Cooltools: Enabling high-resolution Hi-C analysis in Python

Chromosome conformation capture (3C) technologies reveal the incredible complexity of genome organization. Maps of increasing size, depth, and resolution are now used to probe genome architecture across cell states, types, and organisms. Larger datasets add challenges at each step of computational analysis, from storage and memory constraints to researchers' time; however, analysis tools that meet these increased resource demands have not kept pace. Furthermore, existing tools offer limited support for customizing analysis for specific use cases or new biology. Here we introduce cooltools (https://github.com/open2c/cooltools), a suite of computational tools that enables flexible, scalable, and reproducible analysis of high-resolution contact frequency data. Cooltools leverages the widely-adopted cooler format which handles storage and access for high-resolution datasets. Cooltools provides a paired command line interface (CLI) and Python application programming interface (API), which respectively facilitate workflows on high-performance computing clusters and in interactive analysis environments. In short, cooltools enables the effective use of the latest and largest genome folding datasets.

Bioframe: operations on genomic intervals in Pandas dataframes

MOTIVATION

Genomic intervals are one of the most prevalent data structures in computational genome biology, and used to represent features ranging from genes, to DNA binding sites, to disease variants. Operations on genomic intervals provide a language for asking questions about relationships between features. While there are excellent interval arithmetic tools for the command line, they are not smoothly integrated into Python, one of the most popular general-purpose computational and visualization environments.

RESULTS

Bioframe is a library to enable flexible and performant operations on genomic interval dataframes in Python. Bioframe extends the Python data science stack to use cases for computational genome biology by building directly on top of two of the most commonly-used Python libraries, NumPy and Pandas. The bioframe API enables flexible name and column orders, and decouples operations from data formats to avoid unnecessary conversions, a common scourge for bioinformaticians. Bioframe achieves these goals while maintaining high performance and a rich set of features.

AVAILABILITY AND IMPLEMENTATION

Bioframe is open-source under MIT license, cross-platform, and can be installed from the Python Package Index. The source code is maintained by Open2C on GitHub at https://github.com/open2c/bioframe.

The motif composition of variable number tandem repeats impacts gene expression

Understanding the impact of DNA variation on human traits is a fundamental question in human genetics. Variable number tandem repeats (VNTRs) make up ∼3% of the human genome but are often excluded from association analysis owing to poor read mappability or divergent repeat content. Although methods exist to estimate VNTR length from short-read data, it is known that VNTRs vary in both length and repeat (motif) composition. Here, we use a repeat-pangenome graph (RPGG) constructed on 35 haplotype-resolved assemblies to detect variation in both VNTR length and repeat composition. We align population-scale data from the Genotype-Tissue Expression (GTEx) Consortium to examine how variations in sequence composition may be linked to expression, including cases independent of overall VNTR length. We find that 9422 out of 39,125 VNTRs are associated with nearby gene expression through motif variations, of which only 23.4% are accessible from length. Fine-mapping identifies 174 genes to be likely driven by variation in certain VNTR motifs and not overall length. We highlight two genes, CACNA1C and RNF213, that have expression associated with motif variation, showing the utility of RPGG analysis as a new approach for trait association in multiallelic and highly variable loci.

Pairtools: from sequencing data to chromosome contacts

The field of 3D genome organization produces large amounts of sequencing data from Hi-C and a rapidly-expanding set of other chromosome conformation protocols (3C+). Massive and heterogeneous 3C+ data require high-performance and flexible processing of sequenced reads into contact pairs. To meet these challenges, we present pairtools - a flexible suite of tools for contact extraction from sequencing data. Pairtools provides modular command-line interface (CLI) tools that can be flexibly chained into data processing pipelines. Pairtools provides both crucial core tools as well as auxiliary tools for building feature-rich 3C+ pipelines, including contact pair manipulation, filtration, and quality control. Benchmarking pairtools against popular 3C+ data pipelines shows advantages of pairtools for high-performance and flexible 3C+ analysis. Finally, pairtools provides protocol-specific tools for multi-way contacts, haplotype-resolved contacts, and single-cell Hi-C. The combination of CLI tools and tight integration with Python data analysis libraries makes pairtools a versatile foundation for a broad range of 3C+ pipelines.

