The biology and polymer physics underlying large-scale chromosome organization

Exploring protein-mediated compaction of DNA by coarse-grained simulations and unsupervised learning

Protein-DNA interactions and protein-mediated DNA compaction play key roles in a range of biological processes. The length scales typically involved in DNA bending, bridging, looping, and compaction (≥1 kbp) are challenging to address experimentally or by all-atom molecular dynamics simulations, making coarse-grained simulations a natural approach. Here, we present a simple and generic coarse-grained model for DNA-protein and protein-protein interactions and investigate the role of the latter in the protein-induced compaction of DNA. Our approach models the DNA as a discrete worm-like chain. The proteins are treated in the grand canonical ensemble, and the protein-DNA binding strength is taken from experimental measurements. Protein-DNA interactions are modeled as an isotropic binding potential with an imposed binding valency without specific assumptions about the binding geometry. To systematically and quantitatively classify DNA-protein complexes, we present an unsupervised machine learning pipeline that receives a large set of structural order parameters as input, reduces the dimensionality via principal-component analysis, and groups the results using a Gaussian mixture model. We apply our method to recent data on the compaction of viral genome-length DNA by HIV integrase and find that protein-protein interactions are critical to the formation of looped intermediate structures seen experimentally. Our methodology is broadly applicable to DNA-binding proteins and protein-induced DNA compaction and provides a systematic and semi-quantitative approach for analyzing their mesoscale complexes.

Bottom-up data integration in polymer models of chromatin organization

Cellular functions crucially depend on the precise execution of complex biochemical reactions taking place on the chromatin fiber in the tightly packed environment of the cell nucleus. Despite the availability of large datasets probing this process from multiple angles, bottom-up frameworks that allow the incorporation of the sequence-specific nature of biochemistry in a unified model of 3D chromatin structure remain scarce. Here, we propose Sequence-Enhanced Magnetic Polymer (SEMPER), a novel stochastic polymer model that naturally incorporates observational data about sequence-driven biochemical processes, such as binding of transcription factor proteins, in a 3D model of chromatin structure. We introduce a novel approximate Bayesian algorithm to quantify a posteriori the relative importance of various factors, including the polymeric nature of DNA, in determining chromatin epigenetic state, thus providing a transparent way to generate biological hypotheses. Although accurate prediction of contact frequencies (a problem already extensively studied in the literature) is not our main aim, as a by-product of the inference procedure and without additional input from the genome 3D structure, our model can predict with reasonable accuracy some notable and nontrivial conformational features of chromatin folding within the nucleus. Our work highlights the importance of introducing physically realistic statistical models for predicting chromatin states from epigenetic data and opens the way to a new class of more systematic approaches to interpreting epigenomic data.

Mesoscale, long-time mixing of chromosomes and its connection to polymer dynamics

Chromosomes are arranged in distinct territories within the nucleus of animal cells. Recent experiments have shown that these territories overlap at their edges, suggesting partial mixing during interphase. Experiments that knock-down of condensin II proteins during interphase indicate increased chromosome mixing, which demonstrates control of the mixing. In this study, we use a generic polymer simulation to quantify the dynamics of chromosome mixing over time. We introduce the chromosome mixing index, which quantifies the mixing of distinct chromosomes in the nucleus. We find that the chromosome mixing index in a small confinement volume (as a model of the nucleus), increases as a power-law of the time, with the scaling exponent varying non-monotonically with self-interaction and volume fraction. By comparing the chromosome mixing index with both monomer subdiffusion due to (non-topological) intermingling of chromosomes as well as even slower reptation, we show that for relatively large volume fractions, the scaling exponent of the chromosome mixing index is related to Rouse dynamics for relatively weak chromosome attractions and to reptation for strong attractions. In addition, we extend our model to more realistically account for the situation of the Drosophila chromosome by including the heterogeneity of the polymers and their lengths to account for microphase separation of euchromatin and heterochromatin and their interactions with the nuclear lamina. We find that the interaction with the lamina further impedes chromosome mixing.

