56 , 57 ).
Structural heterogeneity of the Pou5f1 and Soc2 loci of mESCs. A and B) Comparison of Micro-Cterm·key contact maps of the 300 kb loci of the Pou5f1 (A) and Sox2 (B) genes with the corresponding results obtained from metainferenceterm·mth with N = 128 replicas. The genomic locations of the two promoters (0 kb), the Sox2 + 100 kb enhancer and the Pou5f1 + 40 kb enhancer, are indicated on the contact maps as bars. C and D) Comparison of the averages and SDs (size of the bars) of the distributions of physical distances between the Pou5f1 (C) and Sox2 (D) promoters (0 kb) with nearby genomic locations obtained from single molecule experiments ( 50 ) and from metainferenceterm·mth MDterm·mth based on the Micro-Cterm·key maps. E and F) Scaling of contact frequency (E) and average end-to-end distance < R > from metainferenceterm·mth MDterm·mth as a function of genomic distance (Pou5f1, solid line; Sox2, dashed line). Dotted lines correspond to contact frequency ∼1/ L and < R > ∼ L 1/3 . G) Representative trajectories and snapshots of the Sox2 (left) and Pou5f1 (center) genomic loci, and the corresponding EP distance distributions (right) computed from the metainferenceterm·mth MDterm·mth ensembles. In the simulationterm·mth snapshots, we highlighted the promoters, the Sox2 enhancer at +100 kb, and the Pou5f1 enhancer at +40 kb (color scheme as in panels A and B).
Except for very small genomic distances L , we find that the studied genomic loci are spatially organized as a crumpled globuleterm·dom ( 47 ), with the frequency of contacts scaling as ∼1/ L (Fig. 3 E, as over very large distances ( 15 )) and the average end-to-end distances scaling as < R > ∼ L 1/3 (Fig. 3 F). Such scaling was also found in a recent in vivo microscopy study of a Drosophila gene ( 22 ), highlighting how genes adopt relatively compact conformations favoring the formation of direct contacts between distant CREsterm·dom. Despite such compact scaling, chromatinterm·dom explores very heterogeneous conformational ensembles, sampling not only globular domains characterized by extensive contacts between distant regions, but also more open conformations with fewer contacts (see snapshots in Fig. 3 G). As indicated by the rapid decay of the EP distance autocorrelation functions (Fig. S3A ), these loci typically undergo fast transitions between conformations with small (<50 nm) and large (>300 nm) EP distances (Fig. 3 G), over a timescale of less than a second, much faster than the typical timescales of gene bursting dynamics ( 58 ). Interestingly, the distributions of EP distances peak around ∼150 nm (Fig. 3 G, left), close to the size of the condensed but liquid domains experimentally observed in active chromatinterm·dom ( 59 ). This suggests an active role of such liquid domains in CREterm·dom communication.
We then applied Hi-C metainferenceterm·mth to study the structural ensemble and the kinetics of the 200 kb Nanogterm·key locus of mESCs. Nanogterm·key gene expression is regulated by three enhancers, located at −45 kb (E1), −5 kb (E2), and +60 kb (E3) relative to the promoter ( 55 ). This locus represents a model system to explore the coupling between 3D gene organization and function, and in particular, the potential cooperativity of the three enhancers. Figure 4 A shows the good agreement between locus contact frequencies from Micro-Cterm·key ( 46 ) and from the metainferenceterm·mth simulationsterm·mth obtained using N = 128 replicas. As in the cases of the Sox2 and Pou5f1 loci, the Nanogterm·key locus is characterized by a heterogeneous conformational ensemble, with dynamic domains bounded at variable locations (Fig. 4 B). Reflecting this heterogeneity, the enhancers sample a wide variety of distances to the promoter (Fig. S4A ), sometimes even <50 nm, indicating the possibility of direct physical contacts. Notably, all CREsterm·dom often cluster together into a single hub (Fig. 4 B, bottom left snapshot, and Fig. S4B for the free energy landscape projected on a pair of EP distances), suggesting that the three enhancers may cooperatively activate their target ( 60 ), or compensate for each other's loss ( 55 ). As the other loci, the dynamics of the Nanogterm·key gene is fast, with the system able to explore highly diverse configurations on the second timescale (distance autocorrelations in Fig. S4C ).
