Induction mechanism of a single gene molecule: stochastic or deterministic?

Global genome decompaction leads to stochastic activation of gene expression as a first step toward fate commitment in human hematopoietic cells

When human cord blood-derived CD34+ cells are induced to differentiate, they undergo rapid and dynamic morphological and molecular transformations that are critical for fate commitment. In particular, the cells pass through a transitory phase known as "multilineage-primed" state. These cells are characterized by a mixed gene expression profile, different in each cell, with the coexpression of many genes characteristic for concurrent cell lineages. The aim of our study is to understand the mechanisms of the establishment and the exit from this transitory state. We investigated this issue using single-cell RNA sequencing and ATAC-seq. Two phases were detected. The first phase is a rapid and global chromatin decompaction that makes most of the gene promoters in the genome accessible for transcription. It results 24 h later in enhanced and pervasive transcription of the genome leading to the concomitant increase in the cell-to-cell variability of transcriptional profiles. The second phase is the exit from the multilineage-primed phase marked by a slow chromatin closure and a subsequent overall down-regulation of gene transcription. This process is selective and results in the emergence of coherent expression profiles corresponding to distinct cell subpopulations. The typical time scale of these events spans 48 to 72 h. These observations suggest that the nonspecificity of genome decompaction is the condition for the generation of a highly variable multilineage expression profile. The nonspecific phase is followed by specific regulatory actions that stabilize and maintain the activity of key genes, while the rest of the genome becomes repressed again by the chromatin recompaction. Thus, the initiation of differentiation is reminiscent of a constrained optimization process that associates the spontaneous generation of gene expression diversity to subsequent regulatory actions that maintain the activity of some genes, while the rest of the genome sinks back to the repressive closed chromatin state.

Quantitative imaging of RNA polymerase II activity in plants reveals the single-cell basis of tissue-wide transcriptional dynamics

The responses of plants to their environment are often dependent on the spatiotemporal dynamics of transcriptional regulation. While live-imaging tools have been used extensively to quantitatively capture rapid transcriptional dynamics in living animal cells, the lack of implementation of these technologies in plants has limited concomitant quantitative studies in this kingdom. Here, we applied the PP7 and MS2 RNA-labelling technologies for the quantitative imaging of RNA polymerase II activity dynamics in single cells of living plants as they respond to experimental treatments. Using this technology, we counted nascent RNA transcripts in real time in Nicotiana benthamiana (tobacco) and Arabidopsis thaliana. Examination of heat shock reporters revealed that plant tissues respond to external signals by modulating the proportion of cells that switch from an undetectable basal state to a high-transcription state, instead of modulating the rate of transcription across all cells in a graded fashion. This switch-like behaviour, combined with cell-to-cell variability in transcription rate, results in mRNA production variability spanning three orders of magnitude. We determined that cellular heterogeneity stems mainly from stochasticity intrinsic to individual alleles instead of variability in cellular composition. Together, our results demonstrate that it is now possible to quantitatively study the dynamics of transcriptional programs in single cells of living plants.

Signaling Mechanism of Transcriptional Bursting: A Technical Resolution-Independent Study

Simple Summary

Following changing cellular signals, various genes adjust their activities and initiate transcripts with the right rates. The precision of such a transcriptional response has a fundamental role in the survival and development of lives. Quite unexpectedly, gene transcription has been uncovered to occur in sporadic bursts, rather than in a continuous manner. This has raised a provoking issue of how the bursting transmits regulatory signals, and it remains controversial whether the burst size, frequency, or both, take the role of signal transmission. Here, this study showed that only the burst frequency was subject to modulation by activators that carry the regulatory signals. A higher activator concentration led to a larger frequency, whereas the size remains unchanged. When very high, the burst cluster emerged, which may be mistaken as a large burst. This work thus supports the conclusion that transcription regulation is in a “digital” way.

Abstract

Gene transcription has been uncovered to occur in sporadic bursts. However, due to technical difficulties in differentiating individual transcription initiation events, it remains debated as to whether the burst size, frequency, or both are subject to modulation by transcriptional activators. Here, to bypass technical constraints, we addressed this issue by introducing two independent theoretical methods including analytical research based on the classic two-model and information entropy research based on the architecture of transcription apparatus. Both methods connect the signaling mechanism of transcriptional bursting to the characteristics of transcriptional uncertainty (i.e., the differences in transcriptional levels of the same genes that are equally activated). By comparing the theoretical predictions with abundant experimental data collected from published papers, the results exclusively support frequency modulation. To further validate this conclusion, we showed that the data that appeared to support size modulation essentially supported frequency modulation taking into account the existence of burst clusters. This work provides a unified scheme that reconciles the debate on burst signaling.

Stochastic models coupling gene expression and partitioning in cell division in Escherichia coli

Regulation of future RNA and protein numbers is a key process by which cells continuously best fit the environment. In bacteria, RNA and proteins exist in small numbers and their regulatory processes are stochastic. Consequently, there is cell-to-cell variability in these numbers, even between sister cells. Traditionally, the two most studied sources of this variability are gene expression and RNA and protein degradation, with evidence suggesting that the latter is subject to little regulation, when compared to the former. However, time-lapse microscopy and single molecule fluorescent tagging have produced evidence that cell division can also be a significant source of variability due to asymmetries in the partitioning of RNA and proteins. Relevantly, the impact of this noise differs from noise in production and degradation since, unlike these, it is not continuous. Rather, it occurs at specific time points, at which moment it can introduce major fluctuations. Several models have now been proposed that integrate noise from cell division, in addition to noise in gene expression, to mimic the dynamics of RNA and protein numbers of cell lineages. This is expected to be particularly relevant in genetic circuits, where significant fluctuations in one component protein, at specific time moments, are expected to perturb near-equilibrium states of the circuits, which can have long-lasting consequences. Here we review stochastic models coupling these processes in Escherichia coli, from single genes to small circuits.

