Ultrasensitive gene regulation by positive feedback loops in nucleosome modification

A review on gene regulatory network reconstruction algorithms based on single cell RNA sequencing

BACKGROUND

Understanding gene regulatory networks (GRNs) is essential for unraveling the molecular mechanisms governing cellular behavior. With the advent of high-throughput transcriptome measurement technology, researchers have aimed to reverse engineer the biological systems, extracting gene regulatory rules from their outputs, which represented by gene expression data. Bulk RNA sequencing, a widely used method for measuring gene expression, has been employed for GRN reconstruction. However, it falls short in capturing dynamic changes in gene expression at the level of individual cells since it averages gene expression across mixed cell populations.

OBJECTIVE

In this review, we provide an overview of 15 GRN reconstruction tools and discuss their respective strengths and limitations, particularly in the context of single cell RNA sequencing (scRNA-seq).

METHODS

Recent advancements in scRNA-seq break new ground of GRN reconstruction. They offer snapshots of the individual cell transcriptomes and capturing dynamic changes. We emphasize how these technological breakthroughs have enhanced GRN reconstruction.

CONCLUSION

GRN reconstructors can be classified based on their requirement for cellular trajectory, which represents a dynamical cellular process including differentiation, aging, or disease progression. Benchmarking studies support the superiority of GRN reconstructors that do not require trajectory analysis in identifying regulator-target relationships. However, methods equipped with trajectory analysis demonstrate better performance in identifying key regulatory factors. In conclusion, researchers should select a suitable GRN reconstructor based on their specific research objectives.

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.

Simulation of receptor triggering by kinetic segregation shows role of oligomers and close-contacts

The activation of T cells, key players of the immune system, involves local evacuation of phosphatase CD45 from a region of the T cell's surface, segregating it from the T cell receptor. What drives this evacuation? In the presence of antigen, what ensures evacuation happens in the subsecond timescales necessary to initiate signaling? In the absence of antigen, what mechanisms ensure that evacuation does not happen spontaneously, which could cause signaling errors? Phenomena known to influence spatial organization of CD45 or similar surface molecules include diffusive motion in the lipid bilayer, oligomerization reactions, and mechanical compression against a nearby surface, such as that of the cell presenting the antigen. Computer simulations can investigate hypothesized spatiotemporal mechanisms of T cell signaling. The challenge to computational studies of evacuation is that the base process, spontaneous evacuation by simple diffusion, is in the extreme rare event limit, meaning direct stochastic simulation is unfeasible. Here, we combine particle-based spatial stochastic simulation with the weighted ensemble method for rare events to compute the mean first passage time for cell surface availability by surface reorganization of CD45. We confirm mathematical estimates that, at physiological concentrations, spontaneous evacuation is extremely rare, roughly 300 years. We find that dimerization decreases the time required for evacuation. A weak bimolecular interaction (dissociation constant estimate 460 μM) is sufficient for an order of magnitude reduction of spontaneous evacuation times, and oligomerization to hexamers reduces times to below 1 s. This introduces a mechanism whereby externally induced CD45 oligomerization could significantly modify T cell function. For large regions of close contact, such as those induced by large microvilli, molecular size and compressibility imply a nonzero reentry probability of 60%, decreasing evacuation times. Simulations show that these reduced evacuation times are still unrealistically long (even with a fourfold variation centered around previous estimates of parameters), suggesting that a yet-to-be-described mechanism, besides compressional exclusion at a close contact, drives evacuation.

A minimal model for gene expression dynamics of bacterial type II toxin-antitoxin systems

Toxin-antitoxin (TA) modules are part of most bacteria's regulatory machinery for stress responses and general aspects of their physiology. Due to the interplay of a long-lived toxin with a short-lived antitoxin, TA modules have also become systems of interest for mathematical modelling. Here we resort to previous modelling efforts and extract from these a minimal model of type II TA system dynamics on a timescale of hours, which can be used to describe time courses derived from gene expression data of TA pairs. We show that this model provides a good quantitative description of TA dynamics for the 11 TA pairs under investigation here, while simpler models do not. Our study brings together aspects of Biophysics with its focus on mathematical modelling and Computational Systems Biology with its focus on the quantitative interpretation of 'omics' data. This mechanistic model serves as a generic transformation of time course information into kinetic parameters. The resulting parameter vector can, in turn, be mechanistically interpreted. We expect that TA pairs with similar mechanisms are characterized by similar vectors of kinetic parameters, allowing us to hypothesize on the mode of action for TA pairs still under discussion.

