General properties of transcriptional time series in Escherichia coli

Growth phase-dependent ribonucleic acid production dynamics

Transcriptional events play a crucial role in major cellular processes that specify the activity of an individual cells and influences cell population behavior in response to environment. Active (ON) and an inactive (OFF) states controls the transcriptional burst. Yet, the mechanism and kinetics of ON/OFF-state across the different growth phases of Escherichia coli remains elusive. Here, we have used a single mRNA detection method in live-cells to comprehend the ON/OFF mechanism of the first transcriptional (TF) and consecutive events (TC) controlled by lactose promoters, Plac and Plac/ara1. We determined that the duration of TF ON/OFF has different modes, exhibiting a close to inverse behavior to that of TC ON/OFF. Dynamics of ON/OFF states in fast and slow-dividing cells were affected by the promoter region during the initiation of transcription. Period of TF ON-state defines the behavior of TC by altering the number and the frequency of mRNAs formed. Furthermore, we have shown that delayed OFF-time in TF affects the dynamics of TC in both states, which is mainly determined by the upstream promoter region. Furthermore, using elongation arrest experiments, we independently validate that mRNA noise in TC is governed by the delayed OFF-period in TF. We have identified the position of the regulatory regions that plays a crucial role in noise (Fano) modulation. Taken together, our results suggest that the dynamics of the first transcriptional event, TF, pre-defines the diversity of the population.

What can we learn when fitting a simple telegraph model to a complex gene expression model?

In experiments, the distributions of mRNA or protein numbers in single cells are often fitted to the random telegraph model which includes synthesis and decay of mRNA or protein, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by crucial biological mechanisms such as feedback regulation, non-exponential gene inactivation durations, and multiple gene activation pathways. Here we investigate the dynamical properties of four relatively complex gene expression models by fitting their steady-state mRNA or protein number distributions to the simple telegraph model. We show that despite the underlying complex biological mechanisms, the telegraph model with three effective parameters can accurately capture the steady-state gene product distributions, as well as the conditional distributions in the active gene state, of the complex models. Some effective parameters are reliable and can reflect realistic dynamic behaviors of the complex models, while others may deviate significantly from their real values in the complex models. The effective parameters can also be applied to characterize the capability for a complex model to exhibit multimodality. Using additional information such as single-cell data at multiple time points, we provide an effective method of distinguishing the complex models from the telegraph model. Furthermore, using measurements under varying experimental conditions, we show that fitting the mRNA or protein number distributions to the telegraph model may even reveal the underlying gene regulation mechanisms of the complex models. The effectiveness of these methods is confirmed by analysis of single-cell data for E. coli and mammalian cells. All these results are robust with respect to cooperative transcriptional regulation and extrinsic noise. In particular, we find that faster relaxation speed to the steady state results in more precise parameter inference under large extrinsic noise.

Using steady-state formula to estimate time-dependent parameters of stochastic gene transcription models

When studying stochastic gene transcription, it is important to understand how system parameters are temporally modulated in response to varying environments. Experimentally, the dynamic distribution data of RNA copy numbers measured at multiple time points are often fitted to stochastic transcription models to estimate time-dependent parameters. However, current methods require determining which parameters are time-dependent, as well as their analytical formulas, before the optimal fit. In this study, we developed a method to estimate time-dependent parameters in a classical two-state model without prior assumptions regarding the system parameters. At each measured time point, the method fitted the dynamic distribution data using a steady-state distribution formula, in which the estimated constant parameters were approximated as time-dependent parameter values at the measured time point. The accuracy of this method can be guaranteed for RNA molecules with relatively high degradation rates and genes with relatively slow responses to induction. We quantify the accuracy of the method and implemented this method on two sets of dynamic distribution data from prokaryotic and eukaryotic cells, and revealed the temporal modulation of transcription burst size in response to environmental changes.

