Polymer physics of chromosome large-scale 3D organisation

Modeling properties of chromosome territories using polymer filaments in diverse confinement geometries

Interphase chromosomes reside within distinct nuclear regions known as chromosome territories (CTs). Recent observations from Hi-C analyses, a method mapping chromosomal interactions, have revealed varied decay in contact probabilities among different chromosomes. Our study explores the relationship between this contact decay and the particular shapes of the chromosome territories they occupy. For this, we employed molecular dynamics (MD) simulations to examine how confined polymers, resembling chromosomes, behave within different confinement geometries similar to chromosome territory boundaries. Our simulations unveil so far unreported relationships between contact probabilities and end-to-end distances varying based on different confinement geometries. These findings highlight the crucial impact of chromosome territories on shaping the larger-scale properties of 3D genome organization. They emphasize the intrinsic connection between the shapes of these territories and the contact behaviors exhibited by chromosomes. Understanding these correlations is key to accurately interpret Hi-C and microscopy data, and offers vital insights into the foundational principles governing genomic organization.

Cohesin-mediated 3D contacts tune enhancer-promoter regulation

Enhancers are key drivers of gene regulation thought to act via 3D physical interactions with the promoters of their target genes. However, genome-wide depletions of architectural proteins such as cohesin result in only limited changes in gene expression, despite a loss of contact domains and loops. Consequently, the role of cohesin and 3D contacts in enhancer function remains debated. Here, we developed CRISPRi of regulatory elements upon degron operation (CRUDO), a novel approach to measure how changes in contact frequency impact enhancer effects on target genes by perturbing enhancers with CRISPRi and measuring gene expression in the presence or absence of cohesin. We systematically perturbed all 1,039 candidate enhancers near five cohesin-dependent genes and identified 34 enhancer-gene regulatory interactions. Of 26 regulatory interactions with sufficient statistical power to evaluate cohesin dependence, 18 show cohesin-dependent effects. A decrease in enhancer-promoter contact frequency upon removal of cohesin is frequently accompanied by a decrease in the regulatory effect of the enhancer on gene expression, consistent with a contact-based model for enhancer function. However, changes in contact frequency and regulatory effects on gene expression vary as a function of distance, with distal enhancers (e.g., >50Kb) experiencing much larger changes than proximal ones (e.g., <50Kb). Because most enhancers are located close to their target genes, these observations can explain how only a small subset of genes - those with strong distal enhancers - are sensitive to cohesin. Together, our results illuminate how 3D contacts, influenced by both cohesin and genomic distance, tune enhancer effects on gene expression.

Polymer physics models reveal structural folding features of single-molecule gene chromatin conformations

Here, we employ polymer physics models of chromatin to investigate the 3D folding of a 2Mb wide genomic region encompassing the human LTN1 gene, a crucial DNA locus involved in key cellular functions. Through extensive Molecular Dynamics simulations, we reconstruct in-silico the ensemble of single-molecule LTN1 3D structures, which we benchmark against recent in-situ Hi-C 2.0 data. The model-derived single molecules are then used to predict structural folding features at the single-cell level, providing testable predictions for super-resolution microscopy experiments.

Combinatorics and topological weights of chromatin loop networks

Polymer physics models suggest that chromatin spontaneously folds into loop networks with transcription units (TUs), such as enhancers and promoters, as anchors. Here we use combinatoric arguments to enumerate the emergent chromatin loop networks, both in the case where TUs are labeled and where they are unlabeled. We then combine these mathematical results with those of computer simulations aimed at finding the inter-TU energy required to form a target loop network. We show that different topologies are vastly different in terms of both their combinatorial weight and energy of formation. We explain the latter result qualitatively by computing the topological weight of a given network-i.e., its partition function in statistical mechanics language-in the approximation where excluded volume interactions are neglected. Our results show that networks featuring local loops are statistically more likely with respect to networks including more nonlocal contacts. We suggest our classification of loop networks, together with our estimate of the combinatorial and topological weight of each network, will be relevant to catalog three-dimensional structures of chromatin fibers around eukaryotic genes, and to estimate their relative frequency in both simulations and experiments.

Effective model of protein-mediated interactions in chromatin

Protein-mediated interactions are ubiquitous in the cellular environment, and particularly in the nucleus, where they are responsible for the structuring of chromatin. We show through molecular-dynamics simulations of a polymer surrounded by binders that the strength of the binder-polymer interaction separates an equilibrium from a nonequilibrium regime. In the equilibrium regime, the system can be efficiently described by an effective model in which the binders are traced out. Even in this case, the polymers display features that are different from those of a standard homopolymer interacting with two-body interactions. We then extend the effective model to deal with the case where binders cannot be regarded as in equilibrium and a new phenomenology appears, including local blobs in the polymer. An effective description of this system can be useful in elucidating the fundamental mechanisms that govern chromatin structuring in particular and indirect interactions in general.

Active transcription and epigenetic reactions synergistically regulate meso-scale genomic organization

In interphase nuclei, chromatin forms dense domains of characteristic sizes, but the influence of transcription and histone modifications on domain size is not understood. We present a theoretical model exploring this relationship, considering chromatin-chromatin interactions, histone modifications, and chromatin extrusion. We predict that the size of heterochromatic domains is governed by a balance among the diffusive flux of methylated histones sustaining them and the acetylation reactions in the domains and the process of loop extrusion via supercoiling by RNAPII at their periphery, which contributes to size reduction. Super-resolution and nano-imaging of five distinct cell lines confirm the predictions indicating that the absence of transcription leads to larger heterochromatin domains. Furthermore, the model accurately reproduces the findings regarding how transcription-mediated supercoiling loss can mitigate the impacts of excessive cohesin loading. Our findings shed light on the role of transcription in genome organization, offering insights into chromatin dynamics and potential therapeutic targets.

Biomarker Selection for Adaptive Systems

Biomarkers enable objective monitoring of a given cell or state in a biological system and are widely used in research, biomanufacturing, and clinical practice. However, identifying appropriate biomarkers that are both robustly measurable and capture a state accurately remains challenging. We present a framework for biomarker identification based upon observability guided sensor selection. Our methods, Dynamic Sensor Selection (DSS) and Structure-Guided Sensor Selection (SGSS), utilize temporal models and experimental data, offering a template for applying observability theory to unconventional data obtained from biological systems. Unlike conventional methods that assume well-known, fixed dynamics, DSS adaptively select biomarkers or sensors that maximize observability while accounting for the time-varying nature of biological systems. Additionally, SGSS incorporates structural information and diverse data to identify sensors which are resilient against inaccuracies in our model of the underlying system. We validate our approaches by performing estimation on high dimensional systems derived from temporal gene expression data from partial observations.

