Effect of promoter architecture on the cell-to-cell variability in gene expression

Anti-correlation of LacI association and dissociation rates observed in living cells

The rate at which transcription factors (TFs) bind their cognate sites has long been assumed to be limited by diffusion, and thus independent of binding site sequence. Here, we systematically test this assumption using cell-to-cell variability in gene expression as a window into the in vivo association and dissociation kinetics of the model transcription factor LacI. Using a stochastic model of the relationship between gene expression variability and binding kinetics, we performed single-cell gene expression measurements to infer association and dissociation rates for a set of 35 different LacI binding sites. We found that both association and dissociation rates differed significantly between binding sites, and moreover observed a clear anticorrelation between these rates across varying binding site strengths. These results contradict the long-standing hypothesis that TF binding site strength is primarily dictated by the dissociation rate, but may confer the evolutionary advantage that TFs do not get stuck in near-operator sequences while searching.

From homogeneity to heterogeneity: Refining stochastic simulations of gene regulation

Cellular processes are intricately controlled through gene regulation, which is significantly influenced by intrinsic noise due to the small number of molecules involved. The Gillespie algorithm, a widely used stochastic simulation method, is pervasively employed to model these systems. However, this algorithm typically assumes that DNA is homogeneously distributed throughout the nucleus, which is not realistic. In this study, we evaluated whether stochastic simulations based on the assumption of spatial homogeneity can accurately capture the dynamics of gene regulation. Our findings indicate that when transcription factors diffuse slowly, these simulations fail to accurately capture gene expression, highlighting the necessity to account for spatial heterogeneity. However, incorporating spatial heterogeneity considerably increases computational time. To address this, we explored various stochastic quasi-steady-state approximations (QSSAs) that simplify the model and reduce simulation time. While both the stochastic total quasi-steady state approximation (stQSSA) and the stochastic low-state quasi-steady-state approximation (slQSSA) reduced simulation time, only the slQSSA provided an accurate model reduction. Our study underscores the importance of utilizing appropriate methods for efficient and accurate stochastic simulations of gene regulatory dynamics, especially when incorporating spatial heterogeneity.

E. coli transcription factors regulate promoter activity by a universal, homeostatic mechanism

Transcription factors (TFs) may activate or repress gene expression through an interplay of different mechanisms, including RNA polymerase (RNAP) recruitment, exclusion, and initiation. TFs often have drastically different regulatory behaviors depending on promoter context and interacting cofactors. However, the detailed mechanisms by which each TF affects transcription and produce promoter-dependent regulation is unclear. Here, we discover that a simple model explains the regulatory effects of E. coli TFs in a range of contexts. Specifically, we measure the relationship between basal promoter activity and its regulation by diverse TFs and find that the contextual changes in TF function are determined entirely by the basal strength of the regulated promoter: TFs exert lower fold-change on stronger promoters under a precise inverse scaling. Remarkably, this scaling relationship holds for both activators and repressors, indicating a universal mechanism of gene regulation. Our data, which spans between 100-fold activation to 1000-fold repression, is consistent with a model of regulation driven by stabilization of RNAP at the promoter for every TF. Crucially, this indicates that TFs naturally act to maintain homeostatic expression levels across genetic or environmental perturbations, ensuring robust expression of regulated genes.

Emergence of temporal noise hierarchy in co-regulated genes of multi-output feed-forward loop

Natural variations in gene expression, called noise, are fundamental to biological systems. The expression noise can be beneficial or detrimental to cellular functions. While the impact of noise on individual genes is well-established, our understanding of how noise behaves when multiple genes are co-expressed by shared regulatory elements within transcription networks remains elusive. This lack of understanding extends to how the architecture and regulatory features of these networks influence noise. To address this gap, we study the multi-output feed-forward loop motif. The motif is prevalent in bacteria and yeast and influences co-expression of multiple genes by shared transcription factors (TFs). Focusing on a two-output variant of the motif, the present study explores the interplay between its architecture, co-expression (symmetric and asymmetric) patterns of the two genes, and the associated noise dynamics. We employ a stochastic modeling approach to investigate how the binding affinities of the TFs influence symmetric and asymmetric expression patterns and the resulting noise dynamics in the co-expressed genes. This knowledge could guide the development of strategies for manipulating gene expression patterns through targeted modulation of TF binding affinities.

Using deep learning to decipher the impact of telomerase promoter mutations on the dynamic metastatic morpholome

Melanoma showcases a complex interplay of genetic alterations and intra- and inter-cellular morphological changes during metastatic transformation. While pivotal, the role of specific mutations in dictating these changes still needs to be fully elucidated. Telomerase promoter mutations (TERTp mutations) significantly influence melanoma's progression, invasiveness, and resistance to various emerging treatments, including chemical inhibitors, telomerase inhibitors, targeted therapy, and immunotherapies. We aim to understand the morphological and phenotypic implications of the two dominant monoallelic TERTp mutations, C228T and C250T, enriched in melanoma metastasis. We developed isogenic clonal cell lines containing the TERTp mutations and utilized dual-color expression reporters steered by the endogenous Telomerase promoter, giving us allelic resolution. This approach allowed us to monitor morpholomic variations induced by these mutations. TERTp mutation-bearing cells exhibited significant morpholome differences from their wild-type counterparts, with increased allele expression patterns, augmented wound-healing rates, and unique spatiotemporal dynamics. Notably, the C250T mutation exerted more pronounced changes in the morpholome than C228T, suggesting a differential role in metastatic potential. Our findings underscore the distinct influence of TERTp mutations on melanoma's cellular architecture and behavior. The C250T mutation may offer a unique morpholomic and systems-driven advantage for metastasis. These insights provide a foundational understanding of how a non-coding mutation in melanoma metastasis affects the system, manifesting in cellular morpholome.