Design of time-delayed safety switches for CRISPR gene therapy

CRISPR system is a powerful gene editing tool which has already been reported to address a variety of gene relevant diseases in different cell lines. However, off-target effect and immune response caused by Cas9 remain two fundamental problems. Inspired by previously reported Cas9 self-elimination systems, time-delayed safety switches are designed in this work. Firstly, ultrasensitive relationship is constructed between Cas9-sgRNA (enzyme) and Cas9 plasmids (substrate), which generates the artificial time delay. Then intrinsic time delay in biomolecular activities is revealed by data fitting and utilized in constructing safety switches. The time-delayed safety switches function by separating the gene editing process and self-elimination process, and the tunable delay time may ensure a good balance between gene editing efficiency and side effect minimization. By addressing gene therapy efficiency, off-target effect, immune response and drug accumulation, we hope our safety switches may offer inspiration in realizing safe and efficient gene therapy in humans.

On the hierarchical design of biochemical-based digital computations

The understanding of the biochemical processes underpinning various biological systems has significantly increased in recent decades and has even prompted reverse engineering of certain of life's more complex processes. The most prominent example is modern computers designed to mimic neuron activity. This work forms part of growing endeavors to return advances in the theory of computation and electronics to biology. In this context, we present a set of requirements sufficient for the design of biochemical analogs of modern electronics in a hierarchical, modular fashion that mimics the design of modern computational devices. This theoretical approach is based on a simple enzymatic analog of the transistor and supported by numerical simulations of biochemical models of enzymatic networks equivalent to complex, and modular, interconnecting electronic circuitry (including clocks, Flip-Flops, adders, decoders, and multiplexers). Furthermore, the proposed approach has been implemented in the form of a Python library capable of creating and testing models of complex bio-analog digital computations based on the execution of an elementary universal logic gate. In tribute to Claude Shannon, our biochemical network materializes his example of a "password" recognition that moves the language of the modern theory of automata beyond combinatorial logic and towards sequential logic.

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

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

Estradiol-Induced Epigenetically Mediated Mechanisms and Regulation of Gene Expression

Gonadal hormone 17β-estradiol (E2) and its receptors are key regulators of gene transcription by binding to estrogen responsive elements in the genome. Besides the classical genomic action, E2 regulates gene transcription via the modification of epigenetic marks on DNA and histone proteins. Depending on the reaction partner, liganded estrogen receptor (ER) promotes DNA methylation at the promoter or enhancer regions. In addition, ERs are important regulators of passive and active DNA demethylation. Furthermore, ERs cooperating with different histone modifying enzymes and chromatin remodeling complexes alter gene transcription. In this review, we survey the basic mechanisms and interactions between estrogen receptors and DNA methylation, demethylation and histone modification processes as well as chromatin remodeling complexes. The particular relevance of these mechanisms to physiological processes in memory formation, embryonic development, spermatogenesis and aging as well as in pathophysiological changes in carcinogenesis is also discussed.

Improvement of the memory function of a mutual repression network in a stochastic environment by negative autoregulation

BACKGROUND

Cellular memory is a ubiquitous function of biological systems. By generating a sustained response to a transient inductive stimulus, often due to bistability, memory is central to the robust control of many important biological processes. However, our understanding of the origins of cellular memory remains incomplete. Stochastic fluctuations that are inherent to most biological systems have been shown to hamper memory function. Yet, how stochasticity changes the behavior of genetic circuits is generally not clear from a deterministic analysis of the network alone. Here, we apply deterministic rate equations, stochastic simulations, and theoretical analyses of Fokker-Planck equations to investigate how intrinsic noise affects the memory function in a mutual repression network.

RESULTS

We find that the addition of negative autoregulation improves the persistence of memory in a small gene regulatory network by reducing stochastic fluctuations. Our theoretical analyses reveal that this improved memory function stems from an increased stability of the steady states of the system. Moreover, we show how the tuning of critical network parameters can further enhance memory.

CONCLUSIONS

Our work illuminates the power of stochastic and theoretical approaches to understanding biological circuits, and the importance of considering stochasticity when designing synthetic circuits with memory function.

Chromatin state switching in a polymer model with mark-conformation coupling

We investigate the phase transition properties of the polymer-Potts model, a chain composed of monomers with magnetic degrees of freedom, with the motivation to study the conformation and mark switching dynamics of chromatin. By the mean-field approximation, we find that the phase transition between the swollen-disordered state and the compact-ordered state is discrete; it is first order as in the long-range Potts model, but with a significantly larger jump in magnetization (i.e., mark coherence) upon the ordering transition. The results imply how small changes in epigenetic writer concentrations can lead to a macroscopic switching of the chromatin state, suggesting a simple mechanism of discrete switching observed, for instance, in cell differentiation.