Multiscale modelling of chromatin 4D organization in SARS-CoV-2 infected cells

SARS-CoV-2 can re-structure chromatin organization and alter the epigenomic landscape of the host genome, but the mechanisms that produce such changes remain unclear. Here, we use polymer physics to investigate how the chromatin of the host genome is re-organized upon infection with SARS-CoV-2. We show that re-structuring of A/B compartments can be explained by a re-modulation of intra-compartment homo-typic affinities, which leads to the weakening of A-A interactions and the enhancement of A-B mixing. At the TAD level, re-arrangements are physically described by a reduction in the loop extrusion activity coupled with an alteration of chromatin phase-separation properties, resulting in more intermingling between different TADs and a spread in space of the TADs themselves. In addition, the architecture of loci relevant to the antiviral interferon response, such as DDX58 or IFIT, becomes more variable within the 3D single-molecule population of the infected model, suggesting that viral infection leads to a loss of chromatin structural specificity. Analysing the time trajectories of pairwise gene-enhancer and higher-order contacts reveals that this variability derives from increased fluctuations in the chromatin dynamics of infected cells. This suggests that SARS-CoV-2 alters gene regulation by impacting the stability of the contact network in time.

A single dose of cocaine rewires the 3D genome structure of midbrain dopamine neurons

Midbrain dopamine neurons (DNs) respond to a first exposure to addictive drugs and play key roles in chronic drug usage1-3. As the synaptic and transcriptional changes that follow an acute cocaine exposure are mostly resolved within a few days4,5, the molecular changes that encode the long-term cellular memory of the exposure within DNs remain unknown. To investigate whether a single cocaine exposure induces long-term changes in the 3D genome structure of DNs, we applied Genome Architecture Mapping and single nucleus transcriptomic analyses in the mouse midbrain. We found extensive rewiring of 3D genome architecture at 24 hours past exposure which remains or worsens by 14 days, outlasting transcriptional responses. The cocaine-induced chromatin rewiring occurs at all genomic scales and affects genes with major roles in cocaine-induced synaptic changes. A single cocaine exposure triggers extensive long-lasting changes in chromatin condensation in post-synaptic and post-transcriptional regulatory genes, for example the unfolding of Rbfox1 which becomes most prominent 14 days post exposure. Finally, structurally remodeled genes are most expressed in a specific DN sub-type characterized by low expression of the dopamine auto-receptor Drd2, a key feature of highly cocaine-sensitive cells. These results reveal an important role for long-lasting 3D genome remodelling in the cellular memory of a single cocaine exposure, providing new hypotheses for understanding the inception of drug addiction and 3D genome plasticity.

Pervasive structural heterogeneity rewires glioblastoma chromosomes to sustain patient-specific transcriptional programs

Glioblastoma multiforme (GBM) encompasses brain malignancies marked by phenotypic and transcriptional heterogeneity thought to render these tumors aggressive, resistant to therapy, and inevitably recurrent. However, little is known about how the spatial organization of GBM genomes underlies this heterogeneity and its effects. Here, we compile a cohort of 28 patient-derived glioblastoma stem cell-like lines (GSCs) known to reflect the properties of their tumor-of-origin; six of these were primary-relapse tumor pairs from the same patient. We generate and analyze 5 kbp-resolution chromosome conformation capture (Hi-C) data from all GSCs to systematically map thousands of standalone and complex structural variants (SVs) and the multitude of neoloops arising as a result. By combining Hi-C, histone modification, and gene expression data with chromatin folding simulations, we explain how the pervasive, uneven, and idiosyncratic occurrence of neoloops sustains tumor-specific transcriptional programs via the formation of new enhancer-promoter contacts. We also show how even moderately recurrent neoloops can relate to patient-specific vulnerabilities. Together, our data provide a resource for dissecting GBM biology and heterogeneity, as well as for informing therapeutic approaches.

Effect of local active fluctuations on structure and dynamics of flexible biopolymers

Active fluctuations play a significant role in the structure and dynamics of biopolymers (e.g. chromatin and cytoskeletal proteins) that are instrumental in the functioning of living cells. For a large range of experimentally accessible length and time scales, these polymers can be represented as flexible chains that are subjected to spatially and temporally varying fluctuating forces. In this work, we introduce a mathematical framework that correlates the spatial and temporal patterns of the fluctuations to different observables that describe the dynamics and conformations of the polymer. We demonstrate the power of this approach by analyzing the case of a point fluctuation on the polymer with an exponential decay of correlation in time with a finite time constant. Specifically, we identify the length and time scale over which the behavior of the polymer exhibits a significant departure from the behavior of a Rouse chain and the range of impact of the fluctuation along the chain. Furthermore, we show that the conformation of the polymer retains the memory of the active fluctuation from earlier times. Altogether, this work sets the basis for understanding and interpreting the role of spatio-temporal patterns of fluctuations in the dynamics, conformation, and functionality of biopolymers in living cells.

Effective modeling of the chromatin structure by coarse-grained methods

The interphase chromatin structure is extremely complex, precise and dynamic. Experimental methods can only show the frequency of interaction of the various parts of the chromatin. Therefore, it is extremely important to develop theoretical methods to predict the chromatin structure. In this publication, we implemented an extended version of the SBS model described by Barbieri et al. and created the ChroMC program that is easy to use and freely available (https://github.com/regulomics/chroMC) to other users. We also describe the necessary factors for the effective modeling of the chromatin structure in Drosophila melanogaster. We compared results of chromatin structure predictions using two methods: Monte Carlo and Molecular Dynamic. Our simulations suggest that incorporating black, non-reactive chromatin is necessary for successful prediction of chromatin structure, while the loop extrusion model with a long range attraction potential or Lennard-Jones (with local attraction force) as well as using Hi-C data as input are not essential for the basic structure reconstruction. We also proposed a new way to calculate the similarity of the properties of contact maps including the calculation of local similarity.Communicated by Ramaswamy H. Sarma.

