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Understanding the mechanistic basis of epigenetic memory has proven to be a difficult task due to the underlying complexity of the systems involved in its establishment and maintenance. Here, we review the role of computational modeling in helping to unlock this complexity, allowing the dissection of intricate feedback dynamics. We focus on three forms of epigenetic memory encoded in gene regulatory networks, DNA methylation, and histone modifications and discuss the important advantages offered by plant systems in their dissection. We summarize the main modeling approaches involved and highlight the principal conceptual advances that the modeling has enabled through iterative cycles of predictive modeling and experiments. Lastly, we discuss remaining gaps in our understanding and how intertwined theory and experimental approaches might help in their resolution. Expected final online publication date for the , Volume 75 is May 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

The shuffling of genetic material facilitated by meiotic crossovers is a critical driver of genetic variation. Therefore, the number and positions of crossover events must be carefully controlled. In , an obligate crossover and repression of nearby crossovers on each chromosome pair are abolished in mutants that lack the synaptonemal complex (SC), a conserved protein scaffold. We use mathematical modelling and quantitative super-resolution microscopy to explore and mechanistically explain meiotic crossover pattering in lines with full, incomplete or abolished synapsis. For mutants, which lack an SC, we develop a coarsening model in which crossover precursors globally compete for a limited pool of the pro-crossover factor HEI10, with dynamic HEI10 exchange mediated through the nucleoplasm. We demonstrate that this model is capable of quantitatively reproducing and predicting experimental crossover patterning and HEI10 foci intensity data. Additionally, we find that a model combining both SC- and nucleoplasm-mediated coarsening can explain crossover patterning in wild-type and in mutants, which display partial synapsis. Together, our results reveal that regulation of crossover patterning in wild-type and SC defective mutants likely act through the same underlying coarsening mechanism, differing only in the spatial compartments through which the pro-crossover factor diffuses.

The maintenance of transcriptional states regulated by histone modifications and controlled switching between these states are fundamental concepts in our understanding of nucleosome-mediated epigenetic memory. Any approach relying on genome-wide bioinformatic analyses alone offers limited scope for dissecting the molecular mechanisms involved in maintenance and switching. Mechanistic mathematical models-describing the dynamics of histone modifications at individual genomic loci-offer an alternative way to investigate these mechanisms. These models, in conjunction with quantitative experimental data-ChIP data, quantification of mRNA levels, and single-cell fluorescence tracking in clonal lineages-can generate predictions that drive more targeted experiments, allowing us to understand mechanisms that would be challenging to unravel by a purely experimental approach. In this chapter, we describe a generic stochastic modeling framework that can be used to capture histone modification dynamics and associated molecular processes-including transcription and read-write feedback by chromatin modifying complexes-at individual genomic loci. Using a specific example-transcriptional silencing by Polycomb-mediated H3K27 methylation-we demonstrate how to construct and simulate a stochastic histone modification model. We provide a step-by-step guide to programming simulations for such a model and discuss how to analyze the simulation output.

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.

The histone modification H3K27me3 plays a central role in Polycomb-mediated epigenetic silencing. H3K27me3 recruits and allosterically activates Polycomb Repressive Complex 2 (PRC2), which adds this modification to nearby histones, providing a read/write mechanism for inheritance through DNA replication. However, for some PRC2 targets, a purely histone-based system for epigenetic inheritance may be insufficient. We address this issue at the Polycomb target in , as a narrow nucleation region of only ~three nucleosomes within mediates epigenetic state switching and subsequent memory over many cell cycles. To explain the memory's unexpected persistence, we introduce a mathematical model incorporating extra protein memory storage elements with positive feedback that persist at the locus through DNA replication, in addition to histone modifications. Our hybrid model explains many features of epigenetic switching/memory at and encapsulates generic mechanisms that may be widely applicable.

Noncoding RNA plays essential roles in transcriptional control and chromatin silencing. At antisense transcription quantitatively influences transcriptional output, but the mechanism by which this occurs is still unclear. Proximal polyadenylation of the antisense transcripts by FCA, an RNA-binding protein that physically interacts with RNA 3' processing factors, reduces transcription. This process genetically requires FLD, a homolog of the H3K4 demethylase LSD1. However, the mechanism linking RNA processing to FLD function had not been established. Here, we show that FLD tightly associates with LUMINIDEPENDENS (LD) and SET DOMAIN GROUP 26 (SDG26) in vivo, and, together, they prevent accumulation of monomethylated H3K4 (H3K4me1) over the gene body. SDG26 interacts with the RNA 3' processing factor FY (WDR33), thus linking activities for proximal polyadenylation of the antisense transcripts to FLD/LD/SDG26-associated H3K4 demethylation. We propose this demethylation antagonizes an active transcription module, thus reducing H3K36me3 accumulation and increasing H3K27me3. Consistent with this view, we show that Polycomb Repressive Complex 2 (PRC2) silencing is genetically required by FCA to repress Overall, our work provides insights into RNA-mediated chromatin silencing.

