Epigenetics meets mathematics: towards a quantitative understanding of chromatin biology

The Trithorax group protein ASH1 requires a combination of BAH domain and AT hooks, but not the SET domain, for mitotic chromatin binding and survival

The Drosophila Trithorax group (TrxG) protein ASH1 remains associated with mitotic chromatin through mechanisms that are poorly understood. ASH1 dimethylates histone H3 at lysine 36 via its SET domain. Here, we identify domains of the TrxG protein ASH1 that are required for mitotic chromatin attachment in living Drosophila. Quantitative live imaging demonstrates that ASH1 requires AT hooks and the BAH domain but not the SET domain for full chromatin binding in metaphase, and that none of these domains are essential for interphase binding. Genetic experiments show that disruptions of the AT hooks and the BAH domain together, but not deletion of the SET domain alone, are lethal. Transcriptional profiling demonstrates that intact ASH1 AT hooks and the BAH domain are required to maintain expression levels of a specific set of genes, including several involved in cell identity and survival. This study identifies in vivo roles for specific ASH1 domains in mitotic binding, gene regulation, and survival that are distinct from its functions as a histone methyltransferase.

The Flowering Season-Meter at FLOWERING LOCUS C Across Life Histories in Crucifers

Many plant species overwinter before they flower. Transition to flowering is aligned to the seasonal transition as a response to the prolonged cold in winter by a process called vernalization. Multiple well-documented vernalization properties in crucifer species with diverse life histories are derived from environmental regulation of a central inhibitor of the flowering gene, Flowering Locus C (FLC). Episode(s) of flowering are prevented during high FLC expression and enabled during low FLC expression. FLC repression outlasts the winter to coincide with spring; this heterochronic aspect is termed "winter memory." In the annual Arabidopsis thaliana, winter memory has long been associated with the highly conserved histone modifiers Polycomb and Trithorax, which have antagonistic roles in transcription. However, there are experimental limitations in determining how dynamic, heterogenous histone modifications within the FLC locus generate the final transcriptional output. Recent theoretical considerations on cell-to-cell variability in gene expression and histone modifications generating bistable states brought support to the hypothesis of chromatin-encoded memory, as with other experimental systems in eukaryotes. Furthermore, these advances unify multiple properties of vernalization, not only the winter memory. Similarly, in the perennial Arabidopsis halleri ssp. gemmifera, recent integration of molecular with mathematical and ecological approaches unifies FLC chromatin features with the all-year-round memory of seasonal temperature. We develop the concept of FLC season-meter to combine existing information from the contrasting annual/perennial and experimental/theoretical sectors into a transitional framework. We highlight simplicity, high conservation, and discrete differences across extreme life histories in crucifers.

Monitoring of switches in heterochromatin-induced silencing shows incomplete establishment and developmental instabilities

Position effect variegation (PEV) in Drosophila results from new juxtapositions of euchromatic and heterochromatic chromosomal regions, and manifests as striking bimodal patterns of gene expression. The semirandom patterns of PEV, reflecting clonal relationships between cells, have been interpreted as gene-expression states that are set in development and thereafter maintained without change through subsequent cell divisions. The rate of instability of PEV is almost entirely unexplored beyond the final expression of the modified gene; thus the origin of the expressivity and patterns of PEV remain unexplained. Many properties of PEV are not predicted from currently accepted biochemical and theoretical models. In this work we investigate the time at which expressivity of silencing is set, and find that it is determined before heterochromatin exists. We employ a mathematical simulation and a corroborating experimental approach to monitor switching (i.e., gains and losses of silencing) through development. In contrast to current views, we find that gene silencing is incompletely set early in embryogenesis, but nevertheless is repeatedly lost and gained in individual cells throughout development. Our data support an alternative to locus-specific "epigenetic" silencing at variegating gene promoters that more fully accounts for the final patterns of PEV.

Polycomb Assemblies Multitask to Regulate Transcription

The Polycomb system is made of an evolutionary ancient group of proteins, present throughout plants and animals. Known initially from developmental studies with the fly Drosophila melanogaster, they were associated with stable sustainment of gene repression and maintenance of cell identity. Acting as multiprotein assemblies with an ability to modify chromatin, through chemical additions to histones and organization of topological domains, they have been involved subsequently in control of developmental transitions and in cell homeostasis. Recent work has unveiled an association of Polycomb components with transcriptionally active loci and the promotion of gene expression, in clear contrast with conventional recognition as repressors. Focusing on mammalian models, I review here advances concerning roles in transcriptional control. Among new findings highlighted is the regulation of their catalytic properties, recruiting to targets, and activities in chromatin organization and compartmentalization. The need for a more integrated approach to the study of the Polycomb system, given its fundamental complexity and its adaptation to cell context, is discussed.