Chromatin phase separated nanoregions explored by polymer cross-linker models and reconstructed from single particle trajectories

Phase separated domains (PSDs) are ubiquitous in cell biology, representing nanoregions of high molecular concentration. PSDs appear at diverse cellular domains, such as neuronal synapses but also in eukaryotic cell nucleus, limiting the access of transcription factors and thus preventing gene expression. We develop a generalized cross-linker polymer model, to study PSDs: we show that increasing the number of cross-linkers induces a polymer condensation, preventing access of diffusing molecules. To investigate how the PSDs restrict the motion of diffusing molecules, we compute the mean residence and first escaping times. Finally, we develop a method based on mean-square-displacement of single particle trajectories to reconstruct the properties of PSDs from the continuum range of anomalous exponents. We also show here that PSD generated by polymers do not induces a long-range attracting field (potential well), in contrast with nanodomains at neuronal synapses. To conclude, PSDs can result from condensed chromatin organization, where the number of cross-linkers controls molecular access.

RNA-mediated symmetry breaking enables singular olfactory receptor choice

Olfactory receptor (OR) choice provides an extreme example of allelic competition for transcriptional dominance, where every olfactory neuron stably transcribes one of approximately 2,000 or more OR alleles1,2. OR gene choice is mediated by a multichromosomal enhancer hub that activates transcription at a single OR3,4, followed by OR-translation-dependent feedback that stabilizes this choice5,6. Here, using single-cell genomics, we show formation of many competing hubs with variable enhancer composition, only one of which retains euchromatic features and transcriptional competence. Furthermore, we provide evidence that OR transcription recruits enhancers and reinforces enhancer hub activity locally, whereas OR RNA inhibits transcription of competing ORs over distance, promoting transition to transcriptional singularity. Whereas OR transcription is sufficient to break the symmetry between equipotent enhancer hubs, OR translation stabilizes transcription at the prevailing hub, indicating that there may be sequential non-coding and coding mechanisms that are implemented by OR alleles for transcriptional prevalence. We propose that coding OR mRNAs possess non-coding functions that influence nuclear architecture, enhance their own transcription and inhibit transcription from their competitors, with generalizable implications for probabilistic cell fate decisions.

The conformational phase diagram of charged polymers in the presence of attractive bridging crowders

Using extensive molecular dynamics simulations, we obtain the conformational phase diagram of a charged polymer in the presence of oppositely charged counterions and neutral attractive crowders for monovalent, divalent, and trivalent counterion valencies. We demonstrate that the charged polymer can exist in three phases: (1) an extended phase for low charge densities and weak polymer-crowder attractive interactions [Charged Extended (CE)]; (2) a collapsed phase for high charge densities and weak polymer-crowder attractive interactions, primarily driven by counterion condensation [Charged Collapsed due to Intra-polymer interactions [(CCI)]; and (3) a collapsed phase for strong polymer-crowder attractive interactions, irrespective of the charge density, driven by crowders acting as bridges or cross-links [Charged Collapsed due to Bridging interactions [(CCB)]. Importantly, simulations reveal that the interaction with crowders can induce collapse, despite the presence of strong repulsive electrostatic interactions, and can replace condensed counterions to facilitate a direct transition from the CCI and CE phases to the CCB phase.

Large-scale data-driven and physics-based models offer insights into the relationships among the structures, dynamics, and functions of chromosomes

The organized three-dimensional chromosome architecture in the cell nucleus provides scaffolding for precise regulation of gene expression. When the cell changes its identity in the cell-fate decision-making process, extensive rearrangements of chromosome structures occur accompanied by large-scale adaptations of gene expression, underscoring the importance of chromosome dynamics in shaping genome function. Over the last two decades, rapid development of experimental methods has provided unprecedented data to characterize the hierarchical structures and dynamic properties of chromosomes. In parallel, these enormous data offer valuable opportunities for developing quantitative computational models. Here, we review a variety of large-scale polymer models developed to investigate the structures and dynamics of chromosomes. Different from the underlying modeling strategies, these approaches can be classified into data-driven ('top-down') and physics-based ('bottom-up') categories. We discuss their contributions to offering valuable insights into the relationships among the structures, dynamics, and functions of chromosomes and propose the perspective of developing data integration approaches from different experimental technologies and multidisciplinary theoretical/simulation methods combined with different modeling strategies.

Leveraging polymer modeling to reconstruct chromatin connectivity from live images

Chromosomal dynamics plays a central role in a number of critical biological processes, such as transcriptional regulation, genetic recombination, and DNA replication. However, visualization of chromatin is generally limited to live imaging of a few fluorescently labeled chromosomal loci or high-resolution reconstruction of multiple loci from a single time frame. To aid in mapping the underlying chromosomal structure based on parsimonious experimental measurements, we present an exact analytical expression for the evolution of the polymer configuration based on a flexible-polymer model, and we propose an algorithm that tracks the polymer configuration from live images of chromatin marked with several fluorescent marks. Our theory identifies the resolution of microscopy needed to achieve high-accuracy tracking for a given spacing of markers, establishing the statistical confidence in the assignment of genome identity to the visualized marks. We then leverage experimental data of locus-tracking measurements to demonstrate the validity of our modeling approach and to establish a basis for the design of experiments with a desired resolution. Altogether, this work provides a computational approach founded on polymer physics that vastly improves the interpretation of in vivo measurements of biopolymer dynamics.

Competition between transcription and loop extrusion modulates promoter and enhancer dynamics

The spatiotemporal configuration of genes with distal regulatory elements, and the impact of chromatin mobility on transcription, remain unclear. Loop extrusion is an attractive model for bringing genetic elements together, but how this functionally interacts with transcription is also largely unknown. We combine live tracking of genomic loci and nascent transcripts with molecular dynamics simulations to assess the spatiotemporal arrangement of the Sox2 gene and its enhancer, in response to a battery of perturbations. We find a close link between chromatin mobility and transcriptional status: active elements display more constrained mobility, consistent with confinement within specialized nuclear sites, and alterations in enhancer mobility distinguish poised from transcribing alleles. Strikingly, we find that whereas loop extrusion and transcription factor-mediated clustering contribute to promoter-enhancer proximity, they have antagonistic effects on chromatin dynamics. This provides an experimental framework for the underappreciated role of chromatin dynamics in genome regulation.

Evaluating the role of the nuclear microenvironment in gene function by population-based modeling

The nuclear folding of chromosomes relative to nuclear bodies is an integral part of gene function. Here, we demonstrate that population-based modeling-from ensemble Hi-C data-provides a detailed description of the nuclear microenvironment of genes and its role in gene function. We define the microenvironment by the subnuclear positions of genomic regions with respect to nuclear bodies, local chromatin compaction, and preferences in chromatin compartmentalization. These structural descriptors are determined in single-cell models, thereby revealing the structural variability between cells. We demonstrate that the microenvironment of a genomic region is linked to its functional potential in gene transcription, replication, and chromatin compartmentalization. Some chromatin regions feature a strong preference for a single microenvironment, due to association with specific nuclear bodies in most cells. Other chromatin shows high structural variability, which is a strong indicator of functional heterogeneity. Moreover, we identify specialized nuclear microenvironments, which distinguish chromatin in different functional states and reveal a key role of nuclear speckles in chromosome organization. We demonstrate that our method produces highly predictive three-dimensional genome structures, which accurately reproduce data from a variety of orthogonal experiments, thus considerably expanding the range of Hi-C data analysis.

