Epigenomics in 3D: importance of long-range spreading and specific interactions in epigenomic maintenance

Role of diffusion and reaction of the constituents in spreading of histone modification marks

Cells switch genes ON or OFF by altering the state of chromatin via histone modifications at specific regulatory locations along the chromatin polymer. These gene regulation processes are carried out by a network of reactions in which the histone marks spread to neighboring regions with the help of enzymes. In the literature, this spreading has been studied as a purely kinetic, non-diffusive process considering the interactions between neighboring nucleosomes. In this work, we go beyond this framework and study the spreading of modifications using a reaction-diffusion (RD) model accounting for the diffusion of the constituents. We quantitatively segregate the modification profiles generated from kinetic and RD models. The diffusion and degradation of enzymes set a natural length scale for limiting the domain size of modification spreading, and the resulting enzyme limitation is inherent in our model. We also demonstrate the emergence of confined modification domains without the explicit requirement of a nucleation site. We explore polymer compaction effects on spreading and show that single-cell domains may differ from averaged profiles. We find that the modification profiles from our model are comparable with existing H3K9me3 data of S. pombe.

Nonequilibrium switching of segmental states can influence compaction of chromatin

Knowledge about the dynamic nature of chromatin organization is essential to understand the regulation of processes like DNA transcription and repair. The existing models of chromatin assume that protein organization and chemical states along chromatin are static and the 3D organization is purely a result of protein-mediated intra-chromatin interactions. Here we present a new hypothesis that certain nonequilibrium processes, such as switching of chemical and physical states due to nucleosome assembly/disassembly or gene repression/activation, can also simultaneously influence chromatin configurations. To understand the implications of this inherent nonequilibrium switching, we present a block copolymer model of chromatin, with switching of its segmental states between two states, mimicking active/repressed or protein unbound/bound states. We show that competition between switching timescale Tt, polymer relaxation timescale τp, and segmental relaxation timescale τs can lead to non-trivial changes in chromatin organization, leading to changes in local compaction and contact probabilities. As a function of the switching timescale, the radius of gyration of chromatin shows a non-monotonic behavior with a prominent minimum when Tt ≈ τp and a maximum when Tt ≈ τs. We find that polymers with a small segment length exhibit a more compact structure than those with larger segment lengths. We also find that the switching can lead to higher contact probability and better mixing of far-away segments. Our study also shows that the nature of the distribution of chromatin clusters varies widely as we change the switching rate.

Dynamical phase transition in models that couple chromatin folding with histone modifications

Genomic regions can acquire heritable epigenetic states through unique histone modifications, which lead to stable gene expression patterns without altering the underlying DNA sequence. However, the relationship between chromatin conformational dynamics and epigenetic stability is poorly understood. In this paper, we propose kinetic models to investigate the dynamic fluctuations of histone modifications and the spatial interactions between nucleosomes. Our model explicitly incorporates the influence of chemical modifications on the structural stability of chromatin and the contribution of chromatin contacts to the cooperative nature of chemical reactions. Through stochastic simulations and analytical theory, we have discovered distinct steady-state outcomes in different kinetic regimes, resembling a dynamical phase transition. Importantly, we have validated that the emergence of this transition, which occurs on biologically relevant timescales, is robust against variations in model design and parameters. Our findings suggest that the viscoelastic properties of chromatin and the timescale at which it transitions from a gel-like to a liquidlike state significantly impact dynamic processes that occur along the one-dimensional DNA sequence.

Two-way feedback between chromatin compaction and histone modification state explains Saccharomyces cerevisiae heterochromatin bistability

Compact chromatin is closely linked with gene silencing in part by sterically masking access to promoters, inhibiting transcription factor binding and preventing polymerase from efficiently transcribing a gene. However, a broader hypothesis suggests that chromatin compaction can be both a cause and a consequence of the locus histone modification state, with a tight bidirectional interaction underpinning bistable transcriptional states. To rigorously test this hypothesis, we developed a mathematical model for the dynamics of the HMR locus in Saccharomyces cerevisiae, that incorporates activating histone modifications, silencing proteins, and a dynamic, acetylation-dependent, three-dimensional locus size. Chromatin compaction enhances silencer protein binding, which in turn feeds back to remove activating histone modifications, leading to further compaction. The bistable output of the model was in good agreement with prior quantitative data, including switching rates from expressed to silent states (and vice versa), and protein binding/histone modification levels within the locus. We then tested the model by predicting changes in switching rates as the genetic length of the locus was increased, which were then experimentally verified. Such bidirectional feedback between chromatin compaction and the histone modification state may be a widespread and important regulatory mechanism given the hallmarks of many heterochromatic regions: physical chromatin compaction and dimerizing (or multivalent) silencing proteins.

Design principles of 3D epigenetic memory systems

Cells remember their identities, in part, by using epigenetic marks-chemical modifications placed along the genome. How can mark patterns remain stable over cell generations despite their constant erosion by replication and other processes? We developed a theoretical model that reveals that three-dimensional (3D) genome organization can stabilize epigenetic memory as long as (i) there is a large density difference between chromatin compartments, (ii) modifying "reader-writer" enzymes spread marks in three dimensions, and (iii) the enzymes are limited in abundance relative to their histone substrates. Analogous to an associative memory that encodes memory in neuronal connectivity, mark patterns are encoded in a 3D network of chromosomal contacts. Our model provides a unified account of diverse observations and reveals a key role of 3D genome organization in epigenetic memory.