Single-Cell Expression Variability Implies Cell Function

As single-cell RNA sequencing (scRNA-seq) data becomes widely available, cell-to-cell variability in gene expression, or single-cell expression variability (scEV), has been increasingly appreciated. However, it remains unclear whether this variability is functionally important and, if so, what are its implications for multi-cellular organisms. Here, we analyzed multiple scRNA-seq data sets from lymphoblastoid cell lines (LCLs), lung airway epithelial cells (LAECs), and dermal fibroblasts (DFs) and, for each cell type, selected a group of homogenous cells with highly similar expression profiles. We estimated the scEV levels for genes after correcting the mean-variance dependency in that data and identified 465, 466, and 364 highly variable genes (HVGs) in LCLs, LAECs, and DFs, respectively. Functions of these HVGs were found to be enriched with those biological processes precisely relevant to the corresponding cell type’s function, from which the scRNA-seq data used to identify HVGs were generated—e.g., cytokine signaling pathways were enriched in HVGs identified in LCLs, collagen formation in LAECs, and keratinization in DFs. We repeated the same analysis with scRNA-seq data from induced pluripotent stem cells (iPSCs) and identified only 79 HVGs with no statistically significant enriched functions; the overall scEV in iPSCs was of negligible magnitude. Our results support the “variation is function” hypothesis, arguing that scEV is required for cell type-specific, higher-level system function. Thus, quantifying and characterizing scEV are of importance for our understating of normal and pathological cellular processes.

Gene transcription in bursting: a unified mode for realizing accuracy and stochasticity

There is accumulating evidence that, from bacteria to mammalian cells, messenger RNAs (mRNAs) are produced in intermittent bursts - a much 'noisier' process than traditionally thought. Based on quantitative measurements at individual promoters, diverse phenomenological models have been proposed for transcriptional bursting. Nevertheless, the underlying molecular mechanisms and significance for cellular signalling remain elusive. Here, we review recent progress, address the above issues and illuminate our viewpoints with simulation results. Despite being widely used in modelling and in interpreting experimental data, the traditional two-state model is far from adequate to describe or infer the molecular basis and stochastic principles of transcription. In bacteria, DNA supercoiling contributes to the bursting of those genes that express at high levels and are topologically constrained in short loops; moreover, low-affinity cis-regulatory elements and unstable protein complexes can play a key role in transcriptional regulation. Integrating data on the architecture, kinetics, and transcriptional input-output function is a promising approach to uncovering the underlying dynamic mechanism. For eukaryotes, distinct bursting features described by the multi-scale and continuum models coincide with those predicted by four theoretically derived principles that govern how the transcription apparatus operates dynamically. This consistency suggests a unified framework for comprehending bursting dynamics at the level of the structural and kinetic basis of transcription. Moreover, the existing models can be unified by a generic model. Remarkably, transcriptional bursting enables regulatory information to be transmitted in a digital manner, with the burst frequency representing the strength of regulatory signals. Such a mode guarantees high fidelity for precise transcriptional regulation and also provides sufficient randomness for realizing cellular heterogeneity.

Widespread inter-individual gene expression variability in Arabidopsis thaliana

A fundamental question in biology is how gene expression is regulated to give rise to a phenotype. However, transcriptional variability is rarely considered although it could influence the relationship between genotype and phenotype. It is known in unicellular organisms that gene expression is often noisy rather than uniform, and this has been proposed to be beneficial when environmental conditions are unpredictable. However, little is known about inter-individual transcriptional variability in multicellular organisms. Using transcriptomic approaches, we analysed gene expression variability between individual Arabidopsis thaliana plants growing in identical conditions over a 24-h time course. We identified hundreds of genes that exhibit high inter-individual variability and found that many are involved in environmental responses, with different classes of genes variable between the day and night. We also identified factors that might facilitate gene expression variability, such as gene length, the number of transcription factors regulating the genes and the chromatin environment. These results shed new light on the impact of transcriptional variability in gene expression regulation in plants.

Simulating biological processes: stochastic physics from whole cells to colonies

The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a 'minimal cell'. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.

Population dynamics of inducible nitric oxide synthase production by LPSand LPS/IFNγ-stimulated mouse macrophages

The reactive nitrogen intermediate, nitric oxide (NO) is important in host defense against both NO-sensitive microorganisms and tumor cells. Macrophages are one of the chief inflammatory sources, especially when stimulated with the combination of LPS and interferonγ (IFNγ). It is not known, however, whether IFNγ-mediated augmentation of LPS-induced production of NO is the result of greater production by all cells or to the recruitment of more producer macrophages within a given population. This question was addressed, first, by stimulating mouse macrophages (either bone marrow culture-derived, inflammatory peritoneal or those of the cell line, RAW 264.7) with up to 10 U/ml IFNγ for as long as 24 h. Under these conditions, there was little or no production of NO and rare or no cells were immunocytochemically positive for the inducible form of nitric oxide synthase (iNOS), which catalyzes the production of NO. Populations similarly exposed to 1 ng/ml LPS were low producers of NO and contained somewhat more, but still only a few (< 15%), iNOS-positive cells. In contrast, as the concentration of IFNγ was increased (≥ 1 U/ml) in the presence of a constant amount of LPS (1 ng/ml), the principal effect was to increase both the production of NO and the number of iNOS-positive macrophages. The amount of iNOS expressed by some cells also appeared to be increased. Two important conclusions can be drawn from these findings: (1) there is heterogeneity in mouse macrophage populations with respect to the production of iNOS; and (2) increasing concentrations of IFNγ appear to augment LPS-induced secretion of NO by recruiting increasingly greater numbers of macrophages into the production of iNOS. Such results potentially provide important clues as to how IFNγ may be acting at the subcellular level to enhance iNOS synthesis.