Multiscale modelling of chromatin 4D organization in SARS-CoV-2 infected cells

SARS-CoV-2 is able to re-structure chromatin organization and alters the epigenomic landscape of the host genome, though the mechanisms that produce such changes are still poorly understood. Here, we investigate with polymer physics chromatin re-organization of the host genome, in space and time upon SARS-CoV-2 viral infection. We show that re-structuring of A/B compartments is well explained by a re-modulation of intra-compartment homotypic affinities, which leads to the weakening of A-A interactions and enhances A-B mixing. At TAD level, re-arrangements are physically described by a general reduction of the loop extrusion activity coupled with an alteration of chromatin phase-separation properties, resulting in more intermingling between different TADs and spread in space of TADs themselves. In addition, the architecture of loci relevant to the antiviral interferon (IFN) response, such as DDX58 or IFIT, results more variable within the 3D single-molecule population of the infected model, suggesting that viral infection leads to a loss of chromatin structural specificity. Analysis of time trajectories of pairwise gene-enhancer and higher-order contacts reveals that such variability derives from a more fluctuating dynamics in infected case, suggesting that SARS-CoV-2 alters gene regulation by impacting the stability of the contact network in time. Overall, our study provides the first polymer-physics based 4D reconstruction of SARS-CoV-2 infected genome with mechanistic insights on the consequent gene mis-regulation.

Phase separation of ecDNA aggregates establishes in-trans contact domains boosting selective MYC regulatory interactions

Extrachromosomal DNAs (ecDNAs) are found in the nucleus of an array of human cancer cells where they can form clusters that were associated to oncogene overexpression, as they carry genes and cis-regulatory elements. Yet, the mechanisms of aggregation and gene amplification beyond copy-number effects remain mostly unclear. Here, we investigate, at the single molecule level, MYC-harboring ecDNAs of COLO320-DM colorectal cancer cells by use of a minimal polymer model of the interactions of ecDNA BRD4 binding sites and BRD4 molecules. We find that BRD4 induces ecDNAs phase separation, resulting in the self-assembly of clusters whose predicted structure is validated against HiChIP data (Hung et al., 2021). Clusters establish in-trans associated contact domains (I-TADs) enriched, beyond copy number, in regulatory contacts among specific ecDNA regions, encompassing its PVT1-MYC fusions but not its other canonical MYC copy. That explains why the fusions originate most of ecDNA MYC transcripts (Hung et al., 2021), and shows that ecDNA clustering per se is important but not sufficient to amplify oncogene expression beyond copy-number, reconciling opposite views on the role of clusters (Hung et al., 2021; Zhu et al., 2021; Purshouse et al. 2022). Regulatory contacts become strongly enriched as soon as half a dozen ecDNAs aggregate, then saturate because of steric hindrance, highlighting that even cells with few ecDNAs can experience pathogenic MYC upregulations. To help drug design and therapeutic applications, with the model we dissect the effects of JQ1, a BET inhibitor. We find that JQ1 reverses ecDNA phase separation hence abolishing I-TADs and extra regulatory contacts, explaining how in COLO320-DM cells it reduces MYC transcription (Hung et al., 2021).

True-to-scale DNA-density maps correlate with major accessibility differences between active and inactive chromatin

Chromatin compaction differences may have a strong impact on accessibility of individual macromolecules and macromolecular assemblies to their DNA target sites. Estimates based on fluorescence microscopy with conventional resolution, however, suggest only modest compaction differences (∼2-10×) between the active nuclear compartment (ANC) and inactive nuclear compartment (INC). Here, we present maps of nuclear landscapes with true-to-scale DNA densities, ranging from <5 to >300 Mbp/μm3. Maps are generated from individual human and mouse cell nuclei with single-molecule localization microscopy at ∼20 nm lateral and ∼100 nm axial optical resolution and are supplemented by electron spectroscopic imaging. Microinjection of fluorescent nanobeads with sizes corresponding to macromolecular assemblies for transcription into nuclei of living cells demonstrates their localization and movements within the ANC and exclusion from the INC.

Enhancer-promoter contact formation requires RNAPII and antagonizes loop extrusion

Homotypic chromatin interactions and loop extrusion are thought to be the two main drivers of mammalian chromosome folding. Here we tested the role of RNA polymerase II (RNAPII) across different scales of interphase chromatin organization in a cellular system allowing for its rapid, auxin-mediated degradation. We combined Micro-C and computational modeling to characterize subsets of loops differentially gained or lost upon RNAPII depletion. Gained loops, extrusion of which was antagonized by RNAPII, almost invariably formed by engaging new or rewired CTCF anchors. Lost loops selectively affected contacts between enhancers and promoters anchored by RNAPII, explaining the repression of most genes. Surprisingly, promoter-promoter interactions remained essentially unaffected by polymerase depletion, and cohesin occupancy was sustained. Together, our findings reconcile the role of RNAPII in transcription with its direct involvement in setting-up regulatory three-dimensional chromatin contacts genome wide, while also revealing an impact on cohesin loop extrusion.

Competition between transcription and loop extrusion modulates promoter and enhancer dynamics

The spatiotemporal configuration of genes with distal regulatory elements, and the impact of chromatin mobility on transcription, remain unclear. Loop extrusion is an attractive model for bringing genetic elements together, but how this functionally interacts with transcription is also largely unknown. We combine live tracking of genomic loci and nascent transcripts with molecular dynamics simulations to assess the 4D arrangement of the Sox2 gene and its enhancer, in response to a battery of perturbations. We find that alterations in chromatin mobility, not promoter-enhancer distance, is more informative about transcriptional status. Active elements display more constrained mobility, consistent with confinement within specialized nuclear sites, and alterations in enhancer mobility distinguish poised from transcribing alleles. Strikingly, we find that whereas loop extrusion and transcription factor-mediated clustering contribute to promoter-enhancer proximity, they have antagonistic effects on chromatin dynamics. This provides an experimental framework for the underappreciated role of chromatin dynamics in genome regulation.