HP1-driven phase separation recapitulates the thermodynamics and kinetics of heterochromatin condensate formation

The spatial segregation of pericentromeric heterochromatin (PCH) into distinct, membrane-less nuclear compartments involves the binding of Heterochromatin Protein 1 (HP1) to H3K9me2/3-rich genomic regions. While HP1 exhibits liquid-liquid phase separation properties in vitro, its mechanistic impact on the structure and dynamics of PCH condensate formation in vivo remains largely unresolved. Here, using a minimal theoretical framework, we systematically investigate the mutual coupling between self-interacting HP1-like molecules and the chromatin polymer. We reveal that the specific affinity of HP1 for H3K9me2/3 loci facilitates coacervation in nucleo and promotes the formation of stable PCH condensates at HP1 levels far below the concentration required to observe phase separation in purified protein assays in vitro. These heterotypic HP1-chromatin interactions give rise to a strong dependence of the nucleoplasmic HP1 density on HP1-H3K9me2/3 stoichiometry, consistent with the thermodynamics of multicomponent phase separation. The dynamical cross talk between HP1 and the viscoelastic chromatin scaffold also leads to anomalously slow equilibration kinetics, which strongly depend on the genomic distribution of H3K9me2/3 domains and result in the coexistence of multiple long-lived, microphase-separated PCH compartments. The morphology of these complex coacervates is further found to be governed by the dynamic establishment of the underlying H3K9me2/3 landscape, which may drive their increasingly abnormal, aspherical shapes during cell development. These findings compare favorably to 4D microscopy measurements of HP1 condensate formation in live Drosophila embryos and suggest a general quantitative model of PCH formation based on the interplay between HP1-based phase separation and chromatin polymer mechanics.

Two-way feedback between chromatin compaction and histone modification state explains S. cerevisiae heterochromatin bistability

Compact chromatin is closely linked with gene silencing in part by sterically masking access to promoters, inhibiting transcription factor binding and preventing polymerase from efficiently transcribing a gene. Here, we propose a broader view: chromatin compaction can be both a cause and a consequence of the histone modification state, and this tight bidirectional interaction can underpin bistable transcriptional states. To test this theory, we developed a mathematical model for the dynamics of the HMR locus in S. cerevisiae, that incorporates activating histone modifications, silencing proteins and a dynamic, acetylation-dependent, three-dimensional locus size. Chromatin compaction enhances silencer protein binding, which in turn feeds back to remove activating histone modifications, leading to further compaction. The bistable output of the model was in good agreement with prior quantitative data, including switching rates from expressed to silent states, and vice versa, and protein binding levels within the locus. We then tested the model by predicting changes in switching rates as the genetic length of the locus was increased, which were then experimentally verified. This bidirectional feedback between chromatin compaction and the histone modification state may be an important regulatory mechanism at many loci.

Epigenetic switching with asymmetric bridging interactions

Gene expression states are often stably sustained in cis despite massively disruptive events like DNA replication. This is achieved by on-going enzymatic activity that maintains parts of the DNA in either heterochromatic (packed) or euchromatic (free) states, each of which is stabilized by both positive feedback and bridging interactions between individual nucleosomes. In contrast to condensed matter, however, the dynamics is not only governed by equilibrium binding interactions but is also mediated by enzymes that recognize and act on specific amino acid tails of the nucleosomes. The mechanical result is that some nucleosomes can bind to one another and form tightly packed polymer configurations, whereas others remain unbound and form free, noncompact polymer configurations. Here, we study the consequences of such an asymmetric interaction pattern on the dynamics of epigenetic switching. We develop a 3D polymer model and show that traits associated with epigenetic switching, such as bistability and epigenetic memory, are permitted by such a model. We find, however, that the experimentally observed burst-like nature of some epigenetic switches is difficult to reproduce by this biologically motivated interaction. Instead, the behavior seen in experiments can be explained by introducing partial confinement, which particularly affects the euchromatic regions of the chromosome.

Phase transitions in heterochromatin organization

Heterochromatin formation has been proposed to involve phase transitions on the level of the three-dimensional folding of heterochromatin regions and the liquid-liquid demixing of heterochromatin proteins. Here, I outline the hallmarks of such transitions and the current challenges to detect them in living cells. I further discuss the abundance and properties of prominent heterochromatin proteins and relate them to their potential role in driving phase transitions. Recent data from mouse fibroblasts indicate that pericentric heterochromatin is organized via a reordering transition on the level of heterochromatin regions that does not necessarily involve liquid-liquid demixing of heterochromatin proteins. Evaluating key hallmarks of the different candidate phase transition mechanisms across cell types and species will be needed to complete the current picture.

4D epigenomics: deciphering the coupling between genome folding and epigenomic regulation with biophysical modeling

Recent experimental observations suggest a strong coupling between the 3D nuclear chromosome organization and epigenomics. However, the mechanistic and functional bases of such interplay remain elusive. In this review, we describe how biophysical modeling has been instrumental in characterizing how genome folding may impact the formation of epigenomic domains and, conversely, how epigenomic marks may affect chromosome conformation. Finally, we discuss how this mutual feedback loop between chromatin organization and epigenome regulation, via the formation of physicochemical nanoreactors, may represent a key functional role of 3D compartmentalization in the assembly and maintenance of stable - but yet plastic - epigenomic landscapes.

Dynamical modeling of the H3K27 epigenetic landscape in mouse embryonic stem cells

The Polycomb system via the methylation of the lysine 27 of histone H3 (H3K27) plays central roles in the silencing of many lineage-specific genes during development. Recent experimental evidence suggested that the recruitment of histone modifying enzymes like the Polycomb repressive complex 2 (PRC2) at specific sites and their spreading capacities from these sites are key to the establishment and maintenance of a proper epigenomic landscape around Polycomb-target genes. Here, to test whether such mechanisms, as a minimal set of qualitative rules, are quantitatively compatible with data, we developed a mathematical model that can predict the locus-specific distributions of H3K27 modifications based on previous biochemical knowledge. Within the biological context of mouse embryonic stem cells, our model showed quantitative agreement with experimental profiles of H3K27 acetylation and methylation around Polycomb-target genes in wild-type and mutants. In particular, we demonstrated the key role of the reader-writer module of PRC2 and of the competition between the binding of activating and repressing enzymes in shaping the H3K27 landscape around transcriptional start sites. The predicted dynamics of establishment and maintenance of the repressive trimethylated H3K27 state suggest a slow accumulation, in perfect agreement with experiments. Our approach represents a first step towards a quantitative description of PcG regulation in various cellular contexts and provides a generic framework to better characterize epigenetic regulation in normal or disease situations.

