Statistical mechanics model for the dynamics of collective epigenetic histone modification

Dynamical phase transition in models that couple chromatin folding with histone modifications

Genomic regions can acquire heritable epigenetic states through unique histone modifications, which lead to stable gene expression patterns without altering the underlying DNA sequence. However, the relationship between chromatin conformational dynamics and epigenetic stability is poorly understood. In this paper, we propose kinetic models to investigate the dynamic fluctuations of histone modifications and the spatial interactions between nucleosomes. Our model explicitly incorporates the influence of chemical modifications on the structural stability of chromatin and the contribution of chromatin contacts to the cooperative nature of chemical reactions. Through stochastic simulations and analytical theory, we have discovered distinct steady-state outcomes in different kinetic regimes, resembling a dynamical phase transition. Importantly, we have validated that the emergence of this transition, which occurs on biologically relevant timescales, is robust against variations in model design and parameters. Our findings suggest that the viscoelastic properties of chromatin and the timescale at which it transitions from a gel-like to a liquidlike state significantly impact dynamic processes that occur along the one-dimensional DNA sequence.

Two-way feedback between chromatin compaction and histone modification state explains Saccharomyces cerevisiae heterochromatin bistability

Compact chromatin is closely linked with gene silencing in part by sterically masking access to promoters, inhibiting transcription factor binding and preventing polymerase from efficiently transcribing a gene. However, a broader hypothesis suggests that chromatin compaction can be both a cause and a consequence of the locus histone modification state, with a tight bidirectional interaction underpinning bistable transcriptional states. To rigorously test this hypothesis, we developed a mathematical model for the dynamics of the HMR locus in Saccharomyces cerevisiae, that incorporates activating histone modifications, silencing proteins, and a dynamic, acetylation-dependent, three-dimensional locus size. Chromatin compaction enhances silencer protein binding, which in turn feeds back to remove activating histone modifications, leading to further compaction. The bistable output of the model was in good agreement with prior quantitative data, including switching rates from expressed to silent states (and vice versa), and protein binding/histone modification levels within the locus. We then tested the model by predicting changes in switching rates as the genetic length of the locus was increased, which were then experimentally verified. Such bidirectional feedback between chromatin compaction and the histone modification state may be a widespread and important regulatory mechanism given the hallmarks of many heterochromatic regions: physical chromatin compaction and dimerizing (or multivalent) silencing proteins.

Modeling of covalent modifications of histones to estimate the binding affinity

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

Nucleosome sliding can influence the spreading of histone modifications

Nucleosomes are the fundamental building blocks of chromatin that not only help in the folding of chromatin, but also in carrying epigenetic information. It is known that nucleosome sliding is responsible for dynamically organizing chromatin structure and the resulting gene regulation. Since sliding can move two neighboring nucleosomes physically close or away, can it play a role in the spreading of histone modifications? We investigate this by simulating a stochastic model that couples nucleosome dynamics with the kinetics of histone modifications. We show that the sliding of nucleosomes can affect the modification pattern as well as the time it takes to modify a given region of chromatin. Exploring different nucleosome densities and modification kinetic parameters, we show that nucleosome sliding can be important for creating histone modification domains. Our model predicts that nucleosome density coupled with sliding dynamics can create an asymmetric histone modification profile around regulatory regions. We also compute the probability distribution of modified nucleosomes and relaxation kinetics of modifications. Our predictions are comparable with known experimental results.

High fidelity epigenetic inheritance: Information theoretic model predicts threshold filling of histone modifications post replication

During cell devision, maintaining the epigenetic information encoded in histone modification patterns is crucial for survival and identity of cells. The faithful inheritance of the histone marks from the parental to the daughter strands is a puzzle, given that each strand gets only half of the parental nucleosomes. Mapping DNA replication and reconstruction of modifications to equivalent problems in communication of information, we ask how well enzymes can recover the parental modifications, if they were ideal computing machines. Studying a parameter regime where realistic enzymes can function, our analysis predicts that enzymes may implement a critical threshold filling algorithm which fills unmodified regions of length at most k. This algorithm, motivated from communication theory, is derived from the maximum à posteriori probability (MAP) decoding which identifies the most probable modification sequence based on available observations. Simulations using our method produce modification patterns similar to what has been observed in recent experiments. We also show that our results can be naturally extended to explain inheritance of spatially distinct antagonistic modifications.