Interpretable prediction of mRNA abundance from promoter sequence using contextual regression models

While machine learning models have been successfully applied to predicting gene expression from promoter sequences, it remains a great challenge to derive intuitive interpretation of the model and reveal DNA motif grammar such as motif cooperation and distance constraint between motif sites. Previous interpretation approaches are often time-consuming or have difficulty to learn the combinatory rules. In this work, we designed interpretable neural network models to predict the mRNA expression levels from DNA sequences. By applying the Contextual Regression framework we developed, we extracted weighted features to cluster samples into different groups, which have different gene expression levels. We performed motif analysis in each cluster and found motifs with active or repressive regulation on gene expression. By comparing the co-occurrence locations of discovered motifs, we also uncovered multiple grammars of motif combination including communities of cooperative motifs and distance constraints between motif pairs. These results revealed new insights of the regulatory architecture of promoter sequences.

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.

Plasmid-mediated phenotypic noise leads to transient antibiotic resistance in bacteria

The rise of antibiotic resistance is a critical public health concern, requiring an understanding of mechanisms that enable bacteria to tolerate antimicrobial agents. Bacteria use diverse strategies, including the amplification of drug-resistance genes. In this paper, we showed that multicopy plasmids, often carrying antibiotic resistance genes in clinical bacteria, can rapidly amplify genes, leading to plasmid-mediated phenotypic noise and transient antibiotic resistance. By combining stochastic simulations of a computational model with high-throughput single-cell measurements of blaTEM-1 expression in Escherichia coli MG1655, we showed that plasmid copy number variability stably maintains populations composed of cells with both low and high plasmid copy numbers. This diversity in plasmid copy number enhances the probability of bacterial survival in the presence of antibiotics, while also rapidly reducing the burden of carrying multiple plasmids in drug-free environments. Our results further support the tenet that multicopy plasmids not only act as vehicles for the horizontal transfer of genetic information between cells but also as drivers of bacterial adaptation, enabling rapid modulation of gene copy numbers. Understanding the role of multicopy plasmids in antibiotic resistance is critical, and our study provides insights into how bacteria can transiently survive lethal concentrations of antibiotics.

A robust ultrasensitive transcriptional switch in noisy cellular environments

Ultrasensitive transcriptional switches enable sharp transitions between transcriptional on and off states and are essential for cells to respond to environmental cues with high fidelity. However, conventional switches, which rely on direct repressor-DNA binding, are extremely noise-sensitive, leading to unintended changes in gene expression. Here, through model simulations and analysis, we discovered that an alternative design combining three indirect transcriptional repression mechanisms, sequestration, blocking, and displacement, can generate a noise-resilient ultrasensitive switch. Although sequestration alone can generate an ultrasensitive switch, it remains sensitive to noise because the unintended transcriptional state induced by noise persists for long periods. However, by jointly utilizing blocking and displacement, these noise-induced transitions can be rapidly restored to the original transcriptional state. Because this transcriptional switch is effective in noisy cellular contexts, it goes beyond previous synthetic transcriptional switches, making it particularly valuable for robust synthetic system design. Our findings also provide insights into the evolution of robust ultrasensitive switches in cells. Specifically, the concurrent use of seemingly redundant indirect repression mechanisms in diverse biological systems appears to be a strategy to achieve noise-resilience of ultrasensitive switches.

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.

Metabolic engineering of Paracoccus denitrificans for dual degradation of sulfamethoxazole and ammonia nitrogen

Sulfamethoxazole (SMX), as one of the most widely used sulfonamide antibiotics, has been frequently detected in the aqueous environment, posing potential risks to the environment and human health. Although microbial degradation methods have been widely applied, some issues remain, including low degradation efficiency and poor environmental adaptability. In this regard, constructing efficient degrading bacteria by metabolic engineering is an ideal solution to these challenges. In this study, we used Paracoccus denitrificans DYTN-1, a superior nitrogen removal environment strain, as chassis to construct an SMX degradation pathway, obtaining a new bacteria for simultaneous degradation of SMX and removal of ammonia nitrogen. In doing this, we first identified and characterized four native promoters of P. denitrificans DYTN-1 with gradient strength to control the expression of the SMX degradation pathway. After degradation pathway expression level optimization and FMN reductase optimization, SMX degradation efficiency was significantly improved. The constructed P. d-pIAB4-PCS-sutR strain exhibited superior co-degradation of SMX and ammonia nitrogen contaminants with degradation rates of 44% and 71%, respectively. This study could pave the way for SMX degradation engineered strain design and evolution of environmental bioremediation. IMPORTANCE The abuse of sulfamethoxazole (SMX) had led to an increased accumulation in the environment, resulting in the disruption of the structure of microbial communities, further disrupting the bio-degradation process of other pollutants, such as ammonia nitrogen. To solve this challenge, we first identified and characterized four native promoters of Paracoccus denitrificans DYTN-1 with gradient strength to control the expression of the SMX degradation pathway. Then SMX degradation efficiency was significantly improved with degradation pathway expression level optimization and FMN reductase optimization. Finally, the superior nitrogen removal environment strain, P. denitrificans DYTN-1, obtained an SMX degradation function. This pioneering study of metabolic engineering to enhance the SMX degradation in microorganisms could pave the way for designing the engineered strains of SMX and nitrogen co-degradation and the environmental bioremediation.

BurstDECONV: a signal deconvolution method to uncover mechanisms of transcriptional bursting in live cells

Monitoring transcription in living cells gives access to the dynamics of this complex fundamental process. It reveals that transcription is discontinuous, whereby active periods (bursts) are separated by one or several types of inactive periods of distinct lifetimes. However, decoding temporal fluctuations arising from live imaging and inferring the distinct transcriptional steps eliciting them is a challenge. We present BurstDECONV, a novel statistical inference method that deconvolves signal traces into individual transcription initiation events. We use the distribution of waiting times between successive polymerase initiation events to identify mechanistic features of transcription such as the number of rate-limiting steps and their kinetics. Comparison of our method to alternative methods emphasizes its advantages in terms of precision and flexibility. Unique features such as the direct determination of the number of promoter states and the simultaneous analysis of several potential transcription models make BurstDECONV an ideal analytic framework for live cell transcription imaging experiments. Using simulated realistic data, we found that our method is robust with regards to noise or suboptimal experimental designs. To show its generality, we applied it to different biological contexts such as Drosophila embryos or human cells.