Painters in chromatin: a unified quantitative framework to systematically characterize epigenome regulation and memory

In eukaryotes, many stable and heritable phenotypes arise from the same DNA sequence, owing to epigenetic regulatory mechanisms relying on the molecular cooperativity of 'reader-writer' enzymes. In this work, we focus on the fundamental, generic mechanisms behind the epigenome memory encoded by post-translational modifications of histone tails. Based on experimental knowledge, we introduce a unified modeling framework, the painter model, describing the mechanistic interplay between sequence-specific recruitment of chromatin regulators, chromatin-state-specific reader-writer processes and long-range spreading mechanisms. A systematic analysis of the model building blocks highlights the crucial impact of tridimensional chromatin organization and state-specific recruitment of enzymes on the stability of epigenomic domains and on gene expression. In particular, we show that enhanced 3D compaction of the genome and enzyme limitation facilitate the formation of ultra-stable, confined chromatin domains. The model also captures how chromatin state dynamics impact the intrinsic transcriptional properties of the region, slower kinetics leading to noisier expression. We finally apply our framework to analyze experimental data, from the propagation of γH2AX around DNA breaks in human cells to the maintenance of heterochromatin in fission yeast, illustrating how the painter model can be used to extract quantitative information on epigenomic molecular processes.

Nucleosome sliding can influence the spreading of histone modifications

Nucleosomes are the fundamental building blocks of chromatin that not only help in the folding of chromatin, but also in carrying epigenetic information. It is known that nucleosome sliding is responsible for dynamically organizing chromatin structure and the resulting gene regulation. Since sliding can move two neighboring nucleosomes physically close or away, can it play a role in the spreading of histone modifications? We investigate this by simulating a stochastic model that couples nucleosome dynamics with the kinetics of histone modifications. We show that the sliding of nucleosomes can affect the modification pattern as well as the time it takes to modify a given region of chromatin. Exploring different nucleosome densities and modification kinetic parameters, we show that nucleosome sliding can be important for creating histone modification domains. Our model predicts that nucleosome density coupled with sliding dynamics can create an asymmetric histone modification profile around regulatory regions. We also compute the probability distribution of modified nucleosomes and relaxation kinetics of modifications. Our predictions are comparable with known experimental results.

Dissecting cell fate dynamics in pediatric glioblastoma through the lens of complex systems and cellular cybernetics

Cancers are complex dynamic ecosystems. Reductionist approaches to science are inadequate in characterizing their self-organized patterns and collective emergent behaviors. Since current approaches to single-cell analysis in cancer systems rely primarily on single time-point multiomics, many of the temporal features and causal adaptive behaviors in cancer dynamics are vastly ignored. As such, tools and concepts from the interdisciplinary paradigm of complex systems theory are introduced herein to decode the cellular cybernetics of cancer differentiation dynamics and behavioral patterns. An intuition for the attractors and complex networks underlying cancer processes such as cell fate decision-making, multiscale pattern formation systems, and epigenetic state-transitions is developed. The applications of complex systems physics in paving targeted therapies and causal pattern discovery in precision oncology are discussed. Pediatric high-grade gliomas are discussed as a model-system to demonstrate that cancers are complex adaptive systems, in which the emergence and selection of heterogeneous cellular states and phenotypic plasticity are driven by complex multiscale network dynamics. In specific, pediatric glioblastoma (GBM) is used as a proof-of-concept model to illustrate the applications of the complex systems framework in understanding GBM cell fate decisions and decoding their adaptive cellular dynamics. The scope of these tools in forecasting cancer cell fate dynamics in the emerging field of computational oncology and patient-centered systems medicine is highlighted.

A Review of Mathematical and Computational Methods in Cancer Dynamics

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems medicine. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems, and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored.

Heterogeneous interactions and polymer entropy decide organization and dynamics of chromatin domains

Chromatin is known to be organized into multiple domains of varying sizes and compaction. While these domains are often imagined as static structures, they are highly dynamic and show cell-to-cell variability. Since processes such as gene regulation and DNA replication occur in the context of these domains, it is important to understand their organization, fluctuation, and dynamics. To simulate chromatin domains, one requires knowledge of interaction strengths among chromatin segments. Here, we derive interaction-strength parameters from experimentally known contact maps and use them to predict chromatin organization and dynamics. Taking two domains on the human chromosome as examples, we investigate its three-dimensional organization, size/shape fluctuations, and dynamics of different segments within a domain, accounting for hydrodynamic effects. Considering different cell types, we quantify changes in interaction strengths and chromatin shape fluctuations in different epigenetic states. Perturbing the interaction strengths systematically, we further investigate how epigenetic-like changes can alter the spatio-temporal nature of the domains. Our results show that heterogeneous weak interactions are crucial in determining the organization of the domains. Computing effective stiffness and relaxation times, we investigate how perturbations in interactions affect the solid- and liquid-like nature of chromatin domains. Quantifying dynamics of chromatin segments within a domain, we show how the competition between polymer entropy and interaction energy influence the timescales of loop formation and maintenance of stable loops.