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

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

Activation of the Notch Signaling Pathway In Vivo Elicits Changes in CSL Nuclear Dynamics

A key feature of Notch signaling is that it directs immediate changes in transcription via the DNA-binding factor CSL, switching it from repression to activation. How Notch generates both a sensitive and accurate response-in the absence of any amplification step-remains to be elucidated. To address this question, we developed real-time analysis of CSL dynamics including single-molecule tracking in vivo. In Notch-OFF nuclei, a small proportion of CSL molecules transiently binds DNA, while in Notch-ON conditions CSL recruitment increases dramatically at target loci, where complexes have longer dwell times conferred by the Notch co-activator Mastermind. Surprisingly, recruitment of CSL-related corepressors also increases in Notch-ON conditions, revealing that Notch induces cooperative or "assisted" loading by promoting local increase in chromatin accessibility. Thus, in vivo Notch activity triggers changes in CSL dwell times and chromatin accessibility, which we propose confer sensitivity to small input changes and facilitate timely shut-down.

Models of life: epigenetics, diversity and cycles

This review emphasizes aspects of biology that can be understood through repeated applications of simple causal rules. The selected topics include perspectives on gene regulation, phage lambda development, epigenetics, microbial ecology, as well as model approaches to diversity and to punctuated equilibrium in evolution. Two outstanding features are repeatedly described. One is the minimal number of rules to sustain specific states of complex systems for a long time. The other is the collapse of such states and the subsequent dynamical cycle of situations that restitute the system to a potentially new metastable state.

Dissecting Embryonic Stem Cell Self-Renewal and Differentiation Commitment from Quantitative Models

To model quantitatively embryonic stem cell (ESC) self-renewal and differentiation by computational approaches, we developed a unified mathematical model for gene expression involved in cell fate choices. Our quantitative model comprised ESC master regulators and lineage-specific pivotal genes. It took the factors of multiple pathways as input and computed expression as a function of intrinsic transcription factors, extrinsic cues, epigenetic modifications, and antagonism between ESC master regulators and lineage-specific pivotal genes. In the model, the differential equations of expression of genes involved in cell fate choices from regulation relationship were established according to the transcription and degradation rates. We applied this model to the Murine ESC self-renewal and differentiation commitment and found that it modeled the expression patterns with good accuracy. Our model analysis revealed that Murine ESC was an attractor state in culture and differentiation was predominantly caused by antagonism between ESC master regulators and lineage-specific pivotal genes. Moreover, antagonism among lineages played a critical role in lineage reprogramming. Our results also uncovered that the ordered expression alteration of ESC master regulators over time had a central role in ESC differentiation fates. Our computational framework was generally applicable to most cell-type maintenance and lineage reprogramming.

Delayed Onset of Symptoms Through Feedback Interference in Chronic Cancers

In many cancers, such as Chronic Myelogenous Leukemia (CML), pancreatic, and colorectal cancer, long delays exist between the initiation of the disease and the onset of debilitating symptoms. The early stages of these diseases present manageable symptoms and, in the case of CML, highly effective treatment options. Progression to the more aggressive stages of the diseases limits effective treatment and significantly exacerbates patient prognosis. The mechanisms causing delay and disease progression are largely unknown. The later stages of these diseases are characterized by excessive build up of primitive cell types, indicating a disruption in the normal cell differentiation process that is commonly regulated through feedback from differentiated types. In this study, we propose a mechanism where mutated primitive cells produce a feedback interference signal that desensitizes them to a normal homeostatic feedback. Using a mathematical model, we show that this mechanism can account for the long delay period between occurrence of genetic changes and symptomatic onset characterized by fast growth of cancerous cell population. Finally, we explore novel concepts for potential treatment of chronic cancers.

Pluripotency, Differentiation, and Reprogramming: A Gene Expression Dynamics Model with Epigenetic Feedback Regulation

Embryonic stem cells exhibit pluripotency: they can differentiate into all types of somatic cells. Pluripotent genes such as Oct4 and Nanog are activated in the pluripotent state, and their expression decreases during cell differentiation. Inversely, expression of differentiation genes such as Gata6 and Gata4 is promoted during differentiation. The gene regulatory network controlling the expression of these genes has been described, and slower-scale epigenetic modifications have been uncovered. Although the differentiation of pluripotent stem cells is normally irreversible, reprogramming of cells can be experimentally manipulated to regain pluripotency via overexpression of certain genes. Despite these experimental advances, the dynamics and mechanisms of differentiation and reprogramming are not yet fully understood. Based on recent experimental findings, we constructed a simple gene regulatory network including pluripotent and differentiation genes, and we demonstrated the existence of pluripotent and differentiated states from the resultant dynamical-systems model. Two differentiation mechanisms, interaction-induced switching from an expression oscillatory state and noise-assisted transition between bistable stationary states, were tested in the model. The former was found to be relevant to the differentiation process. We also introduced variables representing epigenetic modifications, which controlled the threshold for gene expression. By assuming positive feedback between expression levels and the epigenetic variables, we observed differentiation in expression dynamics. Additionally, with numerical reprogramming experiments for differentiated cells, we showed that pluripotency was recovered in cells by imposing overexpression of two pluripotent genes and external factors to control expression of differentiation genes. Interestingly, these factors were consistent with the four Yamanaka factors, Oct4, Sox2, Klf4, and Myc, which were necessary for the establishment of induced pluripotent stem cells. These results, based on a gene regulatory network and expression dynamics, contribute to our wider understanding of pluripotency, differentiation, and reprogramming of cells, and they provide a fresh viewpoint on robustness and control during development.