Unveiling the Machinery behind Chromosome Folding by Polymer Physics Modeling

Understanding the mechanisms underlying the complex 3D architecture of mammalian genomes poses, at a more fundamental level, the problem of how two or multiple genomic sites can establish physical contacts in the nucleus of the cells. Beyond stochastic and fleeting encounters related to the polymeric nature of chromatin, experiments have revealed specific, privileged patterns of interactions that suggest the existence of basic organizing principles of folding. In this review, we focus on two major and recently proposed physical processes of chromatin organization: loop-extrusion and polymer phase-separation, both supported by increasing experimental evidence. We discuss their implementation into polymer physics models, which we test against available single-cell super-resolution imaging data, showing that both mechanisms can cooperate to shape chromatin structure at the single-molecule level. Next, by exploiting the comprehension of the underlying molecular mechanisms, we illustrate how such polymer models can be used as powerful tools to make predictions in silico that can complement experiments in understanding genome folding. To this aim, we focus on recent key applications, such as the prediction of chromatin structure rearrangements upon disease-associated mutations and the identification of the putative chromatin organizing factors that orchestrate the specificity of DNA regulatory contacts genome-wide.

Interphase chromosomes of the Aedes aegypti mosquito are liquid crystalline and can sense mechanical cues

We use data-driven physical simulations to study the three-dimensional architecture of the Aedes aegypti genome. Hi-C maps exhibit both a broad diagonal and compartmentalization with telomeres and centromeres clustering together. Physical modeling reveals that these observations correspond to an ensemble of 3D chromosomal structures that are folded over and partially condensed. Clustering of the centromeres and telomeres near the nuclear lamina appears to be a necessary condition for the formation of the observed structures. Further analysis of the mechanical properties of the genome reveals that the chromosomes of Aedes aegypti, by virtue of their atypical structural organization, are highly sensitive to the deformation of the nuclei. This last finding provides a possible physical mechanism linking mechanical cues to gene regulation.

HiC-GNN: A generalizable model for 3D chromosome reconstruction using graph convolutional neural networks

Chromosome conformation capture (3 C) is a method of measuring chromosome topology in terms of loci interaction. The Hi-C method is a derivative of 3 C that allows for genome-wide quantification of chromosome interaction. From such interaction data, it is possible to infer the three-dimensional (3D) structure of the underlying chromosome. In this paper, we developed a novel method, HiC-GNN, for predicting the 3D structures of chromosomes from Hi-C data. HiC-GNN is unique from other methods for chromosome structure prediction in that the models learned by HiC-GNN can be generalized to data that is distinct from the training data. This aspect of HiC-GNN allows models that were trained on one Hi-C contact map to be used for inference on entirely different maps. To the authors' knowledge, this generalizing capability is not present in any existing methods. HiC-GNN uses a node embedding algorithm and a graph neural network to predict the 3D coordinates of each genomic loci from the corresponding Hi-C contact data. Unlike other methods, our algorithm allows for the storage of pre-trained parameters, thus enabling prediction on data that is entirely different from the training data. We show that our method can accurately generalize a single model across Hi-C resolutions, multiple restriction enzymes, and multiple cell populations while maintaining reconstruction accuracy across three Hi-C datasets. Our algorithm outperforms the state-of-the-art methods in accuracy of prediction and runtime and introduces a novel method for 3D structure prediction from Hi-C data. All our source codes and data are available at https://github.com/OluwadareLab/HiC-GNN.

Multivalent binding proteins can drive collapse and reswelling of chromatin in confinement

Collapsed conformations of chromatin have been long suspected of being mediated by interactions with multivalent binding proteins, which can bring together distant sections of the chromatin fiber. In this study, we use Langevin dynamics simulation of a coarse grained chromatin polymer to show that the role of binding proteins can be more nuanced than previously suspected. In particular, for chromatin polymer in confinement, entropic forces can drive reswelling of collapsed chromatin with increasing binder concentrations, and this reswelling transition happens at physiologically relevant binder concentrations. Both the extent of collapse, and also of reswelling depends on the strength of confinement. We also study the kinetics of collapse and reswelling and show that both processes occur in similar timescales. We characterise this reswelling of chromatin in biologically relevant regimes and discuss the non-trivial role of multivalent binding proteins in mediating the spatial organisation of the genome.

The dynamics of three-dimensional chromatin organization and phase separation in cell fate transitions and diseases

Cell fate transition is a fascinating process involving complex dynamics of three-dimensional (3D) chromatin organization and phase separation, which play an essential role in cell fate decision by regulating gene expression. Phase separation is increasingly being considered a driving force of chromatin folding. In this review, we have summarized the dynamic features of 3D chromatin and phase separation during physiological and pathological cell fate transitions and systematically analyzed recent evidence of phase separation facilitating the chromatin structure. In addition, we discuss current advances in understanding how phase separation contributes to physical and functional enhancer-promoter contacts. We highlight the functional roles of 3D chromatin organization and phase separation in cell fate transitions, and more explorations are required to study the regulatory relationship between 3D chromatin organization and phase separation. 3D chromatin organization (shown by Hi-C contact map) and phase separation are highly dynamic and play functional roles during early embryonic development, cell differentiation, somatic reprogramming, cell transdifferentiation and pathogenetic process. Phase separation can regulate 3D chromatin organization directly, but whether 3D chromatin organization regulates phase separation remains unclear.

Nucleus size and its effect on nucleosome stability in living cells

DNA architectural proteins play a major role in organization of chromosomal DNA in living cells by packaging it into chromatin, whose spatial conformation is determined by an intricate interplay between the DNA-binding properties of architectural proteins and physical constraints applied to the DNA by a tight nuclear space. Yet, the exact effects of the nucleus size on DNA-protein interactions and chromatin structure currently remain obscure. Furthermore, there is even no clear understanding of molecular mechanisms responsible for the nucleus size regulation in living cells. To find answers to these questions, we developed a general theoretical framework based on a combination of polymer field theory and transfer-matrix calculations, which showed that the nucleus size is mainly determined by the difference between the surface tensions of the nuclear envelope and the endoplasmic reticulum membrane as well as the osmotic pressure exerted by cytosolic macromolecules on the nucleus. In addition, the model demonstrated that the cell nucleus functions as a piezoelectric element, changing its electrostatic potential in a size-dependent manner. This effect has been found to have a profound impact on stability of nucleosomes, revealing a previously unknown link between the nucleus size and chromatin structure. Overall, our study provides new insights into the molecular mechanisms responsible for regulation of the nucleus size, as well as the potential role of nuclear organization in shaping the cell response to environmental cues.

