Stochastic models of transcription: from single molecules to single cells

Unified bursting strategies in ectopic and endogenous even-skipped expression patterns

Transcription often occurs in bursts as gene promoters switch stochastically between active and inactive states. Enhancers can dictate transcriptional activity in animal development through the modulation of burst frequency, duration, or amplitude. Previous studies observed that different enhancers can achieve a wide range of transcriptional outputs through the same strategies of bursting control. For example, in Berrocal et al., 2020, we showed that despite responding to different transcription factors, all even-skipped enhancers increase transcription by upregulating burst frequency and amplitude while burst duration remains largely constant. These shared bursting strategies suggest that a unified molecular mechanism constraints how enhancers modulate transcriptional output. Alternatively, different enhancers could have converged on the same bursting control strategy because of natural selection favoring one of these particular strategies. To distinguish between these two scenarios, we compared transcriptional bursting between endogenous and ectopic gene expression patterns. Because enhancers act under different regulatory inputs in ectopic patterns, dissimilar bursting control strategies between endogenous and ectopic patterns would suggest that enhancers adapted their bursting strategies to their trans-regulatory environment. Here, we generated ectopic even-skipped transcription patterns in fruit fly embryos and discovered that bursting strategies remain consistent in endogenous and ectopic even-skipped expression. These results provide evidence for a unified molecular mechanism shaping even-skipped bursting strategies and serve as a starting point to uncover the realm of strategies employed by other enhancers.

Unified bursting strategies in ectopic and endogenous even-skipped expression patterns

Transcription often occurs in bursts as gene promoters switch stochastically between active and inactive states. Enhancers can dictate transcriptional activity in animal development through the modulation of burst frequency, duration, or amplitude. Previous studies observed that different enhancers can achieve a wide range of transcriptional outputs through the same strategies of bursting control. For example, despite responding to different transcription factors, all even-skipped enhancers increase transcription by upregulating burst frequency and amplitude while burst duration remains largely constant. These shared bursting strategies suggest that a unified molecular mechanism constraints how enhancers modulate transcriptional output. Alternatively, different enhancers could have converged on the same bursting control strategy because of natural selection favoring one of these particular strategies. To distinguish between these two scenarios, we compared transcriptional bursting between endogenous and ectopic gene expression patterns. Because enhancers act under different regulatory inputs in ectopic patterns, dissimilar bursting control strategies between endogenous and ectopic patterns would suggest that enhancers adapted their bursting strategies to their trans-regulatory environment. Here, we generated ectopic even-skipped transcription patterns in fruit fly embryos and discovered that bursting strategies remain consistent in endogenous and ectopic even-skipped expression. These results provide evidence for a unified molecular mechanism shaping even-skipped bursting strategies and serve as a starting point to uncover the realm of strategies employed by other enhancers.

Governing principles of transcriptional logic out of equilibrium

To survive, adapt, and develop, cells respond to external and internal stimuli by tightly regulating transcription. Transcriptional regulation involves the combinatorial binding of a repertoire of transcription factors to DNA, which often results in switch-like binary outputs akin to Boolean logic gates. Recent experimental studies have demonstrated that in eukaryotes, transcription factor binding to DNA often involves energy expenditure, thereby driving the system out of equilibrium. The governing principles of transcriptional logic operations out of equilibrium remain unexplored. Here, we employ a simple two-input, single-locus model of transcription that can accommodate both equilibrium and nonequilibrium mechanisms. Using this model, we find that nonequilibrium regimes can give rise to all the logic operations accessible in equilibrium. Strikingly, energy expenditure alters the regulatory function of the two transcription factors in a mutually exclusive manner. This allows for the emergence of new logic operations that are inaccessible in equilibrium. Overall, our results show that energy expenditure can expand the range of cellular decision-making without the need for more complex promoter architectures.