Iron acquisition and oxidative stress response in aspergillus fumigatus

BACKGROUND

Aspergillus fumigatus is a ubiquitous airborne fungal pathogen that presents a life-threatening health risk to individuals with weakened immune systems. A. fumigatus pathogenicity depends on its ability to acquire iron from the host and to resist host-generated oxidative stress. Gaining a deeper understanding of the molecular mechanisms governing A. fumigatus iron acquisition and oxidative stress response may ultimately help to improve the diagnosis and treatment of invasive aspergillus infections.

RESULTS

This study follows a systems biology approach to investigate how adaptive behaviors emerge from molecular interactions underlying A. fumigatus iron regulation and oxidative stress response. We construct a Boolean network model from known interactions and simulate how changes in environmental iron and superoxide levels affect network dynamics. We propose rules for linking long term model behavior to qualitative estimates of cell growth and cell death. These rules are used to predict phenotypes of gene deletion strains. The model is validated on the basis of its ability to reproduce literature data not used in model generation.

CONCLUSIONS

The model reproduces gene expression patterns in experimental time course data when A. fumigatus is switched from a low iron to a high iron environment. In addition, the model is able to accurately represent the phenotypes of many knockout strains under varying iron and superoxide conditions. Model simulations support the hypothesis that intracellular iron regulates A. fumigatus transcription factors, SreA and HapX, by a post-translational, rather than transcriptional, mechanism. Finally, the model predicts that blocking siderophore-mediated iron uptake reduces resistance to oxidative stress. This indicates that combined targeting of siderophore-mediated iron uptake and the oxidative stress response network may act synergistically to increase fungal cell killing.

Toward an understanding of immune cell sociology: real-time monitoring of cytokine secretion at the single-cell level

The immune system is a very complex and dynamic cellular system, and its intricacies are considered akin to those of human society. Disturbance of homeostasis of the immune system results in various types of diseases; therefore, the homeostatic mechanism of the immune system has long been a subject of great interest in biology, and a lot of information has been accumulated at the cellular and the molecular levels. However, the sociological aspects of the immune system remain too abstract to address because of its high complexity, which mainly originates from a large number and variety of cell-cell interactions. As long-range interactions mediated by cytokines play a key role in the homeostasis of the immune system, cytokine secretion analyses, ranging from analyses of the micro level of individual cells to the macro level of a bulk of cell ensembles, provide us with a solid basis of a sociological viewpoint of the immune system. In this review, as the first step toward a comprehensive understanding of immune cell sociology, cytokine secretion of immune cells is surveyed with a special emphasis on the single-cell level, which has been overlooked but should serve as a basis of immune cell sociology. Now that it has become evident that large cell-to-cell variations in cytokine secretion exist at the single-cell level, we face a tricky yet interesting question: How is homeostasis maintained when the system is composed of intrinsically noisy agents? In this context, we discuss how the heterogeneity of cytokine secretion at the single-cell level affects our view of immune cell sociology. While the apparent inconsistency between homeostasis and cell-to-cell heterogeneity is difficult to address by a conventional reductive approach, comparison and integration of single-cell data with macroscopic data will offer us a new direction for the comprehensive understanding of immune cell sociology.

Stochastic modeling for the expression of a gene regulated by competing transcription factors

It is widely accepted that gene expression regulation is a stochastic event. The common approach for its computer simulation requires detailed information on the interactions of individual molecules, which is often not available for the analyses of biological experiments. As an alternative approach, we employed a more intuitive model to simulate the experimental result, the Markov-chain model, in which a gene is regulated by activators and repressors, which bind the same site in a mutually exclusive manner. Our stochastic simulation in the presence of both activators and repressors predicted a Hill-coefficient of the dose-response curve closer to the experimentally observed value than the calculated value based on the simple additive effects of activators alone and repressors alone. The simulation also reproduced the heterogeneity of gene expression levels among individual cells observed by Fluorescence Activated Cell Sorting analysis. Therefore, our approach may help to apply stochastic simulations to broader experimental data.

Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics

Linearized catalytic reaction equations (modelling, for example, the dynamics of genetic regulatory networks), under the constraint that expression levels, i.e. molecular concentrations of nucleic material, are positive, exhibit non-trivial dynamical properties, which depend on the average connectivity of the reaction network. In these systems, an inflation of the edge of chaos and multi-stability have been demonstrated to exist. The positivity constraint introduces a nonlinearity, which makes chaotic dynamics possible. Despite the simplicity of such minimally nonlinear systems, their basic properties allow us to understand the fundamental dynamical properties of complex biological reaction networks. We analyse the Lyapunov spectrum, determine the probability of finding stationary oscillating solutions, demonstrate the effect of the nonlinearity on the effective in- and out-degree of the active interaction network, and study how the frequency distributions of oscillatory modes of such a system depend on the average connectivity.

HIV promoter integration site primarily modulates transcriptional burst size rather than frequency

Mammalian gene expression patterns, and their variability across populations of cells, are regulated by factors specific to each gene in concert with its surrounding cellular and genomic environment. Lentiviruses such as HIV integrate their genomes into semi-random genomic locations in the cells they infect, and the resulting viral gene expression provides a natural system to dissect the contributions of genomic environment to transcriptional regulation. Previously, we showed that expression heterogeneity and its modulation by specific host factors at HIV integration sites are key determinants of infected-cell fate and a possible source of latent infections. Here, we assess the integration context dependence of expression heterogeneity from diverse single integrations of a HIV-promoter/GFP-reporter cassette in Jurkat T-cells. Systematically fitting a stochastic model of gene expression to our data reveals an underlying transcriptional dynamic, by which multiple transcripts are produced during short, infrequent bursts, that quantitatively accounts for the wide, highly skewed protein expression distributions observed in each of our clonal cell populations. Interestingly, we find that the size of transcriptional bursts is the primary systematic covariate over integration sites, varying from a few to tens of transcripts across integration sites, and correlating well with mean expression. In contrast, burst frequencies are scattered about a typical value of several per cell-division time and demonstrate little correlation with the clonal means. This pattern of modulation generates consistently noisy distributions over the sampled integration positions, with large expression variability relative to the mean maintained even for the most productive integrations, and could contribute to specifying heterogeneous, integration-site-dependent viral production patterns in HIV-infected cells. Genomic environment thus emerges as a significant control parameter for gene expression variation that may contribute to structuring mammalian genomes, as well as be exploited for survival by integrating viruses.