An Inactivation Switch Enables Rhythms in a Neurospora Clock Model

Autonomous endogenous time-keeping is ubiquitous across many living organisms, known as the circadian clock when it has a period of about 24 h. Interestingly, the fundamental design principle with a network of interconnected negative and positive feedback loops is conserved through evolution, although the molecular components differ. Filamentous fungus Neurospora crassa is a well-established chrono-genetics model organism to investigate the underlying mechanisms. The core negative feedback loop of the clock of Neurospora is composed of the transcription activator White Collar Complex (WCC) (heterodimer of WC1 and WC2) and the inhibitory element called FFC complex, which is made of FRQ (Frequency protein), FRH (Frequency interacting RNA Helicase) and CK1a (Casein kinase 1a). While exploring their temporal dynamics, we investigate how limit cycle oscillations arise and how molecular switches support self-sustained rhythms. We develop a mathematical model of 10 variables with 26 parameters to understand the interactions and feedback among WC1 and FFC elements in nuclear and cytoplasmic compartments. We performed control and bifurcation analysis to show that our novel model produces robust oscillations with a wild-type period of 22.5 h. Our model reveals a switch between WC1-induced transcription and FFC-assisted inactivation of WC1. Using the new model, we also study the possible mechanisms of glucose compensation. A fairly simple model with just three nonlinearities helps to elucidate clock dynamics, revealing a mechanism of rhythms' production. The model can further be utilized to study entrainment and temperature compensation.

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.

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.

The ATAD2 bromodomain binds different acetylation marks on the histone H4 in similar fuzzy complexes

Bromodomains are protein modules adopting conserved helix bundle folds. Some bromodomain-containing proteins, such as ATPase family AAA domain-containing protein 2 (ATAD2), isoform A, have attracted much interest because they are overexpressed in many types of cancer. Bromodomains bind to acetylated lysine residues on histone tails and thereby facilitate the reading of the histone code. Epigenetic regulators in general have been implicated as indicators, mediators, or causes of a large number of diseases and disorders. To interfere with or modulate these processes, it is therefore of fundamental interest to understand the molecular mechanisms by which epigenetic regulation occurs. Here, we present results from molecular dynamics simulations of a doubly acetylated histone H4 peptide bound to the bromodomain of ATAD2 (hereafter referred to as ATAD2A). These simulations revealed how the flexibility of ATAD2A's major loop, the so-called ZA loop, creates an adaptable interface that preserves the disorder of both peptide and loop in the bound state. We further demonstrate that the binding involves an almost identical average pattern of interactions irrespective of which acetyl mark is inserted into the pocket. In conjunction with a likely mechanism of electrostatically driven recruitment, our simulation results highlight how the bromodomain is built toward promiscuous binding with low specificity. In conclusion, the simulations indicate that disorder and electrostatic steering function jointly to recruit ATAD2A to the histone core and that these fuzzy interactions may promote cooperativity between nearby epigenetic marks.

Epithelial/mesenchymal plasticity: how have quantitative mathematical models helped improve our understanding?

Phenotypic plasticity, the ability of cells to reversibly alter their phenotypes in response to signals, presents a significant clinical challenge to treating solid tumors. Tumor cells utilize phenotypic plasticity to evade therapies, metastasize, and colonize distant organs. As a result, phenotypic plasticity can accelerate tumor progression. A well‐studied example of phenotypic plasticity is the bidirectional conversions among epithelial, mesenchymal, and hybrid epithelial/mesenchymal (E/M) phenotype(s). These conversions can alter a repertoire of cellular traits associated with multiple hallmarks of cancer, such as metabolism, immune evasion, invasion, and metastasis. To tackle the complexity and heterogeneity of these transitions, mathematical models have been developed that seek to capture the experimentally verified molecular mechanisms and act as ‘hypothesis‐generating machines’. Here, we discuss how these quantitative mathematical models have helped us explain existing experimental data, guided further experiments, and provided an improved conceptual framework for understanding how multiple intracellular and extracellular signals can drive E/M plasticity at both the single‐cell and population levels. We also discuss the implications of this plasticity in driving multiple aggressive facets of tumor progression.