Chromatin dynamics controls epigenetic domain formation

In multicellular organisms, nucleosomes carry epigenetic information that defines distinct patterns of gene expression, which are inherited over multiple generations. The enhanced capacity for information storage arises by nucleosome modifications, which are triggered by enzymes. Modified nucleosomes can transfer the mark to others that are in proximity by a positive-feedback (modification begets modification) mechanism. We created a generic polymer model, referred to as 3DSpreader, in which each bead, representing a nucleosome, stochastically switches between unmodified (U) and modified (M) states depending on the states of the neighbors. Modification begins at a specific nucleation site (NS) that is permanently in the M state, and could spread to other loci that is dictated by chromatin dynamics. Transfer of marks among the non-nucleation loci occurs stochastically as chromatin evolves in time. If the spreading rate is slower than the chromatin relaxation rate, which is biologically pertinent, then finite-sized domains form, driven by contacts between nucleosomes through a three-dimensional looping mechanism. Surprisingly, simulations based on the 3DSpreader model result in finite bounded domains that arise without the need for any boundary elements. Maintenance of spatially and temporally stable domains requires the presence of the NS, whose removal eliminates finite-sized modified domains. The theoretical predictions are in excellent agreement with experimental data for H3K9me3 spreading in mouse embryonic stem cells.

The transcription factor Atf1 lowers the transition barrier for nucleosome-mediated establishment of heterochromatin

Transcription factors can exert opposite effects depending on the chromosomal context. The fission yeast transcription factor Atf1 both activates numerous genes in response to stresses and mediates heterochromatic gene silencing in the mating-type region. Investigating this context dependency, we report here that the establishment of silent heterochromatin in the mating-type region occurs at a reduced rate in the absence of Atf1 binding. Quantitative modeling accounts for the observed establishment profiles by a combinatorial recruitment of histone-modifying enzymes: locally by Atf1 at two binding sites and over the whole region by dynamically appearing heterochromatic nucleosomes, a source of which is the RNAi-dependent cenH element. In the absence of Atf1 binding, the synergy is lost, resulting in a slow rate of heterochromatin formation. The system shows how DNA-binding proteins can influence local nucleosome states and thereby potentiate long-range positive feedback on histone-modification reactions to enable heterochromatin formation over large regions in a context-dependent manner.

DNA sequence-dependent formation of heterochromatin nanodomains

The mammalian epigenome contains thousands of heterochromatin nanodomains (HNDs) marked by di- and trimethylation of histone H3 at lysine 9 (H3K9me2/3), which have a typical size of 3–10 nucleosomes. However, what governs HND location and extension is only partly understood. Here, we address this issue by introducing the chromatin hierarchical lattice framework (ChromHL) that predicts chromatin state patterns with single-nucleotide resolution. ChromHL is applied to analyse four HND types in mouse embryonic stem cells that are defined by histone methylases SUV39H1/2 or GLP, transcription factor ADNP or chromatin remodeller ATRX. We find that HND patterns can be computed from PAX3/9, ADNP and LINE1 sequence motifs as nucleation sites and boundaries that are determined by DNA sequence (e.g. CTCF binding sites), cooperative interactions between nucleosomes as well as nucleosome-HP1 interactions. Thus, ChromHL rationalizes how patterns of H3K9me2/3 are established and changed via the activity of protein factors in processes like cell differentiation.

The ability to predict epigenetic regulation is an important challenge in biology. Here the authors describe heterochromatin nanodomains (HNDs) and compare four different types of H3K9me2/3-marked HNDs in mouse embryonic stem cells. They further develop a computational framework to predict genome-wide HND maps from DNA sequence and protein concentrations, at single-nucleotide resolution.

Chromatin Structure and Dynamics: Focus on Neuronal Differentiation and Pathological Implication

Chromatin structure is an essential regulator of gene expression. Its state of compaction contributes to the regulation of genetic programs, in particular during differentiation. Epigenetic processes, which include post-translational modifications of histones, DNA methylation and implication of non-coding RNA, are powerful regulators of gene expression. Neurogenesis and neuronal differentiation are spatio-temporally regulated events that allow the formation of the central nervous system components. Here, we review the chromatin structure and post-translational histone modifications associated with neuronal differentiation. Studying the impact of histone modifications on neuronal differentiation improves our understanding of the pathophysiological mechanisms of chromatinopathies and opens up new therapeutic avenues. In addition, we will discuss techniques for the analysis of histone modifications on a genome-wide scale and the pathologies associated with the dysregulation of the epigenetic machinery.

Epigenetic patterns in a complete human genome

The completion of a telomere-to-telomere human reference genome, T2T-CHM13, has resolved complex regions of the genome, including repetitive and homologous regions. Here, we present a high-resolution epigenetic study of previously unresolved sequences, representing entire acrocentric chromosome short arms, gene family expansions, and a diverse collection of repeat classes. This resource precisely maps CpG methylation (32.28 million CpGs), DNA accessibility, and short-read datasets (166,058 previously unresolved chromatin immunoprecipitation sequencing peaks) to provide evidence of activity across previously unidentified or corrected genes and reveals clinically relevant paralog-specific regulation. Probing CpG methylation across human centromeres from six diverse individuals generated an estimate of variability in kinetochore localization. This analysis provides a framework with which to investigate the most elusive regions of the human genome, granting insights into epigenetic regulation.