Characterization of pluripotent states, in which cells can both self-renew and differentiate, and the irreversible loss of pluripotency are important research areas in developmental biology. In particular, an understanding of these processes is essential to the reprogramming of cells for biomedical applications, i.e., the experimental recovery of pluripotency in differentiated cells. Based on recent advances in dynamical-systems theory for gene expression, we propose a gene-regulatory-network model consisting of several pluripotent and differentiation genes. Our results show that cellular-state transition to differentiated cell types occurs as the number of cells increases, beginning with the pluripotent state and oscillatory expression of pluripotent genes. Cell-cell signaling mediates the differentiation process with robustness to noise, while epigenetic modifications affecting gene expression dynamics fix the cellular state. These modifications ensure the cellular state to be protected against external perturbation, but they also work as an epigenetic barrier to recovery of pluripotency. We show that overexpression of several genes leads to the reprogramming of cells, consistent with the methods for establishing induced pluripotent stem cells. Our model, which involves the inter-relationship between gene expression dynamics and epigenetic modifications, improves our basic understanding of cell differentiation and reprogramming.

Affinity, stoichiometry and cooperativity of heterochromatin protein 1 (HP1) binding to nucleosomal arrays

Heterochromatin protein 1 (HP1) participates in establishing and maintaining heterochromatin via its histone-modification-dependent chromatin interactions. In recent papers HP1 binding to nucleosomal arrays was measured in vitro and interpreted in terms of nearest-neighbour cooperative binding. This mode of chromatin interaction could lead to the spreading of HP1 along the nucleosome chain. Here, we reanalysed previous data by representing the nucleosome chain as a 1D binding lattice and showed how the experimental HP1 binding isotherms can be explained by a simpler model without cooperative interactions between neighboring HP1 dimers. Based on these calculations and spatial models of dinucleosomes and nucleosome chains, we propose that binding stoichiometry depends on the nucleosome repeat length (NRL) rather than protein interactions between HP1 dimers. According to our calculations, more open nucleosome arrays with long DNA linkers are characterized by a larger number of binding sites in comparison to chains with a short NRL. Furthermore, we demonstrate by Monte Carlo simulations that the NRL dependent folding of the nucleosome chain can induce allosteric changes of HP1 binding sites. Thus, HP1 chromatin interactions can be modulated by the change of binding stoichiometry and the type of binding to condensed (methylated) and non-condensed (unmethylated) nucleosome arrays in the absence of direct interactions between HP1 dimers.

Specificity, propagation, and memory of pericentric heterochromatin

The cell establishes heritable patterns of active and silenced chromatin via interacting factors that set, remove, and read epigenetic marks. To understand how the underlying networks operate, we have dissected transcriptional silencing in pericentric heterochromatin (PCH) of mouse fibroblasts. We assembled a quantitative map for the abundance and interactions of 16 factors related to PCH in living cells and found that stably bound complexes of the histone methyltransferase SUV39H1/2 demarcate the PCH state. From the experimental data, we developed a predictive mathematical model that explains how chromatin-bound SUV39H1/2 complexes act as nucleation sites and propagate a spatially confined PCH domain with elevated histone H3 lysine 9 trimethylation levels via chromatin dynamics. This “nucleation and looping” mechanism is particularly robust toward transient perturbations and stably maintains the PCH state. These features make it an attractive model for establishing functional epigenetic domains throughout the genome based on the localized immobilization of chromatin-modifying enzymes.

Compact modeling of allosteric multisite proteins: application to a cell size checkpoint

We explore a framework to model the dose response of allosteric multisite phosphorylation proteins using a single auxiliary variable. This reduction can closely replicate the steady state behavior of detailed multisite systems such as the Monod-Wyman-Changeux allosteric model or rule-based models. Optimal ultrasensitivity is obtained when the activation of an allosteric protein by its individual sites is concerted and redundant. The reduction makes this framework useful for modeling and analyzing biochemical systems in practical applications, where several multisite proteins may interact simultaneously. As an application we analyze a newly discovered checkpoint signaling pathway in budding yeast, which has been proposed to measure cell growth by monitoring signals generated at sites of plasma membrane growth. We show that the known components of this pathway can form a robust hysteretic switch. In particular, this system incorporates a signal proportional to bud growth or size, a mechanism to read the signal, and an all-or-none response triggered only when the signal reaches a threshold indicating that sufficient growth has occurred.

