Dissecting chromatin-mediated gene regulation and epigenetic memory through mathematical modelling

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.

Epigenetic cell memory: The gene's inner chromatin modification circuit

Epigenetic cell memory allows distinct gene expression patterns to persist in different cell types despite a common genotype. Although different patterns can be maintained by the concerted action of transcription factors (TFs), it was proposed that long-term persistence hinges on chromatin state. Here, we study how the dynamics of chromatin state affect memory, and focus on a biologically motivated circuit motif, among histones and DNA modifications, that mediates the action of TFs on gene expression. Memory arises from time-scale separation among three circuit's constituent processes: basal erasure, auto and cross-catalysis, and recruited erasure of modifications. When the two latter processes are sufficiently faster than the former, the circuit exhibits bistability and hysteresis, allowing active and repressed gene states to coexist and persist after TF stimulus removal. The duration of memory is stochastic with a mean value that increases as time-scale separation increases, but more so for the repressed state. This asymmetry stems from the cross-catalysis between repressive histone modifications and DNA methylation and is enhanced by the relatively slower decay rate of the latter. Nevertheless, TF-mediated positive autoregulation can rebalance this asymmetry and even confers robustness of active states to repressive stimuli. More generally, by wiring positively autoregulated chromatin modification circuits under time scale separation, long-term distinct gene expression patterns arise, which are also robust to failure in the regulatory links.

Role of Polycomb in the control of transposable elements

It is generally considered that Polycomb Repressive Complex (PRC)2 deposits the histone mark H3K27me3 on silent protein-coding genes, while transposable elements are repressed by DNA and/or H3K9 methylation. Yet, there is increasing evidence that PRC2 also targets and even silences transposable elements in representatives of several distantly related eukaryotic lineages. In plants and animals, H3K27me3 is present on transposable elements in mutants and specific cell types devoid of DNA methylation. In this Opinion, we summarize the experimental evidence for this phenomenon across the eukaryotic kingdom, and discuss its functional and evolutionary significance. We hypothesize that an ancestral role of Polycomb group (PcG) proteins was to silence transposable elements.

Bivalent chromatin as a therapeutic target in cancer: An in silico predictive approach for combining epigenetic drugs

Tumour cell heterogeneity is a major barrier for efficient design of targeted anti-cancer therapies. A diverse distribution of phenotypically distinct tumour-cell subpopulations prior to drug treatment predisposes to non-uniform responses, leading to the elimination of sensitive cancer cells whilst leaving resistant subpopulations unharmed. Few strategies have been proposed for quantifying the variability associated to individual cancer-cell heterogeneity and minimizing its undesirable impact on clinical outcomes. Here, we report a computational approach that allows the rational design of combinatorial therapies involving epigenetic drugs against chromatin modifiers. We have formulated a stochastic model of a bivalent transcription factor that allows us to characterise three different qualitative behaviours, namely: bistable, high- and low-gene expression. Comparison between analytical results and experimental data determined that the so-called bistable and high-gene expression behaviours can be identified with undifferentiated and differentiated cell types, respectively. Since undifferentiated cells with an aberrant self-renewing potential might exhibit a cancer/metastasis-initiating phenotype, we analysed the efficiency of combining epigenetic drugs against the background of heterogeneity within the bistable sub-ensemble. Whereas single-targeted approaches mostly failed to circumvent the therapeutic problems represented by tumour heterogeneity, combinatorial strategies fared much better. Specifically, the more successful combinations were predicted to involve modulators of the histone H3K4 and H3K27 demethylases KDM5 and KDM6A/UTX. Those strategies involving the H3K4 and H3K27 methyltransferases MLL2 and EZH2, however, were predicted to be less effective. Our theoretical framework provides a coherent basis for the development of an in silico platform capable of identifying the epigenetic drugs combinations best-suited to therapeutically manage non-uniform responses of heterogenous cancer cell populations.

Digital paradigm for Polycomb epigenetic switching and memory

How epigenetic memory states are established and maintained is a central question in gene regulation. A major epigenetic process important for developmental biology involves Polycomb-mediated chromatin silencing. Significant progress has recently been made on elucidating Polycomb silencing in plant systems through analysis of Arabidopsis FLOWERING LOCUS C (FLC). Quantitative silencing of FLC by prolonged cold exposure was shown to represent an ON to OFF switch in an increasing proportion of cells. Here, we review the underlying all-or-nothing, digital paradigm for Polycomb epigenetic silencing. We then examine other Arabidopsis Polycomb-regulated targets where digital regulation may also be relevant.