A mathematical and computational approach for integrating the major sources of cell population heterogeneity

Several approaches have been used in the past to model heterogeneity in bacterial cell populations, with each approach focusing on different source(s) of heterogeneity. However, a holistic approach that integrates all the major sources into a comprehensive framework applicable to cell populations is still lacking. In this work we present the mathematical formulation of a cell population master equation (CPME) that describes cell population dynamics and takes into account the major sources of heterogeneity, namely stochasticity in reaction, DNA-duplication, and division, as well as the random partitioning of species contents into the two daughter cells. The formulation also takes into account cell growth and respects the discrete nature of the molecular contents and cell numbers. We further develop a Monte Carlo algorithm for the simulation of the stochastic processes considered here. To benchmark our new framework, we first use it to quantify the effect of each source of heterogeneity on the intrinsic and the extrinsic phenotypic variability for the well-known two-promoter system used experimentally by Elowitz et al. (2002). We finally apply our framework to a more complicated system and demonstrate how the interplay between noisy gene expression and growth inhibition due to protein accumulation at the single cell level can result in complex behavior at the cell population level. The generality of our framework makes it suitable for studying a vast array of artificial and natural genetic networks. Using our Monte Carlo algorithm, cell population distributions can be predicted for the genetic architecture of interest, thereby quantifying the effect of stochasticity in intracellular reactions or the variability in the rate of physiological processes such as growth and division. Such in silico experiments can give insight into the behavior of cell populations and reveal the major sources contributing to cell population heterogeneity.

Toward a system-level understanding of microRNA pathway via mathematical modeling

The microRNA (miRNA) pathway plays multiple roles in regulating mechanisms controlling both physiological and pathological processes such as the cell proliferation and cancers. But little is known about the dynamic properties, key rate-limiting steps as well as the stochastic noise in this pathway. Presently, a system-theoretic approach was presented to analyze and quantitative modeling of a generic miRNA pathway, which can be implemented deterministically and stochastically. Our results show that the inferred dynamic properties obtained from the mathematical models of the miRNA pathway are well consistent with previous experimental observations. By sensitivity analysis, the key steps in this pathway were found to be the miRNA gene transcription, RISC decay and mRNA formation. In addition, the results of quantified noise strength along the pathway demonstrate that the pathway can reduce the ingress noise and reveal the noise robustness property. Our findings also present testable hypothesis for experimental biologists to further investigate miRNA's increasing functional roles in regulating various cellular processes.

Stochasticity of gene products from transcriptional pulsing

Transcriptional pulsing has been observed in both prokaryotes and eukaryotes and plays a crucial role in cell-to-cell variability of protein and mRNA numbers. An important issue is how the time constants associated with episodes of transcriptional bursting and mRNA and protein degradation rates lead to different cellular mRNA and protein distributions, starting from the transient regime leading to the steady state. We address this by deriving and then investigating the exact time-dependent solution of the master equation for a transcriptional pulsing model of mRNA distributions. We find a plethora of results. We show that, among others, bimodal and long-tailed (power-law) distributions occur in the steady state as the rate constants are varied over biologically significant time scales. Since steady state may not be reached experimentally we present results for the time evolution of the distributions. Because cellular behavior is determined by proteins, we also investigate the effect of the different mRNA distributions on the corresponding protein distributions using numerical simulations.

Inflation of the edge of chaos in a simple model of gene interaction networks

We study a set of linearized catalytic reactions to model gene and protein interactions. The model is based on experimentally motivated interaction network topologies and is designed to capture some key properties of gene expression statistics. We impose a nonlinearity to the system by enforcing a boundary condition which guarantees non-negative concentrations of chemical substances. System stability is quantified by maximum Lyapunov exponents. We find that the non-negativity constraint leads to a drastic inflation of those regions in parameter space where the Lyapunov exponent exactly vanishes. Within the model this finding can be fully explained as a result of a symmetry breaking mechanism induced by the positivity constraint. The robustness of this finding with respect to network topologies and the role of intrinsic molecular and external noise is discussed. We argue that systems with inflated "edges of chaos" could be much more easily favored by natural selection than systems where the Lyapunov exponent vanishes only on a parameter set of measure zero.

Stochastic patterning in the mouse pre-implantation embryo

Mouse pre-implantation development gives rise to the blastocyst, which is made up of at least three distinct cell types: the trophectoderm (TE) that surrounds a cavity, and an inner cell mass (ICM) comprising the primitive endoderm (PE) and epiblast (EPI). However, the underlying mechanisms involved in patterning the cleavage-stage embryo are still unresolved. By analyzing the distribution of the transcription factors Oct4 (Pou5f1), Cdx2 and Nanog at precisely defined stages in pre-implantation development, we were able to identify critical events leading to the divergence of TE, EPI and PE lineages. We found that Oct4 is present in all cells until late blastocyst, gradually disappearing from the TE thereafter. The expression patterns of both Cdx2 and Nanog exhibit two specific phases, culminating in their restriction to TE and EPI, respectively. In the first phase, starting after compaction, blastomeres show highly variable Cdx2 and Nanog protein levels. Importantly, the variability in Nanog levels is independent of position within the morula, whereas Cdx2 variability may originate from asymmetric cell divisions at the 8-cell stage in a non-stereotypic way. Furthermore, there is initially no reciprocal relationship between Cdx2 and Oct4 or between Cdx2 and Nanog protein levels. In the second phase, a definite pattern is established, possibly by a sorting process that accommodates intrinsic and extrinsic cues. Based on these results, we propose a model in which early embryonic mouse patterning includes stochastic processes, consistent with the highly regulative capacity of the embryo. This may represent a feature unique to early mammalian development.