Genome-wide inference reveals that feedback regulations constrain promoter-dependent transcriptional burst kinetics

Gene expression in mammalian cells is highly variable and episodic, resulting in a series of discontinuous bursts of mRNAs. A challenge is to understand how static promoter architecture and dynamic feedback regulations dictate bursting on a genome-wide scale. Although single-cell RNA sequencing (scRNA-seq) provides an opportunity to address this challenge, effective analytical methods are scarce. We developed an interpretable and scalable inference framework, which combined experimental data with a mechanistic model to infer transcriptional burst kinetics (sizes and frequencies) and feedback regulations. Applying this framework to scRNA-seq data generated from embryonic mouse fibroblast cells, we found Simpson's paradoxes, i.e. genome-wide burst kinetics exhibit different characteristics in two cases without and with distinguishing feedback regulations. We also showed that feedbacks differently modulate burst frequencies and sizes and conceal the effects of transcription start site distributions on burst kinetics. Notably, only in the presence of positive feedback, TATA genes are expressed with high burst frequencies and enhancer-promoter interactions mainly modulate burst frequencies. The developed inference method provided a flexible and efficient way to investigate transcriptional burst kinetics and the obtained results would be helpful for understanding cell development and fate decision.

Genome-Wide Analysis of Gene Expression Noise Brought About by Transcriptional Regulation in Pseudomonas aeruginosa

The part of expression noise that is brought about by transcriptional regulation (represented here as NTR) is an important criterion for estimating the regulatory mode of a gene. However, characterization of NTR is an under-explored area, and there is little knowledge regarding the genome-wide NTR in the model pathogen Pseudomonas aeruginosa. Here, with a library of dual-color transcriptional reporters, we estimated the NTR for over 90% of the promoters in P. aeruginosa. Most promoters exhibit low NTR, while 42 and 115 promoters with high NTR were screened out in the exponential and the stationary growth phases, respectively. Specifically, a rearrangement of NTR was found in promoters involved in amino acid metabolism when bacteria enter the exponential phase. In addition, during the stationary phase, high NTR was found in a wide range of iron-related promoters involving siderophore synthesis and heme uptake, ExsA-regulated promoters involving bacterial virulence, and FleQ-regulated promoters involving biofilm development. We also found a large-scale negative dependence of transcriptional regulation between high-NTR promoters belonging to different functional categories. Our findings offer a global view of transcriptional heterogeneity in P. aeruginosa. IMPORTANCE The phenotypic diversity of Pseudomonas aeruginosa is frequently observed in research, suggesting that bacteria adopt strategies such as bet-hedging to survive ever-changing environments. Gene expression noise (GEN) is the major source of phenotypic diversity. Large GEN from transcriptional regulation (represented as NTR) represent an evolutionary necessity to maintain the copy number diversity of certain proteins in the population. Here, we provide a system-wide view of NTR in P. aeruginosa under nutrient-rich and stressed conditions. High NTR was found in genes involved in flagella biosynthesis and amino acid metabolism under both conditions. Specially, iron acquisition genes exhibited high NTR in the stressed condition, suggesting a great diversity of iron physiology in P. aeruginosa. We further revealed a global negative dependence of transcriptional regulation between those high-NTR genes under the stressed condition, suggesting a mutually exclusive relationship between different bacterial survival strategies.

Transcription factor binding process is the primary driver of noise in gene expression

Noise in expression of individual genes gives rise to variations in activity of cellular pathways and generates heterogeneity in cellular phenotypes. Phenotypic heterogeneity has important implications for antibiotic persistence, mutation penetrance, cancer growth and therapy resistance. Specific molecular features such as the presence of the TATA box sequence and the promoter nucleosome occupancy have been associated with noise. However, the relative importance of these features in noise regulation is unclear and how well these features can predict noise has not yet been assessed. Here through an integrated statistical model of gene expression noise in yeast we found that the number of regulating transcription factors (TFs) of a gene was a key predictor of noise, whereas presence of the TATA box and the promoter nucleosome occupancy had poor predictive power. With an increase in the number of regulatory TFs, there was a rise in the number of cooperatively binding TFs. In addition, an increased number of regulatory TFs meant more overlaps in TF binding sites, resulting in competition between TFs for binding to the same region of the promoter. Through modeling of TF binding to promoter and application of stochastic simulations, we demonstrated that competition and cooperation among TFs could increase noise. Thus, our work uncovers a process of noise regulation that arises out of the dynamics of gene regulation and is not dependent on any specific transcription factor or specific promoter sequence.

Controlling gene expression timing through gene regulatory architecture

Gene networks typically involve the regulatory control of multiple genes with related function. This connectivity enables correlated control of the levels and timing of gene expression. Here we study how gene expression timing in the single-input module motif can be encoded in the regulatory DNA of a gene. Using stochastic simulations, we examine the role of binding affinity, TF regulatory function and network size in controlling the mean first-passage time to reach a fixed fraction of steady-state expression for both an auto-regulated TF gene and a target gene. We also examine how the variability in first-passage time depends on these factors. We find that both network size and binding affinity can dramatically speed up or slow down the response time of network genes, in some cases predicting more than a 100-fold change compared to that for a constitutive gene. Furthermore, these factors can also significantly impact the fidelity of this response. Importantly, these effects do not occur at “extremes” of network size or binding affinity, but rather in an intermediate window of either quantity.

Exploring the role of eRNA in regulating gene expression

eRNAs as the products of enhancers can regulate gene expression via various possible ways, but which regulation way is more reasonable is debatable in biology, and in particular, how eRNAs impact gene expression remains unclear. Here we introduce a mechanistic model of gene expression to address these issues. This model considers three possible regulation ways of eRNA: Type-I by which eRNA regulates transcriptional activity by facilitating the formation of enhancer-promoter (E-P) loop, Type-II by which eRNA directly promotes the mRNA production rate, and mixed regulation (i.e., the combination of Type-I and Type-II). We show that with the increase of the E-P loop length, mRNA distribution can transition from unimodality to bimodality or vice versa in all the three regulation cases. However, in contrast to the other two regulations, Type-II regulation can lead to the highest mean mRNA level and the lowest mRNA noise, independent of the E-P loop length. These results would not only reveal the essential mechanism of how eRNA regulates gene expression, but also imply a new mechanism for phenotypic switching, namely the E-P loop can induce phenotypic switching.