Hypothesis-driven probabilistic modelling enables a principled perspective of genomic compartments

The Hi-C method has revolutionized the study of genome organization, yet interpretation of Hi-C interaction frequency maps remains a major challenge. Genomic compartments are a checkered Hi-C interaction pattern suggested to represent the partitioning of the genome into two self-interacting states associated with active and inactive chromatin. Based on a few elementary mechanistic assumptions, we derive a generative probabilistic model of genomic compartments, called deGeco. Testing our model, we find it can explain observed Hi-C interaction maps in a highly robust manner, allowing accurate inference of interaction probability maps from extremely sparse data without any training of parameters. Taking advantage of the interpretability of the model parameters, we then test hypotheses regarding the nature of genomic compartments. We find clear evidence of multiple states, and that these states self-interact with different affinities. We also find that the interaction rules of chromatin states differ considerably within and between chromosomes. Inspecting the molecular underpinnings of a four-state model, we show that a simple classifier can use histone marks to predict the underlying states with 87% accuracy. Finally, we observe instances of mixed-state loci and analyze these loci in single-cell Hi-C maps, finding that mixing of states occurs mainly at the cell level.

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.

A Multigraph-Based Representation of Hi-C Data

Chromatin-chromatin interactions and three-dimensional (3D) spatial structures are involved in transcriptional regulation and have a decisive role in DNA replication and repair. To understand how individual genes and their regulatory elements function within the larger genomic context, and how the genome reacts to environmental stimuli, the linear sequence information needs to be interpreted in three-dimensional space, which is still a challenging task. Here, we propose a novel, heuristic approach to represent Hi-C datasets by a whole-genomic pseudo-structure in 3D space. The baseline of our approach is the construction of a multigraph from genomic-sequence data and Hi-C interaction data, then applying a modified force-directed layout algorithm. The resulting layout is a pseudo-structure. While pseudo-structures are not based on direct observation and their details are inherent to settings, surprisingly, they demonstrate interesting, overall similarities of known genome structures of both barley and rice, namely, the Rabl and Rosette-like conformation. It has an exciting potential to be extended by additional omics data (RNA-seq, Chip-seq, etc.), allowing to visualize the dynamics of the pseudo-structures across various tissues or developmental stages. Furthermore, this novel method would make it possible to revisit most Hi-C data accumulated in the public domain in the last decade.

DNA fluctuations reveal the size and dynamics of topological domains

DNA supercoiling is a key regulatory mechanism that orchestrates DNA readout, recombination, and genome maintenance. DNA-binding proteins often mediate these processes by bringing two distant DNA sites together, thereby inducing (transient) topological domains. In order to understand the dynamics and molecular architecture of protein-induced topological domains in DNA, quantitative and time-resolved approaches are required. Here, we present a methodology to determine the size and dynamics of topological domains in supercoiled DNA in real time and at the single-molecule level. Our approach is based on quantifying the extension fluctuations-in addition to the mean extension-of supercoiled DNA in magnetic tweezers (MT). Using a combination of high-speed MT experiments, Monte Carlo simulations, and analytical theory, we map out the dependence of DNA extension fluctuations as a function of supercoiling density and external force. We find that in the plectonemic regime, the extension variance increases linearly with increasing supercoiling density and show how this enables us to determine the formation and size of topological domains. In addition, we demonstrate how the transient (partial) dissociation of DNA-bridging proteins results in the dynamic sampling of different topological states, which allows us to deduce the torsional stiffness of the plectonemic state and the kinetics of protein-plectoneme interactions. We expect our results to further the understanding and optimization of magnetic tweezer measurements and to enable quantification of the dynamics and reaction pathways of DNA processing enzymes in the context of physiologically relevant forces and supercoiling densities.