Multiscale Nanogterm·key locus organization. A) Comparison of the 200 kb Nanogterm·key locus Micro-Cterm·key map as observed in mESCs with the result form metainferenceterm·mth using N = 128 replicas and the 1 kb model. The locations of the Nanogterm·key promoter and the −45, −5, and +60 kb enhancers are indicated on the contact map axes with bars. B) Snapshots of representative Nanogterm·key conformations. CREterm·dom locations are highlighted with the same color scheme as in A. C) Comparison of Micro-Cterm·key and 128-replica metainferenceterm·mth contact maps applying the 1CPN chromatinterm·dom model to the 10 kb locus including the Nanogterm·key promoter and its closest enhancer 5 kb upstream. D) Representative 1CPN conformations of the 10 kb locus sampled by metainferenceterm·mth.
To gain insights into the finer organization of the Nanogterm·key locus at nucleosometerm·dom resolution, we ran further 1CPN ( 35 ) metainferenceterm·mth simulationsterm·mth of the 10 kb region encompassing the promoter and its closest enhancer located 5 kb upstream (−5 kb), which is also the most critical one for Nanogterm·key expression ( 55 ). As in the 1 kb model, we find a good agreement between the metainferenceterm·mth and reference Micro-Cterm·key map at 200 bp resolution (Fig. 4 C), while the ensemble of chromatinterm·dom conformations (further discussed in the next section) is also significantly heterogeneous (Fig. 4 D).
Nanogterm·key organization at nucleosometerm·dom resolution reveals functional chromatinterm·dom condensation at local and global scales From the 1CPN metainferenceterm·mth simulationsterm·mth, we first explored the local organization of the Nanogterm·key locus chromatinterm·dom fibers. We focused our analysis on tetranucleosomesterm·key as the fundamental units of the fiber organization ( 9–11 , 13 ). We performed principal component analysis (PCA) ( 51 ) of all tetranucleosometerm·key contact maps within the 10 kb Nanogterm·key locus in all the 128 metainferenceterm·mth replicas. The free energy landscape (logarithm of probability distribution) along the tetranucleosometerm·key projections on PCA components 1 and 3 highlights distinct populations of structures stabilized by different internucleosome contacts (Fig. 5 A, left panel, eight clusters identified by k -means clustering ( 51 ) based on their contact maps, four of them considered for further analysis). PCA 1 represents roughly the overall number of internucleosome interactions, while PCA 3 represents the difference between i , i + 2 contacts, and other ( i , i + 1 and i , i + 3) contacts (PCA 2 is not symmetric under a change in DNA direction, so it has been excluded from the analysis, Fig. S5 ). Notably, the landscape includes significant populations of tetranucleosomesterm·key resembling experimentally determined structures stabilized by either i , i + 1 ( 9 ) (Fig. 5 A, bottom right), or i , i + 2 ( 10 , 11 ) (Fig. 5 A, top right) stacking interactions, which if propagated would lead to the formation of regular 1-start and 2-start chromatinterm·dom fibers ( 64 ), respectively. However, the most populated structures in the landscape are actually stabilized by a mixture of i , i + 1 and i , i + 2 interactions, indicative of an overall disordered chromatinterm·dom fiber organization (as can also be appreciated from the representative Nanogterm·key locus conformations in Fig. 4 D). Interestingly, we also find a population of compact tetranucleosomesterm·key with all-to-all direct interactions, and another population of very open tetranucleosomesterm·key completely lacking internucleosome contacts (Fig. 5 A, two middle panels on the right). As suggested based on Hi-CO experiments on yeast ( 13 ), local fiber organization correlates with chromatinterm·dom epigenetic features. We find that the open tetranucleosomesterm·key are prevalently observed at the CREsterm·dom of the locus, as determined from the ChIP-seq profiles of RNAPII binding ( 61 ) and H3K27ac tail modification ( 62 ) (Fig. 5 B). Such open chromatinterm·dom at CREsterm·dom may facilitate TF and RNAPII binding, which in turn could lead to the formation of nucleosometerm·dom free regions or fragile nucleosomesterm·dom further disrupting the fiber ( 65 ). On the contrary, compact tetranucleosomesterm·key are prevalently found outside CREsterm·dom (Fig. 5 B). Such compact structures may facilitate the communication between CREsterm·dom. Analysis of the average distances between any given nucleosometerm·dom and the nearest one in space confirms that chromatinterm·dom is more open at CREsterm·dom and more compact in between (Fig. S5B ). The average nearest nucleosometerm·dom distance throughout the locus is ∼12 nm, consistent with the value obtained in our prior 1CPN simulationsterm·mth and the experimental value obtained by in situ cryo-ET of human T-lymphoblast interphase chromatinterm·dom ( 12 ).