Spatial segregation of heterochromatin: Uncovering functionality in a multicellular organism

Multiple layers of regulation are required to ensure appropriate patterns of gene expression for accurate cell differentiation. Interphase chromatin is non-randomly distributed within the nucleus, with highly compacted, transcriptionally silent heterochromatin enriched at the nuclear and nucleolar periphery. Whether this spatial organization serves a function in organismal physiology, rather than simply being a byproduct of chromatin metabolism, is a fundamental question. Recent work performed in C. elegans embryos characterized the molecular mechanisms that drive the perinuclear anchoring of heterochromatin. Moreover, for the first time it was shown that heterochromatin sequestration helps to restrict cell differentiation programs, while sustaining commitment to a specified fate. Here, we describe and comment on these findings, placing them in a broader context.

Dynamic Chromatin Regulation from a Single Molecule Perspective

Chromatin regulatory processes, like all biological reactions, are dynamic and stochastic in nature but can give rise to stable and inheritable changes in gene expression patterns. A molecular understanding of those processes is key for fundamental biological insight into gene regulation, epigenetic inheritance, lineage determination, and therapeutic intervention in the case of disease. In recent years, great progress has been made in identifying important molecular players involved in key chromatin regulatory pathways. Conversely, we are only beginning to understand the dynamic interplay between protein effectors, transcription factors, and the chromatin substrate itself. Single-molecule approaches employing both highly defined chromatin substrates in vitro, as well as direct observation of complex regulatory processes in vivo, open new avenues for a molecular view of chromatin regulation. This review highlights recent applications of single-molecule methods and related techniques to investigate fundamental chromatin regulatory processes.

Perinuclear Anchoring of H3K9-Methylated Chromatin Stabilizes Induced Cell Fate in C. elegans Embryos

Interphase chromatin is organized in distinct nuclear sub-compartments, reflecting its degree of compaction and transcriptional status. In Caenorhabditis elegans embryos, H3K9 methylation is necessary to silence and to anchor repeat-rich heterochromatin at the nuclear periphery. In a screen for perinuclear anchors of heterochromatin, we identified a previously uncharacterized C. elegans chromodomain protein, CEC-4. CEC-4 binds preferentially mono-, di-, or tri-methylated H3K9 and localizes at the nuclear envelope independently of H3K9 methylation and nuclear lamin. CEC-4 is necessary for endogenous heterochromatin anchoring, but not for transcriptional repression, in contrast to other known H3K9 methyl-binders in worms, which mediate gene repression but not perinuclear anchoring. When we ectopically induce a muscle differentiation program in embryos, cec-4 mutants fail to commit fully to muscle cell fate. This suggests that perinuclear sequestration of chromatin during development helps restrict cell differentiation programs by stabilizing commitment to a specific cell fate. PAPERCLIP.

Multivalency governs HP1α association dynamics with the silent chromatin state

Multivalent interactions between effector proteins and histone post-translational modifications are an elementary mechanism of dynamic chromatin signalling. Here we elucidate the mechanism how heterochromatin protein 1α (HP1α), a multivalent effector, is efficiently recruited to the silent chromatin state (marked by trimethylated H3 at Lys9, H3K9me3) while remaining highly dynamic. Employing chemically defined nucleosome arrays together with single-molecule total internal reflection fluorescence microscopy (smTIRFM), we demonstrate that the HP1α residence time on chromatin depends on the density of H3K9me3, as dissociated factors can rapidly rebind at neighbouring sites. Moreover, by chemically controlling HP1α dimerization we find that effector multivalency prolongs chromatin retention and, importantly, accelerates the association rate. This effect results from increased avidity together with strengthened nonspecific chromatin interactions of dimeric HP1α. We propose that accelerated chromatin binding is a key feature of effector multivalency, allowing for fast and efficient competition for binding sites in the crowded nuclear compartment.

Chromatin effector proteins often employ multivalent interactions with histone post-translational modifications. Here by using chemically defined nucleosome array and single-molecule microscopy, the authors show that effector multivalency prolongs chromatin retention and accelerates the association rate.