Circuit topology analysis of cellular genome reveals signature motifs, conformational heterogeneity, and scaling

Reciprocal regulation of genome topology and function is a fundamental and enduring puzzle in biology. The wealth of data provided by Hi-C libraries offers the opportunity to unravel this relationship. However, there is a need for a comprehensive theoretical framework in order to extract topological information for genome characterization and comparison. Here, we develop a toolbox for topological analysis based on Circuit Topology, allowing for the quantification of inter- and intracellular genomic heterogeneity, at various levels of fold complexity: pairwise contact arrangement, higher-order contact arrangement, and topological fractal dimension. Single-cell Hi-C data were analyzed and characterized based on topological content, revealing not only a strong multiscale heterogeneity but also highly conserved features such as a characteristic topological length scale and topological signature motifs in the genome. We propose that these motifs inform on the topological state of the nucleus and indicate the presence of active loop extrusion.

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Circuit topology quantifies heterogeneity in genomic arrangement

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Scale analysis reveals a characteristic length scale of 10 Mb in genome topology

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We identify highly conserved topological structures related to loop extrusion

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We suggest a topological model of chromatin arrangement for loop extrusion, the L-loop

Slow chromatin dynamics enhances promoter accessibility to transcriptional condensates

Enhancers are DNA sequences at a long genomic distance from target genes. Recent experiments suggest that enhancers are anchored to the surfaces of condensates of transcription machinery and that the loop extrusion process enhances the transcription level of their target genes. Here, we theoretically study the polymer dynamics driven by the loop extrusion of the linker DNA between an enhancer and the promoter of its target gene to calculate the contact probability of the promoter to the transcription machinery in the condensate. Our theory predicts that when the loop extrusion process is active, the contact probability increases with increasing linker DNA length. This finding reflects the fact that the relaxation time, with which the promoter stays in proximity to the surface of the transcriptional condensate, increases as the length of the linker DNA increases. This contrasts the equilibrium case for which the contact probability between the promoter and the transcription machineries is smaller for longer linker DNA lengths.

Longer DNA exhibits greater potential for cell-free gene expression

Cell-free gene expression systems have been valuable tools for understanding how transcription/translation can be regulated in living cells. Many studies have investigated the determining factors that affect gene expression. Here we report the effect of the length of linearized reporter DNAs encoding the firefly luciferase gene so as to exclude the influence of supercoiling. It is found that longer DNA molecules exhibit significantly greater potency in gene expression; for example, the expression level for DNA with 25.7 kbp is 1000-times higher than that for DNA of 1.7 kbp. AFM observation of the DNA conformation indicates that longer DNA takes shrunken conformation with a higher segment density in the reaction mixture for gene expression, in contrast to the stiff conformation of shorter DNA. We propose an underlying mechanism for the favorable effect of longer DNA on gene expression in terms of the enhancement of access of RNA polymerase to the shrunken conformation. It is expected that the enhancement of gene expression efficiency with a shrunken DNA conformation would also be a rather general mechanism in living cellular environments.

HiCEnterprise: identifying long range chromosomal contacts in Hi-C data

Motivation

Computational analysis of chromosomal contact data is currently gaining popularity with the rapid advance in experimental techniques providing access to a growing body of data. An important problem in this area is the identification of long range contacts between distinct chromatin regions. Such loops were shown to exist at different scales, either mediating relatively short range interactions between enhancers and promoters or providing interactions between much larger, distant chromosome domains. A proper statistical analysis as well as availability to a wide research community are crucial in a tool for this task.

Results

We present HiCEnterprise, a first freely available software tool for identification of long range chromatin contacts not only between small regions, but also between chromosomal domains. It implements four different statistical tests for identification of significant contacts for user defined regions or domains as well as necessary functions for input, output and visualization of chromosome contacts.

Availability

The software and the corresponding documentation are available at: github.com/regulomics/HiCEnterprise.

Supplementary information

Supplemental data are available in the online version of the article and at the website regulomics.mimuw.edu.pl/wp/hicenterprise.