Repression and 3D-restructuring resolves regulatory conflicts in evolutionarily rearranged genomes

Regulatory landscapes drive complex developmental gene expression, but it remains unclear how their integrity is maintained when incorporating novel genes and functions during evolution. Here, we investigated how a placental mammal-specific gene, Zfp42, emerged in an ancient vertebrate topologically associated domain (TAD) without adopting or disrupting the conserved expression of its gene, Fat1. In ESCs, physical TAD partitioning separates Zfp42 and Fat1 with distinct local enhancers that drive their independent expression. This separation is driven by chromatin activity and not CTCF/cohesin. In contrast, in embryonic limbs, inactive Zfp42 shares Fat1's intact TAD without responding to active Fat1 enhancers. However, neither Fat1 enhancer-incompatibility nor nuclear envelope-attachment account for Zfp42's unresponsiveness. Rather, Zfp42's promoter is rendered inert to enhancers by context-dependent DNA methylation. Thus, diverse mechanisms enabled the integration of independent Zfp42 regulation in the Fat1 locus. Critically, such regulatory complexity appears common in evolution as, genome wide, most TADs contain multiple independently expressed genes.

Polymer architecture orchestrates the segregation and spatial organization of replicating E. coli chromosomes in slow growth

The mechanism of chromosome segregation and organization in the bacterial cell cycle of E. coli is one of the least understood aspects in its life cycle. The E. coli chromosome is often modelled as a bead spring ring polymer. We introduce cross-links in the DNA-ring polymer, resulting in the formation of loops within each replicating bacterial chromosome. We use simulations to show that the chosen polymer-topology ensures its self-organization along the cell long-axis, such that various chromosomal loci get spatially localized as seen in vivo. The localization of loci arises due to entropic repulsion between polymer loops within each daughter DNA confined in a cylinder. The cellular addresses of the loci in our model are in fair agreement with those seen in experiments as given in J. A. Cass et al., Biophys. J., 2016, 110, 2597-2609. We also show that the adoption of such modified polymer architectures by the daughter DNAs leads to an enhanced propensity of their spatial segregation. Secondly, we match other experimentally reported results, including observation of the cohesion time and the ter-transition. Additionally, the contact map generated from our simulations reproduces the macro-domain like organization as seen in the experimentally obtained Hi-C map. Lastly, we have also proposed a plausible reconciliation of the 'Train Track' and the 'Replication Factory' models which provide conflicting descriptions of the spatial organization of the replication forks. Thus, we reconcile observations from complementary experimental techniques probing bacterial chromosome organization.

Loop-extrusion and polymer phase-separation can co-exist at the single-molecule level to shape chromatin folding

Loop-extrusion and phase-separation have been proposed as mechanisms that shape chromosome spatial organization. It is unclear, however, how they perform relative to each other in explaining chromatin architecture data and whether they compete or co-exist at the single-molecule level. Here, we compare models of polymer physics based on loop-extrusion and phase-separation, as well as models where both mechanisms act simultaneously in a single molecule, against multiplexed FISH data available in human loci in IMR90 and HCT116 cells. We find that the different models recapitulate bulk Hi-C and average multiplexed microscopy data. Single-molecule chromatin conformations are also well captured, especially by phase-separation based models that better reflect the experimentally reported segregation in globules of the considered genomic loci and their cell-to-cell structural variability. Such a variability is consistent with two main concurrent causes: single-cell epigenetic heterogeneity and an intrinsic thermodynamic conformational degeneracy of folding. Overall, the model combining loop-extrusion and polymer phase-separation provides a very good description of the data, particularly higher-order contacts, showing that the two mechanisms can co-exist in shaping chromatin architecture in single cells.

Uncovering the Principles of Genome Folding by 3D Chromatin Modeling

Our understanding of how genomic DNA is tightly packed inside the nucleus, yet is still accessible for vital cellular processes, has grown dramatically over recent years with advances in microscopy and genomics technologies. Computational methods have played a pivotal role in the structural interpretation of experimental data, which helped unravel some organizational principles of genome folding. Here, we give an overview of current computational efforts in mechanistic and data-driven 3D chromatin structure modeling. We discuss strengths and limitations of different methods and evaluate the added value and benefits of computational approaches to infer the 3D structural and dynamic properties of the genome and its underlying mechanisms at different scales and resolution, ranging from the dynamic formation of chromatin loops and topological associated domains to nuclear compartmentalization of chromatin and nuclear bodies.

Biology and Model Predictions of the Dynamics and Heterogeneity of Chromatin-Nuclear Lamina Interactions

Associations of chromatin with the nuclear lamina, at the nuclear periphery, help shape the genome in 3 dimensions. The genomic landscape of lamina-associated domains (LADs) is well characterized, but much remains unknown on the physical and mechanistic properties of chromatin conformation at the nuclear lamina. Computational models of chromatin folding at, and interactions with, a surface representing the nuclear lamina are emerging in attempts to characterize these properties and predict chromatin behavior at the lamina in health and disease. Here, we highlight the heterogeneous nature of the nuclear lamina and LADs, outline the main 3-dimensional chromatin structural modeling methods, review applications of modeling chromatin-lamina interactions and discuss biological insights inferred from these models in normal and disease states. Lastly, we address perspectives on future developments in modeling chromatin interactions with the nuclear lamina.

The Physics of DNA Folding: Polymer Models and Phase-Separation

Within cell nuclei, several biophysical processes occur in order to allow the correct activities of the genome such as transcription and gene regulation. To quantitatively investigate such processes, polymer physics models have been developed to unveil the molecular mechanisms underlying genome functions. Among these, phase-separation plays a key role since it controls gene activity and shapes chromatin spatial structure. In this paper, we review some recent experimental and theoretical progress in the field and show that polymer physics in synergy with numerical simulations can be helpful for several purposes, including the study of molecular condensates, gene-enhancer dynamics, and the three-dimensional reconstruction of real genomic regions.

