Collaboration between CpG sites is needed for stable somatic inheritance of DNA methylation states

EpiAge: a next-generation sequencing-based ELOVL2 epigenetic clock for biological age assessment in saliva and blood across health and disease

This study introduces EpiAgePublic, a new method to estimate biological age using only three specific sites on the gene ELOVL2, known for its connection to aging. Unlike traditional methods that require complex and extensive data, our model uses a simpler approach that is well-suited for next-generation sequencing technology, which is a more advanced method of analyzing DNA methylation. This new model overcomes some of the common challenges found in older methods, such as errors due to sample quality and processing variations. We tested EpiAgePublic with a large and varied group of over 4,600 people to ensure its accuracy. It performed on par with, and sometimes better than, more complicated models that use much more data for age estimation. We examined its effectiveness in understanding how factors like HIV infection and stress affect aging, confirming its usefulness in real-world clinical settings. Our results prove that our simple yet effective model, EpiAgePublic, can capture the subtle signs of aging with high accuracy. We also used this model in a study involving patients with Alzheimer's Disease, demonstrating the practical benefits of next-generation sequencing in making precise age-related assessments. This study lays the groundwork for future research on aging mechanisms and assessing how different interventions might impact the aging process using this clock.

Modeling DNA methyltransferase function to predict epigenetic correlation patterns in healthy and cancer cells

DNA methylation is a crucial epigenetic modification that orchestrates chromatin remodelers that suppress transcription, and aberrations in DNA methylation result in a variety of conditions such as cancers and developmental disorders. While it is understood that methylation occurs at CpG-rich DNA regions, it is less understood how distinct methylation profiles are established within various cell types. In this work, we develop a molecular-transport model that depicts the genomic exploration of DNA methyltransferase within a multiscale DNA environment, incorporating biologically relevant factors like methylation rate and CpG density to predict how patterns are established. Our model predicts DNA methylation-state correlation distributions arising from the transport and kinetic properties that are crucial for the establishment of unique methylation profiles. We model the methylation correlation distributions of nine cancerous human cell types to determine how these properties affect the epigenetic profile. Our theory is capable of recapitulating experimental methylation patterns, suggesting the importance of DNA methyltransferase transport in epigenetic regulation. Through this work, we propose a mechanistic description for the establishment of methylation profiles, capturing the key behavioral characteristics of methyltransferase that lead to aberrant methylation.

Mathematical model of RNA-directed DNA methylation predicts tuning of negative feedback required for stable maintenance

RNA-directed DNA methylation (RdDM) is a plant-specific de novo methylation pathway that is responsible for maintenance of asymmetric methylation (CHH, H = A, T or G) in euchromatin. Loci with CHH methylation produce 24 nucleotide (nt) short interfering (si) RNAs. These siRNAs direct additional CHH methylation to the locus, maintaining methylation states through DNA replication. To understand the necessary conditions to produce stable methylation, we developed a stochastic mathematical model of RdDM. The model describes DNA target search by siRNAs derived from CHH methylated loci bound by an Argonaute. Methylation reinforcement occurs either throughout the cell cycle (steady) or immediately following replication (bursty). We compare initial and final methylation distributions to determine simulation conditions that produce stable methylation. We apply this method to the low CHH methylation case. The resulting model predicts that siRNA production must be linearly proportional to methylation levels, that bursty reinforcement is more stable and that slightly higher levels of siRNA production are required for searching DNA, compared to RNA. Unlike CG methylation, which typically exhibits bi-modality with loci having either 100% or 0% methylation, CHH methylation exists across a range. Our model predicts that careful tuning of the negative feedback in the system is required to enable stable maintenance.

Ultrasensitive Amplification-Free Quantification of a Methyl CpG-Rich Cancer Biomarker by Single-Molecule Kinetic Fingerprinting

The most well-studied epigenetic marker in humans is the 5-methyl modification of cytosine in DNA, which has great potential as a disease biomarker. Currently, quantification of DNA methylation relies heavily on bisulfite conversion followed by PCR amplification and NGS or microarray analysis. PCR is subject to potential bias in differential amplification of bisulfite-converted methylated versus unmethylated sequences. Here, we combine bisulfite conversion with single-molecule kinetic fingerprinting to develop an amplification-free assay for DNA methylation at the branched-chain amino acid transaminase 1 (BCAT1) promoter. Our assay selectively responds to methylated sequences with a limit of detection below 1 fM and a specificity of 99.9999%. Evaluating complex genomic DNA matrices, we reliably distinguish <5% DNA methylation at the BCAT1 promoter in whole blood DNA from completely unmethylated whole-genome amplified DNA. Taken together, these results demonstrate the feasibility and sensitivity of our amplification-free, single-molecule quantification approach to improve the early detection of methylated cancer DNA biomarkers.

Methylation patterns at the adjacent CpG sites within enhancers are a part of cell identity

BACKGROUND

It is generally accepted that methylation status of CpG sites spaced up to 50 bp apart is correlated, and accumulation of locally disordered methylation at adjacent CpG sites is involved in neoplastic transformation, acting in similar way as stochastic accumulation of mutations.

RESULTS

We used EPIC microarray data from 596 samples, representing 12 healthy tissue and cell types, as well as 572 blood cancer specimens to analyze methylation status of adjacent CpG sites across human genome, and subsequently validated our findings with NGS and Sanger sequencing. Our analysis showed that there is a subset of the adjacent CpG sites in human genome, with cytosine at one CpG site methylated and the other devoid of methyl group. These loci map to enhancers that are targeted by families of transcription factors involved in cell differentiation. Moreover, our results suggest that the methylation at these loci differ between alleles within a cell, what allows for remarkable level of heterogeneity of methylation patterns. However, different types of specialized cells acquire only one specific and stable pattern of methylation at each of these loci and that pattern is to a large extent lost during neoplastic transformation.

CONCLUSIONS

We identified a substantial number of adjacent CpG loci in human genome that display remarkably stable and cell type specific methylation pattern. The methylation pattern at these loci appears to reflect different methylation of alleles in cells. Furthermore, we showed that changes of methylation status at those loci are likely to be involved in regulation of the activity of enhancers and contribute to neoplastic transformation.