A computer-guided design tool to increase the efficiency of cellular conversions

Human cell conversion technology has become an important tool for devising new cell transplantation therapies, generating disease models and testing gene therapies. However, while transcription factor over-expression-based methods have shown great promise in generating cell types in vitro, they often endure low conversion efficiency. In this context, great effort has been devoted to increasing the efficiency of current protocols and the development of computational approaches can be of great help in this endeavor. Here we introduce a computer-guided design tool that combines a computational framework for prioritizing more efficient combinations of instructive factors (IFs) of cellular conversions, called IRENE, with a transposon-based genomic integration system for efficient delivery. Particularly, IRENE relies on a stochastic gene regulatory network model that systematically prioritizes more efficient IFs by maximizing the agreement of the transcriptional and epigenetic landscapes between the converted and target cells. Our predictions substantially increased the efficiency of two established iPSC-differentiation protocols (natural killer cells and melanocytes) and established the first protocol for iPSC-derived mammary epithelial cells with high efficiency.

Theoretical analysis of Polycomb-Trithorax systems predicts that poised chromatin is bistable and not bivalent

Polycomb (PcG) and Trithorax (TrxG) group proteins give stable epigenetic memory of silent and active gene expression states, but also allow poised states in pluripotent cells. Here we systematically address the relationship between poised, active and silent chromatin, by integrating 73 publications on PcG/TrxG biochemistry into a mathematical model comprising 144 nucleosome modification states and 8 enzymatic reactions. Our model predicts that poised chromatin is bistable and not bivalent. Bivalent chromatin, containing opposing active and silent modifications, is present as an unstable background population in all system states, and different subtypes co-occur with active and silent chromatin. In contrast, bistability, in which the system switches frequently between stable active and silent states, occurs under a wide range of conditions at the transition between monostable active and silent system states. By proposing that bistability and not bivalency is associated with poised chromatin, this work has implications for understanding the molecular nature of pluripotency.

Polycomb and Trithorax group proteins regulate silent and active gene expression states, but also allow poised states in pluripotent cells. Here the authors present a mathematical model that integrates data on Polycomb/ Trithorax biochemistry into a single coherent framework which predicts that poised chromatin is not bivalent as previously proposed, but is bistable, meaning that the system switches frequently between stable active and silent states.

A multiscale model of epigenetic heterogeneity-driven cell fate decision-making

The inherent capacity of somatic cells to switch their phenotypic status in response to damage stimuli in vivo might have a pivotal role in ageing and cancer. However, how the entry-exit mechanisms of phenotype reprogramming are established remains poorly understood. In an attempt to elucidate such mechanisms, we herein introduce a stochastic model of combined epigenetic regulation (ER)-gene regulatory network (GRN) to study the plastic phenotypic behaviours driven by ER heterogeneity. To deal with such complex system, we additionally formulate a multiscale asymptotic method for stochastic model reduction, from which we derive an efficient hybrid simulation scheme. Our analysis of the coupled system reveals a regime of tristability in which pluripotent stem-like and differentiated steady-states coexist with a third indecisive state, with ER driving transitions between these states. Crucially, ER heterogeneity of differentiation genes is for the most part responsible for conferring abnormal robustness to pluripotent stem-like states. We formulate epigenetic heterogeneity-based strategies capable of unlocking and facilitating the transit from differentiation-refractory (stem-like) to differentiation-primed epistates. The application of the hybrid numerical method validates the likelihood of such switching involving solely kinetic changes in epigenetic factors. Our results suggest that epigenetic heterogeneity regulates the mechanisms and kinetics of phenotypic robustness of cell fate reprogramming. The occurrence of tunable switches capable of modifying the nature of cell fate reprogramming might pave the way for new therapeutic strategies to regulate reparative reprogramming in ageing and cancer.