In , the cold-induced epigenetic regulation of () involves distinct phases of Polycomb repressive complex 2 (PRC2) silencing. During cold, a PHD-PRC2 complex metastably and digitally nucleates H3K27me3 within On return to warm, PHD-PRC2 spreads across the locus delivering H3K27me3 to maintain long-term silencing. Here, we studied natural variation in this process in accessions, exploring Lov-1, which shows reactivation on return to warm, a feature characteristic of in perennial This analysis identifies an additional phase in this Polycomb silencing mechanism downstream from H3K27me3 spreading. In this long-term silencing (perpetuated) phase, the PHD proteins are lost from the nucleation region and silencing is likely maintained by the read-write feedbacks associated with H3K27me3. A combination of noncoding SNPs in the nucleation region mediates instability in this long-term silencing phase with the result that Lov-1 frequently digitally reactivates in individual cells, with a probability that diminishes with increasing cold duration. We propose that this decrease in reactivation probability is due to reduced DNA replication after flowering. Overall, this work defines an additional phase in the Polycomb mechanism instrumental in natural variation of silencing, and provides avenues to dissect broader evolutionary changes at .

Gene silencing by Polycomb complexes is central to eukaryotic development. Cold-induced epigenetic repression of () in the plant provides an opportunity to study initiation and maintenance of Polycomb silencing. Here, we show that a subset of Polycomb repressive complex 2 factors nucleate silencing in a small region within , locally increasing H3K27me3 levels. This nucleation confers a silenced state that is metastably inherited, with memory held in the local chromatin. Metastable memory is then converted to stable epigenetic silencing through separate Polycomb factors, which spread across the locus after cold to enlarge the domain that contains H3K27me3. Polycomb silencing at thus has mechanistically distinct phases, which involve specialization of distinct Polycomb components to deliver first metastable then long-term epigenetic silencing.

Genes targeted by Polycomb repressive complex 2 (PRC2) are regulated in cis by chromatin modifications and also in trans by diffusible regulators such as transcription factors. Here, we introduce a mathematical model in which transcription directly antagonizes Polycomb silencing, thereby linking these cis- and trans-regulatory inputs to gene expression. The model is parameterized by recent experimental data showing that PRC2-mediated repressive chromatin modifications accumulate extremely slowly. The model generates self-perpetuating, bistable active and repressed chromatin states that persist through DNA replication, thereby ensuring high-fidelity transmission of the current chromatin state. However, sufficiently strong, persistent activation or repression of transcription promotes switching between active and repressed chromatin states. We observe that when chromatin modification dynamics are slow, transient pulses of transcriptional activation or repression are effectively filtered, such that epigenetic memory is retained. Noise filtering thus depends on slow chromatin dynamics and may represent an important function of PRC2-based regulation.

Inheritance of gene expression states is fundamental for cells to 'remember' past events, such as environmental or developmental cues. The conserved Polycomb Repressive Complex 2 (PRC2) maintains epigenetic repression of many genes in animals and plants and modifies chromatin at its targets. Histones modified by PRC2 can be inherited through cell division. However, it remains unclear whether this inheritance can direct long-term memory of individual gene expression states (cis memory) or instead if local chromatin states are dictated by the concentrations of diffusible factors (trans memory). By monitoring the expression of two copies of the Arabidopsis Polycomb target gene FLOWERING LOCUS C (FLC) in the same plants, we show that one copy can be repressed while the other is active. Furthermore, this 'mixed' expression state is inherited through many cell divisions as plants develop. These data demonstrate that epigenetic memory of FLC expression is stored not in trans but in cis.

The conserved Polycomb repressive complex 2 (PRC2) generates trimethylation of histone 3 lysine 27 (H3K27me3), a modification associated with stable epigenetic silencing. Much is known about PRC2-induced silencing but key questions remain concerning its nucleation and stability. Vernalization, the perception and memory of winter in plants, is a classic epigenetic process that, in Arabidopsis, involves PRC2-based silencing of the floral repressor FLC. The slow dynamics of vernalization, taking place over weeks in the cold, generate a level of stable silencing of FLC in the subsequent warm that depends quantitatively on the length of the prior cold. These features make vernalization an ideal experimental system to investigate both the maintenance of epigenetic states and the switching between them. Here, using mathematical modelling, chromatin immunoprecipitation and an FLC:GUS reporter assay, we show that the quantitative nature of vernalization is generated by H3K27me3-mediated FLC silencing in the warm in a subpopulation of cells whose number depends on the length of the prior cold. During the cold, H3K27me3 levels progressively increase at a tightly localized nucleation region within FLC. At the end of the cold, numerical simulations predict that such a nucleation region is capable of switching the bistable epigenetic state of an individual locus, with the probability of overall FLC coverage by silencing H3K27me3 marks depending on the length of cold exposure. Thus, the model predicts a bistable pattern of FLC gene expression in individual cells, a prediction we verify using the FLC:GUS reporter system. Our proposed switching mechanism, involving the local nucleation of an opposing histone modification, is likely to be widely relevant in epigenetic reprogramming.