Uncovering the Quantitative Relationships Among Chromosome Fluctuations, Epigenetics, and Gene Expressions of Transdifferentiation on Waddington Landscape

The 3D spatial organization of the chromosomes appears to be linked to the gene function, which is cell type-specific. The chromosome structural ensemble switching model (CSESM) is developed by employing a heteropolymer model on different cell types and the important quantitative relationships among the chromosome ensemble, the epigenetic marks, and the gene expressions are uncovered, that both chromosome fluctuation and epigenetic marks have strong linear correlations with the gene expressions. The results support that the two compartments have different behaviors, corresponding to the relatively sparse and fluctuating phase (compartment A) and the relatively dense and stable phase (compartment B). Importantly, through the investigation of the transdifferentiation processes between the peripheral blood mononuclear cell (PBMC) and the bipolar neuron (BN), a quantitative description for the transdifferentiation is provided, which can be linked to the Waddington landscape. In addition, compared to the direct transdifferentiation between PBMC and BN, the transdifferentiation via the intermediate state neural progenitor cell (NPC) follows a different path (an "uphill" followed by a "downhill"). These theoretical studies bridge the gap among the chromosome fluctuations/ensembles, the epigenetics, and gene expressions in determining the cell fate.

Polymer physics reveals a combinatorial code linking 3D chromatin architecture to 1D chromatin states

The mammalian genome has a complex, functional 3D organization. However, it remains largely unknown how DNA contacts are orchestrated by chromatin organizers. Here, we infer from only Hi-C the cell-type-specific arrangement of DNA binding sites sufficient to recapitulate, through polymer physics, contact patterns genome wide. Our model is validated by its predictions in a set of duplications at Sox9 against available independent data. The binding site types fall in classes that well match chromatin states from segmentation studies, yet they have an overlapping, combinatorial organization along chromosomes necessary to accurately explain contact specificity. The chromatin signatures of the binding site types return a code linking chromatin states to 3D architecture. The code is validated by extensive de novo predictions of Hi-C maps in an independent set of chromosomes. Overall, our results shed light on how 3D information is encrypted in 1D chromatin via the specific combinatorial arrangement of binding sites.

A Polymer Physics Model to Dissect Genome Organization in Healthy and Pathological Phenotypes

Novel technologies revealed a nontrivial spatial organization of the chromosomes within the cell nucleus, which includes different levels of compartmentalization and architectural patterns. Notably, such complex three-dimensional structure plays a crucial role in vital biological functions and its alterations can produce extensive rewiring of genomic regulatory regions, thus leading to gene misexpression and disease. Here, we show that theoretical and computational approaches, based on polymer physics, can be employed to dissect chromatin contacts in three-dimensional space and to predict the effects of pathogenic structural variants on the genome architecture. In particular, we discuss the folding of the human EPHA4 and the murine Pitx1 loci as case studies.

Dynamic and equilibrium properties of finite-size polymer models of chromosome folding

Novel technologies are revealing that chromosomes have a complex three-dimensional organization within the cell nucleus that serves functional purposes. Models from polymer physics have been developed to quantitively understand the molecular principles controlling their structure and folding mechanisms. Here, by using massive molecular-dynamics simulations we show that classical scaling laws combined with finite-size effects of a simple polymer model can effectively explain the scaling behavior that chromatin exhibits at the topologically associating domains level, as revealed by experimental observations. Model results are then validated against recently published high-resolution in situ Hi-C data.

Predicting genome organisation and function with mechanistic modelling

Fitting-free mechanistic models based on polymer simulations predict chromatin folding in 3D by focussing on the underlying biophysical mechanisms. This class of models has been increasingly used in conjunction with experiments to study the spatial organisation of eukaryotic chromosomes. Feedback from experiments to models leads to successive model refinement and has previously led to the discovery of new principles for genome organisation. Here, we review the basis of mechanistic polymer simulations, explain some of the more recent approaches and the contexts in which they have been useful to explain chromosome biology, and speculate on how they might be used in the future.

The interplay of chromatin phase separation and lamina interactions in nuclear organization

The genetic material of eukaryotes is segregated into transcriptionally active euchromatin and silent heterochromatin compartments. The spatial arrangement of chromatin compartments evolves over the course of cellular life in a process that remains poorly understood. The latest nuclear imaging experiments reveal a number of dynamical signatures of chromatin that are reminiscent of active multiphase liquids. This includes the observations of viscoelastic response, coherent motions, Ostwald ripening, and coalescence of chromatin compartments. There is also growing evidence that liquid-liquid phase separation of protein and nucleic acid components is the underlying mechanism for the dynamical behavior of chromatin. To dissect the organizational and dynamical implications of chromatin's liquid behavior, we have devised a phenomenological field-theoretic model of the nucleus as a multiphase condensate of liquid chromatin types. Employing the liquid chromatin model of the Drosophila nucleus, we have carried out an extensive set of simulations with an objective to shed light on the dynamics and chromatin patterning observed in the latest nuclear imaging experiments. Our simulations reveal the emergence of experimentally detected mesoscale chromatin channels and spheroidal droplets which arise from the dynamic interplay of chromatin type to type interactions and intermingling of chromosomal territories. We also quantitatively reproduce coherent motions of chromatin domains observed in displacement correlation spectroscopy measurements which are explained within the framework of our model by phase separation of chromatin types operating within constrained intrachromosomal and interchromosomal boundaries. Finally, we illuminate the role of heterochromatin-lamina interactions in the nuclear organization by showing that these interactions enhance the mobility of euchromatin and indirectly introduce correlated motions of heterochromatin droplets.

Impact of chromosomal organization on epigenetic drift and domain stability revealed by physics-based simulations

We examine the relationship between the size of domains of epigenetic marks and the stability of those domains using our theoretical model that captures the physical mechanisms governing the maintenance of epigenetic modifications. We focus our study on histone H3 lysine-9 trimethylation, one of the most common and consequential epigenetic marks with roles in chromatin compaction and gene repression. Our model combines the effects of methyl spreading by methyltransferases and chromatin segregation into heterochromatin and euchromatin because of preferential heterochromatin protein 1 (HP1) binding. Our model indicates that, although large methylated domains are passed successfully from one chromatin generation to the next, small alterations to the methylation sequence are not maintained during chromatin replication. Using our predictive model, we investigate the size required for an epigenetic domain to persist over chromatin generations while surrounded by a much larger domain of opposite methylation and compaction state. We find that there is a critical size threshold in the hundreds-of-nucleosomes scale above which an epigenetic domain will be reliably maintained over generations. The precise size of the threshold differs for heterochromatic and euchromatic domains. Our results are consistent with natural alterations to the epigenetic sequence occurring during embryonic development and due to age-related epigenetic drift.