Impact of chromosomal organization on epigenetic drift and domain stability revealed by physics-based simulations

We examine the relationship between the size of domains of epigenetic marks and the stability of those domains using our theoretical model that captures the physical mechanisms governing the maintenance of epigenetic modifications. We focus our study on histone H3 lysine-9 trimethylation, one of the most common and consequential epigenetic marks with roles in chromatin compaction and gene repression. Our model combines the effects of methyl spreading by methyltransferases and chromatin segregation into heterochromatin and euchromatin because of preferential heterochromatin protein 1 (HP1) binding. Our model indicates that, although large methylated domains are passed successfully from one chromatin generation to the next, small alterations to the methylation sequence are not maintained during chromatin replication. Using our predictive model, we investigate the size required for an epigenetic domain to persist over chromatin generations while surrounded by a much larger domain of opposite methylation and compaction state. We find that there is a critical size threshold in the hundreds-of-nucleosomes scale above which an epigenetic domain will be reliably maintained over generations. The precise size of the threshold differs for heterochromatic and euchromatic domains. Our results are consistent with natural alterations to the epigenetic sequence occurring during embryonic development and due to age-related epigenetic drift.

Stochastic epigenetic dynamics of gene switching

Epigenetic modifications of histones crucially affect eukaryotic gene activity, while the epigenetic histone state is largely determined by the binding of specific factors such as the transcription factors (TFs) to DNA. Here, the way in which the TFs and the histone state are dynamically correlated is not obvious when the TF synthesis is regulated by the histone state. This type of feedback regulatory relation is ubiquitous in gene networks to determine cell fate in differentiation and other cell transformations. To gain insights into such dynamical feedback regulations, we theoretically analyze a model of epigenetic gene switching by extending the Doi-Peliti operator formalism of reaction kinetics to the problem of coupled molecular processes. Spin-1 and spin-1/2 coherent-state representations are introduced to describe stochastic reactions of histones and binding or unbinding of TFs in a unified way, which provides a concise view of the effects of timescale difference among these molecular processes; even in the case that binding or unbinding of TFs to or from DNA is adiabatically fast, the slow nonadiabatic histone dynamics gives rise to a distinct circular flow of the probability flux around basins in the landscape of the gene state distribution, which leads to hysteresis in gene switching. In contrast to the general belief that the change in the amount of TF precedes the histone state change, flux drives histones to be modified prior to the change in the amount of TF in self-regulating circuits. Flux-landscape analyses shed light on the nonlinear nonadiabatic mechanism of epigenetic cell fate decision making.

Scalable control of developmental timetables by epigenetic switching networks

During development, progenitor cells follow timetables for differentiation that span many cell generations. These developmental timetables are robustly encoded by the embryo, yet scalably adjustable by evolution, facilitating variation in organism size and form. Epigenetic switches, involving rate-limiting activation steps at regulatory gene loci, control gene activation timing in diverse contexts, and could profoundly impact the dynamics of gene regulatory networks controlling developmental lineage specification. Here, we develop a mathematical framework to model regulatory networks with genes controlled by epigenetic switches. Using this framework, we show that such epigenetic switching networks uphold developmental timetables that robustly span many cell generations, and enable the generation of differentiated cells in precisely defined numbers and fractions. Changes to epigenetic switching networks can readily alter the timing of developmental events within a timetable, or alter the overall speed at which timetables unfold, enabling scalable control over differentiated population sizes. With their robust, yet flexibly adjustable nature, epigenetic switching networks could represent central targets on which evolution acts to manufacture diversity in organism size and form.