Molecular basis of CTCF binding polarity in genome folding

Current models propose that boundaries of mammalian topologically associating domains (TADs) arise from the ability of the CTCF protein to stop extrusion of chromatin loops by cohesin. While the orientation of CTCF motifs determines which pairs of CTCF sites preferentially stabilize loops, the molecular basis of this polarity remains unclear. By combining ChIP-seq and single molecule live imaging we report that CTCF positions cohesin, but does not control its overall binding dynamics on chromatin. Using an inducible complementation system, we find that CTCF mutants lacking the N-terminus cannot insulate TADs properly. Cohesin remains at CTCF sites in this mutant, albeit with reduced enrichment. Given the orientation of CTCF motifs presents the N-terminus towards cohesin as it translocates from the interior of TADs, these observations explain how the orientation of CTCF binding sites translates into genome folding patterns.

Principles of meiotic chromosome assembly revealed in S. cerevisiae

During meiotic prophase, chromosomes organise into a series of chromatin loops emanating from a proteinaceous axis, but the mechanisms of assembly remain unclear. Here we use Saccharomyces cerevisiae to explore how this elaborate three-dimensional chromosome organisation is linked to genomic sequence. As cells enter meiosis, we observe that strong cohesin-dependent grid-like Hi-C interaction patterns emerge, reminiscent of mammalian interphase organisation, but with distinct regulation. Meiotic patterns agree with simulations of loop extrusion with growth limited by barriers, in which a heterogeneous population of expanding loops develop along the chromosome. Importantly, CTCF, the factor that imposes similar features in mammalian interphase, is absent in S. cerevisiae, suggesting alternative mechanisms of barrier formation. While grid-like interactions emerge independently of meiotic chromosome synapsis, synapsis itself generates additional compaction that matures differentially according to telomere proximity and chromosome size. Collectively, our results elucidate fundamental principles of chromosome assembly and demonstrate the essential role of cohesin within this evolutionarily conserved process.

Highly structured homolog pairing reflects functional organization of the Drosophila genome

Trans-homolog interactions have been studied extensively in Drosophila, where homologs are paired in somatic cells and transvection is prevalent. Nevertheless, the detailed structure of pairing and its functional impact have not been thoroughly investigated. Accordingly, we generated a diploid cell line from divergent parents and applied haplotype-resolved Hi-C, showing that homologs pair with varying precision genome-wide, in addition to establishing trans-homolog domains and compartments. We also elucidate the structure of pairing with unprecedented detail, observing significant variation across the genome and revealing at least two forms of pairing: tight pairing, spanning contiguous small domains, and loose pairing, consisting of single larger domains. Strikingly, active genomic regions (A-type compartments, active chromatin, expressed genes) correlated with tight pairing, suggesting that pairing has a functional implication genome-wide. Finally, using RNAi and haplotype-resolved Hi-C, we show that disruption of pairing-promoting factors results in global changes in pairing, including the disruption of some interaction peaks.

The genome-wide multi-layered architecture of chromosome pairing in early Drosophila embryos

Genome organization involves cis and trans chromosomal interactions, both implicated in gene regulation, development, and disease. Here, we focus on trans interactions in Drosophila, where homologous chromosomes are paired in somatic cells from embryogenesis through adulthood. We first address long-standing questions regarding the structure of embryonic homolog pairing and, to this end, develop a haplotype-resolved Hi-C approach to minimize homolog misassignment and thus robustly distinguish trans-homolog from cis contacts. This computational approach, which we call Ohm, reveals pairing to be surprisingly structured genome-wide, with trans-homolog domains, compartments, and interaction peaks, many coinciding with analogous cis features. We also find a significant genome-wide correlation between pairing, transcription during zygotic genome activation, and binding of the pioneer factor Zelda. Our findings reveal a complex, highly structured organization underlying homolog pairing, first discovered a century ago in Drosophila. Finally, we demonstrate the versatility of our haplotype-resolved approach by applying it to mammalian embryos.