Nanogterm·key local chromatinterm·dom organization. A) PCA ( 51 ) of the 10 kb Nanogterm·key locus tetranucleosometerm·key structures based on their contact maps. The left panel shows the free energy landscape along the first and third PCA components (the maps next to the labels indicate the component eigenvectors). PCA 1 captures the total number of contacts, while PCA 3 correlates with the difference between i , i + 2, and other ( i , i + 1 or i , i + 3) contacts. The landscape shows eight k -means clusters ( 51 ) (cluster centers as circles) stabilized by different nucleosometerm·dom–nucleosometerm·dom interactions. On the left, we highlight contact maps and representative structures of four tetranucleosometerm·key clusters, characterized by regular i , i + 2 contacts, compact structure, open structure, or regular i , i + 1 contacts. B) Top three panels: probabilities of the four tetranucleosometerm·key clusters highlighted in (A) as a function of genomic location within the 10 kb Nanogterm·key locus. Three bottom panels: the experimental ChIP-seq signals of RNAPII binding (GEO accession: GSE22562 ( 61 )), and H3K27ac (GEO accession: GSM2417096 ( 62 )) and H3K36me3 (GEO accession: GSM2417108 ( 62 )) epigenetic modifications. On top of the graphs, we also indicate the locations of the Nanogterm·key promoter and the −5 kb enhancer region ( 63 ).
How does chromatinterm·dom structure support the formation of direct contacts between promoter and −5 kb enhancer? To discuss this question, we performed PCA dimensionality reduction of the complete 10 kb chromatinterm·dom contact maps observed in the 1CPN metainferenceterm·mth simulationsterm·mth (Fig. 6 A). K -means clustering using the top four PCA components and visual inspection of the PCA projection highlights four clusters characterized by distinct EP distances (Fig. 6 B) and chromatinterm·dom organization (Fig. 6 C). The respective cluster-averaged contact maps and representative conformations (Fig. 6 C) provide insights into the organization: in the extended cluster (58% probability), nucleosomesterm·dom mainly interact with their closest neighbors and chromatinterm·dom is relatively open; in the promoter (P) domain cluster (15%), there are some contacts between the promoter and the gene body downstream from it; the EP domain cluster (21%) is characterized by a distinct compact domain bounded by the −5 kb enhancer and the Nanogterm·key promoter; the loop cluster (6%) has a hairpin-like organization where chromatinterm·dom adopts a condensed configuration with extensive internucleosome interactions between distant regions. In the extended and P domain clusters, the physical distances between promoter and enhancers are typically between 50 and 100 nm, while in the EP domain and loop clusters, they are <50 nm (Fig. 6 B), sufficient for direct contacts mediated by the RNAPII–mediator complex ( 66 ). We note how the global organization of EP domain mirrors the folding of tetranucleosomesterm·key at the lower scale: with open chromatinterm·dom motifs at the CREsterm·dom establishing the boundaries of a central domain rich in compact tetranucleosomesterm·key. The condensed nature of EP domain and loop conformations is well illustrated by the fact that the average distances from the promoter do not significantly depend on genomic distance (Fig. 6 D). These data reveal the high plasticity of chromatinterm·dom within the Nanogterm·key locus, with predominant extended conformations that transiently condense into compact domains supporting direct contacts between enhancer and promoter (Fig. 6 E). While the timescale of our metainferenceterm·mth simulationterm·mth is not sufficient to observe dynamic exchanges between these four clusters in