Time scales in epigenetic dynamics and phenotypic heterogeneity of embryonic stem cells

A remarkable feature of the self-renewing population of embryonic stem cells (ESCs) is their phenotypic heterogeneity: Nanog and other marker proteins of ESCs show large cell-to-cell variation in their expression level, which should significantly influence the differentiation process of individual cells. The molecular mechanism and biological implication of this heterogeneity, however, still remain elusive. We address this problem by constructing a model of the core gene-network of mouse ESCs. The model takes account of processes of binding/unbinding of transcription factors, formation/dissolution of transcription apparatus, and modification of histone code at each locus of genes in the network. These processes are hierarchically interrelated to each other forming the dynamical feedback loops. By simulating stochastic dynamics of this model, we show that the phenotypic heterogeneity of ESCs can be explained when the chromatin at the Nanog locus undergoes the large scale reorganization in formation/dissolution of transcription apparatus, which should have the timescale similar to the cell cycle period. With this slow transcriptional switching of Nanog, the simulated ESCs fluctuate among multiple transient states, which can trigger the differentiation into the lineage-specific cell states. From the simulated transitions among cell states, the epigenetic landscape underlying transitions is calculated. The slow Nanog switching gives rise to the wide basin of ESC states in the landscape. The bimodal Nanog distribution arising from the kinetic flow running through this ESC basin prevents transdifferentiation and promotes the definite decision of the cell fate. These results show that the distribution of timescales of the regulatory processes is decisively important to characterize the fluctuation of cells and their differentiation process. The analyses through the epigenetic landscape and the kinetic flow on the landscape should provide a guideline to engineer cell differentiation.

Embryonic stem cells (ESCs) can proliferate indefinitely by keeping pluripotency, i.e., the ability to differentiate into any cell-lineage. ESCs, therefore, have been the focus of intense biological and medical interests. A remarkable feature of ESCs is their phenotypic heterogeneity: ESCs show large cell-to-cell fluctuation in the expression level of Nanog, which is a key factor to maintain pluripotency. Since Nanog regulates many genes in ESCs, this fluctuation should seriously affect individual cells when they start differentiation. In this paper we analyze this phenotypic fluctuation by simulating the stochastic dynamics of gene network in ESCs. The model takes account of the mutually interrelated processes of gene regulation such as binding/unbinding of transcription factors, formation/dissolution of transcription apparatus, and histone-code modification. We show the distribution of timescales of these processes is decisively important to characterize the dynamical behavior of the gene network, and that the slow formation/dissolution of transcription apparatus at the Nanog locus explains the observed large fluctuation of ESCs. The epigenetic landscapes are calculated based on the stochastic simulation, and the role of the phenotypic fluctuation in the differentiation process is analyzed through the landscape picture.

A computational model for histone mark propagation reproduces the distribution of heterochromatin in different human cell types

Chromatin is a highly compact and dynamic nuclear structure that consists of DNA and associated proteins. The main organizational unit is the nucleosome, which consists of a histone octamer with DNA wrapped around it. Histone proteins are implicated in the regulation of eukaryote genes and they carry numerous reversible post-translational modifications that control DNA-protein interactions and the recruitment of chromatin binding proteins. Heterochromatin, the transcriptionally inactive part of the genome, is densely packed and contains histone H3 that is methylated at Lys 9 (H3K9me). The propagation of H3K9me in nucleosomes along the DNA in chromatin is antagonizing by methylation of H3 Lysine 4 (H3K4me) and acetylations of several lysines, which is related to euchromatin and active genes. We show that the related histone modifications form antagonized domains on a coarse scale. These histone marks are assumed to be initiated within distinct nucleation sites in the DNA and to propagate bi-directionally. We propose a simple computer model that simulates the distribution of heterochromatin in human chromosomes. The simulations are in agreement with previously reported experimental observations from two different human cell lines. We reproduced different types of barriers between heterochromatin and euchromatin providing a unified model for their function. The effect of changes in the nucleation site distribution and of propagation rates were studied. The former occurs mainly with the aim of (de-)activation of single genes or gene groups and the latter has the power of controlling the transcriptional programs of entire chromosomes. Generally, the regulatory program of gene transcription is controlled by the distribution of nucleation sites along the DNA string.