Chromatin organization by an interplay of loop extrusion and compartmental segregation

Mammalian chromatin is spatially organized at many scales showing two prominent features in interphase: (i) alternating regions (1-10 Mb) of active and inactive chromatin that spatially segregate into different compartments, and (ii) domains (<1 Mb), that is, regions that preferentially interact internally [topologically associating domains (TADs)] and are central to gene regulation. There is growing evidence that TADs are formed by active extrusion of chromatin loops by cohesin, whereas compartmentalization is established according to local chromatin states. Here, we use polymer simulations to examine how loop extrusion and compartmental segregation work collectively and potentially interfere in shaping global chromosome organization. A model with differential attraction between euchromatin and heterochromatin leads to phase separation and reproduces compartmentalization as observed in Hi-C. Loop extrusion, essential for TAD formation, in turn, interferes with compartmentalization. Our integrated model faithfully reproduces Hi-C data from puzzling experimental observations where altering loop extrusion also led to changes in compartmentalization. Specifically, depletion of chromatin-associated cohesin reduced TADs and revealed finer compartments, while increased processivity of cohesin strengthened large TADs and reduced compartmentalization; and depletion of the TAD boundary protein CTCF weakened TADs while leaving compartments unaffected. We reveal that these experimental perturbations are special cases of a general polymer phenomenon of active mixing by loop extrusion. Our results suggest that chromatin organization on the megabase scale emerges from competition of nonequilibrium active loop extrusion and epigenetically defined compartment structure.

Emerging Evidence of Chromosome Folding by Loop Extrusion

Chromosome organization poses a remarkable physical problem with many biological consequences: How can molecular interactions between proteins at the nanometer scale organize micron-long chromatinized DNA molecules, insulating or facilitating interactions between specific genomic elements? The mechanism of active loop extrusion holds great promise for explaining interphase and mitotic chromosome folding, yet remains difficult to assay directly. We discuss predictions from our polymer models of loop extrusion with barrier elements and review recent experimental studies that provide strong support for loop extrusion, focusing on perturbations to CTCF and cohesin assayed via Hi-C in interphase. Finally, we discuss a likely molecular mechanism of loop extrusion by structural maintenance of chromosomes complexes.

Two independent modes of chromatin organization revealed by cohesin removal

Imaging and chromosome conformation capture studies have revealed several layers of chromosome organization, including segregation into megabase-sized active and inactive compartments, and partitioning into sub-megabase domains (TADs). It remains unclear, however, how these layers of organization form, interact with one another and influence genome function. Here we show that deletion of the cohesin-loading factor Nipbl in mouse liver leads to a marked reorganization of chromosomal folding. TADs and associated Hi-C peaks vanish globally, even in the absence of transcriptional changes. By contrast, compartmental segregation is preserved and even reinforced. Strikingly, the disappearance of TADs unmasks a finer compartment structure that accurately reflects the underlying epigenetic landscape. These observations demonstrate that the three-dimensional organization of the genome results from the interplay of two independent mechanisms: cohesin-independent segregation of the genome into fine-scale compartments, defined by chromatin state; and cohesin-dependent formation of TADs, possibly by loop extrusion, which helps to guide distant enhancers to their target genes.

SMC complexes differentially compact mitotic chromosomes according to genomic context

Structural maintenance of chromosomes (SMC) protein complexes are key determinants of chromosome conformation. Using Hi-C and polymer modelling, we study how cohesin and condensin, two deeply conserved SMC complexes, organize chromosomes in the budding yeast Saccharomyces cerevisiae. The canonical role of cohesin is to co-align sister chromatids, while condensin generally compacts mitotic chromosomes. We find strikingly different roles for the two complexes in budding yeast mitosis. First, cohesin is responsible for compacting mitotic chromosome arms, independently of sister chromatid cohesion. Polymer simulations demonstrate that this role can be fully accounted for through cis-looping of chromatin. Second, condensin is generally dispensable for compaction along chromosome arms. Instead, it plays a targeted role compacting the rDNA proximal regions and promoting resolution of peri-centromeric regions. Our results argue that the conserved mechanism of SMC complexes is to form chromatin loops and that distinct SMC-dependent looping activities are selectively deployed to appropriately compact chromosomes.