Certain modifications of the structure and functioning of the protein/DNA complex called chromatin can allow adult, fully differentiated, cells to adopt a stem cell-like pluripotent state in a purely epigenetic manner, not involving changes in the underlying DNA sequence. Such reprogramming-like phenomena may constitute an innate reparative route through which human tissues respond to injury and could also serve as a novel regenerative strategy in human pathological situations in which tissue or organ repair is impaired. However, it should be noted that in vivo reprogramming would be capable of maintaining tissue homeostasis provided the acquisition of pluripotency features is strictly transient and accompanied by an accurate replenishment of the specific cell types being lost. Crucially, an excessive reprogramming in the absence of controlled re-differentiation would impair the repair or the replacement of damaged cells, thereby promoting pathological alterations of cell fate. A mechanistic understanding of how the degree of chromatin plasticity dictates the reparative versus pathological behaviour of in vivo reprogramming to rejuvenate aged tissues while preventing tumorigenesis is urgently needed, including especially the intrinsic epigenetic heterogeneity of the tissue resident cells being reprogrammed. We here introduce a novel method that mathematically captures how epigenetic heterogeneity is actually the driving force that governs the routes and kinetics to entry into and exit from a pathological stem-like state. Moreover, our approach computationally validates the likelihood of unlocking chronic, unrestrained plastic states and drive their differentiation down the correct path by solely manipulating the intensity and direction of few epigenetic control switches. Our approach could inspire new therapeutic approaches based on in vivo cell reprogramming for efficient tissue regeneration and rejuvenation and cancer treatment.

Epigenetic regulation of cell fate reprogramming in aging and disease: A predictive computational model

Understanding the control of epigenetic regulation is key to explain and modify the aging process. Because histone-modifying enzymes are sensitive to shifts in availability of cofactors (e.g. metabolites), cellular epigenetic states may be tied to changing conditions associated with cofactor variability. The aim of this study is to analyse the relationships between cofactor fluctuations, epigenetic landscapes, and cell state transitions. Using Approximate Bayesian Computation, we generate an ensemble of epigenetic regulation (ER) systems whose heterogeneity reflects variability in cofactor pools used by histone modifiers. The heterogeneity of epigenetic metabolites, which operates as regulator of the kinetic parameters promoting/preventing histone modifications, stochastically drives phenotypic variability. The ensemble of ER configurations reveals the occurrence of distinct epi-states within the ensemble. Whereas resilient states maintain large epigenetic barriers refractory to reprogramming cellular identity, plastic states lower these barriers, and increase the sensitivity to reprogramming. Moreover, fine-tuning of cofactor levels redirects plastic epigenetic states to re-enter epigenetic resilience, and vice versa. Our ensemble model agrees with a model of metabolism-responsive loss of epigenetic resilience as a cellular aging mechanism. Our findings support the notion that cellular aging, and its reversal, might result from stochastic translation of metabolic inputs into resilient/plastic cell states via ER systems.

Noncoding RNAs in Polycomb and Trithorax Regulation: A Quantitative Perspective

The question of how noncoding RNAs are involved in Polycomb group (PcG) and Trithorax group (TrxG) regulation has been on an extraordinary journey over the last three decades. Favored models have risen and fallen, and healthy debates have swept back and forth. The field has recently reached a critical mass of compelling data that throws light on several previously unresolved issues. The time is ripe for a fruitful combination of these findings with two other long-running avenues of research, namely the biochemical properties of the PcG/TrxG system and the application of theoretical mathematical models toward an understanding of the system's regulatory properties. I propose that integrating our current knowledge of noncoding RNA into a quantitative biochemical and theoretical framework for PcG and TrxG regulation has the potential to reconcile several apparently conflicting models and identifies fascinating questions for future research.

Capturing Environmental Plant Memories in DNA, with a Little Help from Chromatin

Plants are eukaryotes living mostly immotile in harsh environments. On occasion, it is beneficial for their survival to maintain a transcriptional response to an environmental stress longer than the stress lasts (transcriptional memory) and even to reiterate such a response more quickly or more strongly when the same stress is re-encountered (priming memory). In eukaryotes, transcription takes place in the context of chromatin, the packaging material of DNA. Chromatin regulation is often invoked when it comes to environmental transcriptional and priming memory in plants, but rarely chromatin-based regulation can be accurately assigned to a given aspect of transcription in vivo. The conserved eukaryotic chromatin-modifying system Polycomb/Trithorax can support both long-term stability and flexibility of gene expression in Drosophila. The main principles of Polycomb/Trithorax regulation will be outlined and illustrated with the best-studied case of environmental memory from Arabidopsis. Despite being complex, the Polycomb/Trithorax system relies on experimentally tractable elements in the form of DNA, termed Polycomb/Trithorax Responsive Elements. PREs/TREs are essentially memory DNA elements. Here, relevant information to identify PRE/TRE-like elements in plants is highlighted. Examples of priming memory in plants are discussed in relation to the first two reported putative memory DNA elements. Arguably, similar cases from plants can be conducive in dissecting the contribution of DNA-based from chromatin-based regulation of transcription, when two types of DNA elements are defined: those representing binding sites for the transcription factors determining the environmental response and those controlling memory by regulating chromatin modification dynamics, ultimately maintaining the corresponding transcriptional state.