EnhancerNet: a predictive model of cell identity dynamics through enhancer selection

Understanding how cell identity is encoded by the genome and acquired during differentiation is a central challenge in cell biology. I have developed a theoretical framework called EnhancerNet, which models the regulation of cell identity through the lens of transcription factor-enhancer interactions. I demonstrate that autoregulation in these interactions imposes a constraint on the model, resulting in simplified dynamics that can be parameterized from observed cell identities. Despite its simplicity, EnhancerNet recapitulates a broad range of experimental observations on cell identity dynamics, including enhancer selection, cell fate induction, hierarchical differentiation through multipotent progenitor states and direct reprogramming by transcription factor overexpression. The model makes specific quantitative predictions, reproducing known reprogramming recipes and the complex haematopoietic differentiation hierarchy without fitting unobserved parameters. EnhancerNet provides insights into how new cell types could evolve and highlights the functional importance of distal regulatory elements with dynamic chromatin in multicellular evolution.

Dissecting Mechanisms of Epigenetic Memory Through Computational Modeling

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.

T-cell commitment inheritance-an agent-based multi-scale model

T-cell development provides an excellent model system for studying lineage commitment from a multipotent progenitor. The intrathymic development process has been thoroughly studied. The molecular circuitry controlling it has been dissected and the necessary steps like programmed shut off of progenitor genes and T-cell genes upregulation have been revealed. However, the exact timing between decision-making and commitment stage remains unexplored. To this end, we implemented an agent-based multi-scale model to investigate inheritance in early T-cell development. Treating each cell as an agent provides a powerful tool as it tracks each individual cell of a simulated T-cell colony, enabling the construction of lineage trees. Based on the lineage trees, we introduce the concept of the last common ancestors (LCA) of committed cells and analyse their relations, both at single-cell level and population level. In addition to simulating wild-type development, we also conduct knockdown analysis. Our simulations predicted that the commitment is a three-step process that occurs on average over several cell generations once a cell is first prepared by a transcriptional switch. This is followed by the loss of the Bcl11b-opposing function approximately two to three generations later. This is when our LCA analysis indicates that the decision to commit is taken even though in general another one to two generations elapse before the cell actually becomes committed by transitioning to the DN2b state. Our results showed that there is decision inheritance in the commitment mechanism.

A targeted long-read sequencing approach questions the association of OXTR methylation with high-functioning autism

BACKGROUND

DNA sequence variation and altered epigenetic regulation of the oxytocin receptor gene (OXTR) have been implicated in autism and autistic-like behaviors. While previous studies have examined subsegments of OXTR, nanopore Cas9-targeted sequencing (nCATS) allows deep characterization of entire genes with simultaneous assessment of epigenetic 5-methylcytosine (5mC) modification and without the need for prior DNA amplification or bisulfite conversion. This pilot study uses an nCATS approach to sequence the entire OXTR gene and its regulatory construct and screen for 5mC modification to compare results between individuals with high-functioning autism (HFA) and neurotypical controls (NC).

METHODS

Using DNA extracted from peripheral blood, OXTR (Hg38, chr3: 8750381-8770434, 20,054 base pairs) was analyzed by nCATS. 5mC modification probabilities were calculated and visualized across the gene and differential methylation analysis was performed.

RESULTS

Twenty adults with HFA (10 males, 10 females) and 20 age- and sex-matched NC (± 5 years) were included. There were no apparent group differences in the entire OXTR gene sequence, except for the intron variant rs918316, which was clustered in the HFA group. However, differential methylation analysis did not reveal a single significant group-dependent differentially methylated site among the 412 CpG sites captured.

LIMITATIONS

Limitations of this study include the small number of samples due to the pilot nature of the study, which particularly limits the relevance of the sequence variants found. It should also be noted that the use of peripheral blood material limits the ability to draw conclusions about central processes.

CONCLUSIONS

Previous findings of autism-associated OXTR epigenetic alterations were not reproducible with our method. In our opinion, this may lead to a reconsideration of the relevance of altered methylation at individual OXTR CpG positions in autism research. However, given the pilot nature of the study, these results need to be replicated in independent cohorts and with larger sample sizes.

Millennia-long epigenetic fluctuations generate intragenic DNA methylation variance in Arabidopsis populations

Methylation of CG dinucleotides (mCGs), which regulates eukaryotic genome functions, is epigenetically propagated by Dnmt1/MET1 methyltransferases. How mCG is established and transmitted across generations despite imperfect enzyme fidelity is unclear. Whether mCG variation in natural populations is governed by genetic or epigenetic inheritance also remains mysterious. Here, we show that MET1 de novo activity, which is enhanced by existing proximate methylation, seeds and stabilizes mCG in Arabidopsis thaliana genes. MET1 activity is restricted by active demethylation and suppressed by histone variant H2A.Z, producing localized mCG patterns. Based on these observations, we develop a stochastic mathematical model that precisely recapitulates mCG inheritance dynamics and predicts intragenic mCG patterns and their population-scale variation given only CG site spacing. Our results demonstrate that intragenic mCG establishment, inheritance, and variance constitute a unified epigenetic process, revealing that intragenic mCG undergoes large, millennia-long epigenetic fluctuations and can therefore mediate evolution on this timescale.

T-cell commitment inheritance - an agent-based multi-scale model

T-cell development provides an excellent model system for studying lineage commitment from a multipotent progenitor. The intrathymic development process has been thoroughly studied. The molecular circuitry controlling it has been dissected and the necessary steps like programmed shut off of progenitor genes and T-cell genes upregulation have been revealed. However, the exact timing between decision-making and commitment stage remains unexplored. To this end, we implemented an agent-based multi-scale model to investigate inheritance in early T-cell development. Treating each cell as an agent provides a powerful tool as it tracks each individual cell of a simulated T-cell colony, enabling the construction of lineage trees. Based on the lineage trees, we introduce the concept of the last common ancestors (LCA) of committed cells and analyse their relations, both at single-cell level and population level. In addition to simulating wild-type development, we also conduct knockdown analysis. Our simulations showed that the commitment is a three-step process over several cell generations where a cell is first prepared by a transcriptional switch. This is followed by the loss of the Bcl11b-opposing function two to three generations later which is when the decision to commit is taken. Finally, after another one to two generations, the cell becomes committed by transitioning to the DN2b state. Our results showed that there is inheritance in the commitment mechanism.