Effects of microRNA-mediated negative feedback on gene expression noise

MicroRNAs (miRNAs) are small noncoding RNAs that regulate gene expression post-transcriptionally in eukaryotes by binding with target mRNAs and preventing translation. miRNA-mediated feedback motifs are ubiquitous in various genetic networks that control cellular decision making. A key question is how such a feedback mechanism may affect gene expression noise. To answer this, we have developed a mathematical model to study the effects of a miRNA-dependent negative-feedback loop on mean expression and noise in target mRNAs. Combining analytics and simulations, we show the existence of an expression threshold demarcating repressed and expressed regimes in agreement with earlier studies. The steady-state mRNA distributions are bimodal near the threshold, where copy numbers of mRNAs and miRNAs exhibit enhanced anticorrelated fluctuations. Moreover, variation of negative-feedback strength shifts the threshold locations and modulates the noise profiles. Notably, the miRNA-mRNA binding affinity and feedback strength collectively shape the bimodality. We also compare our model with a direct auto-repression motif, where a gene produces its own repressor. Auto-repression fails to produce bimodal mRNA distributions as found in miRNA-based indirect repression, suggesting the crucial role of miRNAs in creating phenotypic diversity. Together, we demonstrate how miRNA-dependent negative feedback modifies the expression threshold and leads to a broader parameter regime of bimodality compared to the no-feedback case.

Inferring gene regulation from stochastic transcriptional variation across single cells at steady state

Regulatory relationships between transcription factors (TFs) and their target genes lie at the heart of cellular identity and function; however, uncovering these relationships is often labor-intensive and requires perturbations. Here, we propose a principled framework to systematically infer gene regulation for all TFs simultaneously in cells at steady state by leveraging the intrinsic variation in the transcriptional abundance across single cells. Through modeling and simulations, we characterize how transcriptional bursts of a TF gene are propagated to its target genes, including the expected ranges of time delay and magnitude of maximum covariation. We distinguish these temporal trends from the time-invariant covariation arising from cell states, and we delineate the experimental and technical requirements for leveraging these small but meaningful cofluctuations in the presence of measurement noise. While current technology does not yet allow adequate power for definitively detecting regulatory relationships for all TFs simultaneously in cells at steady state, we investigate a small-scale dataset to inform future experimental design. This study supports the potential value of mapping regulatory connections through stochastic variation, and it motivates further technological development to achieve its full potential.

Mechanisms of cellular mRNA transcript homeostasis

For most genes, mRNA transcript abundance scales with cell size to ensure a constant concentration. Scaling of mRNA synthesis rates with cell size plays an important role, with regulation of the activity and abundance of RNA polymerase II (Pol II) now emerging as a key point of control. However, there is also considerable evidence for feedback mechanisms that kinetically couple the rates of mRNA synthesis, nuclear export, and degradation to allow cells to compensate for changes in one by adjusting the others. Researchers are beginning to integrate results from these different fields to reveal the mechanisms underlying transcript homeostasis. This will be crucial for moving beyond our current understanding of relative gene expression towards an appreciation of how absolute transcript levels are linked to other aspects of the cellular phenotype.

Stochastic Hazard Analysis of Genetic Circuits in iBioSim and STAMINA

In synthetic biology, combinational circuits are used to program cells for various new applications like biosensors, drug delivery systems, and biofuels. Similar to asynchronous electronic circuits, some combinational genetic circuits may show unwanted switching variations (glitches) caused by multiple input changes. Depending on the biological circuit, glitches can cause irreversible effects and jeopardize the circuit's functionality. This paper presents a stochastic analysis to predict glitch propensities for three implementations of a genetic circuit with known glitching behavior. The analysis uses STochastic Approximate Model-checker for INfinite-state Analysis (STAMINA), a tool for stochastic verification. The STAMINA results were validated by comparison to stochastic simulation in iBioSim resulting in further improvements of STAMINA. This paper demonstrates that stochastic verification can be utilized by genetic designers to evaluate design choices and input restrictions to achieve a desired reliability of operation.

Exact results for queuing models of stochastic transcription with memory and crosstalk

Gene transcription is a complex multistep biochemical process, which can create memory between individual reaction events. On the other hand, many inducible genes, when activated by external cues, are often coregulated by several competitive pathways with crosstalk. This raises an unexplored question: how do molecular memory and crosstalk together affect gene expressions? To address this question, we introduce a queuing model of stochastic transcription, where two crossing signaling pathways are used to direct gene activation in response to external signals and memory functions to model multistep reaction processes involved in transcription. We first establish, based on the total probability principle, the chemical master equation for this queuing model, and then we derive, based on the binomial moment approach, exact expressions for statistical quantities (including distributions) of mRNA, which provide insights into the roles of crosstalk and memory in controlling the mRNA level and noise. We find that molecular memory of gene activation decreases the mRNA level but increases the mRNA noise, and double activation pathways always reduce the mRNA noise in contrast to a single pathway. In addition, we find that molecular memory can make the mRNA bimodality disappear.