Exact distributions for stochastic gene expression models with arbitrary promoter architecture and translational bursting

Gene expression in individual cells is inherently variable and sporadic, leading to cell-to-cell variability in mRNA and protein levels. Recent single-cell and single-molecule experiments indicate that promoter architecture and translational bursting play significant roles in controlling gene expression noise and generating the phenotypic diversity that life exhibits. To quantitatively understand the impact of these factors, it is essential to construct an accurate mathematical description of stochastic gene expression and find the exact analytical results, which is a formidable task. Here, we develop a stochastic model of bursty gene expression, which considers the complex promoter architecture governing the variability in mRNA expression and a general distribution characterizing translational burst. We derive the analytical expression for the corresponding protein steady-state distribution and all moment statistics of protein counts. We show that the total protein noise can be decomposed into three parts: the low-copy noise of protein due to probabilistic individual birth and death events, the noise due to stochastic switching between promoter states, and the noise resulting from translational busting. The theoretical results derived provide quantitative insights into the biochemical mechanisms of stochastic gene expression.

A Core35S Promoter of Cauliflower Mosaic Virus Drives More Efficient Replication of Turnip Crinkle Virus

The 35S promoter with a duplicated enhancer (frequently referred to as 2X35S) is a strong dicotyledonous plant-specific promoter commonly used in generating transgenic plants to enable high-level expression of genes of interest. It is also used to drive the initiation of RNA virus replication from viral cDNA, with the consensus understanding that high levels of viral RNA production powered by 2X35S permit a more efficient initiation of virus replication. Here, we showed that the exact opposite is true. We found that, compared to the Core35S promoter, the 2X35S promoter-driven initiation of turnip crinkle virus (TCV) infection was delayed by at least 24 h. We first compared three versions of 35S promoter, namely 2X35S, 1X35S, and Core35S, for their ability to power the expression of a non-replicating green fluorescent protein (GFP) gene, and confirmed that 2X35S and Core35S correlated with the highest and lowest GFP expression, respectively. However, when inserted upstream of TCV cDNA, 2X35S-driven replication was not detected until 72 h post-inoculation (72 hpi) in inoculated leaves. By contrast, Core35S-driven replication was detected earlier at 48 hpi. A similar delay was also observed in systemically infected leaves (six versus four days post-inoculation). Combining our results, we hypothesized that the stronger 2X35S promoter might enable a higher accumulation of a TCV protein that became a repressor of TCV replication at higher cellular concentration. Extending from these results, we propose that the Core35S (or mini35S) promoter is likely a better choice for generating infectious cDNA clones of TCV.

Stochastic Simulations as a Tool for Assessing Signal Fidelity in Gene Expression in Synthetic Promoter Design

Simple Summary

Synthetic biology is an emerging discipline, offering new perspectives in many industrial fields, from pharma and row-material production to renewable energy. Developing synthetic biology applications is often a lengthy and expensive process with extensive and tedious trial-and-error runs. Computational models can direct the engineering of biological circuits in a computer-aided design setting. By providing a virtual lab environment, in silico models of synthetic circuits can contribute to a quantitative understanding of the underlying molecular pathways before a wet-lab implementation. Here, we illustrate this notion from the point of view of signal fidelity and noise relationship. Noise in gene expression can undermine signal fidelity with implications on the well-functioning of the engineered organisms. For our analysis, we use a specific biological circuit that regulates the gene expression in bacterial inorganic phosphate economy. Applications that use this circuit include those in pollutant detection and wastewater treatment. We provide computational models with different levels of molecular detail as virtual labs. We show that inherent fluctuations in the gene expression machinery can be predicted via stochastic simulations to introduce control in the synthetic promoter design process. Our analysis suggests that noise in the system can be alleviated by strong synthetic promoters with slow unbinding rates. Overall, we provide a recipe for the computer-aided design of synthetic promoter libraries with specific signal to noise characteristics.

Abstract

The design and development of synthetic biology applications in a workflow often involve connecting modular components. Whereas computer-aided design tools are picking up in synthetic biology as in other areas of engineering, the methods for verifying the correct functioning of living technologies are still in their infancy. Especially, fine-tuning for the right promoter strength to match the design specifications is often a lengthy and expensive experimental process. In particular, the relationship between signal fidelity and noise in synthetic promoter design can be a key parameter that can affect the healthy functioning of the engineered organism. To this end, based on our previous work on synthetic promoters for the E. coli PhoBR two-component system, we make a case for using chemical reaction network models for computational verification of various promoter designs before a lab implementation. We provide an analysis of this system with extensive stochastic simulations at a single-cell level to assess the signal fidelity and noise relationship. We then show how quasi-steady-state analysis via ordinary differential equations can be used to navigate between models with different levels of detail. We compare stochastic simulations with our full and reduced models by using various metrics for assessing noise. Our analysis suggests that strong promoters with low unbinding rates can act as control tools for filtering out intrinsic noise in the PhoBR context. Our results confirm that even simpler models can be used to determine promoters with specific signal to noise characteristics.

How subtle changes in 3D structure can create large changes in transcription

Animal genomes are organized into topologically associated domains (TADs). TADs are thought to contribute to gene regulation by facilitating enhancer-promoter (E-P) contacts within a TAD and preventing these contacts across TAD borders. However, the absolute difference in contact frequency across TAD boundaries is usually less than 2-fold, even though disruptions of TAD borders can change gene expression by 10-fold. Existing models fail to explain this hypersensitive response. Here, we propose a futile cycle model of enhancer-mediated regulation that can exhibit hypersensitivity through bistability and hysteresis. Consistent with recent experiments, this regulation does not exhibit strong correlation between E-P contact and promoter activity, even though regulation occurs through contact. Through mathematical analysis and stochastic simulation, we show that this system can create an illusion of E-P biochemical specificity and explain the importance of weak TAD boundaries. It also offers a mechanism to reconcile apparently contradictory results from recent global TAD disruption with local TAD boundary deletion experiments. Together, these analyses advance our understanding of cis-regulatory contacts in controlling gene expression and suggest new experimental directions.