Genome-wide single-molecule analysis of long-read DNA methylation reveals heterogeneous patterns at heterochromatin that reflect nucleosome organisation

High-throughput sequencing technology is central to our current understanding of the human methylome. The vast majority of studies use chemical conversion to analyse bulk-level patterns of DNA methylation across the genome from a population of cells. While this technology has been used to probe single-molecule methylation patterns, such analyses are limited to short reads of a few hundred basepairs. DNA methylation can also be directly detected using Nanopore sequencing which can generate reads measuring megabases in length. However, thus far these analyses have largely focused on bulk-level assessment of DNA methylation. Here, we analyse DNA methylation in single Nanopore reads from human lymphoblastoid cells, to show that bulk-level metrics underestimate large-scale heterogeneity in the methylome. We use the correlation in methylation state between neighbouring sites to quantify single-molecule heterogeneity and find that heterogeneity varies significantly across the human genome, with some regions having heterogeneous methylation patterns at the single-molecule level and others possessing more homogeneous methylation patterns. By comparing the genomic distribution of the correlation to epigenomic annotations, we find that the greatest heterogeneity in single-molecule patterns is observed within heterochromatic partially methylated domains (PMDs). In contrast, reads originating from euchromatic regions and gene bodies have more ordered DNA methylation patterns. By analysing the patterns of single molecules in more detail, we show the existence of a nucleosome-scale periodicity in DNA methylation that accounts for some of the heterogeneity we uncover in long single-molecule DNA methylation patterns. We find that this periodic structure is partially masked in bulk data and correlates with DNA accessibility as measured by nanoNOMe-seq, suggesting that it could be generated by nucleosomes. Our findings demonstrate the power of single-molecule analysis of long-read data to understand the structure of the human methylome.

Tuning Methylation-Dependent Silencing Dynamics by Synthetic Modulation of CpG Density

Methylation of cytosines in CG dinucleotides (CpGs) within promoters has been shown to lead to gene silencing in mammals in natural contexts. Recently, engineered recruitment of methyltransferases (DNMTs) at specific loci was shown to be sufficient to silence synthetic and endogenous gene expression through this mechanism. A critical parameter for DNA methylation-based silencing is the distribution of CpGs within the target promoter. However, how the number or density of CpGs in the target promoter affects the dynamics of silencing by DNMT recruitment has remained unclear. Here, we constructed a library of promoters with systematically varying CpG content, and analyzed the rate of silencing in response to recruitment of DNMT. We observed a tight correlation between silencing rate and CpG content. Further, methylation-specific analysis revealed a constant accumulation rate of methylation at the promoter after DNMT recruitment. We identified a single CpG site between TATA box and transcription start site (TSS) that accounted for a substantial part of the difference in silencing rates between promoters with differing CpG content, indicating that certain residues play disproportionate roles in controlling silencing. Together, these results provide a library of promoters for synthetic epigenetic and gene regulation applications, as well as insights into the regulatory link between CpG content and silencing rate.

Concepts, mechanisms and implications of long-term epigenetic inheritance

Many modes and mechanisms of epigenetic inheritance have been elucidated in eukaryotes. Most of them are relatively short-term, generally not exceeding one or a few organismal generations. However, emerging evidence indicates that one mechanism, cytosine DNA methylation, can mediate epigenetic inheritance over much longer timescales, which are mostly or completely inaccessible in the laboratory. Here we discuss the evidence for, and mechanisms and implications of, such long-term epigenetic inheritance. We argue that compelling evidence supports the long-term epigenetic inheritance of gene body methylation, at least in the model angiosperm Arabidopsis thaliana, and that variation in such methylation can therefore serve as an epigenetic basis for phenotypic variation in natural populations.

Tuning methylation-dependent silencing dynamics by synthetic modulation of CpG density

Methylation of cytosines in CG dinucleotides (CpGs) within promoters has been shown to lead to gene silencing in mammals in natural contexts. Recently, engineered recruitment of methyltransferases (DNMTs) at specific loci was shown to be sufficient to silence synthetic and endogenous gene expression through this mechanism. A critical parameter for DNA methylation-based silencing is the distribution of CpGs within the target promoter. However, how the number or density of CpGs in the target promoter affects the dynamics of silencing by DNMT recruitment has remained unclear. Here we constructed a library of promoters with systematically varying CpG content, and analyzed the rate of silencing in response to recruitment of DNMT. We observed a tight correlation between silencing rate and CpG content. Further, methylation-specific analysis revealed a constant accumulation rate of methylation at the promoter after DNMT recruitment. We identified a single CpG site between TATA box and transcription start site (TSS) that accounted for a substantial part of the difference in silencing rates between promoters with differing CpG content, indicating that certain residues play disproportionate roles in controlling silencing. Together, these results provide a library of promoters for synthetic epigenetic and gene regulation applications, as well as insights into the regulatory link between CpG content and silencing rate.

Extensive de novo activity stabilizes epigenetic inheritance of CG methylation in Arabidopsis transposons

Cytosine methylation within CG dinucleotides (mCG) can be epigenetically inherited over many generations. Such inheritance is thought to be mediated by a semiconservative mechanism that produces binary present/absent methylation patterns. However, we show here that, in Arabidopsis thaliana h1ddm1 mutants, intermediate heterochromatic mCG is stably inherited across many generations and is quantitatively associated with transposon expression. We develop a mathematical model that estimates the rates of semiconservative maintenance failure and de novo methylation at each transposon, demonstrating that mCG can be stably inherited at any level via a dynamic balance of these activities. We find that DRM2-the core methyltransferase of the RNA-directed DNA methylation pathway-catalyzes most of the heterochromatic de novo mCG, with de novo rates orders of magnitude higher than previously thought, whereas chromomethylases make smaller contributions. Our results demonstrate that stable epigenetic inheritance of mCG in plant heterochromatin is enabled by extensive de novo methylation.

MC profiling: a novel approach to analyze DNA methylation heterogeneity in genome-wide bisulfite sequencing data

DNA methylation is an epigenetic mark implicated in crucial biological processes. Most of the knowledge about DNA methylation is based on bulk experiments, in which DNA methylation of genomic regions is reported as average methylation. However, average methylation does not inform on how methylated cytosines are distributed in each single DNA molecule. Here, we propose Methylation Class (MC) profiling as a genome-wide approach to the study of DNA methylation heterogeneity from bulk bisulfite sequencing experiments. The proposed approach is built on the concept of MCs, groups of DNA molecules sharing the same number of methylated cytosines. The relative abundances of MCs from sequencing reads incorporates the information on the average methylation, and directly informs on the methylation level of each molecule. By applying our approach to publicly available bisulfite-sequencing datasets, we individuated cell-to-cell differences as the prevalent contributor to methylation heterogeneity. Moreover, we individuated signatures of loci undergoing imprinting and X-inactivation, and highlighted differences between the two processes. When applying MC profiling to compare different conditions, we identified methylation changes occurring in regions with almost constant average methylation. Altogether, our results indicate that MC profiling can provide useful insights on the epigenetic status and its evolution at multiple genomic regions.