FISH-ing for captured contacts: towards reconciling FISH and 3C

Chromosome conformation capture (3C) and fluorescence in situ hybridization (FISH) are two widely used technologies that provide distinct readouts of 3D chromosome organization. While both technologies can assay locus-specific organization, how to integrate views from 3C, or genome-wide Hi-C, and FISH is far from solved. Contact frequency, measured by Hi-C, and spatial distance, measured by FISH, are often assumed to quantify the same phenomena and used interchangeably. Here, however, we demonstrate that contact frequency is distinct from average spatial distance, both in polymer simulations and in experimental data. Performing a systematic analysis of the technologies, we show that this distinction can create a seemingly paradoxical relationship between 3C and FISH, both in minimal polymer models with dynamic looping interactions and in loop-extrusion simulations. Together, our results indicate that cross-validation of Hi-C and FISH should be carefully designed, and that jointly considering contact frequency and spatial distance is crucial for fully understanding chromosome organization.

Formation of Chromosomal Domains by Loop Extrusion

Topologically associating domains (TADs) are fundamental structural and functional building blocks of human interphase chromosomes, yet the mechanisms of TAD formation remain unclear. Here, we propose that loop extrusion underlies TAD formation. In this process, cis-acting loop-extruding factors, likely cohesins, form progressively larger loops but stall at TAD boundaries due to interactions with boundary proteins, including CTCF. Using polymer simulations, we show that this model produces TADs and finer-scale features of Hi-C data. Each TAD emerges from multiple loops dynamically formed through extrusion, contrary to typical illustrations of single static loops. Loop extrusion both explains diverse experimental observations-including the preferential orientation of CTCF motifs, enrichments of architectural proteins at TAD boundaries, and boundary deletion experiments-and makes specific predictions for the depletion of CTCF versus cohesin. Finally, loop extrusion has potentially far-ranging consequences for processes such as enhancer-promoter interactions, orientation-specific chromosomal looping, and compaction of mitotic chromosomes.

History of chromosome rearrangements reflects the spatial organization of yeast chromosomes

Three-dimensional (3D) organization of genomes affects critical cellular processes such as transcription, replication, and deoxyribo nucleic acid (DNA) repair. While previous studies have investigated the natural role, the 3D organization plays in limiting a possible set of genomic rearrangements following DNA repair, the influence of specific organizational principles on this process, particularly over longer evolutionary time scales, remains relatively unexplored. In budding yeast S.cerevisiae, chromosomes are organized into a Rabl-like configuration, with clustered centromeres and telomeres tethered to the nuclear periphery. Hi-C data for S.cerevisiae show that a consequence of this Rabl-like organization is that regions equally distant from centromeres are more frequently in contact with each other, between arms of both the same and different chromosomes. Here, we detect rearrangement events in Saccharomyces species using an automatic approach, and observe increased rearrangement frequency between regions with higher contact frequencies. Together, our results underscore how specific principles of 3D chromosomal organization can influence evolutionary events.

Super-resolution imaging reveals distinct chromatin folding for different epigenetic states

Metazoan genomes are spatially organized at multiple scales, from packaging of DNA around individual nucleosomes to segregation of whole chromosomes into distinct territories^1–5. At the intermediate scale of kilobases to megabases, which encompasses the sizes of genes, gene clusters and regulatory domains, the three-dimensional (3D) organization of DNA is implicated in multiple gene regulatory mechanisms^2–4,6–8, but understanding this organization remains a challenge. At this scale, the genome is partitioned into domains of different epigenetic states that are essential for regulating gene expression^9–11. Here, we investigate the 3D organization of chromatin in different epigenetic states using super-resolution imaging. We classified genomic domains in Drosophila cells into transcriptionally active, inactive, or Polycomb-repressed states and observed distinct chromatin organizations for each state. Remarkably, all three types of chromatin domains exhibit power-law scaling between their physical sizes in 3D and their domain lengths, but each type has a distinct scaling exponent. Polycomb-repressed chromatin shows the densest packing and most intriguing folding behaviour in which packing density increases with domain length. Distinct from the self-similar organization displayed by transcriptionally active and inactive chromatin, the Polycomb-repressed domains are characterized by a high degree of chromatin intermixing within the domain. Moreover, compared to inactive domains, Polycomb-repressed domains spatially exclude neighbouring active chromatin to a much stronger degree. Computational modelling and knockdown experiments suggest that reversible chromatin interactions mediated by Polycomb-group proteins plays an important role in these unique packaging properties of the repressed chromatin. Taken together, our super-resolution images reveal distinct chromatin packaging for different epigenetic states at the kilobase-to-megabase scale, a length scale that is directly relevant to genome regulation.