Mathematical modeling of histone modifications reveals the formation mechanism and function of bivalent chromatin

Bivalent chromatin is characterized by occupation of both activating and repressive histone modifications. Here, we develop a mathematical model that involves antagonistic histone modifications H3K4me3 and H3K27me3 to capture the key features of bivalent chromatin. Three necessary conditions for the emergence of bivalent chromatin are identified, including advantageous methylating activity over demethylating activity, frequent noise conversions of modifications, and sufficient nonlinearity. The first condition is further confirmed by analyzing the existing experimental data. Investigation of the composition of bivalent chromatin reveals that bivalent nucleosomes carrying both H3K4me3 and H3K27me3 account for no more than half of nucleosomes at the bivalent chromatin domain. We identify that bivalent chromatin not only allows transitions to multiple states but also serves as a stepping stone to facilitate a stepwise transition between repressive chromatin state and activating chromatin state and thus elucidate crucial roles of bivalent chromatin in mediating phenotypical plasticity during cell fate determination.

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Emergence of bivalency needs advantageous writing activity over erasing activity

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Emergence of bivalency is facilitated by noise and nonlinearity

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The proportion of bivalent nucleosomes at bivalent chromatin is no more than 50%

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Bivalent chromatin facilitates chromatin state transitions

A Dimension Reduction Approach for Energy Landscape: Identifying Intermediate States in Metabolism-EMT Network

Dimension reduction is a challenging problem in complex dynamical systems. Here, a dimension reduction approach of landscape (DRL) for complex dynamical systems is proposed, by mapping a high-dimensional system on a low-dimensional energy landscape. The DRL approach is applied to three biological networks, which validates that new reduced dimensions preserve the major information of stability and transition of original high-dimensional systems. The consistency of barrier heights calculated from the low-dimensional landscape and transition actions calculated from the high-dimensional system further shows that the landscape after dimension reduction can quantify the global stability of the system. The epithelial-mesenchymal transition (EMT) and abnormal metabolism are two hallmarks of cancer. With the DRL approach, a quadrastable landscape for metabolism-EMT network is identified, including epithelial (E), abnormal metabolic (A), hybrid E/M (H), and mesenchymal (M) cell states. The quantified energy landscape and kinetic transition paths suggest that for the EMT process, the cells at E state need to first change their metabolism, then enter the M state. The work proposes a general framework for the dimension reduction of a stochastic dynamical system, and advances the mechanistic understanding of the underlying relationship between EMT and cellular metabolism.

Tunable, division-independent control of gene activation timing by a polycomb switch

During development, progenitors often differentiate many cell generations after receiving signals. These delays must be robust yet tunable for precise population size control. Polycomb repressive mechanisms, involving histone H3 lysine-27 trimethylation (H3K27me3), restrain the expression of lineage-specifying genes in progenitors and may delay their activation and ensuing differentiation. Here, we elucidate an epigenetic switch controlling the T cell commitment gene Bcl11b that holds its locus in a heritable inactive state for multiple cell generations before activation. Integrating experiments and modeling, we identify a mechanism where H3K27me3 levels at Bcl11b, regulated by methyltransferase and demethylase activities, set the time delay at which the locus switches from a compacted, silent state to an extended, active state. This activation delay robustly spans many cell generations, is tunable by chromatin modifiers and transcription factors, and is independent of cell division. With their regulatory flexibility, such timed epigenetic switches may broadly control timing in development.

Chromosome Structural Mechanics Dictates the Local Spreading of Epigenetic Marks

We present a theoretical model that demonstrates the integral role chromosome organization and structural mechanics play in the spreading of histone modifications involved in epigenetic regulation. Our model shows that heterogeneous nucleosome positioning, and the resulting position-dependent mechanical properties, must be included to reproduce several qualitative features of experimental data of histone methylation spreading around an artificially induced "nucleation site." We show that our model recreates both the extent of spreading and the presence of a subdominant peak upstream of the transcription start site. Our model indicates that the spreading of epigenetic modifications is sensitive to heterogeneity in chromatin organization and the resulting variability in the chromatin's mechanical properties, suggesting that nucleosome spacing can directly control the conferral of epigenetic marks by modifying the structural mechanics of the chromosome. It further illustrates how the physical organization of the DNA polymer may play a significant role in re-establishing the epigenetic code upon cell division.