Local CpG density affects the trajectory and variance of age-associated DNA methylation changes

BACKGROUND

DNA methylation is an epigenetic mark associated with the repression of gene promoters. Its pattern in the genome is disrupted with age and these changes can be used to statistically predict age with epigenetic clocks. Altered rates of aging inferred from these clocks are observed in human disease. However, the molecular mechanisms underpinning age-associated DNA methylation changes remain unknown. Local DNA sequence can program steady-state DNA methylation levels, but how it influences age-associated methylation changes is unknown.

RESULTS

We analyze longitudinal human DNA methylation trajectories at 345,895 CpGs from 600 individuals aged between 67 and 80 to understand the factors responsible for age-associated epigenetic changes at individual CpGs. We show that changes in methylation with age occur at 182,760 loci largely independently of variation in cell type proportions. These changes are especially apparent at 8322 low CpG density loci. Using SNP data from the same individuals, we demonstrate that methylation trajectories are affected by local sequence polymorphisms at 1487 low CpG density loci. More generally, we find that low CpG density regions are particularly prone to change and do so variably between individuals in people aged over 65. This differs from the behavior of these regions in younger individuals where they predominantly lose methylation.

CONCLUSIONS

Our results, which we reproduce in two independent groups of individuals, demonstrate that local DNA sequence influences age-associated DNA methylation changes in humans in vivo. We suggest that this occurs because interactions between CpGs reinforce maintenance of methylation patterns in CpG dense regions.

Locally correlated kinetics of post-replication DNA methylation reveals processivity and region specificity in DNA methylation maintenance

DNA methylation occurs predominantly on cytosine-phosphate-guanine (CpG) dinucleotides in the mammalian genome, and the methylation landscape is maintained over mitotic cell division. It has been posited that coupling of maintenance methylation activity among neighbouring CpGs is critical to stability over cellular generations; however, the mechanism is unclear. We used mathematical models and stochastic simulation to analyse data from experiments that probe genome-wide methylation of nascent DNA post-replication in cells. We find that DNA methylation maintenance rates on individual CpGs are locally correlated, and the degree of this correlation varies by genomic regional context. By using theory of protein diffusion along DNA, we show that exponential decay of methylation rate correlation with genomic distance is consistent with enzyme processivity. Our results provide quantitative evidence of genome-wide methyltransferase processivity in vivo. We further developed a method to disentangle different mechanistic sources of kinetic correlations. From the experimental data, we estimate that an individual methyltransferase methylates neighbour CpGs processively if they are 36 basepairs apart, on average. But other mechanisms of coupling dominate for longer inter-CpG distances. Our study demonstrates that quantitative insights into enzymatic mechanisms can be obtained from replication-associated, cell-based genome-wide measurements, by combining data-driven statistical analyses with hypothesis-driven mathematical modelling.

Making sense of the ageing methylome

Over time, the human DNA methylation landscape accrues substantial damage, which has been associated with a broad range of age-related diseases, including cardiovascular disease and cancer. Various age-related DNA methylation changes have been described, including at the level of individual CpGs, such as differential and variable methylation, and at the level of the whole methylome, including entropy and correlation networks. Here, we review these changes in the ageing methylome as well as the statistical tools that can be used to quantify them. We detail the evidence linking DNA methylation to ageing phenotypes and the longevity strategies aimed at altering both DNA methylation patterns and machinery to extend healthspan and lifespan. Lastly, we discuss theories on the mechanistic causes of epigenetic ageing.

Cluster mean-field theory accurately predicts statistical properties of large-scale DNA methylation patterns

The accurate establishment and maintenance of DNA methylation patterns is vital for mammalian development and disruption to these processes causes human disease. Our understanding of DNA methylation mechanisms has been facilitated by mathematical modelling, particularly stochastic simulations. Megabase-scale variation in DNA methylation patterns is observed in development, cancer and ageing and the mechanisms generating these patterns are little understood. However, the computational cost of stochastic simulations prevents them from modelling such large genomic regions. Here, we test the utility of three different mean-field models to predict summary statistics associated with large-scale DNA methylation patterns. By comparison to stochastic simulations, we show that a cluster mean-field model accurately predicts the statistical properties of steady-state DNA methylation patterns, including the mean and variance of methylation levels calculated across a system of CpG sites, as well as the covariance and correlation of methylation levels between neighbouring sites. We also demonstrate that a cluster mean-field model can be used within an approximate Bayesian computation framework to accurately infer model parameters from data. As mean-field models can be solved numerically in a few seconds, our work demonstrates their utility for understanding the processes underpinning large-scale DNA methylation patterns.

A mathematical model which examines age-related stochastic fluctuations in DNA maintenance methylation

Due to its complexity and its ubiquitous nature the ageing process remains an enduring biological puzzle. Many molecular mechanisms and biochemical process have become synonymous with ageing. However, recent findings have pinpointed epigenetics as having a key role in ageing and healthspan. In particular age related changes to DNA methylation offer the possibility of monitoring the trajectory of biological ageing and could even be used to predict the onset of diseases such as cancer, Alzheimer's disease and cardiovascular disease. At the molecular level emerging evidence strongly suggests the regulatory processes which govern DNA methylation are subject to intracellular stochasticity. It is challenging to fully understand the impact of stochasticity on DNA methylation levels at the molecular level experimentally. An ideal solution is to use mathematical models to capture the essence of the stochasticity and its outcomes. In this paper we present a novel stochastic model which accounts for specific methylation levels within a gene promoter. Uncertainty of the eventual site-specific methylation levels for different values of methylation age, depending on the initial methylation levels were analysed. Our model predicts the observed bistable levels in CpG islands. In addition, simulations with various levels of noise indicate that uncertainty predominantly spreads through the hypermethylated region of stability, especially for large values of input noise. A key outcome of the model is that CpG islands with high to intermediate methylation levels tend to be more susceptible to dramatic DNA methylation changes due to increasing methylation age.