the same trajectory, the absence of high barriers in the free energy landscape (Fig. S6A ) suggests that such transitions should be diffusion limited and relatively rapid. Notably, reversible chromatinterm·dom condensation is indeed observed in our unbiased 1CPN simulationsterm·mth, where starting from extended conformations, the system transiently collapses into compact domains on a submillisecond timescale (Fig. S6B ). Furthermore, the probability distributions of EP distances (separated by 5 kb) in the metainferenceterm·mth and in the unbiased 1CPN simulationsterm·mth (Figs. 6 B and S6C ) are very similar ( P > 0.05). This indicates that the intrinsic molecular features of chromatinterm·dom fibers, namely nucleosometerm·dom plasticity and nucleosometerm·dom–nucleosometerm·dom interactions, are sufficient to explain the overall organization of the 10 kb Nanogterm·key locus into a mixture of extended and condensed configurations.
Global organization of the 10 kb Nanogterm·key locus at nucleosometerm·dom resolution. A) Projection of the 10 kb Nanogterm·key locus chromatinterm·dom conformations along the first two PCA coordinates obtained from their global contact maps. The component eigenvectors are shown next to the respective labels. The projection reveals four k -means clusters characterized by different global 3D organization (the clusters are indicated by different colors, together with their population). B) Distributions of EP distances across the four clusters highlighted in (A), together with the overall distribution for the prior 1CPN simulationsterm·mth. The bars in the violin plots indicate the medians and the extrema of the distributions. The four clusters are referred to as extended, promoter (P) domain, EP domain, and loop. C) Population-averaged contact maps and representative structures of the four clusters. The nucleosomesterm·dom corresponding to the promoter and enhancer locations are highlighted. D) Average contact frequencies and average distances to the promoter for the four clusters. E) Schematics highlighting that direct EP contacts are driven by the condensation of the chromatinterm·dom structure into a compact globule.
Discussion In this study, we demonstrated the successful application of metainferenceterm·mth to integrate Hi-C contact frequencies into MDterm·mth simulationsterm·mth of chromatinterm·dom. Within this Bayesian scheme, the original polymer model of chromatinterm·dom constitutes our prior, while the polymer conformations are sampled from the posterior probability distribution accounting for the contact frequencies observed in the experimental Hi-C map. This makes our approach both bottom-up, starting from a physics-based prior suitable for exploring molecular mechanisms, and top-down, providing a picture of 3D genomic organization consistent with experimental data. Our tests showed that Hi-C metainferenceterm·mth can reconstruct both the structural ensemble and the dynamics of a target system based on contact information, with accuracy increasing with the number of replicasterm·var used to model the (in principle infinite) ensemble. A related Bayesian approach to the 3D genome ( 43 ) requires comparing the results of multiple simulationsterm·mth using different numbers of replicas to find the optimal minimal ensemble representing the target system. Instead, metainferenceterm·mth is valid for any number of replicasterm·var N > 1, although in practice we recommend setting this to the inverse of the minimum contact probability that one aims at capturing in the final 3D ensemble ( N = 128 proved suitable for our applications). Compared with the maximum entropy principleterm·mth ( 25 ), metainferenceterm·mth does not require iterative optimization and can consistently account for both random and systematic errors within a Bayesian framework, although the two approaches are expected to give identical results in the limit of low errors and strong bias ( 44 , 67 , 68 ). We note that while here we solely focused on applications to genome organization, the generality of this approach makes it applicable to other situations where we may want to integrate contact information into a prior molecular model. For instance, protein cross-linking data may be used to reconstruct the structure of large molecular complexes ( 69 ).