Epigenetic feedback regulation accelerates adaptation and evolution

A simple cell model consisting of a gene regulatory network with epigenetic feedback regulation is studied to evaluate the effect of epigenetic dynamics on adaptation and evolution. We find that, the type of epigenetic dynamics considered enables a cell to adapt to unfamiliar environmental changes, for which no regulatory program has been prepared, through noise-driven selection of a cellular state with a high growth rate. Furthermore, we demonstrate that the inclusion of epigenetic regulation promotes evolutionary development of a regulatory network that can respond to environmental changes in a fast and precise manner. These results strongly suggest that epigenetic feedback regulation in gene expression dynamics provides a significant increase in fitness by engendering an increase in cellular plasticity during adaptation and evolution.

Differentiation of developing olfactory neurons analysed in terms of coupled epigenetic landscapes

The olfactory system integrates signals from receptors expressed in olfactory sensory neurons. Each sensory neuron expresses only one of many similar olfactory receptors (ORs). The choice of receptor is made stochastically early in the differentiation process and is maintained throughout the life of the neuron. The underlying mechanism of this stochastic commitment to one of multiple similar OR genes remains elusive. We present a theoretical analysis of a mechanism that invokes important epigenetic properties of the system. The proposed model combines nucleosomes and associated read-write enzymes as mediators of a cis-acting positive feedback with a trans-acting negative feedback, thereby coupling the local epigenetic landscape of the individual OR genes in a way that allow one and only one gene to be active at any time. The model pinpoint that singular gene selection does not require transient mechanisms, enhancer elements or transcription factors to separate choice from maintenance. In addition, our hypothesis allow us to combine all reported characteristics of singular OR gene selection, in particular that OR genes are silenced from OR transgenes. Intriguingly, it predicts that OR transgenes placed in close proximity should always be expressed simultaneously, though rarely.

Ultrasensitive response motifs: basic amplifiers in molecular signalling networks

Multi-component signal transduction pathways and gene regulatory circuits underpin integrated cellular responses to perturbations. A recurring set of network motifs serve as the basic building blocks of these molecular signalling networks. This review focuses on ultrasensitive response motifs (URMs) that amplify small percentage changes in the input signal into larger percentage changes in the output response. URMs generally possess a sigmoid input–output relationship that is steeper than the Michaelis–Menten type of response and is often approximated by the Hill function. Six types of URMs can be commonly found in intracellular molecular networks and each has a distinct kinetic mechanism for signal amplification. These URMs are: (i) positive cooperative binding, (ii) homo-multimerization, (iii) multistep signalling, (iv) molecular titration, (v) zero-order covalent modification cycle and (vi) positive feedback. Multiple URMs can be combined to generate highly switch-like responses. Serving as basic signal amplifiers, these URMs are essential for molecular circuits to produce complex nonlinear dynamics, including multistability, robust adaptation and oscillation. These dynamic properties are in turn responsible for higher-level cellular behaviours, such as cell fate determination, homeostasis and biological rhythm.

Epigenetics meets mathematics: towards a quantitative understanding of chromatin biology

How fast? How strong? How many? So what? Why do numbers matter in biology? Chromatin binding proteins are forever in motion, exchanging rapidly between bound and free pools. How do regulatory systems whose components are in constant flux ensure stability and flexibility? This review explores the application of quantitative and mathematical approaches to mechanisms of epigenetic regulation. We discuss methods for measuring kinetic parameters and protein quantities in living cells, and explore the insights that have been gained by quantifying and modelling dynamics of chromatin binding proteins.

A simple histone code opens many paths to epigenetics

Nucleosomes can be covalently modified by addition of various chemical groups on several of their exposed histone amino acids. These modifications are added and removed by enzymes (writers) and can be recognized by nucleosome-binding proteins (readers). Linking a reader domain and a writer domain that recognize and create the same modification state should allow nucleosomes in a particular modification state to recruit enzymes that create that modification state on nearby nucleosomes. This positive feedback has the potential to provide the alternative stable and heritable states required for epigenetic memory. However, analysis of simple histone codes involving interconversions between only two or three types of modified nucleosomes has revealed only a few circuit designs that allow heritable bistability. Here we show by computer simulations that a histone code involving alternative modifications at two histone positions, producing four modification states, combined with reader-writer proteins able to distinguish these states, allows for hundreds of different circuits capable of heritable bistability. These expanded possibilities result from multiple ways of generating two-step cooperativity in the positive feedback - through alternative pathways and an additional, novel cooperativity motif. Our analysis reveals other properties of such epigenetic circuits. They are most robust when the dominant nucleosome types are different at both modification positions and are not the type inserted after DNA replication. The dominant nucleosome types often recruit enzymes that create their own type or destroy the opposing type, but never catalyze their own destruction. The circuits appear to be evolutionary accessible; most circuits can be changed stepwise into almost any other circuit without losing heritable bistability. Thus, our analysis indicates that systems that utilize an expanded histone code have huge potential for generating stable and heritable nucleosome modification states and identifies the critical features of such systems.