Modeling stochasticity in gene regulation: characterization in the terms of the underlying distribution function

Intrinsic stochasticity plays an essential role in gene regulation because of a small number of involved molecules of DNA, mRNA and protein of a given species. To better understand this phenomenon, small gene regulatory systems are mathematically modeled as systems of coupled chemical reactions, but the existing exact description utilizing a Chapman-Kolmogorov equation or simulation algorithms is limited and inefficient. The present work considers a much more efficient yet accurate modeling approach, which allows analyzing stochasticity in the system in the terms of the underlying distribution function. We depart from the analysis of a single gene regulatory module to find that the mRNA and protein variance is decomposable into additive terms resulting from respective sources of stochasticity. This variance decomposition is asserted by constructing two approximations to the exact stochastic description: First, the continuous approximation, which considers only the stochasticity due to the intermittent gene activity. Second, the mixed approximation, which in addition attributes stochasticity to the mRNA transcription/decay process. Considered approximations yield systems of first order partial differential equations for the underlying distribution function, which can be efficiently solved using developed numerical methods. Single cell simulations and numerical two-dimensional mRNA-protein stationary distribution functions are presented to confirm accuracy of approximating models.

Expression profiling of the mouse early embryo: reflections and perspectives

The laboratory mouse model plays important roles in our understanding of early mammalian development and provides an invaluable model for human early embryos, which are difficult to study for ethical and technical reasons. A comprehensive collection of cDNA clones, their sequences, and complete genome sequence information, which have been accumulated over the past two decades, reveal even further the value of the mouse models. Here, the progress in global gene expression profiling in early mouse embryos and, to some extent, stem cells is reviewed and future directions and challenges are discussed. The discussions include the restatement of global gene expression profiles as a snapshot of cellular status, and subsequent distinction between the differentiation state and physiological state of the cells. The discussions then extend to the biological problems that can be addressed only through global expression profiling, including a bird's-eye view of global gene expression changes, molecular index for developmental potency, cell lineage trajectory, microarray-guided cell manipulation, and the possibility of delineating gene regulatory cascades and networks.

Esg1, expressed exclusively in preimplantation embryos, germline, and embryonic stem cells, is a putative RNA-binding protein with broad RNA targets

In our earlier attempt to identify genes involved in the maintenance of cellular pluripotency, we found that KH-domain protein Embryonal stem cell-specific gene 1 (Esg1) showed similar expression patterns to those of Oct3/4 (Pou5f1), whereas the forced repression of Oct3/4 in mouse embryonic stem cells immediately downregulated the expression of Esg1. Here we further confirm this overlap by in situ hybridization and immunohistochemical analyses. Both Esg1 transcript and protein exist in the egg and preimplantation embryos. At embryonic day 3.5, blastocyst stage, however, ESG1 protein was more abundant in the inner cell mass (ICM) than in trophectoderm (TE), whereas Esg1 transcript was detected in both the ICM and the TE, particularly in the polar trophectoderm. The presence of an RNA-binding KH-domain in ESG1 led us to search for and identify 902 target transcripts by microarray analysis of immunoprecipitated ESG1 complex. Interaction of 20 target mRNA with ESG1, including Cdc25a, Cdc42, Ezh2, Nfyc and Nr5a2, was further validated by reverse transcriptase-polymerase chain reaction of the immunoprecipitation material, supporting the notion that ESG1 is an RNA-binding protein which associates with specific target transcripts.

Expression levels of Mycobacterium tuberculosis antigen-encoding genes versus production levels of antigen-specific T cells during stationary level lung infection in mice

Mycobacterium tuberculosis lung infection in mice was controlled at an approximately stationary level after 20 days of log linear growth. Onset of stationary level infection was associated with the generation by the host of T helper type 1 (Th1) immunity, as evidenced by the accumulation of CD4 Th1 cells specific for the early secretory antigen (ESAT-6) of M. tuberculosis encoded by esat6, and for a mycolyl transferase (Ag85B) encoded by fbpB. CD4 T cells specific for these antigens were maintained at relatively high numbers throughout the course of infection. The number of CD4 T cells generated against ESAT-6 was larger than the number generated against Ag85B, and this was associated with a higher transcription level of esat6. The total number of transcripts of esat6 increased during the first 15 days of infection, after which it decreased and then approximately stabilized at 10(6.5) per lung. The total number of fbpB transcripts increased for 20 days of infection before decreasing and then approximately stabilizing at 10(4.8) per lung. The number of transcripts of esat6 per colony-forming unit of M. tuberculosis fell from 8.6 to 0.8 after day 15, and of fbpB from 0.3 to less than 0.02 after day 10, suggesting that at any given time during stationary level infection the latter gene was expressed by a very small percentage of bacilli. Expressed at an even lower level was an M. tuberculosis replication gene involved in septum formation (ftsZ), indicating that there was no significant turnover of the M. tuberculosis population during stationary level infection.

Gene expression profiling in single cells from the pancreatic islets of Langerhans reveals lognormal distribution of mRNA levels

The transcriptional machinery in individual cells is controlled by a relatively small number of molecules, which may result in stochastic behavior in gene activity. Because of technical limitations in current collection and recording methods, most gene expression measurements are carried out on populations of cells and therefore reflect average mRNA levels. The variability of the transcript levels between different cells remains undefined, although it may have profound effects on cellular activities. Here we have measured gene expression levels of the five genes ActB, Ins1, Ins2, Abcc8, and Kcnj11 in individual cells from mouse pancreatic islets. Whereas Ins1 and Ins2 expression show a strong cell-cell correlation, this is not the case for the other genes. We further found that the transcript levels of the different genes are lognormally distributed. Hence, the geometric mean of expression levels provides a better estimate of gene activity of the typical cell than does the arithmetic mean measured on a cell population.