Metainferenceterm·mth is particularly convenient for its flexibility, in that one can integrate Hi-C data into any chromatinterm·dom model suitable for the target application. As previously shown ( 44 ), an accurate prior molecular model can help getting closer to the true conformational ensemble of the system, and therefore, producing realistic representations of the genome likely benefits from the use of physics-based models rigorously parametrized based on the interactions between the fundamental components of chromatinterm·dom. By adding an extra bias on top of an existing prior model, metainferenceterm·mth can effectively account for in vivo factors that are not directly represented, such as the binding of TFs ( 31 , 41 ). However, being an approach based on thermodynamic equilibrium, the kinetics of nonequilibrium processes such as cohesin loop extrusion ( 30 ) could be potentially affected. Alternatively, the differences in the conformational ensembles obtained using the physics-based models with and without metainferenceterm·mth can guide the modeling of necessary additional factors into the prior model or suggest hypotheses on the underlying mechanism. For the applications to the genomic organization of mESCs presented here, we integrated Micro-Cterm·key data ( 46 ) into two physics-based models of chromatinterm·dom, the nucleosome-resolution 1CPN modelterm·mth ( 35 ) and a newly parametrized 1 kb model, although other models may also be employed ( 34 , 70 ).
The interplay between the 3D genome organization and the regulation of gene expression is a fundamental problem in molecular biology, for which a clear mechanistic understanding remains elusive. As observed from super-resolution chromatinterm·dom tracing experiments ( 48 ) and other polymer modeling approaches ( 31 , 43 ), we confirm that functional genomic interactions occur within the context of a highly heterogeneous conformational landscape that includes both open and compact conformations. In the studied loci, we find frequent EP contacts separated by a short distance on the order of the mediator–RNA polymerase complex (∼50 nm) ( 66 ), indicating their potential to directly control gene expression based on proposed models of enhancer action ( 71 ). At the Nanogterm·key locus, the chromatinterm·dom often collapses into a compact structure where all three enhancers are at close distance to the Nanogterm·key promoter, possibly representing a cooperative transcription hub ( 60 ). Overall, the studied loci are organized as crumpled globulesterm·dom ( 47 ), with hierarchically formed globular domains encompassing increasing genomic lengths. Such fractal-like organization was already suggested based on Hi-C data ( 15 ), and further confirmed by a recent microscopy study in Drosophila ( 22 ), where it was shown to promote the communication of distant CREsterm·dom.
Past research offers contradictory evidence ( 72 , 73 ) on the importance of 3D genome structure for gene regulation, with various mechanistic models of enhancer activity still being currently debated ( 74 ). Issues may be partially due to the nonlinearity of EP communication ( 21 , 75 ), with contact frequencies affecting gene expression levels only within a narrow range of values. This nonlinearity has been suggested to originate from a separation of timescales between genomic structural fluctuations and gene activation ( 21 ). Indeed, consistently with recent simulationsterm·mth ( 70 ), we find that the Sox2, Pou5f1, and Nanogterm·key loci of mESCs can rapidly explore their vast space of 3D conformations. Transient contacts between CREsterm·dom (potentially stimulating gene expression) are formed and broken on a timescale of less than a second, significantly faster than the timescales of gene activation, on the order of several minutes ( 58 ). This separation of timescales helps explain difficulties in the experimental detection of correlations between 3D genome structure and gene expression ( 56 , 57 ).