First-principles prediction of the information processing capacity of a simple genetic circuit

Given the stochastic nature of gene expression, genetically identical cells exposed to the same environmental inputs will produce different outputs. This heterogeneity has been hypothesized to have consequences for how cells are able to survive in changing environments. Recent work has explored the use of information theory as a framework to understand the accuracy with which cells can ascertain the state of their surroundings. Yet the predictive power of these approaches is limited and has not been rigorously tested using precision measurements. To that end, we generate a minimal model for a simple genetic circuit in which all parameter values for the model come from independently published data sets. We then predict the information processing capacity of the genetic circuit for a suite of biophysical parameters such as protein copy number and protein-DNA affinity. We compare these parameter-free predictions with an experimental determination of protein expression distributions and the resulting information processing capacity of E. coli cells. We find that our minimal model captures the scaling of the cell-to-cell variability in the data and the inferred information processing capacity of our simple genetic circuit up to a systematic deviation.

Reconciling kinetic and thermodynamic models of bacterial transcription

The study of transcription remains one of the centerpieces of modern biology with implications in settings from development to metabolism to evolution to disease. Precision measurements using a host of different techniques including fluorescence and sequencing readouts have raised the bar for what it means to quantitatively understand transcriptional regulation. In particular our understanding of the simplest genetic circuit is sufficiently refined both experimentally and theoretically that it has become possible to carefully discriminate between different conceptual pictures of how this regulatory system works. This regulatory motif, originally posited by Jacob and Monod in the 1960s, consists of a single transcriptional repressor binding to a promoter site and inhibiting transcription. In this paper, we show how seven distinct models of this so-called simple-repression motif, based both on thermodynamic and kinetic thinking, can be used to derive the predicted levels of gene expression and shed light on the often surprising past success of the thermodynamic models. These different models are then invoked to confront a variety of different data on mean, variance and full gene expression distributions, illustrating the extent to which such models can and cannot be distinguished, and suggesting a two-state model with a distribution of burst sizes as the most potent of the seven for describing the simple-repression motif.

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.

Cell-to-cell variability in organelle abundance reveals mechanisms of organelle biogenesis

How cells regulate the number of organelles is a fundamental question in cell biology. While decades of experimental work have uncovered four fundamental processes that regulate organelle biogenesis, namely, de novo synthesis, fission, fusion, and decay, a comprehensive understanding of how these processes together control organelle abundance remains elusive. Recent fluorescence microscopy experiments allow for the counting of organelles at the single-cell level. These measurements provide information about the cell-to-cell variability in organelle abundance in addition to the mean level. Motivated by such measurements, we build upon a recent study and analyze a general stochastic model of organelle biogenesis. We compute the exact analytical expressions for the probability distribution of organelle numbers, their mean, and variance across a population of single cells. It is shown that different mechanisms of organelle biogenesis lead to distinct signatures in the distribution of organelle numbers which allow us to discriminate between these various mechanisms. By comparing our theory against published data for peroxisome abundance measurements in yeast, we show that a widely believed model of peroxisome biogenesis that involves de novo synthesis, fission, and decay is inadequate in explaining the data. Also, our theory predicts bimodality in certain limits of the model. Overall, the framework developed here can be harnessed to gain mechanistic insights into the process of organelle biogenesis.

Decoding the grammar of transcriptional regulation from RNA polymerase measurements: models and their applications

The genomic revolution has indubitably brought about a paradigm shift in the field of molecular biology, wherein we can sequence, write and re-write genomes. In spite of achieving such feats, we still lack a quantitative understanding of how cells integrate environmental and intra-cellular signals at the promoter and accordingly regulate the production of messenger RNAs. This current state of affairs is being redressed by recent experimental breakthroughs which enable the counting of RNA polymerase molecules (or the corresponding nascent RNAs) engaged in the process of transcribing a gene at the single-cell level. Theorists, in conjunction, have sought to unravel the grammar of transcriptional regulation by harnessing the various statistical properties of these measurements. In this review, we focus on the recent progress in developing falsifiable models of transcription that aim to connect the molecular mechanisms of transcription to single-cell polymerase measurements. We discuss studies where the application of such models to the experimental data have led to novel mechanistic insights into the process of transcriptional regulation. Such interplay between theory and experiments will likely contribute towards the exciting journey of unfurling the governing principles of transcriptional regulation ranging from bacteria to higher organisms.