Dot1 histone methyltransferases share a distributive mechanism but have highly diverged catalytic properties

The conserved histone methyltransferase Dot1 establishes an H3K79 methylation pattern consisting of mono-, di- and trimethylation states on histone H3 via a distributive mechanism. This mechanism has been shown to be important for the regulation of the different H3K79 methylation states in yeast. Dot1 enzymes in yeast, Trypanosoma brucei (TbDot1A and TbDot1B, which methylate H3K76) and human (hDot1L) generate very divergent methylation patterns. To understand how these species-specific methylation patterns are generated, the methylation output of the Dot1 enzymes was compared by expressing them in yeast at various expression levels. Computational simulations based on these data showed that the Dot1 enzymes have highly distinct catalytic properties, but share a distributive mechanism. The mechanism of methylation and the distinct rate constants have implications for the regulation of H3K79/K76 methylation. A mathematical model of H3K76 methylation during the trypanosome cell cycle suggests that temporally-regulated consecutive action of TbDot1A and TbDot1B is required for the observed regulation of H3K76 methylation states.

Cooperative stabilization of the SIR complex provides robust epigenetic memory in a model of SIR silencing in Saccharomyces cerevisiae

How alternative chromatin-based regulatory states can be made stable and heritable in order to provide robust epigenetic memory is poorly understood. Here, we develop a stochastic model of the silencing system in Saccharomyces cerevisiae that incorporates cooperative binding of the repressive SIR complex and antisilencing histone modifications, in addition to positive feedback in Sir2 recruitment. The model was able to reproduce key features of SIR regulation of an HM locus, including heritable bistability, dependence on the silencer elements, and sensitivity to SIR dosage. We found that antisilencing methylation of H3K79 by Dot1 was not needed to generate these features, but acted to reduce spreading of SIR binding, consistent with its proposed role in containment of silencing. In contrast, cooperative inter-nucleosome interactions mediated by the SIR complex were critical for concentrating SIR binding around the silencers in the absence of barriers, and for providing bistability in SIR binding. SIR-SIR interactions magnify the cooperativity in the Sir2-histone deacetylation positive feedback reaction and complete a double-negative feedback circuit involving antisilencing modifications. Thus, our modeling underscores the potential importance of cooperative interactions between nucleosome-bound complexes both in the SIR system and in other chromatin-based complexes in epigenetic regulation.

Vernalizing cold is registered digitally at FLC

A fundamental property of many organisms is an ability to sense, evaluate, and respond to environmental signals. In some situations, generation of an appropriate response requires long-term information storage. A classic example is vernalization, where plants quantitatively sense long-term cold and epigenetically store this cold-exposure information to regulate flowering time. In Arabidopsis thaliana, stable epigenetic memory of cold is digital: following long-term cold exposure, cells respond autonomously in an all-or-nothing fashion, with the fraction of cells that stably silence the floral repressor flowering locus C (FLC) increasing with the cold exposure duration. However, during cold exposure itself it is unknown whether vernalizing cold is registered at FLC in individual cells in an all-or-nothing (digital) manner or is continuously varying (analog). Using mathematical modeling, we found that analog registration of cold temperature is problematic due to impaired analog-to-digital conversion into stable memory. This disadvantage is particularly acute when responding to short cold periods, but is absent when cold temperatures are registered digitally at FLC. We tested this prediction experimentally, exposing plants to short periods of cold interrupted with even shorter warm breaks. For FLC expression, we found that the system responds similarly to both interrupted and uninterrupted cold, arguing for a digital mechanism integrating long-term temperature exposure.

Breaking an epigenetic chromatin switch: curious features of hysteresis in Saccharomyces cerevisiae telomeric silencing

In addition to gene network switches, local epigenetic modifications to DNA and histones play an important role in all-or-none cellular decision-making. Here, we study the dynamical design of a well-characterized epigenetic chromatin switch: the yeast SIR system, in order to understand the origin of the stability of epigenetic states. We study hysteresis in this system by perturbing it with a histone deacetylase inhibitor. We find that SIR silencing has many characteristics of a non-linear bistable system, as observed in conventional genetic switches, which are based on activities of a few promoters affecting each other through the abundance of their gene products. Quite remarkably, our experiments in yeast telomeric silencing show a very distinctive pattern when it comes to the transition from bistability to monostability. In particular, the loss of the stable silenced state, upon increasing the inhibitor concentration, does not seem to show the expected saddle node behavior, instead looking like a supercritical pitchfork bifurcation. In other words, the 'off' state merges with the 'on' state at a threshold concentration leading to a single state, as opposed to the two states remaining distinct up to the threshold and exhibiting a discontinuous jump from the 'off' to the 'on' state. We argue that this is an inevitable consequence of silenced and active regions coexisting with dynamic domain boundaries. The experimental observations in our study therefore have broad implications for the understanding of chromatin silencing in yeast and beyond.