Real-time single-cell characterization of the eukaryotic transcription cycle reveals correlations between RNA initiation, elongation, and cleavage

The eukaryotic transcription cycle consists of three main steps: initiation, elongation, and cleavage of the nascent RNA transcript. Although each of these steps can be regulated as well as coupled with each other, their in vivo dissection has remained challenging because available experimental readouts lack sufficient spatiotemporal resolution to separate the contributions from each of these steps. Here, we describe a novel application of Bayesian inference techniques to simultaneously infer the effective parameters of the transcription cycle in real time and at the single-cell level using a two-color MS2/PP7 reporter gene and the developing fruit fly embryo as a case study. Our method enables detailed investigations into cell-to-cell variability in transcription-cycle parameters as well as single-cell correlations between these parameters. These measurements, combined with theoretical modeling, suggest a substantial variability in the elongation rate of individual RNA polymerase molecules. We further illustrate the power of this technique by uncovering a novel mechanistic connection between RNA polymerase density and nascent RNA cleavage efficiency. Thus, our approach makes it possible to shed light on the regulatory mechanisms in play during each step of the transcription cycle in individual, living cells at high spatiotemporal resolution.

Scaling of intrinsic noise in an autocratic reaction network

Biochemical reactions in living cells often produce stochastic trajectories due to the fluctuations of the finite number of the macromolecular species present inside the cell. A significant number of computational and theoretical studies have previously investigated stochasticity in small regulatory networks to understand its origin and regulation. At the systems level regulatory networks have been determined to be hierarchical resembling social networks. In order to determine the stochasticity in networks with hierarchical architecture, here we computationally investigated intrinsic noise in an autocratic reaction network in which only the upstream regulators regulate the downstream regulators. We studied the effects of the qualitative and quantitative nature of regulatory interactions on the stochasticity in the network. We established an unconventional scaling of noise with average abundance in which the noise passes through a minimum indicating that the network can be noisy both in the low and high abundance regimes. We determined that the bursty kinetics of the trajectories are responsible for such scaling. The scaling of noise remains intact for a mixed network that includes democratic subnetworks within the autocratic network.

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.

Kinetic sculpting of the seven stripes of the Drosophila even-skipped gene

We used live imaging to visualize the transcriptional dynamics of the Drosophila melanogaster even-skipped gene at single-cell and high-temporal resolution as its seven stripe expression pattern forms, and developed tools to characterize and visualize how transcriptional bursting varies over time and space. We find that despite being created by the independent activity of five enhancers, even-skipped stripes are sculpted by the same kinetic phenomena: a coupled increase of burst frequency and amplitude. By tracking the position and activity of individual nuclei, we show that stripe movement is driven by the exchange of bursting nuclei from the posterior to anterior stripe flanks. Our work provides a conceptual, theoretical and computational framework for dissecting pattern formation in space and time, and reveals how the coordinated transcriptional activity of individual nuclei shapes complex developmental patterns.

A matter of time: Using dynamics and theory to uncover mechanisms of transcriptional bursting

Eukaryotic transcription generally occurs in bursts of activity lasting minutes to hours; however, state-of-the-art measurements have revealed that many of the molecular processes that underlie bursting, such as transcription factor binding to DNA, unfold on timescales of seconds. This temporal disconnect lies at the heart of a broader challenge in physical biology of predicting transcriptional outcomes and cellular decision-making from the dynamics of underlying molecular processes. Here, we review how new dynamical information about the processes underlying transcriptional control can be combined with theoretical models that predict not only averaged transcriptional dynamics, but also their variability, to formulate testable hypotheses about the molecular mechanisms underlying transcriptional bursting and control.

Exactly solvable models of stochastic gene expression

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

Urn models for stochastic gene expression yield intuitive insights into the probability distributions of single-cell mRNA and protein counts

Fitting the probability mass functions from analytical solutions of stochastic models of gene expression to the single-cell count distributions of mRNA and protein molecules can yield valuable insights into mechanisms underlying gene expression. Solutions of chemical master equations are available for various kinetic schemes but, even for the basic ON-OFF genetic switch, they take complex forms with generating functions given as hypergeometric functions. Interpretation of gene expression dynamics in terms of bursts is not consistent with the complete range of parameters for these functions. Physical insights into the probability mass functions are essential to ensure proper interpretations but are lacking for models considering genetic switches. To fill this gap, we develop urn models for stochastic gene expression. We sample RNA polymerases or ribosomes from a master urn, which represents the cytosol, and assign them to recipient urns of two or more colors, which represent time intervals in which no switching occurs. Colors of the recipient urns represent sub-systems of the promoter states, and the assignments to urns of a specific color represent gene expression. We use elementary principles of discrete probability theory to solve a range of kinetic models without feedback, including the Peccoud-Ycart model, the Shahrezaei-Swain model, and models with an arbitrary number of promoter states. In the last case, we obtain a novel result for the protein distribution. For activated genes, we show that transcriptional lapses, which are events of gene inactivation for short time intervals separated by long active intervals, quantify the transcriptional dynamics better than bursts. We show that the intuition gained from our urn models may also be useful in understanding existing solutions for models with feedback. We contrast our models with urn models for related distributions, discuss a generalization of the Delaporte distribution for single-cell data analysis, and highlight the limitations of our models.

Inherent regulatory asymmetry emanating from network architecture in a prevalent autoregulatory motif

Predicting gene expression from DNA sequence remains a major goal in the field of gene regulation. A challenge to this goal is the connectivity of the network, whose role in altering gene expression remains unclear. Here, we study a common autoregulatory network motif, the negative single-input module, to explore the regulatory properties inherited from the motif. Using stochastic simulations and a synthetic biology approach in E. coli, we find that the TF gene and its target genes have inherent asymmetry in regulation, even when their promoters are identical; the TF gene being more repressed than its targets. The magnitude of asymmetry depends on network features such as network size and TF-binding affinities. Intriguingly, asymmetry disappears when the growth rate is too fast or too slow and is most significant for typical growth conditions. These results highlight the importance of accounting for network architecture in quantitative models of gene expression.