Origins of human disease: the chrono-epigenetic perspective

Epigenetics has enriched human disease studies by adding new interpretations to disease features that cannot be explained by genetic and environmental factors. However, identifying causal mechanisms of epigenetic origin has been challenging. New opportunities have risen from recent findings in intra-individual and cyclical epigenetic variation, which includes circadian epigenetic oscillations. Cytosine modifications display deterministic temporal rhythms, which may drive ageing and complex disease. Temporality in the epigenome, or the 'chrono' dimension, may help the integration of epigenetic, environmental and genetic disease studies, and reconcile several disparities stemming from the arbitrarily delimited research fields. The ultimate goal of chrono-epigenetics is to predict disease risk, age of onset and disease dynamics from within individual-specific temporal dynamics of epigenomes.

Dynamics and inhibition of MLL1 CXXC domain on DNA revealed by single-molecule quantification

CpG islands recruit MLL1 via the CXXC domain to modulate chromatin structure and regulate gene expression. The amino acid motif of CXXC also plays a pivotal role in MLL1's structure and function and serves as a target for drug design. In addition, the CpG pattern in an island governs spatially dependent collaboration among CpGs in recruiting epigenetic enzymes. However, current studies using short DNA fragments cannot probe the dynamics of CXXC on long DNA with crowded CpG motifs. Here, we used single-molecule magnetic tweezers to examine the binding dynamics of MLL1's CXXC domain on a long DNA with a CpG island. The mechanical strand separation assay allows profiling of protein-DNA complexes and reports force-dependent unfolding times. Further design of a hairpin detector reveals the unfolding time of individual CXXC-CpG complexes. Finally, in a proof of concept we demonstrate the inhibiting effect of dimethyl fumarate on the CXXC-DNA complexes by measuring the dose response curve of the unfolding time. This demonstrates the potential feasibility of using single-molecule strand separation as a label-free detector in drug discovery and chemical biology.

Requirement of DNMT1 to orchestrate epigenomic reprogramming for NPM-ALK-driven lymphomagenesis

Malignant transformation depends on genetic and epigenetic events that result in a burst of deregulated gene expression and chromatin changes. To dissect the sequence of events in this process, we used a T-cell-specific lymphoma model based on the human oncogenic nucleophosmin-anaplastic lymphoma kinase (NPM-ALK) translocation. We find that transformation of T cells shifts thymic cell populations to an undifferentiated immunophenotype, which occurs only after a period of latency, accompanied by induction of the MYC-NOTCH1 axis and deregulation of key epigenetic enzymes. We discover aberrant DNA methylation patterns, overlapping with regulatory regions, plus a high degree of epigenetic heterogeneity between individual tumors. In addition, ALK-positive tumors show a loss of associated methylation patterns of neighboring CpG sites. Notably, deletion of the maintenance DNA methyltransferase DNMT1 completely abrogates lymphomagenesis in this model, despite oncogenic signaling through NPM-ALK, suggesting that faithful maintenance of tumor-specific methylation through DNMT1 is essential for sustained proliferation and tumorigenesis.

Environmental and socio-cultural impacts on global DNA methylation in the indigenous Huichol population of Nayarit, Mexico

Alterations of global DNA methylation have been evaluated in several studies worldwide; however, Long Interspersed Nuclear Elements-1 (LINE-1) methylation in genetically conserved populations such as indigenous communities have not, to our knowledge, been reported. The aim of this study was to evaluate the relationship between LINE-1 methylation patterns and factors such as pesticide exposure and socio-cultural characteristics in the Indigenous Huichol Population of Nayarit, Mexico. A cross-sectional study was conducted in 140 Huichol indigenous individuals. A structured questionnaire was used to determine general and anthropometric characteristics, diet, harmful habits, and pesticide exposure. DNA methylation was determined by pyrosequencing of bisulfite-treated DNA. A lower level of LINE-1 methylation was found in the indigenous population when compared to a Mestizo population previously studied by our group. This difference might be due to the influence of the genetic admixture and differing dietary and lifestyle habits. The males in the indigenous population exhibited increased LINE-1 methylation in comparison to the females. Sex and alcohol consumption showed positive associations with LINE-1 methylation, while weight, current work in the field, current pesticide usage, and folate intake exhibited negative associations with LINE-1 methylation. The results suggest that ethnicity, as well as other internal and environmental factors, might influence LINE-1 methylation.

Multi-scale Dynamical Modeling of T Cell Development from an Early Thymic Progenitor State to Lineage Commitment

Intrathymic development of committed progenitor (pro)-T cells from multipotent hematopoietic precursors offers an opportunity to dissect the molecular circuitry establishing cell identity in response to environmental signals. This transition encompasses programmed shutoff of stem/progenitor genes, upregulation of T cell specification genes, proliferation, and ultimately commitment. To explain these features in light of reported cis-acting chromatin effects and experimental kinetic data, we develop a three-level dynamic model of commitment based upon regulation of the commitment-linked gene Bcl11b. The levels are (1) a core gene regulatory network (GRN) architecture from transcription factor (TF) perturbation data, (2) a stochastically controlled chromatin-state gate, and (3) a single-cell proliferation model validated by experimental clonal growth and commitment kinetic assays. Using RNA fluorescence in situ hybridization (FISH) measurements of genes encoding key TFs and measured bulk population dynamics, this single-cell model predicts state-switching kinetics validated by measured clonal proliferation and commitment times. The resulting multi-scale model provides a mechanistic framework for dissecting commitment dynamics.

A Mathematical Model for Inheritance of DNA Methylation Patterns in Somatic Cells

DNA methylation is an essential epigenetic mechanism used by cells to regulate gene expression. Interestingly, DNA replication, a function necessary for cell division, disrupts the methylation pattern. Since perturbed methylation patterns are associated with aberrant gene expression and many diseases, including cancer, restoration of the correct pattern following DNA replication is crucial. However, the exact mechanisms of this restoration remain under investigation. DNA methyltransferases (Dnmts) perform methylation by adding a methyl group to cytosines at CpG sites in the DNA. These CpG sites are found in regions of high density, termed CpG islands (CGIs), and regions of low density in the genome. Nearly, every CpG site in a CGI has the same state, either methylated or unmethylated, and almost all CpG sites in regions of low CpG density are methylated. We propose a stochastic model for the dynamics of the post-replicative restoration of methylation patterns. The model considers the recruitment of Dnmts and demethylating enzymes to regions of hyper- and hypomethylation, respectively. The model also includes the interaction between Dnmt1 and PCNA, an enzyme that localizes Dnmt1 to the replication complex. Using our model, we predict that the methylation of regions of DNA can be bistable. Further, we predict that recruitment mechanisms maintain methylation in CGIs, whereas the Dnmt1-PCNA interaction maintains methylation in low-density regions.