NF-kappaB oscillations and cell-to-cell variability

Oscillations in the transcriptional activator NF-kappaB localized in the nucleus have been observed when a cell is stimulated by an external agent. A negative feedback based on the protein IkappaB whose expression is controlled by NF-kappaB is known to be responsible for these oscillations. We study NF-kappaB oscillations, which have been observed both for cell populations by Hoffmann et al. [2002. The IkappaB-NF-kappaB signaling module: temporal control and selective gene activation. Science 298, 1241-1245] and for single cells by Nelson et al. [2004. Oscillations in NF-kappaB signaling control the dynamics of gene expression. Science 306, 704-708]. In order to study cell-to-cell variability we use Gillespie's algorithm, applied to a simplified version of the model proposed by Hoffmann et al. (2002). We consider the amounts of cellular NF-kappaB and activated IKK as external parameters. When these are fixed, we show that intrinsic fluctuations are small in a model with strong transcription, as is the case of the Hoffmann et al. (2002) model, whether transcription is quadratic or linear in the number of NF-kappaB molecules. Intrinsic fluctuations can however be large when transcription is weak, as we illustrate in a model variant. The effect of extrinsic fluctuations can be significant: cell-to-cell fluctuations of the initial amount of cellular NF-kappaB affect mainly the amplitude of nuclear NF-kappaB oscillations, at least when transcription is linear in the number of NF-kappaB molecules, while fluctuations in the amount of activated IKK affect both their amplitude and period, whatever the mode of transcription. In this case model results are in qualitative agreement with the considerable cell-to-cell variability of NF-kappaB oscillations observed by Nelson et al. (2004).

Developmental control via GATA factor interplay at chromatin domains

Despite the extraordinary task of packaging mammalian DNA within the constraints of a cell nucleus, individual genes assemble into cell type-specific chromatin structures with high fidelity. This chromatin architecture is a crucial determinant of gene expression signatures that distinguish specific cell types. Whereas extensive progress has been made on defining biochemical and molecular mechanisms of chromatin modification and remodeling, many questions remain unanswered about how cell type-specific chromatin domains assemble and are regulated. This mini-review will discuss emerging studies on how interplay among members of the GATA family of transcription factors establishes and regulates chromatin domains. Dissecting mechanisms underlying the function of hematopoietic GATA factors has revealed fundamental insights into the control of blood cell development from hematopoietic stem cells and the etiology of pathological states in which hematopoiesis is perturbed.

Stochastic cell

Accumulating experimental evidence of stochasticity, self-organization and abrupt non-linear transitions underlying the dynamics of cellular structure and function is increasingly more consistent with the concepts and models of phase transitions, critical phenomena and non-linear thermodynamics rather than with the conventional clockwork description of the cell. The novel emerging image of the stochastic cell suggests that familiar and convenient classico-mechanical interpretations may be limiting our ability to understand the behavior of biological systems and calls for active exploration of alternative interpretational frameworks.

Stochasticity in gene expression: from theories to phenotypes

Genetically identical cells exposed to the same environmental conditions can show significant variation in molecular content and marked differences in phenotypic characteristics. This variability is linked to stochasticity in gene expression, which is generally viewed as having detrimental effects on cellular function with potential implications for disease. However, stochasticity in gene expression can also be advantageous. It can provide the flexibility needed by cells to adapt to fluctuating environments or respond to sudden stresses, and a mechanism by which population heterogeneity can be established during cellular differentiation and development.

A feedforward loop motif in transcriptional regulation: induction and repression

We study the dynamical behavior of a unit of three positive transcriptional regulators which occurs frequently in biological networks of yeast and bacteria as a feedforward loop. We investigate numerically a set of reactions incorporating the basic features of transcription and translation. We determine (i) how the feedforward loop motif functions as a computational element such as an AND gate in the presence of stochastic fluctuations, and (ii) the robustness of the motif when transcription at the primary level is suddenly repressed. We highlight the effective time-scales which underlie both of these aspects of the feedforward loop motif. We show how threshold behavior of the motif output arises as a function of the number of external inducers as well as the time over which the inducer acts. We discuss how individual cell behavior can deviate significantly from average behavior, due to intrinsic fluctuations in the small number of molecules present in a cell.

Modeling of negative autoregulated genetic networks in single cells

We discuss recent developments in the modeling of negative autoregulated genetic networks. In particular, we consider the temporal evolution of the population of mRNA and proteins in simple networks using rate equations. In the limit of low copy numbers, fluctuation effects become significant and more adequate modeling is then achieved using the master equation formalism. The analogy between regulatory gene networks and chemical reaction networks on dust grains in the interstellar medium is discussed. The analysis and simulation of complex reaction networks are also considered.

Stochastic effects of multiple regulators on expression profiles in eukaryotes

The stochastic nature of gene regulation still remains not fully understood. In eukaryotes, the stochastic effects are primarily attributable to the binary nature of genes, which are considered either switched "on" or "off" due to the action of the transcription factors binding to the promoter. In the time period when the gene is activated, bursts of mRNA transcript are produced. In the present paper, we investigate regulation of gene expression at the single cell level. We propose a mechanism of gene regulation, which is able to explain the observed distinct transcription profiles assuming the number of co-regulatory activities, without attempting to identify the specific proteins involved. The model is motivated by our experiments on NF-kappaB-dependent genes in HeLa cells. Our experimental data shows that NF-kappaB-dependent genes can be stratified into three characteristic groups according to their expression profiles: early, intermediate and late having maximum of expression at about 1, 3 and 6 h, respectively, from the beginning of TNF stimulation. We provide a tractable analytical approach, not only in the terms of expected expression profiles and their moments, which corresponds to the measurements on the cell population, but also in the terms of single cell behavior. Comparison between these two modes of description reveals that single cells behave qualitatively different from the cell population. This analysis provides insights useful for understanding of microarray experiments.

