On the spontaneous stochastic dynamics of a single gene: complexity of the molecular interplay at the promoter

Single-cell transcriptional uncertainty landscape of cell differentiation

Background: Single-cell studies have demonstrated the presence of significant cell-to-cell heterogeneity in gene expression. Whether such heterogeneity is only a bystander or has a functional role in the cell differentiation process is still hotly debated. Methods: In this study, we quantified and followed single-cell transcriptional uncertainty - a measure of gene transcriptional stochasticity in single cells - in 10 cell differentiation systems of varying cell lineage progressions, from single to multi-branching trajectories, using the stochastic two-state gene transcription model. Results: By visualizing the transcriptional uncertainty as a landscape over a two-dimensional representation of the single-cell gene expression data, we observed universal features in the cell differentiation trajectories that include: (i) a peak in single-cell uncertainty during transition states, and in systems with bifurcating differentiation trajectories, each branching point represents a state of high transcriptional uncertainty; (ii) a positive correlation of transcriptional uncertainty with transcriptional burst size and frequency; (iii) an increase in RNA velocity preceding the increase in the cell transcriptional uncertainty. Conclusions: Our findings suggest a possible universal mechanism during the cell differentiation process, in which stem cells engage stochastic exploratory dynamics of gene expression at the start of the cell differentiation by increasing gene transcriptional bursts, and disengage such dynamics once cells have decided on a particular terminal cell identity. Notably, the peak of single-cell transcriptional uncertainty signifies the decision-making point in the cell differentiation process.

Forecasting cellular states: from descriptive to predictive biology via single-cell multiomics

As the single cell field races to characterize each cell type, state, and behavior, the complexity of the computational analysis approaches the complexity of the biological systems. Single cell and imaging technologies now enable unprecedented measurements of state transitions in biological systems, providing high-throughput data that capture tens-of-thousands of measurements on hundreds-of-thousands of samples. Thus, the definition of cell type and state is evolving to encompass the broad range of biological questions now attainable. To answer these questions requires the development of computational tools for integrated multi-omics analysis. Merged with mathematical models, these algorithms will be able to forecast future states of biological systems, going from statistical inferences of phenotypes to time course predictions of the biological systems with dynamic maps analogous to weather systems. Thus, systems biology for forecasting biological system dynamics from multi-omic data represents the future of cell biology empowering a new generation of technology-driven predictive medicine.

Noise and the molecular processes underlying cell fate decision-making

Cell fate decision-making events involve the interplay of many molecular processes, ranging from signal transduction to genetic regulation, as well as a set of molecular and physiological feedback loops. Each aspect offers a rich field of investigation in its own right, but to understand the whole process, even in simple terms, we need to consider them together. Here we attempt to characterise this process by focussing on the roles of noise during cell fate decisions. We use a range of recent results to develop a view of the sequence of events by which a cell progresses from a pluripotent or multipotent to a differentiated state: chromatin organisation, transcription factor stoichiometry, and cellular signalling all change during this progression, and all shape cellular variability, which becomes maximal at the transition state.

Exactly solvable models of stochastic gene expression

Stochastic models are key to understanding the intricate dynamics of gene expression. However, the simplest models that only account for active and inactive states of a gene fail to capture common observations in both prokaryotic and eukaryotic organisms. Here, we consider multistate models of gene expression that generalize the canonical Telegraph process and are capable of capturing the joint effects of transcription factors, heterochromatin state, and DNA accessibility (or, in prokaryotes, sigma-factor activity) on transcript abundance. We propose two approaches for solving classes of these generalized systems. The first approach offers a fresh perspective on a general class of multistate models and allows us to "decompose" more complicated systems into simpler processes, each of which can be solved analytically. This enables us to obtain a solution of any model from this class. Next, we develop an approximation method based on a power series expansion of the stationary distribution for an even broader class of multistate models of gene transcription. We further show that models from both classes cannot have a heavy-tailed distribution in the absence of extrinsic noise. The combination of analytical and computational solutions for these realistic gene expression models also holds the potential to design synthetic systems and control the behavior of naturally evolved gene expression systems in guiding cell-fate decisions.

What Is a Transcriptional Burst?

The idea that gene activity can be discontinuous will not surprise many biologists - many genes are restricted in when and where they can be expressed. Yet during the past 15 years, a collection of observations compiled under the umbrella term 'transcriptional bursting' has received considerable interest. Direct visualization of the dynamics of discontinuous transcription has expanded our understanding of basic transcriptional mechanisms and their regulation and provides a real-time readout of gene activity during the life of a cell. In this review, we try to reconcile the different views of the transcriptional process emerging from studies of bursting, and how this work contextualizes the relative importance of different regulatory inputs to normal dynamic ranges of gene activity.