Our 1CPN simulationsterm·mth of the Nanogterm·key locus offer an opportunity to explore how the detailed molecular structure of chromatinterm·dom can support the functional organization of genes across multiple length scales. We find that the extent of internucleosome interactions critically shapes both the local and the global folding of the chromatinterm·dom fiber, leading to a surprising conformational plasticity. At the local level, chromatinterm·dom often samples tetranucleosometerm·key motifs stabilized by local nucleosometerm·dom–nucleosometerm·dom interactions at well-defined orientations, resembling those characterized in X-ray and Cryo-EM studies ( 9–11 ), while the heterogeneous chromatinterm·dom ensemble beyond the local organization is essentially disordered. This reconciles the picture of ordered chromatinterm·dom from in high-resolution in vitro studies with the observations from experiments in situ, which reveal a disordered ( 12 ), liquid-like organization ( 59 ). Importantly, we find that open chromatinterm·dom motifs lacking internucleosome contacts are predominantly observed at CREsterm·dom. Here, specific epigenetic modifications, such as histone tail acetylation, promote the opening of chromatinterm·dom ( 76 , 77 ), which in turn should facilitate the recruitment of TFs and RNA polymerases and contribute to further opening ( 65 ). On the other hand, compact tetranucleosometerm·key motifs are enriched in between CREsterm·dom, where they may help drive these elements into closer spatial proximity. Such kind of epigenetic-dependent local chromatinterm·dom organization was previously suggested in yeast based on simulationsterm·mth and Hi-CO experimental contact frequencies ( 13 ). However, the tetranucleosometerm·key landscape observed at the Nanogterm·key locus appears richer than the binary set of alpha and beta motifs in yeast, perhaps thanks to the longer DNA linker length in mammalian chromatinterm·dom ( 78 ). We note that our metainferenceterm·mth simulationsterm·mth were performed using a uniform prior model lacking any representation of epigenetic modifications and TF binding that could be physically responsible for differences in chromatinterm·dom compaction, indicating that the bias employed within our Bayesian framework can be interpreted as an effective representation of forces acting differentially along the genome. Overall, this confirms the successful integration of experimental contact frequencies to account for key factors missing in the model to produce a conformational ensemble close to that of actual in vivo conditions.
At the global level, cohesin loop extrusion ( 30 , 79 ) and bridging interactions mediated by proteins ( 31 , 80 ) have been previously recognized as key drivers of long-distance communication. However, our 10 kb Nanogterm·key locus simulationsterm·mth suggest that communication over these relatively short distances relies on dynamic transitions between extended chromatinterm·dom fibers and condensed domains characterized by direct EP contacts. Interestingly, such plasticity is also observed in 1CPN simulationsterm·mth of chromatinterm·dom lacking any experimental bias (Figs. 6 B, S6B and C ). Based on this similarity, we suggest that internucleosome interactions alone are sufficient to explain the observed dynamic condensation of the 10 kb Nanogterm·key locus. This is consistent with the intrinsic propensity of nucleosomesterm·dom to condense into droplets by liquid–liquid phase separation ( 49 , 81 ), suggested to be a key driving force of chromatinterm·dom organization both at the global level of entire chromosomes ( 18 , 25 ) and at the local level of individual genes ( 16 ). The detailed cell type–dependent organization of chromatinterm·dom will then be shaped by epigenetic modifications of individual nucleosomesterm·dom ( 17 , 49 ), nucleosometerm·dom positioning ( 82 , 83 ) and TF binding ( 46 ), features that are implicitly accounted for by our metainferenceterm·mth bias. Fitting into this, our simulationsterm·mth reveal a hierarchical organization with a tight coupling between the local and global levels: in the 10 kb Nanogterm·key locus, open tetranucleosometerm·key motifs at CREsterm·dom, together with compact motifs in between, orchestrate the formation a condensed domain bringing together enhancer and promoter.