Modeling chromosomes: Beyond pretty pictures

Recently, Chromosome Conformation Capture (3C) based experiments have highlighted the importance of computational models for the study of chromosome organization. In this review, we propose that current computational models can be grouped into roughly four classes, with two classes of data-driven models: consensus structures and data-driven ensembles, and two classes of de novo models: structural ensembles and mechanistic ensembles. Finally, we highlight specific questions mechanistic ensembles can address.

Genome-wide maps of nuclear lamina interactions in single human cells

Mammalian interphase chromosomes interact with the nuclear lamina (NL) through hundreds of large lamina-associated domains (LADs). We report a method to map NL contacts genome-wide in single human cells. Analysis of nearly 400 maps reveals a core architecture consisting of gene-poor LADs that contact the NL with high cell-to-cell consistency, interspersed by LADs with more variable NL interactions. The variable contacts tend to be cell-type specific and are more sensitive to changes in genome ploidy than the consistent contacts. Single-cell maps indicate that NL contacts involve multivalent interactions over hundreds of kilobases. Moreover, we observe extensive intra-chromosomal coordination of NL contacts, even over tens of megabases. Such coordinated loci exhibit preferential interactions as detected by Hi-C. Finally, the consistency of NL contacts is inversely linked to gene activity in single cells and correlates positively with the heterochromatic histone modification H3K9me3. These results highlight fundamental principles of single-cell chromatin organization. VIDEO ABSTRACT.

Cohesin-dependent globules and heterochromatin shape 3D genome architecture in S. pombe

Eukaryotic genomes are folded into three-dimensional structures, such as self-associating topological domains, the borders of which are enriched in cohesin and CCCTC-binding factor (CTCF) required for long-range interactions. How local chromatin interactions govern higher-order folding of chromatin fibres and the function of cohesin in this process remain poorly understood. Here we perform genome-wide chromatin conformation capture (Hi-C) analysis to explore the high-resolution organization of the Schizosaccharomyces pombe genome, which despite its small size exhibits fundamental features found in other eukaryotes. Our analyses of wild-type and mutant strains reveal key elements of chromosome architecture and genome organization. On chromosome arms, small regions of chromatin locally interact to form 'globules'. This feature requires a function of cohesin distinct from its role in sister chromatid cohesion. Cohesin is enriched at globule boundaries and its loss causes disruption of local globule structures and global chromosome territories. By contrast, heterochromatin, which loads cohesin at specific sites including pericentromeric and subtelomeric domains, is dispensable for globule formation but nevertheless affects genome organization. We show that heterochromatin mediates chromatin fibre compaction at centromeres and promotes prominent inter-arm interactions within centromere-proximal regions, providing structural constraints crucial for proper genome organization. Loss of heterochromatin relaxes constraints on chromosomes, causing an increase in intra- and inter-chromosomal interactions. Together, our analyses uncover fundamental genome folding principles that drive higher-order chromosome organization crucial for coordinating nuclear functions.