Automated cell cycle and cell size measurements for single-cell gene expression studies

OBJECTIVES

Recent rise of single-cell studies revealed the importance of understanding the role of cell-to-cell variability, especially at the transcriptomic level. One of the numerous sources of cell-to-cell variation in gene expression is the heterogeneity in cell proliferation state. In order to identify how cell cycle and cell size influences gene expression variability at the single-cell level, we provide an universal and automatic toxic-free label method, compatible with single-cell high-throughput RT-qPCR. The method consists of isolating cells after a double-stained, analyzing their morphological parameters and performing a transcriptomic analysis on the same identified cells.

RESULTS

This led to an unbiased gene expression analysis and could be also used for improving single-cell tracking and imaging when combined with cell isolation. As an application for this technique, we showed that cell-to-cell variability in chicken erythroid progenitors was negligibly influenced by cell size nor cell cycle.

Inferring gene regulatory networks from single-cell data: a mechanistic approach

Background

The recent development of single-cell transcriptomics has enabled gene expression to be measured in individual cells instead of being population-averaged. Despite this considerable precision improvement, inferring regulatory networks remains challenging because stochasticity now proves to play a fundamental role in gene expression. In particular, mRNA synthesis is now acknowledged to occur in a highly bursty manner.

Results

We propose to view the inference problem as a fitting procedure for a mechanistic gene network model that is inherently stochastic and takes not only protein, but also mRNA levels into account. We first explain how to build and simulate this network model based upon the coupling of genes that are described as piecewise-deterministic Markov processes. Our model is modular and can be used to implement various biochemical hypotheses including causal interactions between genes. However, a naive fitting procedure would be intractable. By performing a relevant approximation of the stationary distribution, we derive a tractable procedure that corresponds to a statistical hidden Markov model with interpretable parameters. This approximation turns out to be extremely close to the theoretical distribution in the case of a simple toggle-switch, and we show that it can indeed fit real single-cell data. As a first step toward inference, our approach was applied to a number of simple two-gene networks simulated in silico from the mechanistic model and satisfactorily recovered the original networks.

Conclusions

Our results demonstrate that functional interactions between genes can be inferred from the distribution of a mechanistic, dynamical stochastic model that is able to describe gene expression in individual cells. This approach seems promising in relation to the current explosion of single-cell expression data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0487-0) contains supplementary material, which is available to authorized users.

Transcriptional precision and accuracy in development: from measurements to models and mechanisms

During development, genes are transcribed at specific times, locations and levels. In recent years, the emergence of quantitative tools has significantly advanced our ability to measure transcription with high spatiotemporal resolution in vivo. Here, we highlight recent studies that have used these tools to characterize transcription during development, and discuss the mechanisms that contribute to the precision and accuracy of the timing, location and level of transcription. We attempt to disentangle the discrepancies in how physicists and biologists use the term ‘precision' to facilitate interactions using a common language. We also highlight selected examples in which the coupling of mathematical modeling with experimental approaches has provided important mechanistic insights, and call for a more expansive use of mathematical modeling to exploit the wealth of quantitative data and advance our understanding of animal transcription.

Summary: This Review highlights how high-resolution quantitative tools and theoretical models have formed our current view of the mechanisms determining precision and accuracy in the timing, location and level of transcription in the Drosophila embryo.

SINCERITIES: inferring gene regulatory networks from time-stamped single cell transcriptional expression profiles

Motivation

Single cell transcriptional profiling opens up a new avenue in studying the functional role of cell-to-cell variability in physiological processes. The analysis of single cell expression profiles creates new challenges due to the distributive nature of the data and the stochastic dynamics of gene transcription process. The reconstruction of gene regulatory networks (GRNs) using single cell transcriptional profiles is particularly challenging, especially when directed gene-gene relationships are desired.

Results

We developed SINCERITIES (SINgle CEll Regularized Inference using TIme-stamped Expression profileS) for the inference of GRNs from single cell transcriptional profiles. We focused on time-stamped cross-sectional expression data, commonly generated from transcriptional profiling of single cells collected at multiple time points after cell stimulation. SINCERITIES recovers directed regulatory relationships among genes by employing regularized linear regression (ridge regression), using temporal changes in the distributions of gene expressions. Meanwhile, the modes of the gene regulations (activation and repression) come from partial correlation analyses between pairs of genes. We demonstrated the efficacy of SINCERITIES in inferring GRNs using in silico time-stamped single cell expression data and single cell transcriptional profiles of THP-1 monocytic human leukemia cells. The case studies showed that SINCERITIES could provide accurate GRN predictions, significantly better than other GRN inference algorithms such as TSNI, GENIE3 and JUMP3. Moreover, SINCERITIES has a low computational complexity and is amenable to problems of extremely large dimensionality. Finally, an application of SINCERITIES to single cell expression data of T2EC chicken erythrocytes pointed to BATF as a candidate novel regulator of erythroid development.