The Nucleome Data Bank: web-based resources to simulate and analyze the three-dimensional genome

We introduce the Nucleome Data Bank (NDB), a web-based platform to simulate and analyze the three-dimensional (3D) organization of genomes. The NDB enables physics-based simulation of chromosomal structural dynamics through the MEGABASE + MiChroM computational pipeline. The input of the pipeline consists of epigenetic information sourced from the Encode database; the output consists of the trajectories of chromosomal motions that accurately predict Hi-C and fluorescence insitu hybridization data, as well as multiple observations of chromosomal dynamics in vivo. As an intermediate step, users can also generate chromosomal sub-compartment annotations directly from the same epigenetic input, without the use of any DNA-DNA proximity ligation data. Additionally, the NDB freely hosts both experimental and computational structural genomics data. Besides being able to perform their own genome simulations and download the hosted data, users can also analyze and visualize the same data through custom-designed web-based tools. In particular, the one-dimensional genetic and epigenetic data can be overlaid onto accurate 3D structures of chromosomes, to study the spatial distribution of genetic and epigenetic features. The NDB aims to be a shared resource to biologists, biophysicists and all genome scientists. The NDB is available at https://ndb.rice.edu.

The rich inner life of the cell nucleus: dynamic organization, active flows, and emergent rheology

The cell nucleus stores the genetic material essential for life, and provides the environment for transcription, maintenance, and replication of the genome. Moreover, the nucleoplasm is filled with subnuclear bodies such as nucleoli that are responsible for other vital functions. Overall, the nucleus presents a highly heterogeneous and dynamic environment with diverse functionality. Here, we propose that its biophysical complexity can be organized around three inter-related and interactive facets: heterogeneity, activity, and rheology. Most nuclear constituents are sites of active, ATP-dependent processes and are thus inherently dynamic: The genome undergoes constant rearrangement, the nuclear envelope flickers and fluctuates, nucleoli migrate and coalesce, and many of these events are mediated by nucleoplasmic flows and interactions. And yet there is spatiotemporal organization in terms of hierarchical structure of the genome, its coherently moving regions and membrane-less compartmentalization via phase-separated nucleoplasmic constituents. Moreover, the non-equilibrium or activity-driven nature of the nucleus gives rise to emergent rheology and material properties that impact all cellular processes via the central dogma of molecular biology. New biophysical insights into the cell nucleus can come from appreciating this rich inner life.

Robust and efficient gene regulation through localized nuclear microenvironments

Developmental enhancers drive gene expression in specific cell types during animal development. They integrate signals from many different sources mediated through the binding of transcription factors, producing specific responses in gene expression. Transcription factors often bind low-affinity sequences for only short durations. How brief, low-affinity interactions drive efficient transcription and robust gene expression is a central question in developmental biology. Localized high concentrations of transcription factors have been suggested as a possible mechanism by which to use these enhancer sites effectively. Here, we discuss the evidence for such transcriptional microenvironments, mechanisms for their formation and the biological consequences of such sub-nuclear compartmentalization for developmental decisions and evolution.

A sporadic case of congenital aniridia caused by pericentric inversion inv(11)(p13q14) associated with a 977 kb deletion in the 11p13 region

Background

Because of the significant occurrence of “WAGR-region” deletions among de novo mutations detected in congenital aniridia, DNA diagnosis is critical for all sporadic cases of aniridia due to its help in making an early diagnosis of WAGR syndrome. Standard cytogenetic karyotype study is a necessary step of molecular diagnostics in patients with deletions and in the patients’ parents as it reveals complex chromosomal rearrangements and the risk of having another affected child, as well as to provide prenatal and/or preimplantation diagnostics.