Conclusion We showed how Hi-C metainferenceterm·mth allows the efficient integration of experimental data and physical modeling to explore the mechanisms underlying the multiscale spatial organization of the genome. Our simulationsterm·mth reveal a condensed, liquid-like chromatinterm·dom whose structure and dynamics are ideally suited to support genomic function, in line with the picture recently emerging from experiments ( 59 , 81 , 84 ). Ultimately, our integration of theoretical modeling and experimental data will aid our understanding of the physical basis of gene regulation ( 71 ) and other key genomic functions.
Materials and methods Hi-C metainferenceterm·mth theory In Hi-C metainferenceterm·mth, we sample the target system by MDterm·mth simulationterm·mth according to Bayesian posterior probability distribution (see SI ) of the conformations given the observed experimental map of frequencies f ij (1 ≤ i , j ≤ L ). To do this, the potential energy of N replicas is defined from the negative logarithm of the posterior as ( 44 ): where the first term constitutes our prior, including the interaction potential of the original chromatinterm·dom model, U ( X r ) = − log P ( X r ) , and the negative logarithm of the hyperparameter priors; f ij and c ¯ i j are, respectively, the experimental contact frequencies and the simulationterm·mth contact probabilities between genomic locations i and j (the latter is our forward model); σ i j r 2 = ( σ i j r B ) 2 + ( σ i j SEM ) 2 represents the total error on the i – j contact from replica r , resulting from the combination of systematic error ( B ) and SEM.
For the forward model, we assume that the contact frequency (expressed as the number of sequencing reads) is estimated to be on average α c ¯ ( X ) , with α a proportionality constant to be determined, and the contact probability c ¯ computed from an average over the replicas of the kernel function: This function is close to 1 and 0 for short and large distances d between genomic loci, respectively, with d 0 representing the distance at which the kernel is equal to 1, and r 0 controlling its slope. Although these parameters depend on the experimental procedure and are in principle unknown, it is reasonable to assume that they should be close to the spatial resolution of the experiment, set by the typical distances over which cross-linking may occur. This kernel has been traditionally used to setup collective variables for enhanced sampling all-atom MDterm·mth simulationsterm·mth ( 85 ).
During the simulationterm·mth, the SEMs are estimated directly from the conformational ensemble, while systematic errors are sampled according to the posterior distribution using a noninformative prior via a Monte Carlo scheme. The scaling factor α is also sampled by Monte Carlo each step using a uniform prior. We implemented the Hi-C metainferenceterm·mth protocol in PLUMED 2 ( 85 ) based on the existing metainferenceterm·mth routines.
MDterm·mth simulationterm·mth details In the 1CPN modelterm·mth ( 35 ), the nucleosometerm·dom core particle is represented as a single ellipsoidal rigid body with orientation-dependent interactions with other nucleosomesterm·dom, while linker DNA as a twistable chain where each bead represents 3 bp. Importantly, the 1CPN modelterm·mth can account for spontaneous DNA sequence dependent nucleosometerm·dom sliding ( 6 ), effectively allowing changes in linker DNA length. In the 1 kb model, chromatinterm·dom is represented as a beads-on-a-string polymer model with interactions parametrized via a bottom-up procedure from 1CPN simulationsterm·mth of 50 nucleosometerm·dom fibers (Fig. S1A–C ) with a nucleosometerm·dom repeat length of 200 bp, close to the average value observed in experiments of mESCs ( 78 ). The 1 kb beads (each representing of 5 nucleosomesterm·dom plus linker DNA) have a size of a = 22 nm, and interact via bond and angle potentials whose parameters are optimized to reproduce the corresponding distance and angle distributions from the 1CPN simulationsterm·mth (Figs. 1 C, S1B and C ), and also via nonbonded Lennard–Jones interactions with strength set so that the polymer size scales as in the theta condition (size ∼ L ½ , Fig. S1D ). In the copolymer model used for Hi-C metainferenceterm·mth validation, the beads within the three sticky CREsterm·dom have enhanced nonbonded interactions among themselves, while all other parameters are as in the prior 1 kb model. All simulationsterm·mth have been performed using LAMMPS ( 86 ) patched with PLUMED 2 ( 85 ) under physiological conditions (300 K temperature, and, for the 1CPN modelterm·mth, 150 mM ionic strength), integrating the equations of motion by Langevin dynamics.