Specialized enzymes add and remove chemical modifications to the histone proteins that package DNA into nucleosomes. These modifications act as labels to recruit various proteins to the DNA locations where they are needed to control DNA functions, such as gene expression. The modifications are usually made and maintained in response to specific signals. However, if a modifying enzyme is itself recruited by the modification it makes, then this positive feedback could cause the modification or its absence to be self-sustaining, and even heritable, once the signal has gone. We used computer simulations to systematically explore the possibilities for such epigenetic states when there is an expanded modification ‘code’ - one that involves the presence or absence of two different modifications rather than just one. We found that this small expansion of the histone code allows hundreds of different modification and enzyme recruitment schemes to give alternative stable and heritable states. These worked best when the nucleosomes in alternative states were differently modified at both positions. All working schemes involved positive feedback and cooperativity between nucleosomes. Thus, even a simple histone code could be used in many ways to make stable and heritable, yet reversible, marks on DNA.

Modeling the dynamic epigenome: from histone modifications towards self-organizing chromatin

Epigenetic mechanisms play an important role in regulating and stabilizing functional states of living cells. However, in spite of an increasing amount of experimental data, models of transcriptional regulation by epigenetic processes, in particular by histone modifications, are rather rare. In this article, we focus on epigenetic modes of transcriptional regulation based on histone modifications and their potential dynamical interplay with DNA methylation and higher-order chromatin structure. The main purpose of this article is to review recent formal modeling approaches to the dynamics and propagation of histone modifications and to relate them to available experimental data. We evaluate their assumptions with respect to recruitment of relevant modifiers, establishment and processing of modifications, and compare the emerging stability properties and memory effects. Theoretical predictions that await experimental validation are highlighted and potential extensions of these models towards multiscale models of self-organizing chromatin are discussed.

Barriers and silencers: a theoretical toolkit for control and containment of nucleosome-based epigenetic states

Positive feedback in nucleosome modification has been proposed to allow large chromatin regions to exist stably and heritably in distinct expression states. However, modeling has shown that such epigenetic bistability requires that modifying enzymes recruited by nucleosomes are active on distant nucleosomes, potentially allowing uncontrollable spreading of modification. By modeling the silencing of mating-type loci in Saccharomyces cerevisiae, we show that a modification reaction that combines a long-range component and a locally acting component can provide bistability and can be blocked by simple barriers that interrupt the nucleosome chain. We find that robust containment of the silenced region could be achieved by the presence of a number of weak simple barriers in the surrounding chromatin and a limited capacity of the positive feedback reaction. In addition, we show that the state of the silenced region can be regulated by silencer elements acting only on neighboring nucleosomes. Thus, a relatively simple set of nucleosome-modifying enzymes and recognition domains is all that is needed to make chromatin-based epigenetics useful and safe.

Robust network topologies for generating switch-like cellular responses

Signaling networks that convert graded stimuli into binary, all-or-none cellular responses are critical in processes ranging from cell-cycle control to lineage commitment. To exhaustively enumerate topologies that exhibit this switch-like behavior, we simulated all possible two- and three-component networks on random parameter sets, and assessed the resulting response profiles for both steepness (ultrasensitivity) and extent of memory (bistability). Simulations were used to study purely enzymatic networks, purely transcriptional networks, and hybrid enzymatic/transcriptional networks, and the topologies in each class were rank ordered by parametric robustness (i.e., the percentage of applied parameter sets exhibiting ultrasensitivity or bistability). Results reveal that the distribution of network robustness is highly skewed, with the most robust topologies clustering into a small number of motifs. Hybrid networks are the most robust in generating ultrasensitivity (up to 28%) and bistability (up to 18%); strikingly, a purely transcriptional framework is the most fragile in generating either ultrasensitive (up to 3%) or bistable (up to 1%) responses. The disparity in robustness among the network classes is due in part to zero-order ultrasensitivity, an enzyme-specific phenomenon, which repeatedly emerges as a particularly robust mechanism for generating nonlinearity and can act as a building block for switch-like responses. We also highlight experimentally studied examples of topologies enabling switching behavior, in both native and synthetic systems, that rank highly in our simulations. This unbiased approach for identifying topologies capable of a given response may be useful in discovering new natural motifs and in designing robust synthetic gene networks.