Availability and implementation

MATLAB and R version of SINCERITIES are freely available from the following websites: http://www.cabsel.ethz.ch/tools/sincerities.html and https://github.com/CABSEL/SINCERITIES. The single cell THP-1 and T2EC transcriptional profiles are available from the original publications (Kouno et al., 2013; Richard et al., 2016). The in silico single cell data are available on SINCERITIES websites.

Supplementary information

Supplementary data are available at Bioinformatics online.

Discrete distributional differential expression (D3E)--a tool for gene expression analysis of single-cell RNA-seq data

Background

The advent of high throughput RNA-seq at the single-cell level has opened up new opportunities to elucidate the heterogeneity of gene expression. One of the most widespread applications of RNA-seq is to identify genes which are differentially expressed between two experimental conditions.

Results

We present a discrete, distributional method for differential gene expression (D³E), a novel algorithm specifically designed for single-cell RNA-seq data. We use synthetic data to evaluate D³E, demonstrating that it can detect changes in expression, even when the mean level remains unchanged. Since D³E is based on an analytically tractable stochastic model, it provides additional biological insights by quantifying biologically meaningful properties, such as the average burst size and frequency. We use D³E to investigate experimental data, and with the help of the underlying model, we directly test hypotheses about the driving mechanism behind changes in gene expression.

Conclusion

Evaluation using synthetic data shows that D³E performs better than other methods for identifying differentially expressed genes since it is designed to take full advantage of the information available from single-cell RNA-seq experiments. Moreover, the analytical model underlying D³E makes it possible to gain additional biological insights.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-0944-6) contains supplementary material, which is available to authorized users.

Gene expression variability in clonal populations: Causes and consequences

During the last decade it has been shown that among cell variation in gene expression plays an important role within clonal populations. Here, we provide an overview of the different mechanisms contributing to gene expression variability in clonal populations. These are ranging from inherent variations in the biochemical process of gene expression itself, such as intrinsic noise, extrinsic noise and bistability to individual responses to variations in the local micro-environment, a phenomenon called phenotypic plasticity. Also genotypic variations caused by clonal evolution and phase variation can contribute to gene expression variability. Consequently, gene expression studies need to take these fluctuations in expression into account. However, frequently used techniques for expression quantification, such as microarrays, RNA sequencing, quantitative PCR and gene reporter fusions classically determine the population average of gene expression. Here, we discuss how these techniques can be adapted towards single cell analysis by integration with single cell isolation, RNA amplification and microscopy. Alternatively more qualitative selection-based techniques, such as mutant screenings, in vivo expression technology (IVET) and recombination-based IVET (RIVET) can be applied for detection of genes expressed only within a subpopulation. Finally, differential fluorescence induction (DFI), a protocol specially designed for single cell expression is discussed.

Fundamental principles of energy consumption for gene expression

How energy is consumed in gene expression is largely unknown mainly due to complexity of non-equilibrium mechanisms affecting expression levels. Here, by analyzing a representative gene model that considers complexity of gene expression, we show that negative feedback increases energy consumption but positive feedback has an opposite effect; promoter leakage always reduces energy consumption; generating more bursts needs to consume more energy; and the speed of promoter switching is at the cost of energy consumption. We also find that the relationship between energy consumption and expression noise is multi-mode, depending on both the type of feedback and the speed of promoter switching. Altogether, these results constitute fundamental principles of energy consumption for gene expression, which lay a foundation for designing biologically reasonable gene modules. In addition, we discuss possible biological implications of these principles by combining experimental facts.

Temperature-induced variation in gene expression burst size in metazoan cells

Background

Gene expression is an inherently stochastic process, owing to its dynamic molecular nature. Protein amount distributions, which can be acquired by cytometry using a reporter gene, can inform about the mechanisms of the underlying microscopic molecular system.

Results

By using different clones of chicken erythroid progenitor cells harboring different integration sites of a CMV-driven mCherry protein, we investigated the dynamical behavior of such distributions. We show that, on short term, clone distributions can be quickly regenerated from small population samples with a high accuracy. On longer term, on the contrary, we show variations manifested by correlated fluctuation in the Mean Fluorescence Intensity. In search for a possible cause of this correlation, we demonstrate that in response to small temperature variations cells are able to adjust their gene expression rate: a modest (2 °C) increase in external temperature induces a significant down regulation of mean expression values, with a reverse effect observed when the temperature is decreased. Using a two-state model of gene expression we further demonstrate that temperature acts by modifying the size of transcription bursts, while the burst frequency of the investigated promoter is less systematically affected.

Conclusions

For the first time, we report that transcription burst size is a key parameter for gene expression that metazoan cells from homeotherm animals can modify in response to an external thermal stimulus.

Electronic supplementary material

The online version of this article (doi:10.1186/s12867-015-0048-2) contains supplementary material, which is available to authorized users.