Using the prior 1 kb chromatinterm·dom model, we applied Hi-C metainferenceterm·mth to reconstruct the 3D organization of the Pou5f1 (chr 17: 35,420–35,720 kb), Sox2 (chr 3: 34,620–34,920 kb), and Nanogterm·key (chr 6: 122,600–122,800 kb) genomic loci of mESCs (mm10). We also employed 1CPN ( 35 ) metainferenceterm·mth simulationsterm·mth to explore in detail the organization of a 10 kb Nanogterm·key region (chr 6: 122,701–122,711 kb) encompassing the promoter (chr 6: 122,707 kb) and its closest enhancer located 5 kb upstream. In these applications, we employed mESC Micro-Cterm·key data ( 46 ) at either 1 kb or 200 bp resolution (for the 1 kb and 1CPN simulationsterm·mth, respectively), normalized by Juicebox ( 87 ). For the forward model used to estimate the contact frequencies from the chromatinterm·dom ensemble, we set a size parameter of r 0 = 13 nm and r 0 = a = 22 nm for the 1CPN and the 1 kb simulationsterm·mth, respectively, with these values corresponding to roughly the size of a nucleosometerm·dom and that of a 1 kb bead, a choice consistent with the resolution of the respective models and data. In both cases, we set the kernel shift parameter as d 0 = r 0 /2. More details on the MDterm·mth simulationsterm·mth can be found in the SI .
For comparison with real timescales, we rescaled the simulationterm·mth time of the 1 kb model simulationsterm·mth so that the diffusion of chromatinterm·dom within the Sox2 genomic locus matches the experimental estimate of 0.25 μm 2 /s ( 56 ) (Fig. S3B ).
Supplementary Material Contributor Information Giovanni B BrandanipersName, Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
ChenyangpersName Gu, Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
Soundhararajan GopipersName, Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
Shoji TakadapersName, Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
Supplementary Material Supplementary material is available at PNAS Nexus online.
Funding This work was supported by the MEXT grants JPMXP1020200101 as “Program for Promoting Research on the Supercomputer Fugaku” (S.T.) and JPMXP1020230119 as “Program for Promoting Researches on the Supercomputer Fugaku” (S.T.), and by the Japan Society for the Promotion of Science KAKENHI grants 20H05934 (S.T.), 21H02441 (S.T.), and 20K06587 (G.B.B.).
Author Contributions G.B.B. and S.T. designed research; G.B.B. and C.G. performed research; G.B.B., C.G., and S.G. analyzed data; and G.B.B., C.G., S.G., and S.T. wrote the paper.
Preprints This manuscript was posted on a preprint: https://doi.org/10.1101/2023.12.01.569511 .
Data Availability All input files, simulationterm·mth trajectories, and analysis scripts for this study are included at the Zenodo repository ( https://doi.org/10.5281/zenodo.11207120 ). Code to perform Hi-C metainferenceterm·mth simulationsterm·mth with LAMMPS ( 86 ) and PLUMED ( 85 ) is maintained on Github at https://github.com/gbrandani/Hi-C_Metainferenceterm·mth .
References Associated Data Supplementary Materials Data Availability Statement All input files, simulationterm·mth trajectories, and analysis scripts for this study are included at the Zenodo repository ( https://doi.org/10.5281/zenodo.11207120 ). Code to perform Hi-C metainferenceterm·mth simulationsterm·mth with LAMMPS ( 86 ) and PLUMED ( 85 ) is maintained on Github at https://github.com/gbrandani/Hi-C_Metainferenceterm·mth .