Nucleosome-mediated cooperativity between transcription factors

Cooperative binding of transcription factors (TFs) to promoters and other regulatory regions is essential for precise gene expression. The classical model of cooperativity requires direct interactions between TFs, thus constraining the arrangement of TF sites in regulatory regions. Recent genomic and functional studies, however, demonstrate a great deal of flexibility in such arrangements with variable distances, numbers of sites, and identities of TF sites located in cis-regulatory regions. Such flexibility is inconsistent with cooperativity by direct interactions between TFs. Here, we demonstrate that strong cooperativity among noninteracting TFs can be achieved by their competition with nucleosomes. We find that the mechanism of nucleosome-mediated cooperativity is analogous to cooperativity in another multimolecular complex: hemoglobin. This surprising analogy provides deep insights, with parallels between the heterotropic regulation of hemoglobin (e.g., the Bohr effect) and the roles of nucleosome-positioning sequences and chromatin modifications in gene expression. Nucleosome-mediated cooperativity is consistent with several experimental studies, is equally applicable to repressors and activators, allows substantial flexibility in and modularity of regulatory regions, and provides a rationale for a broad range of genomic and evolutionary observations. Striking parallels between cooperativity in hemoglobin and in transcriptional regulation point to a general mechanism that can be used in various biological systems.

Statistical-mechanical lattice models for protein-DNA binding in chromatin

Statistical-mechanical lattice models for protein-DNA binding are well established as a method to describe complex ligand binding equilibria measured in vitro with purified DNA and protein components. Recently, a new field of applications has opened up for this approach since it has become possible to experimentally quantify genome-wide protein occupancies in relation to the DNA sequence. In particular, the organization of the eukaryotic genome by histone proteins into a nucleoprotein complex termed chromatin has been recognized as a key parameter that controls the access of transcription factors to the DNA sequence. New approaches have to be developed to derive statistical-mechanical lattice descriptions of chromatin-associated protein-DNA interactions. Here, we present the theoretical framework for lattice models of histone-DNA interactions in chromatin and investigate the (competitive) DNA binding of other chromosomal proteins and transcription factors. The results have a number of applications for quantitative models for the regulation of gene expression.

Condensed DNA: condensing the concepts

DNA is stored in vivo in a highly compact, so-called condensed phase, where gene regulatory processes are governed by the intricate interplay between different states of DNA compaction. These systems often have surprising properties, which one would not predict from classical concepts of dilute solutions. The mechanistic details of DNA packing are essential for its functioning, as revealed by the recent developments coming from biochemistry, electrostatics, statistical mechanics, and molecular and cell biology. Different aspects of condensed DNA behavior are linked to each other, but the links are often hidden in the bulk of experimental and theoretical details. Here we try to condense some of these concepts and provide interconnections between the different fields. After a brief description of main experimental features of DNA condensation inside viruses, bacteria, eukaryotes and the test tube, main theoretical approaches for the description of these systems are presented. We end up with an extended discussion of the role of DNA condensation in the context of gene regulation and mention potential applications of DNA condensation in gene therapy and biotechnology.

Simplified models of biological networks

The function of living cells is controlled by complex regulatory networks that are built of a wide diversity of interacting molecular components. The sheer size and intricacy of molecular networks of even the simplest organisms are obstacles toward understanding network functionality. This review discusses the achievements and promise of a bottom-up approach that uses well-characterized subnetworks as model systems for understanding larger networks. It highlights the interplay between the structure, logic, and function of various types of small regulatory circuits. The bottom-up approach advocates understanding regulatory networks as a collection of entangled motifs. We therefore emphasize the potential of negative and positive feedback, as well as their combinations, to generate robust homeostasis, epigenetics, and oscillations.

Transcriptional interaction-assisted identification of dynamic nucleosome positioning

Background

Nucleosomes regulate DNA accessibility and therefore play a central role in transcription control. Computational methods have been developed to predict static nucleosome positions from DNA sequences, but nucleosomes are dynamic in vivo.

Results

Motivated by our observation that transcriptional interaction is discriminative information for nucleosome occupancy, we developed a novel computational approach to identify dynamic nucleosome positions at promoters by combining transcriptional interaction and genomic sequence information. Our approach successfully identified experimentally determined nucleosome positioning dynamics available in three cellular conditions, and significantly improved the prediction accuracy which is based on sequence information alone. We then applied our approach to various cellular conditions and established a comprehensive landscape of dynamic nucleosome positioning in yeast.

Conclusion

Analysis of this landscape revealed that the majority of nucleosome positions are maintained during most conditions. However, nucleosome occupancy at most promoters fluctuates with the corresponding gene expression level and is reduced specifically at the phase of peak expression. Further investigation into properties of nucleosome occupancy identified two gene groups associated with distinct modes of nucleosome modulation. Our results suggest that both the intrinsic sequence and regulatory proteins modulate nucleosomes in an altered manner.