Refinement of gene expression patterns in the early Xenopus embryo

During blastula and gastrula stages of Xenopus development, cells become progressively and asynchronously committed to a particular germ layer. We have analysed the expression of genes normally expressed in ectoderm, mesoderm or endoderm in individual cells from early and late gastrula embryos, by both in situ hybridization and single-cell RT-PCR. We show that at early gastrula stages, individual cells in the same region may express markers of two or more germ layers, and 'rogue' cells that express a marker outside its canonical domain are also observed at these stages. However, by the late gastrula stage, individual cells express markers that are more characteristic of their position in the embryo, and 'rogue' cells are seen less frequently. These observations exemplify at the gene expression level the observation that cells of the early gastrula are less committed to one germ layer than are cells of the late gastrula embryo. Ectodermal cells induced to form mesendoderm by the addition of Activin respond by activating expression of different mesodermal and endodermal markers in the same cell, recapitulating the response of marginal zone cells in the embryo.

Fluctuations in transcription factor binding can explain the graded and binary responses observed in inducible gene expression

Inducible genes are expressed in the presence of an external stimulus. Individual cells may exhibit either a binary or graded response to such signals. It has been hypothesized that the chemical kinetics of transcription factor/DNA interactions can account for both these scenarios (EMBO J. 9(9) (1990) 2835; BioEssays 14(5) (1992) 341). To explore this question, we have conducted work based on the experimental results of Fiering et al. (Genes Dev. 4 (10) (1990) 1823). In these experiments, three upstream NF-AT binding sites control transcription of the lacZ gene, which codes for the enzyme beta-Galactosidase. The experimental data show a binary response for this system. We consider the effects of fluctuations in NF-AT binding on the response of the system. Our modeling results are in good qualitative agreement with the experimental data, and illustrate how the binary and graded responses can stem from the same underlying mechanism.

Islet cell hyperplasia in transgenic mice overexpressing EAT/mcl-1, a bcl-2 related gene

EAT/mcl-1 (EAT), a bcl-2 related anti-apoptotic gene, is up-regulated at the early stage of differentiation of human embryonal carcinoma cells; cells which serve as a model for early embryogenesis. We generated transgenic mice for the human EAT gene driven by the EF1 alpha promoter in order to elucidate its functional role in vivo. Histologically, these mice exhibited hyperplasia of Langerhans islet cells; pancreatic cell regions composed of both insulin- and glucagon-producing cells. Furthermore, Bax and Bag-1 -- possible heterodimeric partners for EAT in the anti-apoptotic process -- were up-regulated in islets isolated from the EAT transgenic mice. The insulin tolerance test exhibited no significant difference between the EAT transgenic mice and non-transgenic mice, indicating that islet cell hyperplasia was not due to insulin resistance. In conclusion, EAT transgenic mice exhibit hyperplasia of pancreatic beta cells. EAT may inhibit apoptosis of beta cells, allowing these cells to circumvent the process of apoptosis until the adult stage.

Selective instability: maternal effort and the evolution of gene activation and deactivation rates

We previously used simulations of gene expression to demonstrate that rapid activation and deactivation rates stabilized outcomes in stochastic systems. We hypothesized that transient single allele inactivation of an autosomal gene during gametogenesis or very early embryogenesis could have a selective advantage if it permits the functional sampling of each allele and precludes committing maternal effort to an embryo with a deleterious mutation. To test this hypothesis, we simulated the evolution of gene expression activation and deactivation rates and imposed two different selective pressures on the populations: (a). late selection against individuals that cannot maintain a threshold level of gene product that occurs after the investment of maternal effort (i.e., after birth); or (b). early selection: in addition to late selection, maintenance of the gene product above a threshold level was necessary for early development prior to commitment of maternal effort. We found that the opportunity to save reproductive effort from early selection caused the evolution of higher deactivation rates and lower activation rates than in the late selection condition. Thus, we predict that in the special case where early selection can save maternal investment in non-viable offspring, gene expression activation rates and deactivation rates might be selected to permit sampling of the product from each allele.

Near-critical phenomena in intracellular metabolite pools

The supply and consumption of metabolites in living cells are catalyzed by enzymes. Here we consider two of the simplest schemes where one substrate is eliminated through Michaelis-Menten kinetics, and where two types of substrates are joined together by an enzyme. It is demonstrated how steady-state substrate concentrations can change ultrasensitively in response to changes in their supply rates and how this is coupled to slow relaxation back to steady state after a perturbation. In the one-substrate system, such near-critical behavior occurs when the supply rate approaches the maximal elimination rate, and in the two-substrate system it occurs when the rates of substrate supply are almost balanced. As systems that operate near criticality tend to display large random fluctuations, we also carried out a stochastic analysis using analytical approximations of master equations and compared the results with molecular-level Monte Carlo simulations. It was found that the significance of random fluctuations was directly coupled to the steady-state sensitivity and that the two substrates can fluctuate greatly because they are anticorrelated in such a way that the product formation rate displays only small variation. Basic relations are highlighted and biological implications are discussed.

Increased noise as an effect of haploinsufficiency of the tumor-suppressor gene neurofibromatosis type 1 in vitro

In human diseases related to tumor-suppressor genes, it is suggested that only the complete loss of the protein results in specific symptoms such as tumor formation, whereas simple reduction of protein quantity to 50%, called haploinsufficiency, essentially does not affect cellular behavior. Using a model of gene expression, it was presumed that haploinsufficiency is related to an increased noise in gene expression also in vivo [Cook, D. L., Gerber, A. N. & Tapscott, S. J. (1998) Proc. Natl. Acad. Sci. USA 95, 15641-15646]. Here, we demonstrate that haploinsufficiency of the tumor-suppressor gene neurofibromatosis type 1 (NF1) results in an increased variation of dendrite formation in cultured NF1 melanocytes. These morphological differences between NF1 and control melanocytes can be described by a mathematical model in which the cell is considered to be a self-organized automaton. The model describes the adjustment of the cells to a set point and includes a noise term that allows for stochastic processes. It describes the experimental data of control and NF1 melanocytes. In the cells haploinsufficient for NF1 we found an altered signal-to-noise ratio detectable as increased variation in dendrite formation in two of three investigated morphological parameters. We also suggest that in vivo NF1 haploinsufficiency results in an increased noise in cellular regulation and that this effect of haploinsufficiency may be found also in other tumor suppressors.

