Using computational modelling to reveal mechanisms of epigenetic Polycomb control

Proximal termination generates a transcriptional state that determines the rate of establishment of Polycomb silencing

The mechanisms and timescales controlling de novo establishment of chromatin-mediated transcriptional silencing by Polycomb repressive complex 2 (PRC2) are unclear. Here, we investigate PRC2 silencing at Arabidopsis FLOWERING LOCUS C (FLC), known to involve co-transcriptional RNA processing, histone demethylation activity, and PRC2 function, but so far not mechanistically connected. We develop and test a computational model describing proximal polyadenylation/termination mediated by the RNA-binding protein FCA that induces H3K4me1 removal by the histone demethylase FLD. H3K4me1 removal feeds back to reduce RNA polymerase II (RNA Pol II) processivity and thus enhance early termination, thereby repressing productive transcription. The model predicts that this transcription-coupled repression controls the level of transcriptional antagonism to PRC2 action. Thus, the effectiveness of this repression dictates the timescale for establishment of PRC2/H3K27me3 silencing. We experimentally validate these mechanistic model predictions, revealing that co-transcriptional processing sets the level of productive transcription at the locus, which then determines the rate of the ON-to-OFF switch to PRC2 silencing.

Polycomb repression of Hox genes involves spatial feedback but not domain compaction or phase transition

Polycomb group proteins have a critical role in silencing transcription during development. It is commonly proposed that Polycomb-dependent changes in genome folding, which compact chromatin, contribute directly to repression by blocking the binding of activating complexes. Recently, it has also been argued that liquid-liquid demixing of Polycomb proteins facilitates this compaction and repression by phase-separating target genes into a membraneless compartment. To test these models, we used Optical Reconstruction of Chromatin Architecture to trace the Hoxa gene cluster, a canonical Polycomb target, in thousands of single cells. Across multiple cell types, we find that Polycomb-bound chromatin frequently explores decompact states and partial mixing with neighboring chromatin, while remaining uniformly repressed, challenging the repression-by-compaction or phase-separation models. Using polymer simulations, we show that these observed flexible ensembles can be explained by 'spatial feedback'-transient contacts that contribute to the propagation of the epigenetic state (epigenetic memory), without inducing a globular organization.

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.

Modeling of covalent modifications of histones to estimate the binding affinity

Covalent histone modifications such as methylation, acetylation, phosphorylation, and other epigenetic modifications of the chromatin play an essential role in regulating eukaryotic cells of which most of these reactions are catalyzed by the enzymes. The binding energy of enzymes is often determined by experimental data via mathematical and statistical models due to specific modifications. Many theoretical models have been introduced to study histone modifications and reprogramming experiments in mammalian cells, in which all efforts in determining the affinity binding are essential part of the work. Here, we introduce a one-dimensional statistical Potts model to accurately determine the enzyme's binding free energy using the experimental data for various types of cells. We study the methylation of lysine 4 and 27 on histone H3 and suppose that each histone has one modification site with one of the seven states: H3K27me3, H3K27me2, H3K27me1, unmodified, H3K4me1, H3K4me2, and H3K4me3. Based on this model, the histone covalent modification is described. Moreover, by using simulation data, the histone's binding free energy and the energy of chromatin states are determined, when they are subject to changes from unmodified to active or repressive states, by finding the probability of the transition.

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.

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.

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.

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.

Histone H1 prevents non-CG methylation-mediated small RNA biogenesis in Arabidopsis heterochromatin

Flowering plants utilize small RNA (sRNA) molecules to guide DNA methyltransferases to genomic sequences. This RNA-directed DNA methylation (RdDM) pathway preferentially targets euchromatic transposable elements. However, RdDM is thought to be recruited by methylation of histone H3 at lysine 9 (H3K9me), a hallmark of heterochromatin. How RdDM is targeted to euchromatin despite an affinity for H3K9me is unclear. Here, we show that loss of histone H1 enhances heterochromatic RdDM, preferentially at nucleosome linker DNA. Surprisingly, this does not require SHH1, the RdDM component that binds H3K9me. Furthermore, H3K9me is dispensable for RdDM, as is CG DNA methylation. Instead, we find that non-CG methylation is specifically associated with sRNA biogenesis, and without H1 sRNA production quantitatively expands to non-CG-methylated loci. Our results demonstrate that H1 enforces the separation of euchromatic and heterochromatic DNA methylation pathways by excluding the sRNA-generating branch of RdDM from non-CG-methylated heterochromatin.

Cells adapt to different roles by turning different groups of genes on and off. One way cells control which genes are on or off is by creating regions of active and inactive DNA, which are created and maintained by different groups of proteins. Genes in active DNA regions can be turned on, while genes in inactive regions are switched off or silenced. Silenced DNA regions also turn off ‘transposable elements’: pieces of DNA that can copy themselves and move to other regions of the genome if they become active. Transposons can be dangerous if they are activated, because they can disrupt genes or regulatory sequences when they move.

There are different types of active and inactive DNA, but it is not always clear why these differences exist, or how they are maintained over time. In plants, such as the commonly-studied weed Arabidopsis thaliana, there are two types of inactive DNA, called E and H, that can silence transposons. In both types, DNA has small chemicals called methyl groups attached to it, which help inactivate the DNA. Type E DNA is methylated by a process called RNA-directed DNA methylation (RdDM), but RdDM is rarely seen in type H DNA.

Choi, Lyons and Zilberman showed that RdDM is attracted to E and H regions by previously existing methylated DNA. However, in the H regions, a protein called histone H1 blocks RdDM from attaching methyl groups. This helps focus RdDM onto E regions where it is most needed, because E regions contain the types of transposons RdDM is best suited to silence.

When Choi, Lyons and Zilberman examined genetically modified A. thaliana plants that do not produce histone H1, they found that RdDM happened in both E and H regions. There are many more H regions than E regions, so stretching RdDM across both made it less effective at silencing DNA.

This work shows how different DNA silencing processes are focused onto specific genetic regions, helping explain why there are different types of active and inactive DNA within cells. RdDM has been studied as a way to affect crop growth and yield by altering DNA methylation. These results may help such studies by explaining how RdDM is naturally targeted.

A cis-acting mechanism mediates transcriptional memory at Polycomb target genes in mammals

Epigenetic inheritance of gene expression states enables a single genome to maintain distinct cellular identities. How histone modifications contribute to this process remains unclear. Using global chromatin perturbations and local, time-controlled modulation of transcription, we establish the existence of epigenetic memory of transcriptional activation for genes that can be silenced by the Polycomb group. This property emerges during cell differentiation and allows genes to be stably switched after a transient transcriptional stimulus. This transcriptional memory state at Polycomb targets operates in cis; however, rather than relying solely on read-and-write propagation of histone modifications, the memory is also linked to the strength of activating inputs opposing Polycomb proteins, and therefore varies with the cellular context. Our data and computational simulations suggest a model whereby transcriptional memory arises from double-negative feedback between Polycomb-mediated silencing and active transcription. Transcriptional memory at Polycomb targets thus depends not only on histone modifications but also on the gene-regulatory network and underlying identity of a cell.