Methylation of Subtelomeric Chromatin Modifies the Expression of the lncRNA TERRA, Disturbing Telomere Homeostasis

The long noncoding RNA (lncRNA) telomeric repeat-containing RNA (TERRA) has been associated with telomeric homeostasis, telomerase recruitment, and the process of chromosome healing; nevertheless, the impact of this association has not been investigated during the carcinogenic process. Determining whether changes in TERRA expression are a cause or a consequence of cell transformation is a complex task because studies are usually carried out using either cancerous cells or tumor samples. To determine the role of this lncRNA in cellular aging and chromosome healing, we evaluated telomeric integrity and TERRA expression during the establishment of a clone of untransformed myeloid cells. We found that reduced expression of TERRA disturbed the telomeric homeostasis of certain loci, but the expression of the lncRNA was affected only when the methylation of subtelomeric bivalent chromatin domains was compromised. We conclude that the disruption in TERRA homeostasis is a consequence of cellular transformation and that changes in its expression profile can lead to telomeric and genomic instability.

Does the Expression and Epigenetics of Genes Involved in Monogenic Forms of Parkinson’s Disease Influence Sporadic Forms?

Parkinson’s disease (PD) is a disorder characterized by a triad of motor symptoms (akinesia, rigidity, resting tremor) related to loss of dopaminergic neurons mainly in the Substantia nigra pars compacta. Diagnosis is often made after a substantial loss of neurons has already occurred, and while dopamine replacement therapies improve symptoms, they do not modify the course of the disease. Although some biological mechanisms involved in the disease have been identified, such as oxidative stress and accumulation of misfolded proteins, they do not explain entirely PD pathophysiology, and a need for a better understanding remains. Neurodegenerative diseases, including PD, appear to be the result of complex interactions between genetic and environmental factors. The latter can alter gene expression by causing epigenetic changes, such as DNA methylation, post-translational modification of histones and non-coding RNAs. Regulation of genes responsible for monogenic forms of PD may be involved in sporadic PD. This review will focus on the epigenetic mechanisms regulating their expression, since these are the genes for which we currently have the most information available. Despite technical challenges, epigenetic epidemiology offers new insights on revealing altered biological pathways and identifying predictive biomarkers for the onset and progression of PD.

Non-cooperative mechanism for bounded and ultrasensitive chromatin remodeling

Chromatin remodeling is an essential form of gene regulation that is involved in a variety of biological processes. We develop a theoretical model that takes advantage of percolation effects at the level of nucleosome interactions, which allows for ultrasensitive chromatin expansion. This model is non-cooperative and readily provides spatial bounds to the expansion region, preventing uncontrolled remodeling events. We explore different chromatin architectures and the ultrasensitivity of the chromatin density as a function of transcription factor concentration. We also compare our model with experimental data involving an inhibitor of nucleosome acetylation. These results suggest a novel mechanism for spatially-bounded chromatin remodeling and they provide means for quantitative comparisons between proposed models of chromatin architecture.

High fidelity epigenetic inheritance: Information theoretic model predicts threshold filling of histone modifications post replication

During cell devision, maintaining the epigenetic information encoded in histone modification patterns is crucial for survival and identity of cells. The faithful inheritance of the histone marks from the parental to the daughter strands is a puzzle, given that each strand gets only half of the parental nucleosomes. Mapping DNA replication and reconstruction of modifications to equivalent problems in communication of information, we ask how well enzymes can recover the parental modifications, if they were ideal computing machines. Studying a parameter regime where realistic enzymes can function, our analysis predicts that enzymes may implement a critical threshold filling algorithm which fills unmodified regions of length at most k. This algorithm, motivated from communication theory, is derived from the maximum à posteriori probability (MAP) decoding which identifies the most probable modification sequence based on available observations. Simulations using our method produce modification patterns similar to what has been observed in recent experiments. We also show that our results can be naturally extended to explain inheritance of spatially distinct antagonistic modifications.

A Liquid State Perspective on Dynamics of Chromatin Compartments

The interior of the eukaryotic cell nucleus has a crowded and heterogeneous environment packed with chromatin polymers, regulatory proteins, and RNA molecules. Chromatin polymer, assisted by epigenetic modifications, protein and RNA binders, forms multi-scale compartments which help regulate genes in response to cellular signals. Furthermore, chromatin compartments are dynamic and tend to evolve in size and composition in ways that are not fully understood. The latest super-resolution imaging experiments have revealed a much more dynamic and stochastic nature of chromatin compartments than was appreciated before. An emerging mechanism explaining chromatin compartmentalization dynamics is the phase separation of protein and nucleic acids into membraneless liquid condensates. Consequently, concepts and ideas from soft matter and polymer systems have been rapidly entering the lexicon of cell biology. In this respect, the role of computational models is crucial for establishing a rigorous and quantitative foundation for the new concepts and disentangling the complex interplay of forces that contribute to the emergent patterns of chromatin dynamics and organization. Several multi-scale models have emerged to address various aspects of chromatin dynamics, ranging from equilibrium polymer simulations, hybrid non-equilibrium simulations coupling protein binding and chromatin folding, and mesoscopic field-theoretic models. Here, we review these emerging theoretical paradigms and computational models with a particular focus on chromatin’s phase separation and liquid-like properties as a basis for nuclear organization and dynamics.

Spatial organization of chromosomes leads to heterogeneous chromatin motion and drives the liquid- or gel-like dynamical behavior of chromatin

Chromosome organization and dynamics are involved in regulating many fundamental processes such as gene transcription and DNA repair. Experiments unveiled that chromatin motion is highly heterogeneous inside cell nuclei, ranging from a liquid-like, mobile state to a gel-like, rigid regime. Using polymer modeling, we investigate how these different physical states and dynamical heterogeneities may emerge from the same structural mechanisms. We found that the formation of topologically associating domains (TADs) is a key driver of chromatin motion heterogeneity. In particular, we showed that the local degree of compaction of the TAD regulates the transition from a weakly compact, fluid state of chromatin to a more compact, gel state exhibiting anomalous diffusion and coherent motion. Our work provides a comprehensive study of chromosome dynamics and a unified view of chromatin motion enabling interpretation of the wide variety of dynamical behaviors observed experimentally across different biological conditions, suggesting that the "liquid" or "solid" state of chromatin are in fact two sides of the same coin.