Shadow enhancers can suppress input transcription factor noise through distinct regulatory logic

Shadow enhancers, groups of seemingly redundant enhancers, are found in a wide range of organisms and are critical for robust developmental patterning. However, their mechanism of action is unknown. We hypothesized that shadow enhancers drive consistent expression levels by buffering upstream noise through a separation of transcription factor (TF) inputs at the individual enhancers. By measuring the transcriptional dynamics of several Kruppel shadow enhancer configurations in live Drosophila embryos, we showed that individual member enhancers act largely independently. We found that TF fluctuations are an appreciable source of noise that the shadow enhancer pair can better buffer than duplicated enhancers. The shadow enhancer pair is also uniquely able to maintain low levels of expression noise across a wide range of temperatures. A stochastic model demonstrated the separation of TF inputs is sufficient to explain these findings. Our results suggest the widespread use of shadow enhancers is partially due to their noise suppressing ability.

Information transmission from NFkB signaling dynamics to gene expression

The dynamic signal encoding paradigm suggests that information flows from the extracellular environment into specific signaling patterns (encoding) that are then read by downstream effectors to control cellular behavior. Previous work empirically quantified the information content of dynamic signaling patterns. However, whether this information can be faithfully transmitted to the gene expression level is unclear. Here we used NFkB signaling as a model to understand the accuracy of information transmission from signaling dynamics into gene expression. Using a detailed mathematical model, we simulated realistic NFkB signaling patterns with different degrees of variability. The NFkB patterns were used as an input to a simple gene expression model. Analysis of information transmission between ligand and NFkB and ligand and gene expression allows us to determine information loss in transmission between receptors to dynamic signaling patterns and between signaling dynamics to gene expression. Information loss could occur due to biochemical noise or due to a lack of specificity. We found that noise-free gene expression has very little information loss suggesting that gene expression can preserve specificity in NFkB patterns. As expected, the addition of noise to the gene expression model results in information loss. Interestingly, this effect can be mitigated by a specific choice of parameters that can substantially reduce information loss due to biochemical noise during gene expression. Overall our results show that the cellular capacity for information transmission from dynamic signaling patterns to gene expression can be high enough to preserve ligand specificity and thereby the accuracy of cellular response to environmental cues.

Probing Mechanisms of Transcription Elongation Through Cell-to-Cell Variability of RNA Polymerase

The process of transcription initiation and elongation are primary points of control in the regulation of gene expression. Although biochemical studies have uncovered the mechanisms involved in controlling transcription at each step, how these mechanisms manifest in vivo at the level of individual genes is still unclear. Recent experimental advances have enabled single-cell measurements of RNA polymerase (RNAP) molecules engaged in the process of transcribing a gene of interest. In this article, we use Gillespie simulations to show that measurements of cell-to-cell variability of RNAP numbers and interpolymerase distances can reveal the prevailing mode of regulation of a given gene. Mechanisms of regulation at each step, from initiation to elongation dynamics, produce qualitatively distinct signatures, which can further be used to discern between them. Most intriguingly, depending on the initiation kinetics, stochastic elongation can either enhance or suppress cell-to-cell variability at the RNAP level. To demonstrate the value of this framework, we analyze RNAP number distribution data for ribosomal genes in Saccharomyces cerevisiae from three previously published studies and show that this approach provides crucial mechanistic insights into the transcriptional regulation of these genes.

What Is a Transcriptional Burst?

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

Control strategies for the timing of intracellular events

While the timing of intracellular events is essential for many cellular processes, gene expression inside a single cell can exhibit substantial cell-to-cell variability, raising the question of how cells ensure precision in event timing despite such stochasticity. We address this question by analyzing a biologically reasonable model of gene expression in the context of first passage time (FPT), focusing on two experimentally measurable statistics: mean FPT (MFPT) and timing variability (TV). We show that (1) transcriptional burst size (BS) and burst frequency (BF) can minimize the TV; (2) translational BS monotonically reduces the MFPT to a nonzero low bound; (3) the timescale of promoter kinetics can minimize both the MFPT and the TV, depending on the ratio of the on-switching rate over the off-switching rate; and (4) positive feedback regulation of any form can all minimize the TV, whereas negative feedback regulation of transcriptional BF or BS always enhances the TV. These control strategies can have broad implications for diverse cellular processes relying on precise temporal triggering of events.

Multisite phosphorylation drives phenotypic variation in (p)ppGpp synthetase-dependent antibiotic tolerance

Isogenic populations of cells exhibit phenotypic variability that has specific physiological consequences. Individual bacteria within a population can differ in antibiotic tolerance, but whether this variability can be regulated or is generally an unavoidable consequence of stochastic fluctuations is unclear. Here we report that a gene encoding a bacterial (p)ppGpp synthetase in Bacillus subtilis, sasA, exhibits high levels of extrinsic noise in expression. We find that sasA is regulated by multisite phosphorylation of the transcription factor WalR, mediated by a Ser/Thr kinase-phosphatase pair PrkC/PrpC, and a Histidine kinase WalK of a two-component system. This regulatory intersection is crucial for controlling the appearance of outliers; rare cells with unusually high levels of sasA expression, having increased antibiotic tolerance. We create a predictive model demonstrating that the probability of a given cell surviving antibiotic treatment increases with sasA expression. Therefore, multisite phosphorylation can be used to strongly regulate variability in antibiotic tolerance.

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.