Transcriptional processes: Models and inference

Many biochemical events involve multistep reactions. One of the most important biological processes that involve multistep reaction is the transcriptional process. Models for multistep reaction necessarily need multiple states and it is a challenge to compute model parameters that best agree with experimental data. Therefore, the aim of this work is to design a multistep promoter model which accurately characterizes transcriptional bursting and is consistent with observed data. To address this issue, we develop a model for promoters with several OFF states and a single ON state using Erlang distribution. To explore the combined effects of model and data, we combine Monte Carlo extension of Expectation Maximization (MCEM) and delay Stochastic Simulation Algorithm (DSSA) and call the resultant algorithm as delay Bursty MCEM. We apply this algorithm to time-series data of endogenous mouse glutaminase promoter to validate the model assumptions and infer the kinetic parameters. Our results show that with multiple OFF states, we are able to infer and produce a model which is more consistent with experimental data. Our results also show that delay Bursty MCEM inference is more efficient.

Distribution of Initiation Times Reveals Mechanisms of Transcriptional Regulation in Single Cells

Transcription is the dominant point of control of gene expression. Biochemical studies have revealed key molecular components of transcription and their interactions, but the dynamics of transcription initiation in cells is still poorly understood. This state of affairs is being remedied with experiments that observe transcriptional dynamics in single cells using fluorescent reporters. Quantitative information about transcription initiation dynamics can also be extracted from experiments that use electron micrographs of RNA polymerases caught in the act of transcribing a gene (Miller spreads). Inspired by these data, we analyze a general stochastic model of transcription initiation and elongation and compute the distribution of transcription initiation times. We show that different mechanisms of initiation leave distinct signatures in the distribution of initiation times that can be compared to experiments. We analyze published data from micrographs of RNA polymerases transcribing ribosomal RNA genes in Escherichia coli and compare the observed distributions of interpolymerase distances with the predictions from previously hypothesized mechanisms for the regulation of these genes. Our analysis demonstrates the potential of measuring the distribution of time intervals between initiation events as a probe for dissecting mechanisms of transcription initiation in live cells.

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.

Nascent RNA kinetics: Transient and steady state behavior of models of transcription

Regulation of transcription is a vital process in cells, but mechanistic details of this regulation still remain elusive. The dominant approach to unravel the dynamics of transcriptional regulation is to first develop mathematical models of transcription and then experimentally test the predictions these models make for the distribution of mRNA and protein molecules at the individual cell level. However, these measurements are affected by a multitude of downstream processes which make it difficult to interpret the measurements. Recent experimental advancements allow for counting the nascent mRNA number of a gene as a function of time at the single-cell level. These measurements closely reflect the dynamics of transcription. In this paper, we consider a general mechanism of transcription with stochastic initiation and deterministic elongation and probe its impact on the temporal behavior of nascent RNA levels. Using techniques from queueing theory, we derive exact analytical expressions for the mean and variance of the nascent RNA distribution as functions of time. We apply these analytical results to obtain the mean and variance of nascent RNA distribution for specific models of transcription. These models of initiation exhibit qualitatively distinct transient behaviors for both the mean and variance which further allows us to discriminate between them. Stochastic simulations confirm these results. Overall the analytical results presented here provide the necessary tools to connect mechanisms of transcription initiation to single-cell measurements of nascent RNA.

Single-cell systems biology: probing the basic unit of information flow

Gene expression varies across cells in a population or a tissue. This heterogeneity has come into sharp focus in recent years through developments in new imaging and sequencing technologies. However, our ability to measure variation has outpaced our ability to interpret it. Much of the variability may arise from random effects occurring in the processes of gene expression (transcription, RNA processing and decay, translation). The molecular basis of these effects is largely unknown. Likewise, a functional role of this variability in growth, differentiation and disease has only been elucidated in a few cases. In this review, we highlight recent experimental and theoretical advances for measuring and analyzing stochastic variation.

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.