Poisson representation: a bridge between discrete and continuous models of stochastic gene regulatory networks

Stochastic gene expression dynamics can be modelled either discretely or continuously. Previous studies have shown that the mRNA or protein number distributions of some simple discrete and continuous gene expression models are related by Gardiner's Poisson representation. Here, we systematically investigate the Poisson representation in complex stochastic gene regulatory networks. We show that when the gene of interest is unregulated, the discrete and continuous descriptions of stochastic gene expression are always related by the Poisson representation, no matter how complex the model is. This generalizes the results obtained in Dattani & Barahona (Dattani & Barahona 2017 J. R. Soc. Interface 14, 20160833 (doi:10.1098/rsif.2016.0833)). In addition, using a simple counter-example, we find that the Poisson representation in general fails to link the two descriptions when the gene is regulated. However, for a general stochastic gene regulatory network, we demonstrate that the discrete and continuous models are approximately related by the Poisson representation in the limit of large protein numbers. These theoretical results are further applied to analytically solve many complex gene expression models whose exact distributions are previously unknown.

DNA supercoiling in bacteria: state of play and challenges from a viewpoint of physics based modeling

DNA supercoiling is central to many fundamental processes of living organisms. Its average level along the chromosome and over time reflects the dynamic equilibrium of opposite activities of topoisomerases, which are required to relax mechanical stresses that are inevitably produced during DNA replication and gene transcription. Supercoiling affects all scales of the spatio-temporal organization of bacterial DNA, from the base pair to the large scale chromosome conformation. Highlighted in vitro and in vivo in the 1960s and 1970s, respectively, the first physical models were proposed concomitantly in order to predict the deformation properties of the double helix. About fifteen years later, polymer physics models demonstrated on larger scales the plectonemic nature and the tree-like organization of supercoiled DNA. Since then, many works have tried to establish a better understanding of the multiple structuring and physiological properties of bacterial DNA in thermodynamic equilibrium and far from equilibrium. The purpose of this essay is to address upcoming challenges by thoroughly exploring the relevance, predictive capacity, and limitations of current physical models, with a specific focus on structural properties beyond the scale of the double helix. We discuss more particularly the problem of DNA conformations, the interplay between DNA supercoiling with gene transcription and DNA replication, its role on nucleoid formation and, finally, the problem of scaling up models. Our primary objective is to foster increased collaboration between physicists and biologists. To achieve this, we have reduced the respective jargon to a minimum and we provide some explanatory background material for the two communities.

Assessing in vivo the impact of gene context on transcription through DNA supercoiling

Gene context can have significant impact on gene expression but is currently not integrated in quantitative models of gene regulation despite known biophysical principles and quantitative in vitro measurements. Conceptually, the simplest gene context consists of a single gene framed by two topological barriers, known as the twin transcriptional-loop model, which illustrates the interplay between transcription and DNA supercoiling. In vivo, DNA supercoiling is additionally modulated by topoisomerases, whose modus operandi remains to be quantified. Here, we bridge the gap between theory and in vivo properties by realizing in Escherichia coli the twin transcriptional-loop model and by measuring how gene expression varies with promoters and distances to the topological barriers. We find that gene expression depends on the distance to the upstream barrier but not to the downstream barrier, with a promoter-dependent intensity. We rationalize these findings with a first-principle biophysical model of DNA transcription. Our results are explained if TopoI and gyrase both act specifically, respectively upstream and downstream of the gene, with antagonistic effects of TopoI, which can repress initiation while facilitating elongation. Altogether, our work sets the foundations for a systematic and quantitative description of the impact of gene context on gene regulation.

Uncovering the effect of RNA polymerase steric interactions on gene expression noise: Analytical distributions of nascent and mature RNA numbers