Data-driven dynamical model indicates that the heat shock response in Chlamydomonas reinhardtii is tailored to handle natural temperature variation

Global warming exposes plants to severe heat stress, with consequent crop yield reduction. Organisms exposed to high temperature stresses typically protect themselves with a heat shock response (HSR), where accumulation of unfolded proteins initiates the synthesis of heat shock proteins through the heat shock transcription factor HSF1. While the molecular mechanisms are qualitatively well characterized, our quantitative understanding of the underlying dynamics is still very limited. Here, we study the dynamics of HSR in the photosynthetic model organism Chlamydomonas reinhardtii with a data-driven mathematical model of HSR. We based our dynamical model mostly on mass action kinetics, with a few nonlinear terms. The model was parametrized and validated by several independent datasets obtained from the literature. We demonstrate that HSR quantitatively and significantly differs if an increase in temperature of the same magnitude occurs abruptly, as often applied under laboratory conditions, or gradually, which would rather be expected under natural conditions. In contrast to rapid temperature increases, under gradual changes only negligible amounts of misfolded proteins accumulate, indicating that the HSR of C. reinhardtii efficiently avoids the accumulation of misfolded proteins under conditions most likely to prevail in nature. The mathematical model we developed is a flexible tool to simulate the HSR to different conditions and complements the current experimental approaches.

Analytical Expressions and Physics for Single-Cell mRNA Distributions of the lac Operon of E. coli

Mechanistic models of stochastic gene expression are of considerable interest, but their complexity often precludes tractable analytical expressions for messenger RNA (mRNA) and protein distributions. The lac operon of Escherichia coli is a model system with regulatory elements such as multiple operators and DNA looping that are shared by many operons. Although this system is complex, intuition suggests that fast DNA looping may simplify it by causing the repressor-bound states of the operon to equilibrate rapidly, thus ensuring that the subsequent dynamics are governed by slow transitions between the repressor-free and the equilibrated repressor-bound states. Here, we show that this intuition is correct by applying singular perturbation theory to a mechanistic model of lac transcription with the scaled time constant of DNA looping as the perturbation parameter. We find that at steady state, the repressor-bound states satisfy detailed balance and are dominated by the looped states; moreover, the interaction between the repressor-free and the equilibrated repressor-bound states is described by an extension of the Peccoud-Ycart two-state model in which both (repressor-free and repressor-bound) states support transcription. The solution of this extended two-state model reveals that the steady-state mRNA distribution is a mixture of the Poisson and negative hypergeometric distributions, which reflects mRNAs obtained by transcription from the repressor-bound and repressor-free states. Finally, we show that the physics revealed by perturbation theory makes it easy to derive the extended two-state model equations for complex regulatory architectures.

Analytical results for a generalized model of bursty gene expression with molecular memory

The activation of a gene is a complex biochemical process and could involve small steps, creating a memory between individual events. However, the effect of this molecular memory was often neglected in previous work. How the molecular memory affects gene expression remains not fully explored. We analyze a stochastic model of bursty gene expression, where the waiting time from inactivation to activation is assumed to follow a nonexponential (in fact, Erlang) distribution. We derive the analytical expression for the gene-product distribution, which explicitly traces the effect of molecule memory. Interestingly, we find that the effect of molecular memory is equivalent to the introduction of feedback. In addition, we analytically show that the stationary distribution is always super-Poissonian, independent of the detail of the waiting-time distribution, and there is the optimal step size that minimizes the Fano factor for any given mean burst size and is a decreasing function of the mean burst size. These analytical results indicate that molecular memory is an unneglectable factor affecting gene expression.

Effects of mRNA Degradation and Site-Specific Transcriptional Pausing on Protein Expression Noise

Genetically identical cells exhibit diverse phenotypes even when experiencing the same environment. This phenomenon in part originates from cell-to-cell variability (noise) in protein expression. Although various kinetic schemes of stochastic transcription initiation are known to affect gene expression noise, how posttranscription initiation events contribute to noise at the protein level remains incompletely understood. To address this question, we developed a stochastic simulation-based model of bacterial gene expression that integrates well-known dependencies between transcription initiation, transcription elongation dynamics, mRNA degradation, and translation. We identified realistic conditions under which mRNA lifetime and transcriptional pauses modulate the protein expression noise initially introduced by the promoter architecture. For instance, we found that the short lifetime of bacterial mRNAs facilitates the production of protein bursts. Conversely, RNA polymerase (RNAP) pausing at specific sites during transcription elongation can attenuate protein bursts by fluidizing the RNAP traffic to the point of erasing the effect of a bursty promoter. Pause-prone sites, if located close to the promoter, can also affect noise indirectly by reducing both transcription and translation initiation due to RNAP and ribosome congestion. Our findings highlight how the interplay between transcription initiation, transcription elongation, translation, and mRNA degradation shapes the distribution in protein numbers. They also have implications for our understanding of gene evolution and suggest combinatorial strategies for modulating phenotypic variability by genetic engineering.

Control of Hox transcription factor concentration and cell-to-cell variability by an auto-regulatory switch

The variability in transcription factor concentration among cells is an important developmental determinant, yet how variability is controlled remains poorly understood. Studies of variability have focused predominantly on monitoring mRNA production noise. Little information exists about transcription factor protein variability, as this requires the use of quantitative methods with single-molecule sensitivity. Using Fluorescence Correlation Spectroscopy (FCS), we have characterized the concentration and variability of 14 endogenously tagged TFs in live Drosophila imaginal discs. For the Hox TF Antennapedia, we investigated whether protein variability results from random stochastic events or is developmentally regulated. We found that Antennapedia transitioned from low concentration/high variability early, to high concentration/low variability later, in development. FCS and temporally resolved genetic studies uncovered that Antennapedia itself is necessary and sufficient to drive a developmental regulatory switch from auto-activation to auto-repression, thereby reducing variability. This switch is controlled by progressive changes in relative concentrations of preferentially activating and repressing Antennapedia isoforms, which bind chromatin with different affinities. Mathematical modeling demonstrated that the experimentally supported auto-regulatory circuit can explain the increase of Antennapedia concentration and suppression of variability over time.

Summary: Preferentially repressing and activating isoforms of the Hox transcription factor Antennapedia elicit a developmental regulatory switch from auto-activation to auto-repression that increases concentration and suppresses cell-to-cell variability over time.