Physical modeling of the heritability and maintenance of epigenetic modifications

We develop a predictive theoretical model of the physical mechanisms that govern the heritability and maintenance of epigenetic modifications. This model focuses on a particular modification, methylation of lysine-9 of histone H3 (H3K9), which is one of the most representative and critical epigenetic marks that affects chromatin organization and gene expression. Our model combines the effect of segregation and compaction on chromosomal organization with the effect of the interaction between proteins that compact the chromatin (heterochromatin protein 1) and the methyltransferases that affect methyl spreading. Our chromatin model demonstrates that a block of H3K9 methylations in the epigenetic sequence determines the compaction state at any particular location in the chromatin. Using our predictive model for chromatin compaction, we develop a methylation model to address the reestablishment of the methylation sequence following DNA replication. Our model reliably maintains methylation over generations, thereby establishing the robustness of the epigenetic code.

Quantifying epigenetic stability with minimum action paths

Chromatin can adopt multiple stable, heritable states with distinct histone modifications and varying levels of gene expression. Insight on the stability and maintenance of such epigenetic states can be gained by mathematical modeling of stochastic reaction networks for histone modifications. Analytical results for the kinetic networks are particularly valuable. Compared to computationally demanding numerical simulations, they often are more convenient at evaluating the robustness of conclusions with respect to model parameters. In this communication, we developed a second-quantization-based approach that can be used to analyze discrete stochastic models with a fixed, finite number of particles using a representation of the SU(2) algebra. We applied the approach to a kinetic model of chromatin states that captures the feedback between nucleosomes and the enzymes conferring histone modifications. Using a path-integral expression for the transition probability, we computed the epigenetic landscape that helps to identify the emergence of bistability and the most probable path connecting the two steady states. We anticipate the generalizability of the approach will make it useful for studying more complicated models that couple epigenetic modifications with transcription factors and chromatin structure.

Cancer Stem Cell Functions in Hepatocellular Carcinoma and Comprehensive Therapeutic Strategies

Hepatocellular carcinoma (HCC) is a significant cause of cancer-related mortality owing to resistance to traditional treatments and tumor recurrence after therapy, which leads to poor therapeutic outcomes. Cancer stem cells (CSC) are a small subset of tumor cells with the capability to influence self-renewal, differentiation, and tumorigenesis. A number of surface markers for liver cancer stem cell (LCSC) subpopulations (EpCAM, CD133, CD44, CD13, CD90, OV-6, CD47, and side populations) in HCC have been identified. LCSCs play critical roles in regulating HCC stemness, self-renewal, tumorigenicity, metastasis, recurrence, and therapeutic resistance via genetic mutations, epigenetic disruption, signaling pathway dysregulation, or alterations microenvironment. Accumulating studies have shown that biomarkers for LCSCs contribute to diagnosis and prognosis prediction of HCC, supporting their utility in clinical management and development of therapeutic strategies. Preclinical and clinical analyses of therapeutic approaches for HCC using small molecule inhibitors, oncolytic measles viruses, and anti-surface marker antibodies have demonstrated selective, efficient, and safe targeting of LCSC populations. The current review focuses on recent reports on the influence of LCSCs on HCC stemness, tumorigenesis, and multiple drug resistance (MDR), along with LCSC-targeted therapeutic strategies for HCC.