The telegraph model is the standard model of stochastic gene expression, which can be solved exactly to obtain the distribution of mature RNA numbers per cell. A modification of this model also leads to an analytical distribution of nascent RNA numbers. These solutions are routinely used for the analysis of single-cell data, including the inference of transcriptional parameters. However, these models neglect important mechanistic features of transcription elongation, such as the stochastic movement of RNA polymerases and their steric (excluded-volume) interactions. Here we construct a model of gene expression describing promoter switching between inactive and active states, binding of RNA polymerases in the active state, their stochastic movement including steric interactions along the gene, and their unbinding leading to a mature transcript that subsequently decays. We derive the steady-state distributions of the nascent and mature RNA numbers in two important limiting cases: constitutive expression and slow promoter switching. We show that RNA fluctuations are suppressed by steric interactions between RNA polymerases, and that this suppression can in some instances even lead to sub-Poissonian fluctuations; these effects are most pronounced for nascent RNA and less prominent for mature RNA, since the latter is not a direct sensor of transcription. We find a relationship between the parameters of our microscopic mechanistic model and those of the standard models that ensures excellent consistency in their prediction of the first and second RNA number moments over vast regions of parameter space, encompassing slow, intermediate, and rapid promoter switching, provided the RNA number distributions are Poissonian or super-Poissonian. Furthermore, we identify the limitations of inference from mature RNA data, specifically showing that it cannot differentiate between highly distinct RNA polymerase traffic patterns on a gene.

Monte Carlo samplers for efficient network inference

Accessing information on an underlying network driving a biological process often involves interrupting the process and collecting snapshot data. When snapshot data are stochastic, the data's structure necessitates a probabilistic description to infer underlying reaction networks. As an example, we may imagine wanting to learn gene state networks from the type of data collected in single molecule RNA fluorescence in situ hybridization (RNA-FISH). In the networks we consider, nodes represent network states, and edges represent biochemical reaction rates linking states. Simultaneously estimating the number of nodes and constituent parameters from snapshot data remains a challenging task in part on account of data uncertainty and timescale separations between kinetic parameters mediating the network. While parametric Bayesian methods learn parameters given a network structure (with known node numbers) with rigorously propagated measurement uncertainty, learning the number of nodes and parameters with potentially large timescale separations remain open questions. Here, we propose a Bayesian nonparametric framework and describe a hybrid Bayesian Markov Chain Monte Carlo (MCMC) sampler directly addressing these challenges. In particular, in our hybrid method, Hamiltonian Monte Carlo (HMC) leverages local posterior geometries in inference to explore the parameter space; Adaptive Metropolis Hastings (AMH) learns correlations between plausible parameter sets to efficiently propose probable models; and Parallel Tempering takes into account multiple models simultaneously with tempered information content to augment sampling efficiency. We apply our method to synthetic data mimicking single molecule RNA-FISH, a popular snapshot method in probing transcriptional networks to illustrate the identified challenges inherent to learning dynamical models from these snapshots and how our method addresses them.

Nearly maximal information gain due to time integration in central dogma reactions

Living cells process information about their environment through the central dogma processes of transcription and translation, which drive the cellular response to stimuli. Here, we study the transfer of information from environmental input to the transcript and protein expression levels. Evaluation of both experimental and analogous simulation data reveals that transcription and translation are not two simple information channels connected in series. Instead, we demonstrate that the central dogma reactions often create a time-integrating information channel, where the translation channel receives and integrates multiple outputs from the transcription channel. This information channel model of the central dogma provides new information-theoretic selection criteria for the central dogma rate constants. Using the data for four well-studied species we show that their central dogma rate constants achieve information gain because of time integration while also keeping the loss because of stochasticity in translation relatively low (<0.5 bits).

Understanding spatiotemporal coupling of gene expression using single molecule RNA imaging technologies

Across all kingdoms of life, gene regulatory mechanisms underlie cellular adaptation to ever-changing environments. Regulation of gene expression adjusts protein synthesis and, in turn, cellular growth. Messenger RNAs are key molecules in the process of gene expression. Our ability to quantitatively measure mRNA expression in single cells has improved tremendously over the past decades. This revealed an unexpected coordination between the steps that control the life of an mRNA, from transcription to degradation. Here, we provide an overview of the state-of-the-art imaging approaches for measurement and quantitative understanding of gene expression, starting from the early visualizations of single genes by electron microscopy to current fluorescence-based approaches in single cells, including live-cell RNA-imaging approaches to FISH-based spatial transcriptomics across model organisms. We also highlight how these methods have shaped our current understanding of the spatiotemporal coupling between transcriptional and post-transcriptional events in prokaryotes. We conclude by discussing future challenges of this multidisciplinary field.Abbreviations: mRNA: messenger RNA; rRNA: ribosomal rDNA; tRNA: transfer RNA; sRNA: small RNA; FISH: fluorescence in situ hybridization; RNP: ribonucleoprotein; smFISH: single RNA molecule FISH; smiFISH: single molecule inexpensive FISH; HCR-FISH: Hybridization Chain-Reaction-FISH; RCA: Rolling Circle Amplification; seqFISH: Sequential FISH; MERFISH: Multiplexed error robust FISH; UTR: Untranslated region; RBP: RNA binding protein; FP: fluorescent protein; eGFP: enhanced GFP, MCP: MS2 coat protein; PCP: PP7 coat protein; MB: Molecular beacons; sgRNA: single guide RNA.