A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration

Stem cell heterogeneity is essential for homeostasis in tissue development. This paper establishes a general mathematical framework to model the dynamics of stem cell regeneration with cell heterogeneity and random transitions of epigenetic states. The framework generalizes the classical G0 cell cycle model and incorporates the epigenetic states of individual cells represented by a continuous multidimensional variable. In the model, the kinetic rates of cell behaviors, including proliferation, differentiation, and apoptosis, are dependent on their epigenetic states, and the random transitions of epigenetic states between cell cycles are represented by an inheritance probability function that describes the conditional probability of cell state changes. Moreover, the model can be extended to include genotypic changes and describe the process of gene mutation-induced tumor development. The proposed mathematical framework provides a generalized formula that helps us to understand various dynamic processes of stem cell regeneration, including tissue development, degeneration, and abnormal growth.

DNA Methylation Heterogeneity Induced by Collaborations Between Enhancers

During mammalian embryo development, reprogramming of DNA methylation plays important roles in the erasure of parental epigenetic memory and the establishment of naive pluripotent cells. Multiple enzymes that regulate the processes of methylation and demethylation work together to shape the pattern of genome-scale DNA methylation and guide the process of cell differentiation. Recent availability of methylome information from single-cell whole genome bisulfite sequencing (scBS-seq) provides an opportunity to study DNA methylation dynamics in the whole genome in individual cells, which reveal the heterogeneous methylation distributions of enhancers in embryo stem cells. In this study, we developed a computational model of enhancer methylation inheritance to study the dynamics of genome-scale DNA methylation reprogramming during exit from pluripotency. The model enables us to track genome-scale DNA methylation reprogramming at single-cell level during the embryo development process and reproduce the DNA methylation heterogeneity reported by scBS-seq. Model simulations show that DNA methylation heterogeneity is an intrinsic property driven by cell division along the development process, and the collaboration between neighboring enhancers is required for heterogeneous methylation. Our study suggests that the mechanism of genome-scale oscillation might not be necessary for the DNA methylation heterogeneity during exit from pluripotency.

Stochastic modeling reveals kinetic heterogeneity in post-replication DNA methylation

DNA methylation is a heritable epigenetic modification that plays an essential role in mammalian development. Genomic methylation patterns are dynamically maintained, with DNA methyltransferases mediating inheritance of methyl marks onto nascent DNA over cycles of replication. A recently developed experimental technique employing immunoprecipitation of bromodeoxyuridine labeled nascent DNA followed by bisulfite sequencing (Repli-BS) measures post-replication temporal evolution of cytosine methylation, thus enabling genome-wide monitoring of methylation maintenance. In this work, we combine statistical analysis and stochastic mathematical modeling to analyze Repli-BS data from human embryonic stem cells. We estimate site-specific kinetic rate constants for the restoration of methyl marks on >10 million uniquely mapped cytosines within the CpG (cytosine-phosphate-guanine) dinucleotide context across the genome using Maximum Likelihood Estimation. We find that post-replication remethylation rate constants span approximately two orders of magnitude, with half-lives of per-site recovery of steady-state methylation levels ranging from shorter than ten minutes to five hours and longer. Furthermore, we find that kinetic constants of maintenance methylation are correlated among neighboring CpG sites. Stochastic mathematical modeling provides insight to the biological mechanisms underlying the inference results, suggesting that enzyme processivity and/or collaboration can produce the observed kinetic correlations. Our combined statistical/mathematical modeling approach expands the utility of genomic datasets and disentangles heterogeneity in methylation patterns arising from replication-associated temporal dynamics versus stable cell-to-cell differences.

DNA sequence context as a marker of CpG methylation instability in normal and cancer tissues

DNA methylation alterations are related to multiple molecular mechanisms. The DNA context of CpG sites plays a crucial role in the maintenance and stability of methylation patterns. The quantitative relationship between DNA composition and DNA methylation has been studied in normal as well as pathological conditions, showing that DNA methylation status is highly dependent on the local sequence context. In this work, we describe this relationship by analyzing the DNA sequence context associated to methylation profiles in both physiological and pathological conditions. In particular, we used DNA motifs to describe methylation stability patterns in normal tissues and aberrant methylation events in cancer lesions. In this manuscript, we show how different groups of DNA sequences can be related to specific epigenetic events, across normal and cancer tissues, and provide a thorough structural and functional characterization of these sequences.

Genome-Scale Oscillations in DNA Methylation during Exit from Pluripotency

Pluripotency is accompanied by the erasure of parental epigenetic memory, with naïve pluripotent cells exhibiting global DNA hypomethylation both in vitro and in vivo. Exit from pluripotency and priming for differentiation into somatic lineages is associated with genome-wide de novo DNA methylation. We show that during this phase, co-expression of enzymes required for DNA methylation turnover, DNMT3s and TETs, promotes cell-to-cell variability in this epigenetic mark. Using a combination of single-cell sequencing and quantitative biophysical modeling, we show that this variability is associated with coherent, genome-scale oscillations in DNA methylation with an amplitude dependent on CpG density. Analysis of parallel single-cell transcriptional and epigenetic profiling provides evidence for oscillatory dynamics both in vitro and in vivo. These observations provide insights into the emergence of epigenetic heterogeneity during early embryo development, indicating that dynamic changes in DNA methylation might influence early cell fate decisions.