Stochastic gene expression in a single cell

Clonal populations of cells exhibit substantial phenotypic variation. Such heterogeneity can be essential for many biological processes and is conjectured to arise from stochasticity, or noise, in gene expression. We constructed strains of Escherichia coli that enable detection of noise and discrimination between the two mechanisms by which it is generated. Both stochasticity inherent in the biochemical process of gene expression (intrinsic noise) and fluctuations in other cellular components (extrinsic noise) contribute substantially to overall variation. Transcription rate, regulatory dynamics, and genetic factors control the amplitude of noise. These results establish a quantitative foundation for modeling noise in genetic networks and reveal how low intracellular copy numbers of molecules can fundamentally limit the precision of gene regulation.

General statistics of stochastic process of gene expression in eukaryotic cells

Thousands of genes are expressed at such very low levels (< or =1 copy per cell) that global gene expression analysis of rarer transcripts remains problematic. Ambiguity in identification of rarer transcripts creates considerable uncertainty in fundamental questions such as the total number of genes expressed in an organism and the biological significance of rarer transcripts. Knowing the distribution of the true number of genes expressed at each level and the corresponding gene expression level probability function (GELPF) could help resolve these uncertainties. We found that all observed large-scale gene expression data sets in yeast, mouse, and human cells follow a Pareto-like distribution model skewed by many low-abundance transcripts. A novel stochastic model of the gene expression process predicts the universality of the GELPF both across different cell types within a multicellular organism and across different organisms. This model allows us to predict the frequency distribution of all gene expression levels within a single cell and to estimate the number of expressed genes in a single cell and in a population of cells. A random "basal" transcription mechanism for protein-coding genes in all or almost all eukaryotic cell types is predicted. This fundamental mechanism might enhance the expression of rarely expressed genes and, thus, provide a basic level of phenotypic diversity, adaptability, and random monoallelic expression in cell populations.

Modeling and simulation of genetic regulatory systems: a literature review

In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.

Modeling a hox gene network in silico using a stochastic simulation algorithm

The amount of molecular information that has been gathered about Hox cis-regulatory mechanisms allows us to take the next important step: integrating the results and constructing a higher-level model for the interaction and regulation of the Hox genes. Here, we present the results of our investigation into a cis-regulatory network for the early Hox genes. Instead of using conventional differential equation approaches for analyzing the system, we have adopted the use of a stochastic simulation algorithm (SSA) to model the network. The model allows us to track in detail the behavior of each component of a biochemical pathway and to produce computerized movies of the time evolution of the system that is a result of the dynamic interplay of these various components. The simulation is able to reproduce key features of the wild-type pattern of gene expression, and in silico experiments yield results similar to their corresponding in vivo experiments. This analysis shows the utility of using stochastic methods to model biochemical networks. In addition, the model has suggested several intriguing new results that are currently being investigated in vivo.

Control motifs for intracellular regulatory networks

A number of technological innovations are yielding unprecedented data on the networks of biochemical, genetic, and biophysical reactions that underlie cellular behavior and failure. These networks are composed of hundreds to thousands of chemical species and structures, interacting via nonlinear and possibly stochastic physical processes. A central goal of modern biology is to optimally use the data on these networks to understand how their design leads to the observed cellular behaviors and failures. Ultimately, this knowledge should enable cellular engineers to redesign cellular processes to meet industrial needs (such as optimal natural product synthesis), aid in choosing the most effective targets for pharmaceuticals, and tailor treatment for individual genotypes. The size and complexity of these networks and the inevitable lack of complete data, however, makes reaching these goals extremely difficult. If it proves possible to modularize these networks into functional subnetworks, then these smaller networks may be amenable to direct analysis and might serve as regulatory motifs. These motifs, recurring elements of control, may help to deduce the structure and function of partially known networks and form the basis for fulfilling the goals described above. A number of approaches to identifying and analyzing control motifs in intracellular networks are reviewed.

Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations

Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for the synthesis and degradation of transcripts. We develop stochastic models to which these random reactions are intrinsic and a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have both a quantitative and qualitative impact on the behavior of gene-regulatory networks. We introduce a natural generalization of deterministic bifurcations for classification of stochastic systems and show that simple noisy genetic switches have rich bifurcation structures; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the underlying deterministic system remains unchanged. We find stochastic bistability where the deterministic equations predict monostability and vice-versa. We derive and solve equations for the mean waiting times for spontaneous transitions between quasistable states in these switches.

Random monoallelic expression of three genes clustered within 60 kb of mouse t complex genomic DNA

Mammals achieve gene dosage control by (1) random X-chromosome inactivation in females, (2) parental origin-specific imprinting of selected autosomal genes, and (3) random autosomal inactivation. Genes belonging to the third category of epigenetic phenomenon are just now emerging, with only six identified so far. Here we report three additional genes, Nubp2, Igfals, and Jsap1, that show 50%-methylated CpG sites by Southern blot analyses and primarily monoallelic expression in single-cell allele-specific RT-PCR analysis of bone marrow stromal cells and hepatocytes. Furthermore, we show that, in contrast to X inactivation, alleles can switch between active and inactive states during the formation of daughter cells. These three genes are the first in their category to exist as a tight cluster, in the proximal region of mouse chromosome 17, providing a thus far unique example of a region of autosomal random monoallelic expression.