Imaging biofilms using fluorescence in situ hybridization: seeing is believing

Biofilms are complex structures with an intricate relationship between the resident microorganisms, the extracellular matrix, and the surrounding environment. Interest in biofilms is growing exponentially given its ubiquity in so diverse fields such as healthcare, environmental and industry. Molecular techniques (e.g., next-generation sequencing, RNA-seq) have been used to study biofilm properties. However, these techniques disrupt the spatial structure of biofilms; therefore, they do not allow to observe the location/position of biofilm components (e.g., cells, genes, metabolites), which is particularly relevant to explore and study the interactions and functions of microorganisms. Fluorescence in situ hybridization (FISH) has been arguably the most widely used method for an in situ analysis of spatial distribution of biofilms. In this review, an overview on different FISH variants already applied on biofilm studies (e.g., CLASI-FISH, BONCAT-FISH, HiPR-FISH, seq-FISH) will be explored. In combination with confocal laser scanning microscopy, these variants emerged as a powerful approach to visualize, quantify and locate microorganisms, genes, and metabolites inside biofilms. Finally, we discuss new possible research directions for the development of robust and accurate FISH-based approaches that will allow to dig deeper into the biofilm structure and function.

The minimal intrinsic stochasticity of constitutively expressed eukaryotic genes is sub-Poissonian

Stochastic variation in gene products ("noise") is an inescapable by-product of gene expression. Noise must be minimized to allow for the reliable execution of cellular functions. However, noise cannot be suppressed beyond an intrinsic lower limit. For constitutively expressed genes, this limit is believed to be Poissonian, meaning that the variance in mRNA numbers cannot be lower than their mean. Here, we show that several cell division genes in fission yeast have mRNA variances significantly below this limit, which cannot be explained by the classical gene expression model for low-noise genes. Our analysis reveals that multiple steps in both transcription and mRNA degradation are essential to explain this sub-Poissonian variance. The sub-Poissonian regime differs qualitatively from previously characterized noise regimes, a hallmark being that cytoplasmic noise is reduced when the mRNA export rate increases. Our study re-defines the lower limit of eukaryotic gene expression noise and identifies molecular requirements for ultra-low noise which are expected to support essential cell functions.

Gene expression model inference from snapshot RNA data using Bayesian non-parametrics

Gene expression models, which are key towards understanding cellular regulatory response, underlie observations of single-cell transcriptional dynamics. Although RNA expression data encode information on gene expression models, existing computational frameworks do not perform simultaneous Bayesian inference of gene expression models and parameters from such data. Rather, gene expression models-composed of gene states, their connectivities and associated parameters-are currently deduced by pre-specifying gene state numbers and connectivity before learning associated rate parameters. Here we propose a method to learn full distributions over gene states, state connectivities and associated rate parameters, simultaneously and self-consistently from single-molecule RNA counts. We propagate noise from fluctuating RNA counts over models by treating models themselves as random variables. We achieve this within a Bayesian non-parametric paradigm. We demonstrate our method on the Escherichia coli lacZ pathway and the Saccharomyces cerevisiae STL1 pathway, and verify its robustness on synthetic data.