Mechanism of long noncoding RNAs as transcriptional regulators in cancer

Dysregulation of gene expression, often interpreted by gene transcription as an endpoint response, is tightly associated with human cancer. Long noncoding RNAs (lncRNAs), derived from the noncoding elements in the genome and appeared no less than 200nt in length, have emerged as a novel class of pivotal regulatory component. Recently, great attention has been paid to the cancer-related lncRNAs and growing evidence have shown that lncRNAs act as key transcriptional regulators in cancer cells through diverse mechanisms. Here, we focus on the nucleus-expressed lncRNAs and summarize their molecular mechanisms in transcriptional control during tumorigenesis and cancer metastasis. Six major mechanisms will be discussed in this review: association with transcriptional factor, modulating DNA methylation or histone modification enzyme, influencing on chromatin remodelling complex, facilitating chromosomal looping, interaction with RNA polymerase and direct association with promoter.

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.

Epigenetic regulation of histone H3 in the process of hepatocellular tumorigenesis

Better understanding of epigenetic regulation of hepatocellular carcinoma (HCC) will help us to cure this most common malignant liver cancer worldwide. The underlying mechanisms of HCC tumorigenesis are genomic aberrations regulated by genetic and epigenetic modifications. Histone H3 lysine modifications regulate histone structure and modulate transcriptional factor binding with target gene promoters. Targetting genes include VASH2, fatty acids synthase, RIZ1, FBP1, MPP1/3, YAP, which affect tumorigenesis, metabolisms, angiogenesis, and metastasis. Signal pathway studies demonstrate that the HGF-MET-MLL axis, phosphatase and tensin homolog (PTEN)-PI3K-Akt axis; WNT-β-catenin signal pathway is involved in histone H3 modification. A variety of factors such as virus infection, reactive oxygen species, food-borne toxins, irradiation, or non-coding RNA cause hepatocellular DNA damage or modification. Dysfunctional DNA repair mechanisms, including those at the epigenetic level are also major causes of HCC tumorigenesis. The development of therapies based on epigenetic regulatory mechanisms has great potential to advance the care of HCC patients in the future.

Learning the Formation Mechanism of Domain-Level Chromatin States with Epigenomics Data

Epigenetic modifications can extend over long genomic regions to form domain-level chromatin states that play critical roles in gene regulation. The molecular mechanism for the establishment and maintenance of these states is not fully understood and remains challenging to study with existing experimental techniques. Here, we took a data-driven approach and parameterized an information-theoretic model to infer the formation mechanism of domain-level chromatin states from genome-wide epigenetic modification profiles. This model reproduces statistical correlations among histone modifications and identifies well-known states. Importantly, it predicts drastically different mechanisms and kinetic pathways for the formation of euchromatin and heterochromatin. In particular, long, strong enhancer and promoter states grow gradually from short but stable regulatory elements via a multistep process. On the other hand, the formation of heterochromatin states is highly cooperative, and no intermediate states are found along the transition path. This cooperativity can arise from a chromatin looping-mediated spreading of histone methylation mark and supports collapsed, globular three-dimensional conformations rather than regular fibril structures for heterochromatin. We further validated these predictions using changes of epigenetic profiles along cell differentiation. Our study demonstrates that information-theoretic models can go beyond statistical analysis to derive insightful kinetic information that is otherwise difficult to access.

Investigating epithelial-to-mesenchymal transition with integrated computational and experimental approaches

The transition between epithelial and mesenchymal (EMT) is a fundamental cellular process that plays critical roles in development, cancer metastasis, and tissue wound healing. EMT is not a binary process but involves multiple partial EMT states that give rise to a high degree of cell state plasticity. Here, we first reviewed several studies on theoretical predictions and experimental verification of these intermediate states, the role of partial EMT on kidney fibrosis development, and how quantitative signaling information controls cell commitment to partial or full EMT upon transient signals. Next, we summarized existing knowledge and open questions on the coupling between EMT and other biological processes, such as the cell cycle, epigenetic regulation, stemness, and apoptosis. Taken together, EMT is a model system that has attracted increasing interests for quantitative experimental and theoretical studies.