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.

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.

Integration of Epigenetic Mechanisms into Non-Genotoxic Carcinogenicity Hazard Assessment: Focus on DNA Methylation and Histone Modifications

Epigenetics involves a series of mechanisms that entail histone and DNA covalent modifications and non-coding RNAs, and that collectively contribute to programing cell functions and differentiation. Epigenetic anomalies and DNA mutations are co-drivers of cellular dysfunctions, including carcinogenesis. Alterations of the epigenetic system occur in cancers whether the initial carcinogenic events are from genotoxic (GTxC) or non-genotoxic (NGTxC) carcinogens. NGTxC are not inherently DNA reactive, they do not have a unifying mode of action and as yet there are no regulatory test guidelines addressing mechanisms of NGTxC. To fil this gap, the Test Guideline Programme of the Organisation for Economic Cooperation and Development is developing a framework for an integrated approach for the testing and assessment (IATA) of NGTxC and is considering assays that address key events of cancer hallmarks. Here, with the intent of better understanding the applicability of epigenetic assays in chemical carcinogenicity assessment, we focus on DNA methylation and histone modifications and review: (1) epigenetic mechanisms contributing to carcinogenesis, (2) epigenetic mechanisms altered following exposure to arsenic, nickel, or phenobarbital in order to identify common carcinogen-specific mechanisms, (3) characteristics of a series of epigenetic assay types, and (4) epigenetic assay validation needs in the context of chemical hazard assessment. As a key component of numerous NGTxC mechanisms of action, epigenetic assays included in IATA assay combinations can contribute to improved chemical carcinogen identification for the better protection of public health.

Understanding 3D genome organization by multidisciplinary methods

Understanding how chromatin is folded in the nucleus is fundamental to understanding its function. Although 3D genome organization has been historically difficult to study owing to a lack of relevant methodologies, major technological breakthroughs in genome-wide mapping of chromatin contacts and advances in imaging technologies in the twenty-first century considerably improved our understanding of chromosome conformation and nuclear architecture. In this Review, we discuss methods of 3D genome organization analysis, including sequencing-based techniques, such as Hi-C and its derivatives, Micro-C, DamID and others; microscopy-based techniques, such as super-resolution imaging coupled with fluorescence in situ hybridization (FISH), multiplex FISH, in situ genome sequencing and live microscopy methods; and computational and modelling approaches. We describe the most commonly used techniques and their contribution to our current knowledge of nuclear architecture and, finally, we provide a perspective on up-and-coming methods that open possibilities for future major discoveries.

3D genome organisation in Drosophila

Ever since Thomas Hunt Morgan's discovery of the chromosomal basis of inheritance by using Drosophila melanogaster as a model organism, the fruit fly has remained an essential model system in studies of genome biology, including chromatin organisation. Very much as in vertebrates, in Drosophila, the genome is organised in territories, compartments and topologically associating domains (TADs). However, these domains might be formed through a slightly different mechanism than in vertebrates due to the presence of a large and potentially redundant set of insulator proteins and the minor role of dCTCF in TAD boundary formation. Here, we review the different levels of chromatin organisation in Drosophila and discuss mechanisms and factors that might be involved in TAD formation. The dynamics of TADs and enhancer-promoter interactions in the context of transcription are covered in the light of currently conflicting results. Finally, we illustrate the value of polymer modelling approaches to infer the principles governing the three-dimensional organisation of the Drosophila genome.

Multiscale modeling of genome organization with maximum entropy optimization

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.

The hierarchical packing of euchromatin domains can be described as multiplicative cascades

The genome is packed into the cell nucleus in the form of chromatin. Biochemical approaches have revealed that chromatin is packed within domains, which group into larger domains, and so forth. Such hierarchical packing is equally visible in super-resolution microscopy images of large-scale chromatin organization. While previous work has suggested that chromatin is partitioned into distinct domains via microphase separation, it is unclear how these domains organize into this hierarchical packing. A particular challenge is to find an image analysis approach that fully incorporates such hierarchical packing, so that hypothetical governing mechanisms of euchromatin packing can be compared against the results of such an analysis. Here, we obtain 3D STED super-resolution images from pluripotent zebrafish embryos labeled with improved DNA fluorescence stains, and demonstrate how the hierarchical packing of euchromatin in these images can be described as multiplicative cascades. Multiplicative cascades are an established theoretical concept to describe the placement of ever-smaller structures within bigger structures. Importantly, these cascades can generate artificial image data by applying a single rule again and again, and can be fully specified using only four parameters. Here, we show how the typical patterns of euchromatin organization are reflected in the values of these four parameters. Specifically, we can pinpoint the values required to mimic a microphase-separated state of euchromatin. We suggest that the concept of multiplicative cascades can also be applied to images of other types of chromatin. Here, cascade parameters could serve as test quantities to assess whether microphase separation or other theoretical models accurately reproduce the hierarchical packing of chromatin.

Establishment of heterochromatin in domain-size-dependent bursts

Methylation of histone H3K9 is a hallmark of epigenetic silencing in eukaryotes. Nucleosome modifications often rely on positive feedback where enzymes are recruited by modified nucleosomes. A combination of local and global feedbacks has been proposed to account for some dynamic properties of heterochromatin, but the range at which the global feedbacks operate and the exact mode of heterochromatin propagation are not known. We investigated these questions in fission yeast. Guided by mathematical modeling, we incrementally increased the size of the mating-type region and profiled heterochromatin establishment over time. We observed exponential decays in the proportion of cells with active reporters, with rates that decreased with domain size. Establishment periods varied from a few generations in wild type to >200 generations in the longest region examined, and highly correlated silencing of two reporters located outside the nucleation center was observed. On a chromatin level, this indicates that individual regions are silenced in sudden bursts. Mathematical modeling accounts for these bursts if heterochromatic nucleosomes facilitate a deacetylation or methylation reaction at long range, in a distance-independent manner. A likely effector of three-dimensional interactions is the evolutionarily conserved Swi6^HP1 H3K9me reader, indicating the bursting behavior might be a general mode of heterochromatin propagation.