Effect of transcription factor resource sharing on gene expression noise

Gene expression is intrinsically a stochastic (noisy) process with important implications for cellular functions. Deciphering the underlying mechanisms of gene expression noise remains one of the key challenges of regulatory biology. Theoretical models of transcription often incorporate the kinetics of how transcription factors (TFs) interact with a single promoter to impact gene expression noise. However, inside single cells multiple identical gene copies as well as additional binding sites can compete for a limiting pool of TFs. Here we develop a simple kinetic model of transcription, which explicitly incorporates this interplay between TF copy number and its binding sites. We show that TF sharing enhances noise in mRNA distribution across an isogenic population of cells. Moreover, when a single gene copy shares it’s TFs with multiple competitor sites, the mRNA variance as a function of the mean remains unaltered by their presence. Hence, all the data for variance as a function of mean expression collapse onto a single master curve independent of the strength and number of competitor sites. However, this result does not hold true when the competition stems from multiple copies of the same gene. Therefore, although previous studies showed that the mean expression follows a universal master curve, our findings suggest that different scenarios of competition bear distinct signatures at the level of variance. Intriguingly, the introduction of competitor sites can transform a unimodal mRNA distribution into a multimodal distribution. These results demonstrate the impact of limited availability of TF resource on the regulation of noise in gene expression.

Genetically identical cells, even when they are exposed to the same environmental conditions, display incredible diversity. Gene expression noise is attributed to be a key source of this phenotypic diversity. Transcriptional dynamics is a dominant source of expression noise. Although scores of theoretical and experimental studies have explored how noise is regulated at the level of transcription, most of them focus on the gene specific, cis regulatory elements, such as the number of transcription factor (TF) binding sites, their binding strength, etc. However, how the global properties of transcription, such as the limited availability of TFs impact noise in gene expression remains rather elusive. Here we build a theoretical model that incorporates the effect of limiting TF pool on gene expression noise. We find that competition between genes for TFs leads to enhanced variability in mRNA copy number across an isogenic population. Moreover, for gene copies sharing TFs with other competitor sites, mRNA variance as a function of the mean shows distinct imprints for one gene copy and multiple gene copies respectively. This stands in sharp contrast to the universal behavior found in mean expression irrespective of the different scenarios of competition. An interesting feature of competition is that introduction of competitor sites can transform a unimodal mRNA distribution into a multimodal distribution, which could lead to phenotypic variability.

A moment-convergence method for stochastic analysis of biochemical reaction networks

Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in terms of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.

Mechanical bounds to transcriptional noise

Over the past several decades it has been increasingly recognized that stochastic processes play a central role in transcription. Although many stochastic effects have been explained, the source of transcriptional bursting (one of the most well-known sources of stochasticity) has continued to evade understanding. Recent results have pointed to mechanical feedback as the source of transcriptional bursting, but a reconciliation of this perspective with preexisting views of transcriptional regulation is lacking. In this article, we present a simple phenomenological model that is able to incorporate the traditional view of gene expression within a framework with mechanical limits to transcription. By introducing a simple competition between mechanical arrest and relaxation copy number probability distributions collapse onto a shared universal curve under shifting and rescaling and a lower limit of intrinsic noise for any mean expression level is found.

Dissecting the stochastic transcription initiation process in live Escherichia coli

We investigate the hypothesis that, in Escherichia coli, while the concentration of RNA polymerases differs in different growth conditions, the fraction of RNA polymerases free for transcription remains approximately constant within a certain range of these conditions. After establishing this, we apply a standard model-fitting procedure to fully characterize the in vivo kinetics of the rate-limiting steps in transcription initiation of the Plac/ara-1 promoter from distributions of intervals between transcription events in cells with different RNA polymerase concentrations. We find that, under full induction, the closed complex lasts ∼788 s while subsequent steps last ∼193 s, on average. We then establish that the closed complex formation usually occurs multiple times prior to each successful initiation event. Furthermore, the promoter intermittently switches to an inactive state that, on average, lasts ∼87 s. This is shown to arise from the intermittent repression of the promoter by LacI. The methods employed here should be of use to resolve the rate-limiting steps governing the in vivo dynamics of initiation of prokaryotic promoters, similar to established steady-state assays to resolve the in vitro dynamics.