Reciprocal regulation between mRNA and microRNA enables a bistable switch that directs cell fate decisions

Micro RNAs (miRNAs) serve as crucial post-transcriptional regulators in a variety of essential cell fate decisions. However, the contribution of mRNA-miRNA mutual regulation to bistability is not fully understood. In the present study, we built a set of mathematical models of mRNA-miRNA interactions and systematically analyzed the sensitivity of the response curves under various conditions. Our findings indicate that mRNA-miRNA reciprocal regulation could manifest ultrasensitivity to subserve the generation of bistability when equipped with a positive feedback loop. We also find that the region of bistability is expanded by a stronger competing endogenous mRNA. Interestingly, bistability can be generated without a feedback loop if multiple miRNA binding sites exist on a target mRNA. Thus, we demonstrate the importance of simple mRNA-miRNA reciprocal regulation in cell fate decisions.

Multiple coupled landscapes and non-adiabatic dynamics with applications to self-activating genes

Many physical, chemical and biochemical systems (e.g. electronic dynamics and gene regulatory networks) are governed by continuous stochastic processes (e.g. electron dynamics on a particular electronic energy surface and protein (gene product) synthesis) coupled with discrete processes (e.g. hopping among different electronic energy surfaces and on and off switching of genes). One can also think of the underlying dynamics as the continuous motion on a particular landscape and discrete hoppings among different landscapes. The main difference of such systems from the intra-landscape dynamics alone is the emergence of the timescale involved in transitions among different landscapes in addition to the timescale involved in a particular landscape. The adiabatic limit when inter-landscape hoppings are fast compared to continuous intra-landscape dynamics has been studied both analytically and numerically, but the analytical treatment of the non-adiabatic regime where the inter-landscape hoppings are slow or comparable to continuous intra-landscape dynamics remains challenging. In this study, we show that there exists mathematical mapping of the dynamics on 2(N) discretely coupled N continuous dimensional landscapes onto one single landscape in 2N dimensional extended continuous space. On this 2N dimensional landscape, eddy current emerges as a sign of non-equilibrium non-adiabatic dynamics and plays an important role in system evolution. Many interesting physical effects such as the enhancement of fluctuations, irreversibility, dissipation and optimal kinetics emerge due to non-adiabaticity manifested by the eddy current illustrated for an N = 1 self-activator. We further generalize our theory to the N-gene network with multiple binding sites and multiple synthesis rates for discretely coupled non-equilibrium stochastic physical and biological systems.

Achieving diverse and monoallelic olfactory receptor selection through dual-objective optimization design

Multiple-objective optimization is common in biological systems. In the mammalian olfactory system, each sensory neuron stochastically expresses only one out of up to thousands of olfactory receptor (OR) gene alleles; at the organism level, the types of expressed ORs need to be maximized. Existing models focus only on monoallele activation, and cannot explain recent observations in mutants, especially the reduced global diversity of expressed ORs in G9a/GLP knockouts. In this work we integrated existing information on OR expression, and constructed a comprehensive model that has all its components based on physical interactions. Analyzing the model reveals an evolutionarily optimized three-layer regulation mechanism, which includes zonal segregation, epigenetic barrier crossing coupled to a negative feedback loop that mechanistically differs from previous theoretical proposals, and a previously unidentified enhancer competition step. This model not only recapitulates monoallelic OR expression, but also elucidates how the olfactory system maximizes and maintains the diversity of OR expression, and has multiple predictions validated by existing experimental results. Through making an analogy to a physical system with thermally activated barrier crossing and comparative reverse engineering analyses, the study reveals that the olfactory receptor selection system is optimally designed, and particularly underscores cooperativity and synergy as a general design principle for multiobjective optimization in biology.