"Student-led workshop strengthens perceived discussion skills and community in an interdisciplinary graduate program"

The Integrated Graduate Program in Physical and Engineering Biology (IGPPEB) at Yale University brings together Ph.D. students from the physical, engineering, and biological sciences. The main goals of this program are for students to become comfortable working in an interdisciplinary and collaborative research environment and adept at communicating with scientists and nonscientists. To fill a student-identified learning gap in engaging in inclusive discussions, IGPPEB students developed a communication workshop to improve skills in visual engagement, citing specific content, constructive conversation entrances, and encouragement of peers. Based on short- and long-term assessment of the workshop, 100% of students reported that it should be offered to future cohorts and 63% of students perceived it to be personally helpful. Additionally, 92% of participants reported using one or more of the core skills beyond the course, with skills in "Encouraging peers" and "Constructive conversation entrances" rated the highest in perceived improvement. Based on the highest average rating of 76 ± 24 (on a scale of 0-100), students agreed that the workshop made them feel more welcome in the IGPPEB community. With a rating of 68 ± 13, they also agreed that the workshop had a positive impact on their graduate school experience. Participants provided suggestions for future improvements, such as increasing student involvement in leading discussions of course material. This study demonstrates that a student-led workshop can improve perceived discussion skills and build community across an interdisciplinary program in the sciences.

STREAMING-Tag System: Technology to Enable Visualization of Transcriptional Activity and Subnuclear Localization of Specific Endogenous Genes

The Spliced TetO REpeAt, MS2 repeat, and INtein sandwiched reporter Gene tag (STREAMING-tag) system enables imaging of nuclear localization as well as the transcription activity of a specific endogenous gene at sub-100-nm resolution in living cells. The use of this system combined with imaging of epigenome states enables a detailed analysis of the impact of epigenome status on transcriptional dynamics. In this chapter, we describe a method for quantifying distances between Nanog gene and clusters of cofactor BRD4 using the STREAMING-tag system in mouse embryonic stem cells.

Concordance of MERFISH spatial transcriptomics with bulk and single-cell RNA sequencing

Spatial transcriptomics extends single-cell RNA sequencing (scRNA-seq) by providing spatial context for cell type identification and analysis. Imaging-based spatial technologies such as multiplexed error-robust fluorescence in situ hybridization (MERFISH) can achieve single-cell resolution, directly mapping single-cell identities to spatial positions. MERFISH produces a different data type than scRNA-seq, and a technical comparison between the two modalities is necessary to ascertain how to best integrate them. We performed MERFISH on the mouse liver and kidney and compared the resulting bulk and single-cell RNA statistics with those from the Tabula Muris Senis cell atlas and from two Visium datasets. MERFISH quantitatively reproduced the bulk RNA-seq and scRNA-seq results with improvements in overall dropout rates and sensitivity. Finally, we found that MERFISH independently resolved distinct cell types and spatial structure in both the liver and kidney. Computational integration with the Tabula Muris Senis atlas did not enhance these results. We conclude that MERFISH provides a quantitatively comparable method for single-cell gene expression and can identify cell types without the need for computational integration with scRNA-seq atlases.

Collective polymerase dynamics emerge from DNA supercoiling during transcription

All biological processes ultimately come from physical interactions. The mechanical properties of DNA play a critical role in transcription. RNA polymerase can over or under twist DNA (referred to as DNA supercoiling) when it moves along a gene, resulting in mechanical stresses in DNA that impact its own motion and that of other polymerases. For example, when enough supercoiling accumulates, an isolated polymerase halts, and transcription stops. DNA supercoiling can also mediate nonlocal interactions between polymerases that shape gene expression fluctuations. Here, we construct a comprehensive model of transcription that captures how RNA polymerase motion changes the degree of DNA supercoiling, which in turn feeds back into the rate at which polymerases are recruited and move along the DNA. Surprisingly, our model predicts that a group of three or more polymerases move together at a constant velocity and sustain their motion (forming what we call a polymeton), whereas one or two polymerases would have halted. We further show that accounting for the impact of DNA supercoiling on both RNA polymerase recruitment and velocity recapitulates empirical observations of gene expression fluctuations. Finally, we propose a mechanical toggle switch whereby interactions between genes are mediated by DNA twisting as opposed to proteins. Understanding the mechanical regulation of gene expression provides new insights into how endogenous genes can interact and informs the design of new forms of engineered interactions.