Signal integration by the CYP1A1 promoter--a quantitative study

Genes involved in detoxification of foreign compounds exhibit complex spatiotemporal expression patterns in liver. Cytochrome P450 1A1 (CYP1A1), for example, is restricted to the pericentral region of liver lobules in response to the interplay between aryl hydrocarbon receptor (AhR) and Wnt/β-catenin signaling pathways. However, the mechanisms by which the two pathways orchestrate gene expression are still poorly understood. With the help of 29 mutant constructs of the human CYP1A1 promoter and a mathematical model that combines Wnt/β-catenin and AhR signaling with the statistical mechanics of the promoter, we systematically quantified the regulatory influence of different transcription factor binding sites on gene induction within the promoter. The model unveils how different binding sites cooperate and how they establish the promoter logic; it quantitatively predicts two-dimensional stimulus-response curves. Furthermore, it shows that crosstalk between Wnt/β-catenin and AhR signaling is crucial to understand the complex zonated expression patterns found in liver lobules. This study exemplifies how statistical mechanical modeling together with combinatorial reporter assays has the capacity to disentangle the promoter logic that establishes physiological gene expression patterns.

Reinitiation enhances reliable transcriptional responses in eukaryotes

Gene transcription is a noisy process carried out by the transcription machinery recruited to the promoter. Noise reduction is a fundamental requirement for reliable transcriptional responses which in turn are crucial for signal transduction. Compared with the relatively simple transcription initiation in prokaryotes, eukaryotic transcription is more complex partially owing to its additional reinitiation mechanism. By theoretical analysis, we showed that reinitiation reduces noise in eukaryotic transcription independent of the transcription level. Besides, a higher reinitiation rate enables a stable scaffold complex an advantage in noise reduction. Finally, we showed that the coupling between scaffold formation and transcription can further reduce transcription noise independent of the transcription level. Furthermore, compared with the reinitiation mechanism, the noise reduction effect of the coupling can be of more significance in the case that the transcription level is low and the intrinsic noise dominates. Our results uncover a mechanistic route which eukaryotes may use to facilitate a more reliable response in the noisy transcription process.

Stochastic oscillations induced by intrinsic fluctuations in a self-repressing gene

Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Thus, it is important to understand how regularity can emerge from noise. Here, we study the stochastic dynamics of a self-repressing gene with arbitrarily long or short response time. We find that when the mRNA and protein half-lives are approximately equal to the gene response time, fluctuations can induce relatively regular oscillations in the protein concentration. To gain insight into this phenomenon at the crossroads of determinism and stochasticity, we use an intermediate theoretical approach, based on a moment-closure approximation of the master equation, which allows us to take into account the binary character of gene activity. We thereby obtain differential equations that describe how nonlinearity can feed-back fluctuations into the mean-field equations to trigger oscillations. Finally, our results suggest that the self-repressing Hes1 gene circuit exploits this phenomenon to generate robust oscillations, inasmuch as its time constants satisfy precisely the conditions we have identified.

Noise and information transmission in promoters with multiple internal States

Based on the measurements of noise in gene expression performed during the past decade, it has become customary to think of gene regulation in terms of a two-state model, where the promoter of a gene can stochastically switch between an ON and an OFF state. As experiments are becoming increasingly precise and the deviations from the two-state model start to be observable, we ask about the experimental signatures of complex multistate promoters, as well as the functional consequences of this additional complexity. In detail, we i), extend the calculations for noise in gene expression to promoters described by state transition diagrams with multiple states, ii), systematically compute the experimentally accessible noise characteristics for these complex promoters, and iii), use information theory to evaluate the channel capacities of complex promoter architectures and compare them with the baseline provided by the two-state model. We find that adding internal states to the promoter generically decreases channel capacity, except in certain cases, three of which (cooperativity, dual-role regulation, promoter cycling) we analyze in detail.

Promoter-mediated transcriptional dynamics

Genes in eukaryotic cells are typically regulated by complex promoters containing multiple binding sites for a variety of transcription factors, but how promoter dynamics affect transcriptional dynamics has remained poorly understood. In this study, we analyze gene models at the transcriptional regulation level, which incorporate the complexity of promoter structure (PS) defined as transcriptional exits (i.e., ON states of the promoter) and the transition pattern (described by a matrix consisting of transition rates among promoter activity states). We show that multiple exits of transcription are the essential origin of generating multimodal distributions of mRNA, but promoters with the same transition pattern can lead to multimodality of different modes, depending on the regulation of transcriptional factors. In turn, for similar mRNA distributions in the models, the mean ON or OFF time distributions may exhibit different characteristics, thus providing the supplemental information on PS. In addition, we demonstrate that the transcriptional noise can be characterized by a nonlinear function of mean ON and OFF times. These results not only reveal essential characteristics of promoter-mediated transcriptional dynamics but also provide signatures useful for inferring PS based on characteristics of transcriptional outputs.