Transcription organizes euchromatin via microphase separation

In eukaryotes, DNA is packed inside the cell nucleus in the form of chromatin, which consists of DNA, proteins such as histones, and RNA. Euchromatin, which is permissive for transcription, is spatially organized into transcriptionally inactive domains interspersed with pockets of transcriptional activity. While transcription and RNA have been implicated in euchromatin organization, it remains unclear how their interplay forms and maintains transcription pockets. Here we combine theory and experiment to analyze the dynamics of euchromatin organization as pluripotent zebrafish cells exit mitosis and begin transcription. We show that accumulation of RNA induces formation of transcription pockets which displace transcriptionally inactive chromatin. We propose that the accumulating RNA recruits RNA-binding proteins that together tend to separate from transcriptionally inactive euchromatin. Full phase separation is prevented because RNA remains tethered to transcribed euchromatin through RNA polymerases. Instead, smaller scale microphases emerge that do not grow further and form the typical pattern of euchromatin organization.

Using computational modelling to reveal mechanisms of epigenetic Polycomb control

The Polycomb system is essential for stable gene silencing in many organisms. This regulation is achieved in part through addition of the histone modifications H3K27me2/me3 by Polycomb Repressive Complex 2 (PRC2). These modifications are believed to be the causative epigenetic memory elements of PRC2-mediated silencing. As these marks are stored locally in the chromatin, PRC2-based memory is a cis-acting system. A key feature of stable epigenetic memory in cis is PRC2-mediated, self-reinforcing feedback from K27-methylated histones onto nearby histones in a read-write paradigm. However, it was not clear under what conditions such feedback can lead to stable memory, able, for example, to survive the perturbation of histone dilution at DNA replication. In this context, computational modelling has allowed a rigorous exploration of possible underlying memory mechanisms and has also greatly accelerated our understanding of switching between active and silenced states. Specifically, modelling has predicted that switching and memory at Polycomb loci is digital, with a locus being either active or inactive, rather than possessing intermediate, smoothly varying levels of activation. Here, we review recent advances in models of Polycomb control, focusing on models of epigenetic switching through nucleation and spreading of H3K27me2/me3. We also examine models that incorporate transcriptional feedback antagonism and those including bivalent chromatin states. With more quantitative experimental data on histone modification kinetics, as well as single-cell resolution data on transcription and protein levels for PRC2 targets, we anticipate an expanded need for modelling to help dissect increasingly interconnected and complex memory mechanisms.

From whole-mount to single-cell spatial assessment of gene expression in 3D

Unravelling spatio-temporal patterns of gene expression is crucial to understanding core biological principles from embryogenesis to disease. Here we review emerging technologies, providing automated, high-throughput, spatially resolved quantitative gene expression data. Novel techniques expand on current benchmark protocols, expediting their incorporation into ongoing research. These approaches digitally reconstruct patterns of embryonic expression in three dimensions, and have successfully identified novel domains of expression, cell types, and tissue features. Such technologies pave the way for unbiased and exhaustive recapitulation of gene expression levels in spatial and quantitative terms, promoting understanding of the molecular origin of developmental defects, and improving medical diagnostics.

Chromosome Structural Mechanics Dictates the Local Spreading of Epigenetic Marks

We present a theoretical model that demonstrates the integral role chromosome organization and structural mechanics play in the spreading of histone modifications involved in epigenetic regulation. Our model shows that heterogeneous nucleosome positioning, and the resulting position-dependent mechanical properties, must be included to reproduce several qualitative features of experimental data of histone methylation spreading around an artificially induced "nucleation site." We show that our model recreates both the extent of spreading and the presence of a subdominant peak upstream of the transcription start site. Our model indicates that the spreading of epigenetic modifications is sensitive to heterogeneity in chromatin organization and the resulting variability in the chromatin's mechanical properties, suggesting that nucleosome spacing can directly control the conferral of epigenetic marks by modifying the structural mechanics of the chromosome. It further illustrates how the physical organization of the DNA polymer may play a significant role in re-establishing the epigenetic code upon cell division.

Physical modeling of the heritability and maintenance of epigenetic modifications

We develop a predictive theoretical model of the physical mechanisms that govern the heritability and maintenance of epigenetic modifications. This model focuses on a particular modification, methylation of lysine-9 of histone H3 (H3K9), which is one of the most representative and critical epigenetic marks that affects chromatin organization and gene expression. Our model combines the effect of segregation and compaction on chromosomal organization with the effect of the interaction between proteins that compact the chromatin (heterochromatin protein 1) and the methyltransferases that affect methyl spreading. Our chromatin model demonstrates that a block of H3K9 methylations in the epigenetic sequence determines the compaction state at any particular location in the chromatin. Using our predictive model for chromatin compaction, we develop a methylation model to address the reestablishment of the methylation sequence following DNA replication. Our model reliably maintains methylation over generations, thereby establishing the robustness of the epigenetic code.