What are memories made of? How Polycomb and Trithorax proteins mediate epigenetic memory

In any biological system with memory, the state of the system depends on its history. Epigenetic memory maintains gene expression states through cell generations without a change in DNA sequence and in the absence of initiating signals. It is immensely powerful in biological systems - it adds long-term stability to gene expression states and increases the robustness of gene regulatory networks. The Polycomb group (PcG) and Trithorax group (TrxG) proteins can confer long-term, mitotically heritable memory by sustaining silent and active gene expression states, respectively. Several recent studies have advanced our understanding of the molecular mechanisms of this epigenetic memory during DNA replication and mitosis.

Engineering chromatin states: chemical and synthetic biology approaches to investigate histone modification function

Patterns of histone post-translational modifications (PTMs) and DNA modifications establish a landscape of chromatin states with regulatory impact on gene expression, cell differentiation and development. These diverse modifications are read out by effector protein complexes, which ultimately determine their functional outcome by modulating the activity state of underlying genes. From genome-wide studies employing high-throughput ChIP-Seq methods as well as proteomic mass spectrometry studies, a large number of PTMs are known and their coexistence patterns and associations with genomic regions have been mapped in a large number of different cell types. Conversely, the molecular interplay between chromatin effector proteins and modified chromatin regions as well as their resulting biological output is less well understood on a molecular level. Within the last decade a host of chemical approaches has been developed with the goal to produce synthetic chromatin with a defined arrangement of PTMs. These methods now permit systematic functional studies of individual histone and DNA modifications, and additionally provide a discovery platform to identify further interacting nuclear proteins. Complementary chemical- and synthetic-biology methods have emerged to directly observe and modulate the modification landscape in living cells and to readily probe the effect of altered PTM patterns on biological processes. Herein, we review current methodologies allowing chemical and synthetic biological engineering of distinct chromatin states in vitro and in vivo with the aim of obtaining a molecular understanding of histone and DNA modification function. This article is part of a Special Issue entitled: Molecular mechanisms of histone modification function.

Statistical mechanics model for the dynamics of collective epigenetic histone modification

Epigenetic histone modifications play an important role in the maintenance of different cell phenotypes. The exact molecular mechanism for inheritance of the modification patterns over cell generations remains elusive. We construct a Potts-type model based on experimentally observed nearest-neighbor enzyme lateral interactions and nucleosome covalent modification state biased enzyme recruitment. The model can lead to effective nonlocal interactions among nucleosomes suggested in previous theoretical studies, and epigenetic memory is robustly inheritable against stochastic cellular processes.

Quantitative in vivo analysis of chromatin binding of Polycomb and Trithorax group proteins reveals retention of ASH1 on mitotic chromatin

The Polycomb (PcG) and Trithorax (TrxG) group proteins work antagonistically on several hundred developmentally important target genes, giving stable mitotic memory, but also allowing flexibility of gene expression states. How this is achieved in quantitative terms is poorly understood. Here, we present a quantitative kinetic analysis in living Drosophila of the PcG proteins Enhancer of Zeste, (E(Z)), Pleiohomeotic (PHO) and Polycomb (PC) and the TrxG protein absent, small or homeotic discs 1 (ASH1). Fluorescence recovery after photobleaching and fluorescence correlation spectroscopy reveal highly dynamic chromatin binding behaviour for all proteins, with exchange occurring within seconds. We show that although the PcG proteins substantially dissociate from mitotic chromatin, ASH1 remains robustly associated with chromatin throughout mitosis. Finally, we show that chromatin binding by ASH1 and PC switches from an antagonistic relationship in interphase, to a cooperative one during mitosis. These results provide quantitative insights into PcG and TrxG chromatin-binding dynamics and have implications for our understanding of the molecular nature of epigenetic memory.