Case presentation

DNA samples were obtained from the proband (a 2-year-old boy) and his two healthy parents. Molecular analysis revealed a 977.065 kb deletion that removed loci of the ELP4, PAX6, and RCN1 genes but did not affect the coding sequence of the WT1 gene. The deletion occurred de novo on the paternal allele. The patient had normal karyotype 46,XY and a de novo pericentric inversion of chromosome 11, inv(11)(p13q14).

Conclusions

We confirmed the diagnosis of congenital aniridia at the molecular level. For the patient, the risk of developing Wilms’ tumor is similar to that in the general population. The recurrence risk for sibs in the family is low, but considering the possibility of gonadal mosaicism, it is higher than in the general population.

Circuit Topology Analysis of Polymer Folding Reactions

Circuit topology is emerging as a versatile measure to classify the internal structures of folded linear polymers such as proteins and nucleic acids. The topology framework can be applied to a wide range of problems, most notably molecular folding reactions that are central to biology and molecular engineering. In this Outlook, we discuss the state-of-the art of the technology and elaborate on the opportunities and challenges that lie ahead.

The self-stirred genome: large-scale chromatin dynamics, its biophysical origins and implications

The organization and dynamics of human genome govern all cellular processes - directly impacting the central dogma of biology - yet are poorly understood, especially at large length scales. Chromatin, the functional form of DNA in cells, undergoes frequent local remodeling and rearrangements to accommodate processes such as transcription, replication and DNA repair. How these local activities contribute to nucleus-wide coherent chromatin motion, where micron-scale regions of chromatin move together over several seconds, remains unclear. Activity of nuclear enzymes was found to drive the coherent chromatin dynamics, however, its biological nature and physical mechanism remain to be revealed. The coherent dynamics leads to a perpetual stirring of the genome, leading to collective gene dynamics over microns and seconds, thus likely contributing to local and global gene-expression patterns. Hence, a possible biological role of chromatin coherence may involve gene regulation.

Chromosome organization by a conserved condensin-ParB system in the actinobacterium Corynebacterium glutamicum

Higher-order chromosome folding and segregation are tightly regulated in all domains of life. In bacteria, details on nucleoid organization regulatory mechanisms and function remain poorly characterized, especially in non-model species. Here, we investigate the role of DNA-partitioning protein ParB and SMC condensin complexes in the actinobacterium Corynebacterium glutamicum. Chromosome conformation capture reveals SMC-mediated long-range interactions around ten centromere-like parS sites clustered at the replication origin (oriC). At least one oriC-proximal parS site is necessary for reliable chromosome segregation. We use chromatin immunoprecipitation and photoactivated single-molecule localization microscopy to show the formation of distinct, parS-dependent ParB-nucleoprotein subclusters. We further show that SMC/ScpAB complexes, loaded via ParB at parS sites, mediate chromosomal inter-arm contacts (as previously shown in Bacillus subtilis). However, the MukBEF-like SMC complex MksBEFG does not contribute to chromosomal DNA-folding; instead, this complex is involved in plasmid maintenance and interacts with the polar oriC-tethering factor DivIVA. Our results complement current models of ParB-SMC/ScpAB crosstalk and show that some condensin complexes evolved functions that are apparently uncoupled from chromosome folding.

The regulation of higher-order chromosome folding and segregation in bacteria is poorly understood. Here, Böhm et al. provide insights into the roles of DNA partitioning protein ParB and SMC condensin complexes in Corynebacterium glutamicum.

Translational nucleosome positioning: A computational study

About three-quarters of eukaryotic DNA is wrapped into nucleosomes; DNA spools with a protein core. The affinity of a given DNA stretch to be incorporated into a nucleosome is known to depend on the base-pair sequence-dependent geometry and elasticity of the DNA double helix. This causes the rotational and translational positioning of nucleosomes. In this study we ask the question whether the latter can be predicted by a simple coarse-grained DNA model with sequence-dependent elasticity, the rigid base-pair model. Whereas this model is known to be rather robust in predicting rotational nucleosome positioning, we show that the translational positioning is a rather subtle effect that is dominated by the guanine-cytosine content dependence of entropy rather than energy. A correct qualitative prediction within the rigid base-pair framework can only be achieved by assuming that DNA elasticity effectively changes on complexation into the nucleosome complex. With that extra assumption we arrive at a model which gives an excellent quantitative agreement to experimental in vitro nucleosome maps, under the additional assumption that nucleosomes equilibrate their positions only locally.