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Co-expression of DNMT3s and TETs promotes genome-scale oscillations in DNA methylation

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Oscillation amplitude is greatest at a CpG density characteristic of enhancers

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Cell synchronization reveals oscillation period and link with primary transcripts

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Multi-omic single-cell profiling provides evidence for oscillatory dynamics in vivo

Hidden Markov Modelling Reveals Neighborhood Dependence of Dnmt3a and 3b Activity

DNA methylation is an epigenetic mark whose important role in development has been widely recognized. This epigenetic modification results in heritable information not encoded by the DNA sequence. The underlying mechanisms controlling DNA methylation are only partly understood. Several mechanistic models of enzyme activities responsible for DNA methylation have been proposed. Here, we extend existing Hidden Markov Models (HMMs) for DNA methylation by describing the occurrence of spatial methylation patterns over time and propose several models with different neighborhood dependences. Furthermore, we investigate correlations between the neighborhood dependence and other genomic information. We perform numerical analysis of the HMMs applied to comprehensive hairpin and non-hairpin bisulfite sequencing measurements and accurately predict wild-type data. We find evidence that the activities of Dnmt3a and Dnmt3b responsible for de novo methylation depend on 5' (left) but not on 3' (right) neighboring CpGs in a sequencing string.

A single-cell epigenetic model for paternal psychological stress-induced transgenerational reprogramming in offspring

Experimental evidence shows that parental psychological stress affects the long-term health of offspring in an inheritable fashion. Although epigenetic mechanisms, including DNA methylation, miRNA, and histone modifications, are involved in transgenerational programming, the underlining mechanisms of transgenerational inheritance remain unsolved. Here, we present a single-cell-based computational model for transgenerational inheritance for investigating the long-term dynamics of phenotype changes in response to parental stress. The model is based on a recent study that has identified the imprinted sperm gene Sfmbt2 as a key target, and incorporates crosstalks among drastically different time scales in mammalian development, including DNA methylation, transcription, cell division, and population dynamics. Computational analysis of the model suggests a positive feedback to DNA methylation in the promoter region of sperm Sfmbt2 gene that provides a possible mechanism to mediate the parental psychological stress reprogramming in offspring. This approach provides a modeling framework for the understanding of the roles that epigenetics play in transgenerational inheritance.

Nucleotide distance influences co-methylation between nearby CpG sites

The tendency of individual CpG sites to be methylated is distinctive, non-random and well-regulated throughout the genome. We investigated the structural and spatial factors influencing CpGs methylation by performing an ultra-deep targeted methylation analysis on human, mouse and zebrafish genes. We found that methylation is not a random process and that closer neighboring CpG sites are more likely to share the same methylation status. Moreover, if the distance between CpGs increases, the degree of co-methylation decreases. We set up a simulation model to analyze the contribution of both the intrinsic susceptibility and the distance effect on the probability of a CpG to be methylated. Our finding suggests that the establishment of a specific methylation pattern follows a universal rule that must take into account of the synergistic and dynamic interplay of these two main factors: the intrinsic methylation susceptibility of specific CpG and the nucleotide distance between two CpG sites.

Within-sample co-methylation patterns in normal tissues

Background

DNA methylation is an epigenetic event that may regulate gene expression. Because of this regulation role, aberrant DNA methylation is often associated with many diseases. Within-sample DNA co-methylation is the similarity of methylation in nearby cytosine sites of a chromosome. It is important to study co-methylation patterns. However, it is not well studied yet, and it is unclear to us what co-methylation patterns normal DNA samples have. Are the co-methylation patterns of the same tissue across several samples different? Are the co-methylation patterns of various tissues of the same sample different? To answer these questions, we conduct analyses using two sets of data: 3-sample-1-tissue (3S1T) and 1-sample-8-tissue (1S8T).

Results

To study the co-methylation patterns of the two datasets, 3S1T and 1S8T, we investigate the following questions: How often does one methylation state change to other methylation states and how is this change associated with chromosome distance? Based on the 3S1T data, we find there is not significant co-methylation difference among the same spleen tissues of three different samples. However, the analysis results of 1S8T data show that there were significant differences among eight tissues of one sample. For both 3S1T and 1S8T data, we find that the no/low methylation state A and high/full methylation state D tend to remain the same along a chromosome region. We also find that the low/partial methylation state B and partial/high methylation state C tend to change to higher methylation states along a chromosome. Finally, we find that lengths of most co-methylation regions are very short with only a few hundred base pairs. In fact, only a small proportion of methylated regions are longer than 1000 base pairs.

Conclusions

In this paper, we have addressed a few questions regarding within-sample co-methylation patterns in normal tissues. Our statistical analysis results and answers may help researchers to better understand the biological process of DNA methylation. This may pave the way to develop better analysis methods for future methylation research.

Electronic supplementary material

The online version of this article (10.1186/s13040-019-0198-8) contains supplementary material, which is available to authorized users.

Computational modelling folate metabolism and DNA methylation: implications for understanding health and ageing

Dietary folates have a key role to play in health, as deficiencies in the intake of these B vitamins have been implicated in a wide variety of clinical conditions. The reason for this is folates function as single carbon donors in the synthesis of methionine and nucleotides. Moreover, folates have a vital role to play in the epigenetics of mammalian cells by supplying methyl groups for DNA methylation reactions. Intriguingly, a growing body of experimental evidence suggests that DNA methylation status could be a central modulator of the ageing process. This has important health implications because the methylation status of the human genome could be used to infer age-related disease risk. Thus, it is imperative we further our understanding of the processes which underpin DNA methylation and how these intersect with folate metabolism and ageing. The biochemical and molecular mechanisms, which underpin these processes, are complex. However, computational modelling offers an ideal framework for handling this complexity. A number of computational models have been assembled over the years, but to date, no model has represented the full scope of the interaction between the folate cycle and the reactions, which governs the DNA methylation cycle. In this review, we will discuss several of the models, which have been developed to represent these systems. In addition, we will present a rationale for developing a combined model of folate metabolism and the DNA methylation cycle.

Data-driven selection and parameter estimation for DNA methylation mathematical models

Epigenetics is coming to the fore as a key process which underpins health. In particular emerging experimental evidence has associated alterations to DNA methylation status with healthspan and aging. Mammalian DNA methylation status is maintained by an intricate array of biochemical and molecular processes. It can be argued changes to these fundamental cellular processes ultimately drive the formation of aberrant DNA methylation patterns, which are a hallmark of diseases, such as cancer, Alzheimer's disease and cardiovascular disease. In recent years mathematical models have been used as effective tools to help advance our understanding of the dynamics which underpin DNA methylation. In this paper we present linear and nonlinear models which encapsulate the dynamics of the molecular mechanisms which define DNA methylation. Applying a recently developed Bayesian algorithm for parameter estimation and model selection, we are able to estimate distributions of parameters which include nominal parameter values. Using limited noisy observations, the method also identified which methylation model the observations originated from, signaling that our method has practical applications in identifying what models best match the biological data for DNA methylation.