Spatially coordinated dynamic gene transcription in living pituitary tissue

Transcription at individual genes in single cells is often pulsatile and stochastic. A key question emerges regarding how this behaviour contributes to tissue phenotype, but it has been a challenge to quantitatively analyse this in living cells over time, as opposed to studying snap-shots of gene expression state. We have used imaging of reporter gene expression to track transcription in living pituitary tissue. We integrated live-cell imaging data with statistical modelling for quantitative real-time estimation of the timing of switching between transcriptional states across a whole tissue. Multiple levels of transcription rate were identified, indicating that gene expression is not a simple binary 'on-off' process. Immature tissue displayed shorter durations of high-expressing states than the adult. In adult pituitary tissue, direct cell contacts involving gap junctions allowed local spatial coordination of prolactin gene expression. Our findings identify how heterogeneous transcriptional dynamics of single cells may contribute to overall tissue behaviour.

A cell size- and cell cycle-aware stochastic model for predicting time-dynamic gene network activity in individual cells

Background

Despite the development of various modeling approaches to predict gene network activity, a time dynamic stochastic model taking into account real-time changes in cell volume and cell cycle stages is still missing.

Results

Here we present a stochastic single-cell model that can be applied to any eukaryotic gene network with any number of components. The model tracks changes in cell volume, DNA replication, and cell division, and dynamically adjusts rates of stochastic reactions based on this information. By tracking cell division, the model can maintain cell lineage information, allowing the researcher to trace the descendants of any single cell and therefore study cell lineage effects. To test the predictive power of our model, we applied it to the canonical galactose network of the yeast Saccharomyces cerevisiae. Using a minimal set of free parameters and across several galactose induction conditions, the model effectively captured several details of the experimentally-obtained single-cell network activity levels as well as phenotypic switching rates.

Conclusion

Our model can readily be customized to model any gene network in any of the commonly used cells types, offering a novel and user-friendly stochastic modeling capability to the systems biology field.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0240-5) contains supplementary material, which is available to authorized users.

Deciphering Transcriptional Dynamics In Vivo by Counting Nascent RNA Molecules

Deciphering how the regulatory DNA sequence of a gene dictates its expression in response to intra and extracellular cues is one of the leading challenges in modern genomics. The development of novel single-cell sequencing and imaging techniques, as well as a better exploitation of currently available single-molecule imaging techniques, provides an avenue to interrogate the process of transcription and its dynamics in cells by quantifying the number of RNA polymerases engaged in the transcription of a gene (or equivalently the number of nascent RNAs) at a given moment in time. In this paper, we propose that measurements of the cell-to-cell variability in the number of nascent RNAs provide a mostly unexplored method for deciphering mechanisms of transcription initiation in cells. We propose a simple kinetic model of transcription initiation and elongation from which we calculate nascent RNA copy-number fluctuations. To demonstrate the usefulness of this approach, we test our theory against published nascent RNA data for twelve constitutively expressed yeast genes. Rather than transcription being initiated through a single rate limiting step, as it had been previously proposed, our single-cell analysis reveals the presence of at least two rate limiting steps. Surprisingly, half of the genes analyzed have nearly identical rates of transcription initiation, suggesting a common mechanism. Our analytical framework can be used to extract quantitative information about dynamics of transcription from single-cell sequencing data, as well as from single-molecule imaging and electron micrographs of fixed cells, and provides the mathematical means to exploit the quantitative power of these technologies.

A model for aryl hydrocarbon receptor-activated gene expression shows potency and efficacy changes and predicts squelching due to competition for transcription co-activators

A stochastic model of nuclear receptor-mediated transcription was developed based on activation of the aryl hydrocarbon receptor (AHR) by 2,3,7,8-tetrachlorodibenzodioxin (TCDD) and subsequent binding the activated AHR to xenobiotic response elements (XREs) on DNA. The model was based on effects observed in cells lines commonly used as in vitro experimental systems. Following ligand binding, the AHR moves into the cell nucleus and forms a heterodimer with the aryl hydrocarbon nuclear translocator (ARNT). In the model, a requirement for binding to DNA is that a generic coregulatory protein is subsequently bound to the AHR-ARNT dimer. Varying the amount of coregulator available within the nucleus altered both the potency and efficacy of TCDD for inducing for transcription of CYP1A1 mRNA, a commonly used marker for activation of the AHR. Lowering the amount of available cofactor slightly increased the EC50 for the transcriptional response without changing the efficacy or maximal response. Further reduction in the amount of cofactor reduced the efficacy and produced non-monotonic dose-response curves (NMDRCs) at higher ligand concentrations. The shapes of these NMDRCs were reminiscent of the phenomenon of squelching. Resource limitations for transcriptional machinery are becoming apparent in eukaryotic cells. Within single cells, nuclear receptor-mediated gene expression appears to be a stochastic process; however, intercellular communication and other aspects of tissue coordination may represent a compensatory process to maintain an organism’s ability to respond on a phenotypic level to various stimuli within an inconstant environment.