Organization of Chromosomal DNA by SMC Complexes

Structural maintenance of chromosomes (SMC) complexes are key organizers of chromosome architecture in all kingdoms of life. Despite seemingly divergent functions, such as chromosome segregation, chromosome maintenance, sister chromatid cohesion, and mitotic chromosome compaction, it appears that these complexes function via highly conserved mechanisms and that they represent a novel class of DNA translocases.

Structural and Dynamical Signatures of Local DNA Damage in Live Cells

The dynamic organization of chromatin inside the cell nucleus plays a key role in gene regulation and genome replication, as well as maintaining genome integrity. Although the static folded state of the genome has been extensively studied, dynamical signatures of processes such as transcription or DNA repair remain an open question. Here, we investigate the interphase chromatin dynamics in human cells in response to local DNA damage, specifically, DNA double-strand breaks (DSBs). Using simultaneous two-color spinning-disk confocal microscopy, we monitor the DSB dynamics and the compaction of the surrounding chromatin, visualized by fluorescently labeled 53BP1 and histone H2B, respectively. Our study reveals a surprising difference between the mobility of DSBs located in the nuclear interior versus periphery (less than 1 μm from the nuclear envelope), with the interior DSBs being almost twice as mobile as the periphery DSBs. Remarkably, we find that the DSB sites possess a robust structural signature in a form of a unique chromatin compaction profile. Moreover, our data show that the DSB motion is subdiffusive and ATP-dependent and exhibits unique dynamical signatures, different from those of undamaged chromatin. Our findings reveal that the DSB mobility follows a universal relationship defined solely by the physical parameters describing the DSBs and their local environment, such as the DSB focus size (represented by the local accumulation of 53BP1), DSB density, and the local chromatin compaction. This suggests that the DSB-related repair processes are robust and likely deterministic because the observed dynamical signatures (DSB mobility) can be explained solely by their structural features (DSB focus size, local chromatin compaction). Such knowledge might help in detecting local DNA damage in live cells, as well as in aiding our biophysical understanding of genome integrity in health and disease.

How the Genome Folds: The Biophysics of Four-Dimensional Chromatin Organization

The genetic information that instructs transcription and other cellular functions is carried by the chromosomes, polymers of DNA in complex with histones and other proteins. These polymers are folded inside nuclei five orders of magnitude smaller than their linear length, and many facets of this folding correlate with or are causally related to transcription and other cellular functions. Recent advances in sequencing and imaging-based techniques have enabled new views into several layers of chromatin organization. These experimental findings are accompanied by computational modeling efforts based on polymer physics that can provide mechanistic insights and quantitative predictions. Here, we review current knowledge of the main levels of chromatin organization, from the scale of nucleosomes to the entire nucleus, our current understanding of their underlying biophysical and molecular mechanisms, and some of their functional implications.

The biology and polymer physics underlying large-scale chromosome organization

Chromosome large-scale organization is a beautiful example of the interplay between physics and biology. DNA molecules are polymers and thus belong to the class of molecules for which physicists have developed models and formulated testable hypotheses to understand their arrangement and dynamic properties in solution, based on the principles of polymer physics. Biologists documented and discovered the biochemical basis for the structure, function and dynamic spatial organization of chromosomes in cells. The underlying principles of chromosome organization have recently been revealed in unprecedented detail using high-resolution chromosome capture technology that can simultaneously detect chromosome contact sites throughout the genome. These independent lines of investigation have now converged on a model in which DNA loops, generated by the loop extrusion mechanism, are the basic organizational and functional units of the chromosome.