Effects of Collective Histone State Dynamics on Epigenetic Landscape and Kinetics of Cell Reprogramming

Cell reprogramming is a process of transitions from differentiated to pluripotent cell states via transient intermediate states. Within the epigenetic landscape framework, such a process is regarded as a sequence of transitions among basins on the landscape; therefore, theoretical construction of a model landscape which exhibits experimentally consistent dynamics can provide clues to understanding epigenetic mechanism of reprogramming. We propose a minimal gene-network model of the landscape, in which each gene is regulated by an integrated mechanism of transcription-factor binding/unbinding and the collective chemical modification of histones. We show that the slow collective variation of many histones around each gene locus alters topology of the landscape and significantly affects transition dynamics between basins. Differentiation and reprogramming follow different transition pathways on the calculated landscape, which should be verified experimentally via single-cell pursuit of the reprogramming process. Effects of modulation in collective histone state kinetics on transition dynamics and pathway are examined in search for an efficient protocol of reprogramming.

Putting it all on pigmentation: Heuristics of a bold and stochastic cell fate decision

Gradients of transmembrane potential coordinate cell-fate decisions and patterning during embryogenesis and wound-healing. Bioelectrical signaling may also be more important for adult pathologies than currently recognized. In this issue of Science Signaling, Lobikin et al. describe a role for bioelectric signals during the development of Xenopus leavis embryos to instruct an organism-level response reminiscent of neoplastic progression in melanoma.

Effect of replication on epigenetic memory and consequences on gene transcription

Gene activity in eukaryotes is in part regulated at the level of chromatin through the assembly of local chromatin states that are more or less permissive to transcription. How do these chromatin states achieve their functions and whether or not they contribute to the epigenetic inheritance of the transcriptional program remain to be elucidated. In cycling cells, stability is indeed strongly challenged by the periodic occurrence of replication and cell division. To address this question, we perform simulations of the stochastic dynamics of chromatin states when driven out-of-equilibrium by periodic perturbations. We show how epigenetic memory is significantly affected by the cell cycle length. In addition, we develop a simple model to connect the epigenetic state to the transcriptional state and gene activity. In particular, it suggests that replication may induce transcriptional bursting at repressive loci. Finally, we discuss how our findings-effect of replication and link to gene transcription-have original and deep implications to various biological contexts of epigenetic memory.

Transgenerational epigenetic inheritance requires a much deeper analysis

In his article, Szyf [1] has addressed the key challenges in and the controversies surrounding nongenetic inheritance. However, crucial findings that are important to counter two major criticisms held against transgenerational inheritance, especially in mammals--namely epigenetic memory survival across generations, and soma-to-germline transfer of heritable information--need additional discussion. Given the far-reaching implications of nongenetic inheritance on the one hand, and the skepticisms about its existence on the other, it is important that the advances concerned are examined deeply. The following discussion fills the gap left by Szyf [1] and provides an integrated perspective.

Universal flux-fluctuation law in small systems

The relation between flux and fluctuation is fundamental to complex physical systems that support and transport flows. A recently obtained law predicts monotonous enhancement of fluctuation as the average flux is increased, which in principle is valid but only for large systems. For realistic complex systems of small sizes, this law breaks down when both the average flux and fluctuation become large. Here we demonstrate the failure of this law in small systems using real data and model complex networked systems, derive analytically a modified flux-fluctuation law, and validate it through computations of a large number of complex networked systems. Our law is more general in that its predictions agree with numerics and it reduces naturally to the previous law in the limit of large system size, leading to new insights into the flow dynamics in small-size complex systems with significant implications for the statistical and scaling behaviors of small systems, a topic of great recent interest.

Physicochemical modifications of histones and their impact on epigenomics

The study of histone post-translational modifications (PTMs) has made extraordinary progress over the past few years and many epigenetic modifications have been identified and found to be associated with fundamental biological processes and pathological conditions. Most histone-modifying enzymes produce specific covalent modifications on histone tails that, taken together, elicit complex and concerted processes. An even higher level of complexity is generated by the action of small molecules that are able to modulate pharmacologically epigenetic enzymes and interfere with these biochemical mechanisms. In this article, we provide an overview of histone PTMs by reviewing and discussing them in terms of their physicochemical properties, emphasizing these concepts in view of recent research efforts to elucidate epigenetic mechanisms and devise future epigenetic drugs.