A Genetic Circuit Compiler: Generating Combinatorial Genetic Circuits with Web Semantics and Inference

A central strategy of synthetic biology is to understand the basic processes of living creatures through engineering organisms using the same building blocks. Biological machines described in terms of parts can be studied by computer simulation in any of several languages or robotically assembled in vitro. In this paper we present a language, the Genetic Circuit Description Language (GCDL) and a compiler, the Genetic Circuit Compiler (GCC). This language describes genetic circuits at a level of granularity appropriate both for automated assembly in the laboratory and deriving simulation code. The GCDL follows Semantic Web practice, and the compiler makes novel use of the logical inference facilities that are therefore available. We present the GCDL and compiler structure as a study of a tool for generating κ-language simulations from semantic descriptions of genetic circuits.

Added value of autoregulation and multi-step kinetics of transcription initiation

Bacterial gene expression regulation occurs mostly during transcription, which has two main rate-limiting steps: the close complex formation, when the RNA polymerase binds to an active promoter, and the subsequent open complex formation, after which it follows elongation. Tuning these steps' kinetics by the action of e.g. transcription factors, allows for a wide diversity of dynamics. For example, adding autoregulation generates single-gene circuits able to perform more complex tasks. Using stochastic models of transcription kinetics with empirically validated parameter values, we investigate how autoregulation and the multi-step transcription initiation kinetics of single-gene autoregulated circuits can be combined to fine-tune steady state mean and cell-to-cell variability in protein expression levels, as well as response times. Next, we investigate how they can be jointly tuned to control complex behaviours, namely, time counting, switching dynamics and memory storage. Overall, our finding suggests that, in bacteria, jointly regulating a single-gene circuit's topology and the transcription initiation multi-step dynamics allows enhancing complex task performance.

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.

Dynamic interplay between enhancer-promoter topology and gene activity

A long-standing question in gene regulation is how remote enhancers communicate with their target promoters, and specifically how chromatin topology dynamically relates to gene activation. Here, we combine genome editing and multi-color live imaging to simultaneously visualize physical enhancer-promoter interaction and transcription at the single-cell level in Drosophila embryos. By examining transcriptional activation of a reporter by the endogenous even-skipped enhancers, which are located 150 kb away, we identify three distinct topological conformation states and measure their transition kinetics. We show that sustained proximity of the enhancer to its target is required for activation. Transcription in turn affects the three-dimensional topology as it enhances the temporal stability of the proximal conformation and is associated with further spatial compaction. Furthermore, the facilitated long-range activation results in transcriptional competition at the locus, causing corresponding developmental defects. Our approach offers quantitative insight into the spatial and temporal determinants of long-range gene regulation and their implications for cellular fates.

Bursting onto the scene? Exploring stochastic mRNA production in bacteria

Recent large-scale measurements of gene expression variability (or noise) in E. coli have led to the unexpected conclusion that the variability is in large part dictated by and increasing with the mean level of expression. Here we review the evidence for this apparent universal trend in variability, as well as for the related idea that transcription is fundamentally bursty. We examine recently proposed mechanisms for burstiness and universality and argue that they do not explain important features of observed data. Finally, we discuss potential limitations and pitfalls in the interpretation of experimental measurements of cell-to-cell variability.

Stochastic models of gene transcription with upstream drives: exact solution and sample path characterization

Gene transcription is a highly stochastic and dynamic process. As a result, the mRNA copy number of a given gene is heterogeneous both between cells and across time. We present a framework to model gene transcription in populations of cells with time-varying (stochastic or deterministic) transcription and degradation rates. Such rates can be understood as upstream cellular drives representing the effect of different aspects of the cellular environment. We show that the full solution of the master equation contains two components: a model-specific, upstream effective drive, which encapsulates the effect of cellular drives (e.g. entrainment, periodicity or promoter randomness) and a downstream transcriptional Poissonian part, which is common to all models. Our analytical framework treats cell-to-cell and dynamic variability consistently, unifying several approaches in the literature. We apply the obtained solution to characterize different models of experimental relevance, and to explain the influence on gene transcription of synchrony, stationarity, ergodicity, as well as the effect of time scales and other dynamic characteristics of drives. We also show how the solution can be applied to the analysis of noise sources in single-cell data, and to reduce the computational cost of stochastic simulations.

The free-energy cost of interaction between DNA loops

From the viewpoint of thermodynamics, the formation of DNA loops and the interaction between them, which are all non-equilibrium processes, result in the change of free energy, affecting gene expression and further cell-to-cell variability as observed experimentally. However, how these processes dissipate free energy remains largely unclear. Here, by analyzing a mechanic model that maps three fundamental topologies of two interacting DNA loops into a 4-state model of gene transcription, we first show that a longer DNA loop needs more mean free energy consumption. Then, independent of the type of interacting two DNA loops (nested, side-by-side or alternating), the promotion between them always consumes less mean free energy whereas the suppression dissipates more mean free energy. More interestingly, we find that in contrast to the mechanism of direct looping between promoter and enhancer, the facilitated-tracking mechanism dissipates less mean free energy but enhances the mean mRNA expression, justifying the facilitated-tracking hypothesis, a long-standing debate in biology. Based on minimal energy principle, we thus speculate that organisms would utilize the mechanisms of loop-loop promotion and facilitated tracking to survive in complex environments. Our studies provide insights into the understanding of gene expression regulation mechanism from the view of energy consumption.

Stochastic gene expression conditioned on large deviations

The intrinsic stochasticity of gene expression can give rise to large fluctuations and rare events that drive phenotypic variation in a population of genetically identical cells. Characterizing the fluctuations that give rise to such rare events motivates the analysis of large deviations in stochastic models of gene expression. Recent developments in non-equilibrium statistical mechanics have led to a framework for analyzing Markovian processes conditioned on rare events and for representing such processes by conditioning-free driven Markovian processes. We use this framework, in combination with approaches based on queueing theory, to analyze a general class of stochastic models of gene expression. Modeling gene expression as a Batch Markovian Arrival Process (BMAP), we derive exact analytical results quantifying large deviations of time-integrated random variables such as promoter activity fluctuations. We find that the conditioning-free driven process can also be represented by a BMAP that has the same form as the original process, but with renormalized parameters. The results obtained can be used to quantify the likelihood of large deviations, to characterize system fluctuations conditional on rare events and to identify combinations of model parameters that can give rise to dynamical phase transitions in system dynamics.