Analytic approaches to stochastic gene expression in multicellular systems

Deterministic thermodynamic models of the complex systems, which control gene expression in metazoa, are helping researchers identify fundamental themes in the regulation of transcription. However, quantitative single cell studies are increasingly identifying regulatory mechanisms that control variability in expression. Such behaviors cannot be captured by deterministic models and are poorly suited to contemporary stochastic approaches that rely on continuum approximations, such as Langevin methods. Fortunately, theoretical advances in the modeling of transcription have assembled some general results that can be readily applied to systems being explored only through a deterministic approach. Here, I review some of the recent experimental evidence for the importance of genetically regulating stochastic effects during embryonic development and discuss key results from Markov theory that can be used to model this regulation. I then discuss several pairs of regulatory mechanisms recently investigated through a Markov approach. In each case, a deterministic treatment predicts no difference between the mechanisms, but the statistical treatment reveals the potential for substantially different distributions of transcriptional activity. In this light, features of gene regulation that seemed needlessly complex evolutionary baggage may be appreciated for their key contributions to reliability and precision of gene expression.

Can we negotiate with a tumor?

Recent progress in deciphering the molecular portraits of tumors promises an era of more personalized drug choices. However, current protocols still follow standard fixed-time schedules, which is not entirely coherent with the common observation that most tumors do not grow continuously. This unpredictability of the increases in tumor mass is not necessarily an obstacle to therapeutic efficiency, particularly if tumor dynamics could be exploited. We propose a model of tumor mass evolution as the integrated result of the dynamics of two linked complex systems, tumor cell population and tumor microenvironment, and show the practical relevance of this nonlinear approach.

Suppression and enhancement of transcriptional noise by DNA looping

DNA looping has been observed to enhance and suppress transcriptional noise but it is uncertain which of these two opposite effects is to be expected for given conditions. Here, we derive analytical expressions for the main quantifiers of transcriptional noise in terms of the molecular parameters and elucidate the role of DNA looping. Our results rationalize paradoxical experimental observations and provide the first quantitative explanation of landmark individual-cell measurements at the single molecule level on the classical lac operon genetic system [Choi, L. Cai, K. Frieda, and X. S. Xie, Science 322, 442 (2008)].

Reconciling the concurrent fast and slow cycling of proteins on gene promoters

During gene transcription, proteins appear to cycle on and off some gene promoters with both long (tens of minutes) and short periods (no more than several minutes). The essence of these phenomena still remains unclear. Here, we propose a stochastic model for the state evolution of promoters in terms of DNA-protein interactions. The model associates the characteristics of microscopic molecular interactions with macroscopic measurable quantities. Through theoretical derivation, we reconcile the contradictory viewpoints on the concurrent fast and slow cycling; both the cycling phenomena are further reproduced by fitting simulation results to the experimental data on the pS2 gene. Our results suggest that the fast cycling dictates how the proteins behave on the promoter and that stable binding hardly occurs. Different kinds of proteins rapidly bind/unbind the promoter at distinct transcriptional stages fulfilling specific functions; this feature is essentially manifested as the slow cycling of proteins when detected by chromatin immunoprecipitation assays. Thus, the slow cycling represents neither stable binding of proteins nor external modulation of the fast cycling. This work also reveals the relationship between the essence and measurement of transcriptional dynamics.

Systems biophysics of gene expression

Gene expression is a process central to any form of life. It involves multiple temporal and functional scales that extend from specific protein-DNA interactions to the coordinated regulation of multiple genes in response to intracellular and extracellular changes. This diversity in scales poses fundamental challenges to the use of traditional approaches to fully understand even the simplest gene expression systems. Recent advances in computational systems biophysics have provided promising avenues to reliably integrate the molecular detail of biophysical process into the system behavior. Here, we review recent advances in the description of gene regulation as a system of biophysical processes that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. There is now basic mechanistic understanding on how promoters controlled by multiple, local and distal, DNA binding sites for transcription factors can actively control transcriptional noise, cell-to-cell variability, and other properties of gene regulation, including precision and flexibility of the transcriptional responses.

Dual gating mechanism and function of P2X7 receptor channels

The ATP-gated P2X7 receptor channel (P2X7R) operates as a cytolytic and apoptotic receptor but also controls sustained cellular responses, including cell growth and proliferation. However, it has not been clarified how the same receptor mediates such opposing effects. To address this question, we have combined electrophysiological, imaging, and mathematical studies using wild-type and mutant rat P2X7Rs. Activation of naïve (not previously stimulated) receptors by low agonist concentrations caused monophasic slow desensitizing currents and internalization of receptors without other changes in the cellular morphology, much like other P2XRs. In contrast, saturating agonist concentrations induced high-amplitude biphasic currents, reflecting pore dilation and causing rapid cell swelling and lysis. The existence of these two signaling patterns was accounted for using a revised Markov-state model that included, in addition to naïve and sensitized states, desensitized states. Occupancy of one or two ATP-binding sites of naïve receptors favored a slow transition to desensitized states, whereas occupancy of the third binding site favored a transition to sensitized/dilated states. Consistent with model predictions, nondilating P2X7R mutants always generated desensitizing currents. These results suggest that the level of saturation of the ligand binding sites determines the nature of the P2X7R gating and cellular actions.