Cell-type specialization is encoded by specific chromatin topologies

The three-dimensional (3D) structure of chromatin is intrinsically associated with gene regulation and cell function1-3. Methods based on chromatin conformation capture have mapped chromatin structures in neuronal systems such as in vitro differentiated neurons, neurons isolated through fluorescence-activated cell sorting from cortical tissues pooled from different animals and from dissociated whole hippocampi4-6. However, changes in chromatin organization captured by imaging, such as the relocation of Bdnf away from the nuclear periphery after activation7, are invisible with such approaches8. Here we developed immunoGAM, an extension of genome architecture mapping (GAM)2,9, to map 3D chromatin topology genome-wide in specific brain cell types, without tissue disruption, from single animals. GAM is a ligation-free technology that maps genome topology by sequencing the DNA content from thin (about 220 nm) nuclear cryosections. Chromatin interactions are identified from the increased probability of co-segregation of contacting loci across a collection of nuclear slices. ImmunoGAM expands the scope of GAM to enable the selection of specific cell types using low cell numbers (approximately 1,000 cells) within a complex tissue and avoids tissue dissociation2,10. We report cell-type specialized 3D chromatin structures at multiple genomic scales that relate to patterns of gene expression. We discover extensive 'melting' of long genes when they are highly expressed and/or have high chromatin accessibility. The contacts most specific of neuron subtypes contain genes associated with specialized processes, such as addiction and synaptic plasticity, which harbour putative binding sites for neuronal transcription factors within accessible chromatin regions. Moreover, sensory receptor genes are preferentially found in heterochromatic compartments in brain cells, which establish strong contacts across tens of megabases. Our results demonstrate that highly specific chromatin conformations in brain cells are tightly related to gene regulation mechanisms and specialized functions.

The 3D Genome: From Structure to Function

The genome is the most functional part of a cell, and genomic contents are organized in a compact three-dimensional (3D) structure. The genome contains millions of nucleotide bases organized in its proper frame. Rapid development in genome sequencing and advanced microscopy techniques have enabled us to understand the 3D spatial organization of the genome. Chromosome capture methods using a ligation approach and the visualization tool of a 3D genome browser have facilitated detailed exploration of the genome. Topologically associated domains (TADs), lamin-associated domains, CCCTC-binding factor domains, cohesin, and chromatin structures are the prominent identified components that encode the 3D structure of the genome. Although TADs are the major contributors to 3D genome organization, they are absent in Arabidopsis. However, a few research groups have reported the presence of TAD-like structures in the plant kingdom.

Polymer models are a versatile tool to study chromatin 3D organization

The development of new experimental technologies is opening the way to a deeper investigation of the three-dimensional organization of chromosomes inside the cell nucleus. Genome architecture is linked to vital functional purposes, yet a full comprehension of the mechanisms behind DNA folding is still far from being accomplished. Theoretical approaches based on polymer physics have been employed to understand the complexity of chromatin architecture data and to unveil the basic mechanisms shaping its structure. Here, we review some recent advances in the field to discuss how Polymer Physics, combined with numerical Molecular Dynamics simulation and Machine Learning based inference, can capture important aspects of genome organization, including the description of tissue-specific structural rearrangements, the detection of novel, regulatory-linked architectural elements and the structural variability of chromatin at the single-cell level.

Computational methods for predicting 3D genomic organization from high-resolution chromosome conformation capture data

The advent of high-resolution chromosome conformation capture assays (such as 5C, Hi-C and Pore-C) has allowed for unprecedented sequence-level investigations into the structure-function relationship of the genome. In order to comprehensively understand this relationship, computational tools are required that utilize data generated from these assays to predict 3D genome organization (the 3D genome reconstruction problem). Many computational tools have been developed that answer this need, but a comprehensive comparison of their underlying algorithmic approaches has not been conducted. This manuscript provides a comprehensive review of the existing computational tools (from November 2006 to September 2019, inclusive) that can be used to predict 3D genome organizations from high-resolution chromosome conformation capture data. Overall, existing tools were found to use a relatively small set of algorithms from one or more of the following categories: dimensionality reduction, graph/network theory, maximum likelihood estimation (MLE) and statistical modeling. Solutions in each category are far from maturity, and the breadth and depth of various algorithmic categories have not been fully explored. While the tools for predicting 3D structure for a genomic region or single chromosome are diverse, there is a general lack of algorithmic diversity among computational tools for predicting the complete 3D genome organization from high-resolution chromosome conformation capture data.

Hi-C analyses with GENOVA: a case study with cohesin variants

Conformation capture-approaches like Hi-C can elucidate chromosome structure at a genome-wide scale. Hi-C datasets are large and require specialised software. Here, we present GENOVA: a user-friendly software package to analyse and visualise chromosome conformation capture (3C) data. GENOVA is an R-package that includes the most common Hi-C analyses, such as compartment and insulation score analysis. It can create annotated heatmaps to visualise the contact frequency at a specific locus and aggregate Hi-C signal over user-specified genomic regions such as ChIP-seq data. Finally, our package supports output from the major mapping-pipelines. We demonstrate the capabilities of GENOVA by analysing Hi-C data from HAP1 cell lines in which the cohesin-subunits SA1 and SA2 were knocked out. We find that ΔSA1 cells gain intra-TAD interactions and increase compartmentalisation. ΔSA2 cells have longer loops and a less compartmentalised genome. These results suggest that cohesin^SA1 forms longer loops, while cohesin^SA2 plays a role in forming and maintaining intra-TAD interactions. Our data supports the model that the genome is provided structure in 3D by the counter-balancing of loop formation on one hand, and compartmentalization on the other hand. By differentially controlling loops, cohesin^SA1 and cohesin^SA2 therefore also affect nuclear compartmentalization. We show that GENOVA is an easy to use R-package, that allows researchers to explore Hi-C data in great detail.

Comparison of the Hi-C, GAM and SPRITE methods using polymer models of chromatin

Hi-C, split-pool recognition of interactions by tag extension (SPRITE) and genome architecture mapping (GAM) are powerful technologies utilized to probe chromatin interactions genome wide, but how faithfully they capture three-dimensional (3D) contacts and how they perform relative to each other is unclear, as no benchmark exists. Here, we compare these methods in silico in a simplified, yet controlled, framework against known 3D structures of polymer models of murine and human loci, which can recapitulate Hi-C, GAM and SPRITE experiments and multiplexed fluorescence in situ hybridization (FISH) single-molecule conformations. We find that in silico Hi-C, GAM and SPRITE bulk data are faithful to the reference 3D structures whereas single-cell data reflect strong variability among single molecules. The minimal number of cells required in replicate experiments to return statistically similar contacts is different across the technologies, being lowest in SPRITE and highest in GAM under the same conditions. Noise-to-signal levels follow an inverse power law with detection efficiency and grow with genomic distance differently among the three methods, being lowest in GAM for genomic separations >1 Mb.