Effect of Genotype and Maternal Affective Disorder on Intronic Methylation of FK506 Binding Protein 5 in Cord Blood DNA

A single nucleotide polymorphism (SNP: rs1360780) in FKBP5 (FK506 Binding Protein 5) has been shown to interact with exposure to childhood adversity to promote loss of methylation and increase in gene expression in adults. We asked whether rs1360780 can influence FKBP5 intronic methylation in the context of exposure to maternal affective disorders in utero. Sixty cord blood DNA samples from the Boston Birth Cohort were genotyped at rs1360780 and studied for methylation changes as they relate to genotype and exposure to affective disorders during pregnancy. Linear regression was employed to contrast the risk (TT) genotype to the heterozygous (CT) and homozygous (CC) genotypes with adjustment for potential confounders. The recessive genotype (TT) was associated with increased methylation at multiple CpGs in the FKBP5 intron 5 region (p < 0.01). These findings were enhanced among cases exposed to maternal affective disorders (p = 0.02). A human cell line treated with cortisol showed that changes in intron 5 CpG methylation and FKBP5 expression were inversely associated. These findings suggest that rs1360780 can influence FKBP5 intronic methylation by acting in cis as a methylation quantitative locus and highlight the impact of genotypic risk on methylation in utero. Additionally, prenatal stress exposure compounded with the risk genotype may lead to a compensatory increase in methylation.

Proof of concept study of age-dependent DNA methylation markers across different tissues by massive parallel sequencing

The use of DNA methylation (DNAm) for chronological age determination has been widely investigated within the last few years for its application within the field of forensic genetics. The majority of forensic studies are based on blood, saliva, and buccal cell samples, respectively. Although these types of samples represent an extensive amount of traces found at a crime scene or are readily available from individuals, samples from other tissues can be relevant for forensic investigations. Age determination could be important for cases involving unidentifiable bodies and based on remaining soft tissue e.g. brain and muscle, or completely depend on hard tissue such as bone. However, due to the cell type specificity of DNAm, it is not evident whether cell type specific age-dependent CpG positions are also applicable for age determination in other cell types. Within this pilot study, we investigated whether 13 previously selected age-dependent loci based on whole blood analysis including amongst others ELOVL2, TRIM59, F5, and KLF14 also have predictive value in other forensically relevant tissues. Samples of brain, bone, muscle, buccal swabs, and whole blood of 29 deceased individuals (age range 0-87 years) were analyzed for these 13 age-dependent markers using massive parallel sequencing. Seven of these loci did show age-dependency in all five tissues. The change of DNAm during lifetime was different in the set of tissues analyzed, and sometimes other CpG sites within the loci showed a higher age-dependency. This pilot study shows the potential of existing blood DNAm markers for age-determination to analyze other tissues than blood. We identified seven known blood-based DNAm markers for use in muscle, brain, bone, buccal swabs, and blood. Nevertheless, a different reference set for each tissue is needed to adapt for tissue-specific changes of the DNAm over time.

Modeling Methylation Patterns with Long Read Sequencing Data

Variation in cytosine methylation at CpG dinucleotides is often observed in genomic regions, and analysis typically focuses on estimating the proportion of methylated sites observed in a given region and comparing these levels across samples to determine association with conditions of interest. While sites are tacitly treated as independent, when observed at the level of individual molecules methylation patterns exhibit strong evidence of local spatial dependence. We previously developed a neighboring sites model to account for correlation and clustering behavior observed in two tandem repeat regions in a collection of ovarian carcinomas. We now introduce extensions of the model that account for the effect of distance between sites as well as asymmetric correlation in de novo methylation and demethylation rates. We apply our models to published data from a whole genome bisulfite sequencing experiment using long reads, estimating model parameters for a selection of CpG-dense regions spanning between 21 and 67 sites. Our methods detect evidence of local spatial correlation as a function of site-to-site distance and demonstrate the added value of employing long read sequencing data in epigenetic research.

Exploring the Link between Nucleosome Occupancy and DNA Methylation

Near promoters, both nucleosomes and CpG sites form characteristic spatial patterns. Previously, nucleosome depleted regions were observed upstream of transcription start sites and nucleosome occupancy was reported to correlate both with CpG density and the level of CpG methylation. Several studies imply a causal link where CpG methylation might induce nucleosome formation, whereas others argue the opposite, i.e., that nucleosome occupancy might influence CpG methylation. Correlations are indeed evident between nucleosomes, CpG density and CpG methylation—at least near promoter sites. It is however less established whether there is an immediate causal relation between nucleosome occupancy and the presence of CpG sites—or if nucleosome occupancy could be influenced by other factors. In this work, we test for such causality in human genomes by analyzing the three quantities both near and away from promoter sites. For data from the human genome we compare promoter regions with given CpG densities with genomic regions without promoters but of similar CpG densities. We find the observed correlation between nucleosome occupancy and CpG density, respectively CpG methylation, to be specific to promoter regions. In other regions along the genome nucleosome occupancy is statistically independent of the positioning of CpGs or their methylation levels. Anti-correlation between CpG density and methylation level is however similarly strong in both regions. On promoters, nucleosome occupancy is more strongly affected by the level of gene expression than CpG density or CpG methylation—calling into question any direct causal relation between nucleosome occupancy and CpG organization. Rather, our results suggest that for organisms with cytosine methylation nucleosome occupancy might be primarily linked to gene expression, with no strong impact on methylation.

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.

Noise-induced polarization switching in complex networks

The combination of bistability and noise is ubiquitous in complex systems, from biology to social interactions, and has important implications for their functioning and resilience. Here we use a simple three-state dynamical process, in which nodes go from one pole to another through an intermediate state, to show that noise can induce polarization switching in bistable systems if dynamical correlations are significant. In large, fully connected networks, where dynamical correlations can be neglected, increasing noise yields a collapse of bistability to an unpolarized configuration where the three possible states of the nodes are equally likely. In contrast, increased noise induces abrupt and irreversible polarization switching in sparsely connected networks. In multiplexes, where each layer can have a different polarization tendency, one layer is dominant and progressively imposes its polarization state on the other, offsetting or promoting the ability of noise to switch its polarization. Overall, we show that the interplay of noise and dynamical correlations can yield discontinuous transitions between extremes, which cannot be explained by a simple mean-field description.