Eukaryotic transcriptional dynamics: from single molecules to cell populations

Transcriptional regulation is achieved through combinatorial interactions between regulatory elements in the human genome and a vast range of factors that modulate the recruitment and activity of RNA polymerase. Experimental approaches for studying transcription in vivo now extend from single-molecule techniques to genome-wide measurements. Parallel to these developments is the need for testable quantitative and predictive models for understanding gene regulation. These conceptual models must also provide insight into the dynamics of transcription and the variability that is observed at the single-cell level. In this Review, we discuss recent results on transcriptional regulation and also the models those results engender. We show how a non-equilibrium description informs our view of transcription by explicitly considering time- and energy-dependence at the molecular level.

Multidimensional control of cell structural robustness

Ample adaptive and functional opportunities of a living cell are determined by the complexity of its structural organisation. However, such complexity gives rise to a problem of maintenance of the coherence of inner processes in macroscopic interims and in macroscopic volumes which is necessary to support the structural robustness of a cell. The solution to this problem lies in multidimensional control of the adaptive and functional changes of a cell as well as its self-renewing processes in the context of environmental conditions. Six mechanisms (principles) form the basis of this multidimensional control: regulatory circuits with feedback loops, redundant inner diversity within a cell, multilevel distributed network organisation of a cell, molecular selection within a cell, continuous informational flows and functioning with a reserve of power. In the review we provide detailed analysis of these mechanisms, discuss their specific functions and the role of the superposition of these mechanisms in the maintenance of cell structural robustness in a wide range of environmental conditions.

Stochastic models of transcription: from single molecules to single cells

Genes in prokaryotic and eukaryotic cells are typically regulated by complex promoters containing multiple binding sites for a variety of transcription factors leading to a specific functional dependence between regulatory inputs and transcriptional outputs. With increasing regularity, the transcriptional outputs from different promoters are being measured in quantitative detail in single-cell experiments thus providing the impetus for the development of quantitative models of transcription. We describe recent progress in developing models of transcriptional regulation that incorporate, to different degrees, the complexity of multi-state promoter dynamics, and its effect on the transcriptional outputs of single cells. The goal of these models is to predict the statistical properties of transcriptional outputs and characterize their variability in time and across a population of cells, as a function of the input concentrations of transcription factors. The interplay between mathematical models of different regulatory mechanisms and quantitative biophysical experiments holds the promise of elucidating the molecular-scale mechanisms of transcriptional regulation in cells, from bacteria to higher eukaryotes.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Quantifying the contribution of chromatin dynamics to stochastic gene expression reveals long, locus-dependent periods between transcriptional bursts

BACKGROUND

A number of studies have established that stochasticity in gene expression may play an important role in many biological phenomena. This therefore calls for further investigations to identify the molecular mechanisms at stake, in order to understand and manipulate cell-to-cell variability. In this work, we explored the role played by chromatin dynamics in the regulation of stochastic gene expression in higher eukaryotic cells.

RESULTS

For this purpose, we generated isogenic chicken-cell populations expressing a fluorescent reporter integrated in one copy per clone. Although the clones differed only in the genetic locus at which the reporter was inserted, they showed markedly different fluorescence distributions, revealing different levels of stochastic gene expression. Use of chromatin-modifying agents showed that direct manipulation of chromatin dynamics had a marked effect on the extent of stochastic gene expression. To better understand the molecular mechanism involved in these phenomena, we fitted these data to a two-state model describing the opening/closing process of the chromatin. We found that the differences between clones seemed to be due mainly to the duration of the closed state, and that the agents we used mainly seem to act on the opening probability.

CONCLUSIONS

In this study, we report biological experiments combined with computational modeling, highlighting the importance of chromatin dynamics in stochastic gene expression. This work sheds a new light on the mechanisms of gene expression in higher eukaryotic cells, and argues in favor of relatively slow dynamics with long (hours to days) periods of quiet state.

Transcription stochasticity of complex gene regulation models

Transcription is regulated by a multitude of factors that concertedly induce genes to switch between activity states. Eukaryotic transcription involves a multitude of complexes that sequentially assemble on chromatin under the influence of transcription factors and the dynamic state of chromatin. Prokaryotic transcription depends on transcription factors, sigma-factors, and, in some cases, on DNA looping. We present a stochastic model of transcription that considers these complex regulatory mechanisms. We coarse-grain the molecular details in such a way that the model can describe a broad class of gene-regulation mechanisms. We solve this model analytically for various measures of stochastic transcription and compare alternative gene-regulation designs. We find that genes with complex multiprotein regulation can have peaked burst-size distributions in contrast to the geometric distributions found for simple models of transcription regulation. Burst-size distributions are, in addition, shaped by mRNA degradation during transcription bursts. We derive the stochastic properties of genes in the limit of deterministic switch times. These genes typically have reduced transcription noise. Severe timescale separation between gene regulation and transcription initiation enhances noise and leads to bimodal mRNA copy number distributions. In general, complex mechanisms for gene regulation lead to nonexponential waiting-time distributions for gene switching and transcription initiation, which typically reduce noise in mRNA copy numbers and burst size. Finally, we discuss that qualitatively different gene regulation models can often fit the same experimental data on single-cell mRNA abundance even though they have qualitatively different burst-size statistics and regulatory parameters.