Chromatin loops as allosteric modulators of enhancer-promoter interactions

The classic model of eukaryotic gene expression requires direct spatial contact between a distal enhancer and a proximal promoter. Recent Chromosome Conformation Capture (3C) studies show that enhancers and promoters are embedded in a complex network of looping interactions. Here we use a polymer model of chromatin fiber to investigate whether, and to what extent, looping interactions between elements in the vicinity of an enhancer-promoter pair can influence their contact frequency. Our equilibrium polymer simulations show that a chromatin loop, formed by elements flanking either an enhancer or a promoter, suppresses enhancer-promoter interactions, working as an insulator. A loop formed by elements located in the region between an enhancer and a promoter, on the contrary, facilitates their interactions. We find that different mechanisms underlie insulation and facilitation; insulation occurs due to steric exclusion by the loop, and is a global effect, while facilitation occurs due to an effective shortening of the enhancer-promoter genomic distance, and is a local effect. Consistently, we find that these effects manifest quite differently for in silico 3C and microscopy. Our results show that looping interactions that do not directly involve an enhancer-promoter pair can nevertheless significantly modulate their interactions. This phenomenon is analogous to allosteric regulation in proteins, where a conformational change triggered by binding of a regulatory molecule to one site affects the state of another site.

In eukaryotes, enhancers directly contact promoters over large genomic distances to regulate gene expression. Characterizing the principles underlying these long-range enhancer-promoter contacts is crucial for a full understanding of gene expression. Recent experimental mapping of chromosomal interactions by the Hi-C method shows an intricate network of local looping interactions surrounding enhancers and promoters. We model a region of chromatin fiber as a long polymer and study how the formation of loops between certain regulatory elements can insulate or facilitate enhancer-promoter interactions. We find 2–5 fold insulation or facilitation, depending on the location of looping elements relative to an enhancer-promoter pair. These effects originate from the polymer nature of chromatin, without requiring additional mechanisms beyond the formation of a chromatin loop. Our findings suggest that loop-mediated gene regulation by elements in the vicinity of an enhancer-promoter pair can be understood as an allosteric effect. This highlights the complex effects that local chromatin organization can have on gene regulation.

Organization of the mitotic chromosome

Mitotic chromosomes are among the most recognizable structures in the cell, yet for over a century their internal organization remains largely unsolved. We applied chromosome conformation capture methods, 5C and Hi-C, across the cell cycle and revealed two distinct three-dimensional folding states of the human genome. We show that the highly compartmentalized and cell type-specific organization described previously for nonsynchronous cells is restricted to interphase. In metaphase, we identified a homogenous folding state that is locus-independent, common to all chromosomes, and consistent among cell types, suggesting a general principle of metaphase chromosome organization. Using polymer simulations, we found that metaphase Hi-C data are inconsistent with classic hierarchical models and are instead best described by a linearly organized longitudinally compressed array of consecutive chromatin loops.

Higher-order chromatin structure: bridging physics and biology

Advances in microscopy and genomic techniques have provided new insight into spatial chromatin organization inside of the nucleus. In particular, chromosome conformation capture data has highlighted the relevance of polymer physics for high-order chromatin organization. In this context, we review basic polymer states, discuss how an appropriate polymer model can be determined from experimental data, and examine the success and limitations of various polymer models of higher-order interphase chromatin organization. By taking into account topological constraints acting on the chromatin fiber, recently developed polymer models of interphase chromatin can reproduce the observed scaling of distances between genomic loci, chromosomal territories, and probabilities of contacts between loci measured by chromosome conformation capture methods. Polymer models provide a framework for the interpretation of experimental data as ensembles of conformations rather than collections of loops, and will be crucial for untangling functional implications of chromosomal organization.

Bayesian image recovery for dendritic structures under low signal-to-noise conditions

Experimental research seeking to quantify neuronal structure constantly contends with restrictions on image resolution and variability. In particular, experimentalists often need to analyze images with very low signal-to-noise ratio (SNR). In many experiments, dye toxicity scales with the light intensity; this leads experimentalists to reduce image SNR in order to preserve the viability of the specimen. In this paper, we present a Bayesian approach for estimating the neuronal shape given low-SNR observations. This Bayesian framework has two major advantages. First, the method effectively incorporates known facts about 1) the image formation process, including blur and the Poisson nature of image noise at low intensities, and 2) dendritic shape, including the fact that dendrites are simply-connected geometric structures with smooth boundaries. Second, we may employ standard Markov chain Monte Carlo techniques for quantifying the posterior uncertainty in our estimate of the dendritic shape. We describe an efficient computational implementation of these methods and demonstrate the algorithm's performance on simulated noisy two-photon laser-scanning microscopy images.