Single cell analysis pushes the boundaries of TAD formation and function

Eukaryotic genomes encode genetic information in their linear sequence, but appropriate expression of their genes requires chromosomes to fold into complex three-dimensional structures. Fueled by a growing collection of sequencing and imaging-based technologies, studies have uncovered a hierarchy of DNA interactions, from small chromatin loops that connect genes and enhancers to larger topologically associated domains (TADs) and compartments. However, despite the remarkable conservation of these organizational features, we have a very limited understanding of how this organization influences gene expression. This issue is further complicated in the context of single-cell heterogeneity, as has recently been revealed at both the level of gene activation and chromatin topology. Here, we provide a perspective on recent studies that address cell-to-cell variability and the relationship between structural heterogeneity and gene expression. We propose that transcription is regulated by variable 3D structures driven by at least two independent and partially redundant mechanisms. Collectively, this may provide flexibility to transcriptional regulation at the level of individual cells as well as reproducibility across whole tissues.

Nonequilibrium Theory of Epigenomic Microphase Separation in the Cell Nucleus

Understanding the spatial organization of the genome in the cell nucleus is one of the current grand challenges in biophysics. Certain biochemical-or epigenetic-marks that are deposited along the genome are thought to play an important, yet poorly understood, role in determining genome organization and cell identity. The physical principles underlying the interplay between epigenetic dynamics and genome folding remain elusive. Here we propose and study a theory that assumes a coupling between epigenetic mark and genome densities, and which can be applied at the scale of the whole nucleus. We show that equilibrium models are not compatible with experiments and a qualitative agreement is recovered by accounting for nonequilibrium processes that can stabilize microphase separated epigenomic domains. We finally discuss the potential biophysical origin of these terms.

Magnetic polymer models for epigenetics-driven chromosome folding

Epigenetics is a driving force of important and ubiquitous phenomena in nature such as cell differentiation or even metamorphosis. Opposite to its widespread role, understanding the biophysical principles that allow epigenetics to control and rewire gene regulatory networks remains an open challenge. In this work we study the effects of epigenetic modifications on the spatial folding of chromosomes-and hence on the expression of the underlying genes-by mapping the problem to a class of models known as magnetic polymers. In this work we show that a first order phase transition underlies the simultaneous spreading of certain epigenetic marks and the conformational collapse of a chromosome. Further, we describe Brownian dynamics simulations of the model in which the topology of the polymer and thermal fluctuations are fully taken into account and that confirm our mean field predictions. Extending our models to allow for nonequilibrium terms yields new stable phases which qualitatively agrees with observations in vivo. Our results show that statistical mechanics techniques applied to models of magnetic polymers can be successfully exploited to rationalize the outcomes of experiments designed to probe the interplay between a dynamic epigenetic landscape and chromatin organization.

Two major mechanisms of chromosome organization

The spatial organization of chromosomes has long been connected to their polymeric nature and is believed to be important for their biological functions, including the control of interactions between genomic elements, the maintenance of genetic information, and the compaction and safe transfer of chromosomes to cellular progeny. chromosome conformation capture techniques, particularly Hi-C, have provided a comprehensive picture of spatial chromosome organization and revealed new features and elements of chromosome folding. Furthermore, recent advances in microscopy have made it possible to obtain distance maps for extensive regions of chromosomes (Bintu et al., 2018; Nir et al., 2018 [2^••,3]), providing information complementary to, and in excellent agreement with, Hi-C maps. Not only has the resolution of both techniques advanced significantly, but new perturbation data generated in the last two years have led to the identification of molecular mechanisms behind large-scale genome organization. Two major mechanisms that have been proposed to govern chromosome organization are (i) the active (ATP-dependent) process of loop extrusion by Structural Maintenance of Chromosomes (SMC) complexes, and (ii) the spatial compartmentalization of the genome, which is likely mediated by affinity interactions between heterochromatic regions (Falk et al., 2019 [76^••]) rather than by ATP-dependent processes. Here, we review existing evidence that these two processes operate together to fold chromosomes in interphase and that loop extrusion alone drives mitotic compaction. We discuss possible implications of these mechanisms for chromosome function.

The Ising model in swollen vs. compact polymers: Mean-field approach and computer simulations

We study the properties of the classical Ising model with nearest-neighbor interaction for spins located at the monomers of long polymer chains in 2 and 3 dimensions. We compare results for two ensembles of polymers with very different single chain properties: 1) swollen, self-avoiding linear polymer chains in good solvent conditions and 2) compact, space-filling randomly branching polymers in melt. By employing a mean-field approach and Monte Carlo computer simulations, we show that swollen polymers cannot sustain an ordered phase. On the contrary, compact polymers may indeed produce an observable phase transition. Finally, we briefly consider the statistical properties of the ordered phase by comparing polymer chains within the same universality class but characterized by very different shapes.

How epigenome drives chromatin folding and dynamics, insights from efficient coarse-grained models of chromosomes

The 3D organization of chromosomes is crucial for regulating gene expression and cell function. Many experimental and polymer modeling efforts are dedicated to deciphering the mechanistic principles behind chromosome folding. Chromosomes are long and densely packed-topologically constrained-polymers. The main challenges are therefore to develop adequate models and simulation methods to investigate properly the multi spatio-temporal scales of such macromolecules. Here, we proposed a generic strategy to develop efficient coarse-grained models for self-avoiding polymers on a lattice. Accounting accurately for the polymer entanglement length and the volumic density, we show that our simulation scheme not only captures the steady-state structural and dynamical properties of the system but also tracks the same dynamics at different coarse-graining. This strategy allows a strong power-law gain in numerical efficiency and offers a systematic way to define reliable coarse-grained null models for chromosomes and to go beyond the current limitations by studying long chromosomes during an extended time period with good statistics. We use our formalism to investigate in details the time evolution of the 3D organization of chromosome 3R (20 Mbp) in drosophila during one cell cycle (20 hours). We show that a combination of our coarse-graining strategy with a one-parameter block copolymer model integrating epigenomic-driven interactions quantitatively reproduce experimental data at the chromosome-scale and predict that chromatin motion is very dynamic during the cell cycle.