Behavior genetics and postgenomics

The science of genetics is undergoing a paradigm shift. Recent discoveries, including the activity of retrotransposons, the extent of copy number variations, somatic and chromosomal mosaicism, and the nature of the epigenome as a regulator of DNA expressivity, are challenging a series of dogmas concerning the nature of the genome and the relationship between genotype and phenotype. According to three widely held dogmas, DNA is the unchanging template of heredity, is identical in all the cells and tissues of the body, and is the sole agent of inheritance. Rather than being an unchanging template, DNA appears subject to a good deal of environmentally induced change. Instead of identical DNA in all the cells of the body, somatic mosaicism appears to be the normal human condition. And DNA can no longer be considered the sole agent of inheritance. We now know that the epigenome, which regulates gene expressivity, can be inherited via the germline. These developments are particularly significant for behavior genetics for at least three reasons: First, epigenetic regulation, DNA variability, and somatic mosaicism appear to be particularly prevalent in the human brain and probably are involved in much of human behavior; second, they have important implications for the validity of heritability and gene association studies, the methodologies that largely define the discipline of behavior genetics; and third, they appear to play a critical role in development during the perinatal period and, in particular, in enabling phenotypic plasticity in offspring. I examine one of the central claims to emerge from the use of heritability studies in the behavioral sciences, the principle of minimal shared maternal effects, in light of the growing awareness that the maternal perinatal environment is a critical venue for the exercise of adaptive phenotypic plasticity. This consideration has important implications for both developmental and evolutionary biology.

Complex dynamics of transcription regulation

Transcription is a tightly regulated cellular function which can be triggered by endogenous (intrinsic) or exogenous (extrinsic) signals. The development of novel techniques to examine the dynamic behavior of transcription factors and the analysis of transcriptional activity at the single cell level with increased temporal resolution has revealed unexpected elements of stochasticity and dynamics of this process. Emerging research reveals a complex picture, wherein a wide range of time scales and temporal transcription patterns overlap to generate transcriptional programs. The challenge now is to develop a perspective that can guide us to common underlying mechanisms, and consolidate these findings. Here we review the recent literature on temporal dynamics and stochastic gene regulation patterns governed by intrinsic or extrinsic signals, utilizing the glucocorticoid receptor (GR)-mediated transcriptional model to illustrate commonality of these emerging concepts. This article is part of a Special Issue entitled: Chromatin in time and space.

The impact of transcriptional cycling on gene regulation

Research of the past decade showed that transcriptional regulation could be a highly dynamic and cyclical process. Many transcription factors and their co-regulators cyclically associate with a periodicity of 30-75 min with regulatory chromatin regions resulting in dynamically changing chromatin marks and cyclical activities of RNA polymerase II in mRNA synthesis.

Genes at work in random bouts: stochastically discontinuous gene activity makes cell cycle duration and cell fate decisions variable, thus providing for stem cells plasticity

Cell interdivision periods (IDP) in homogenous cell populations vary stochastically. Another aspect of probabilistic cell behavior is randomness in cell differentiation. These features are suggested to result from competing stochastic events of assembly/disassembly of the transcription pre-initiation complex (PIC) at gene promoters. The time needed to assemble a proper PIC from different proteins, which must be numerous enough to make their combination gene specific, may be comparable to the IDP. Nascent mRNA visualization at defined genes and inferences from protein level fluctuations in single cells suggest that some genes do operate in this way. The onset of mRNA production by such genes may miss the time windows provided by the cell cycle, resulting in cells differentiating into those in which the respective mRNAs are either present or absent. This creates a way to generate cell phenotype diversity in multicellular organisms.

What do expression dynamics tell us about the mechanism of transcription?

Single-cell microscopy studies have the potential to provide an unprecedented view of gene expression with exquisite spatial and temporal sensitivity. However, there is a challenge to connect the holistic cellular view with a reductionist biochemical view. In particular, experimental efforts to characterize the in vivo regulation of transcription have focused primarily on measurements of the dynamics of transcription factors and chromatin modifying factors. Such measurements have elucidated the transient nature of many nuclear interactions. In the past few years, experimental approaches have emerged that allow for interrogation of the output of transcription at the single-molecule, single-cell level. Here, I summarize the experimental results and models that aim to provide an integrated view of transcriptional regulation.

Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression

Gene expression at the single-cell level incorporates reaction mechanisms which are intrinsically stochastic as they involve molecular species present at low copy numbers. The dynamics of these mechanisms can be described quantitatively using stochastic master-equation modelling; in this paper we study a generic gene-expression model of this kind which explicitly includes the representations of the processes of transcription and translation. For this model we determine the generating function of the steady-state distribution of mRNA and protein counts and characterise the underlying probability law using a combination of analytic, asymptotic and numerical approaches, finding that the distribution may assume a number of qualitatively distinct forms. The results of the analysis are suitable for comparison with single-molecule resolution gene-expression data emerging from recent experimental studies.

Nuclear proteins: finding and binding target sites in chromatin

Fluorescent protein labelling, as well as impressive progress in live cell imaging have revolutionised the view on how essential nuclear functions like gene transcription regulation and DNA repair are organised. Here, we address questions like how DNA-interacting molecules find and bind their target sequences in the vast amount of DNA. In addition, we discuss methods that have been developed for quantitative analysis of data from fluorescence recovery after photobleaching experiments (FRAP).

Transcriptional regulation: effects of promoter proximal pausing on speed, synchrony and reliability

Recent whole genome polymerase binding assays in the Drosophila embryo have shown that a substantial proportion of uninduced genes have pre-assembled RNA polymerase-II transcription initiation complex (PIC) bound to their promoters. These constitute a subset of promoter proximally paused genes for which mRNA elongation instead of promoter access is regulated. This difference can be described as a rearrangement of the regulatory topology to control the downstream transcriptional process of elongation rather than the upstream transcriptional initiation event. It has been shown experimentally that genes with the former mode of regulation tend to induce faster and more synchronously, and that promoter-proximal pausing is observed mainly in metazoans, in accord with a posited impact on synchrony. However, it has not been shown whether or not it is the change in the regulated step per se that is causal. We investigate this question by proposing and analyzing a continuous-time Markov chain model of PIC assembly regulated at one of two steps: initial polymerase association with DNA, or release from a paused, transcribing state. Our analysis demonstrates that, over a wide range of physical parameters, increased speed and synchrony are functional consequences of elongation control. Further, we make new predictions about the effect of elongation regulation on the consistent control of total transcript number between cells. We also identify which elements in the transcription induction pathway are most sensitive to molecular noise and thus possibly the most evolutionarily constrained. Our methods produce symbolic expressions for quantities of interest with reasonable computational effort and they can be used to explore the interplay between interaction topology and molecular noise in a broader class of biochemical networks. We provide general-purpose code implementing these methods.

Gene activation is an inherently random process because numerous diffusing proteins and DNA must first interact by random association before transcription can begin. For many genes the necessary protein–DNA associations only begin after activation, but it has recently been noted that a large class of genes in multicellular organisms can assemble the initiation complex of proteins on the core promoter prior to activation. For these genes, activation merely releases polymerase from the preassembled complex to transcribe the gene. It has been proposed on the basis of experiments that such a mechanism, while possibly costly, increases both the speed and the synchrony of the process of gene transcription. We study a realistic model of gene transcription, and show that this conclusion holds for all but a tiny fraction of the space of physical rate parameters that govern the process. The improved control of cell-to-cell variations afforded by regulation through a paused polymerase may help multicellular organisms achieve the high degree of coordination required for development. Our approach has also generated tools with which one can study the effects of analogous changes in other molecular networks and determine the relative importance of various molecular binding rates to particular system properties.

Random discrete competing events vs. dynamic bistable switches in cell proliferation in differentiation

Several recent experiments related to fundamental aspects of cell behaviour, such as passing of the restriction point of cell cycle, which are generally interpreted in accordance with the dynamic paradigm implying the use of differential equations operating with the concentrations of cellular components and rate constants of their interactions, are shown in the present paper to be consistent with a simple model based on discrete competing stochastic events interpreted as assembly of alternative complexes of transcription factors at gene promoters. The model conforms to the transition probability model of cell cycle and to the stochastic approaches to cell differentiation and integrates them with the restriction point concept.

Dynamics of nuclear receptor target gene regulation

Ligand-regulated nuclear receptors, such as estrogen receptors, glucocorticoid receptor, vitamin D receptor, and peroxisome proliferator-activated receptors, belong to the most widely studied and best understood transcription factors. Therefore, the dynamic nature of transcriptional regulation was observed first with different members of the nuclear receptor superfamily, but is now also extended to other transcription factors, such as nuclear factor κB. Dynamic and in part cyclical processes were observed on the level of translocation into the nucleus, association with genomic binding sites, exchange of co-regulators and chromatin modifiers, occurrence of chromatin marks, and activities of RNA polymerase II resulting in mRNA synthesis. In this review, we summarize recent findings on the dynamic regulation of nuclear receptor target genes in the chromatin context.