A stochastic transcriptional switch model for single cell imaging data

Gene expression is made up of inherently stochastic processes within single cells and can be modeled through stochastic reaction networks (SRNs). In particular, SRNs capture the features of intrinsic variability arising from intracellular biochemical processes. We extend current models for gene expression to allow the transcriptional process within an SRN to follow a random step or switch function which may be estimated using reversible jump Markov chain Monte Carlo (MCMC). This stochastic switch model provides a generic framework to capture many different dynamic features observed in single cell gene expression. Inference for such SRNs is challenging due to the intractability of the transition densities. We derive a model-specific birth–death approximation and study its use for inference in comparison with the linear noise approximation where both approximations are considered within the unifying framework of state-space models. The methodology is applied to synthetic as well as experimental single cell imaging data measuring expression of the human prolactin gene in pituitary cells.

Effects of promoter leakage on dynamics of gene expression

Background

Quantitative analysis of simple molecular networks is an important step forward understanding fundamental intracellular processes. As network motifs occurring recurrently in complex biological networks, gene auto-regulatory circuits have been extensively studied but gene expression dynamics remain to be fully understood, e.g., how promoter leakage affects expression noise is unclear.

Results

In this work, we analyze a gene model with auto regulation, where the promoter is assumed to have one active state with highly efficient transcription and one inactive state with very lowly efficient transcription (termed as promoter leakage). We first derive the analytical distribution of gene product, and then analyze effects of promoter leakage on expression dynamics including bursting kinetics. Interestingly, we find that promoter leakage always reduces expression noise and that increasing the leakage rate tends to simplify phenotypes. In addition, higher leakage results in fewer bursts.

Conclusions

Our results reveal the essential role of promoter leakage in controlling expression dynamics and further phenotype. Specifically, promoter leakage is a universal mechanism of reducing expression noise, controlling phenotypes in different environments and making the gene produce generate fewer bursts.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0157-z) contains supplementary material, which is available to authorized users.

Inferring single-cell gene expression mechanisms using stochastic simulation

MOTIVATION

Stochastic promoter switching between transcriptionally active (ON) and inactive (OFF) states is a major source of noise in gene expression. It is often implicitly assumed that transitions between promoter states are memoryless, i.e. promoters spend an exponentially distributed time interval in each of the two states. However, increasing evidence suggests that promoter ON/OFF times can be non-exponential, hinting at more complex transcriptional regulatory architectures. Given the essential role of gene expression in all cellular functions, efficient computational techniques for characterizing promoter architectures are critically needed.

RESULTS

We have developed a novel model reduction for promoters with arbitrary numbers of ON and OFF states, allowing us to approximate complex promoter switching behavior with Weibull-distributed ON/OFF times. Using this model reduction, we created bursty Monte Carlo expectation-maximization with modified cross-entropy method ('bursty MCEM(2)'), an efficient parameter estimation and model selection technique for inferring the number and configuration of promoter states from single-cell gene expression data. Application of bursty MCEM(2) to data from the endogenous mouse glutaminase promoter reveals nearly deterministic promoter OFF times, consistent with a multi-step activation mechanism consisting of 10 or more inactive states. Our novel approach to modeling promoter fluctuations together with bursty MCEM(2) provides powerful tools for characterizing transcriptional bursting across genes under different environmental conditions.

AVAILABILITY AND IMPLEMENTATION

R source code implementing bursty MCEM(2) is available upon request.

CONTACT

absingh@udel.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

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.

Division time-based amplifiers for stochastic gene expression

While cell-to-cell variability is a phenotypic consequence of gene expression noise, sources of this noise may be complex – apart from intrinsic sources such as the random birth/death of mRNA and stochastic switching between promoter states, there are also extrinsic sources of noise such as cell division where division times are either constant or random.

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.