Molecular Origins of Transcriptional Heterogeneity in Diazotrophic Klebsiella oxytoca

Phenotypic heterogeneity in clonal bacterial batch cultures has been shown for a range of bacterial systems; however, the molecular origins of such heterogeneity and its magnitude are not well understood. Under conditions of extreme low-nitrogen stress in the model diazotroph Klebsiella oxytoca, we found remarkably high heterogeneity of nifHDK gene expression, which codes for the structural genes of nitrogenase, one key enzyme of the global nitrogen cycle. This heterogeneity limited the bulk observed nitrogen-fixing capacity of the population. Using dual-probe, single-cell RNA fluorescent in situ hybridization, we correlated nifHDK expression with that of nifLA and glnK-amtB, which code for the main upstream regulatory components. Through stochastic transcription models and mutual information analysis, we revealed likely molecular origins for heterogeneity in nitrogenase expression. In the wild type and regulatory variants, we found that nifHDK transcription was inherently bursty, but we established that noise propagation through signaling was also significant. The regulatory gene glnK had the highest discernible effect on nifHDK variance, while noise from factors outside the regulatory pathway were negligible. Understanding the basis of inherent heterogeneity of nitrogenase expression and its origins can inform biotechnology strategies seeking to enhance biological nitrogen fixation. Finally, we speculate on potential benefits of diazotrophic heterogeneity in natural soil environments. IMPORTANCE Nitrogen is an essential micronutrient for both plant and animal life and naturally exists in both reactive and inert chemical forms. Modern agriculture is heavily reliant on nitrogen that has been "fixed" into a reactive form via the energetically expensive Haber-Bosch process, with significant environmental consequences. Nitrogen-fixing bacteria provide an alternative source of fixed nitrogen for use in both biotechnological and agricultural settings, but this relies on a firm understanding of how the fixation process is regulated within individual bacterial cells. We examined the cell-to-cell variability in the nitrogen-fixing behavior of Klebsiella oxytoca, a free-living bacterium. The significance of our research is in identifying not only the presence of marked variability but also the specific mechanisms that give rise to it. This understanding gives insight into both the evolutionary advantages of variable behavior as well as strategies for biotechnological applications.

RNase HI Depletion Strongly Potentiates Cell Killing by Rifampicin in Mycobacteria

Multidrug-resistant (MDR) tuberculosis (TB) is defined by the resistance of Mycobacterium tuberculosis, the causative organism, to the first-line antibiotics rifampicin and isoniazid. Mitigating or reversing resistance to these drugs offers a means of preserving and extending their use in TB treatment. R-loops are RNA/DNA hybrids that are formed in the genome during transcription, and they can be lethal to the cell if not resolved. RNase HI is an enzyme that removes R-loops, and this activity is essential in M. tuberculosis: knockouts of rnhC, the gene encoding RNase HI, are nonviable. This essentiality makes it a candidate target for the development of new antibiotics. In the model organism Mycolicibacterium smegmatis, RNase HI activity is provided by two enzymes, RnhA and RnhC. We show that the partial depletion of RNase HI activity in M. smegmatis, by knocking out either of the genes encoding RnhA or RnhC, led to the accumulation of R-loops. The sensitivity of the knockout strains to the antibiotics moxifloxacin, streptomycin, and rifampicin was increased, the latter by a striking near 100-fold. We also show that R-loop accumulation accompanies partial transcriptional inhibition, suggesting a mechanistic basis for the synergy between RNase HI depletion and rifampicin. A model of how transcriptional inhibition can potentiate R-loop accumulation is presented. Finally, we identified four small molecules that inhibit recombinant RnhC activity and that also potentiated rifampicin activity in whole-cell assays against M. tuberculosis, supporting an on-target mode of action and providing the first step in developing a new class of antimycobacterial drug.

A spatially resolved stochastic model reveals the role of supercoiling in transcription regulation

In Escherichia coli, translocation of RNA polymerase (RNAP) during transcription introduces supercoiling to DNA, which influences the initiation and elongation behaviors of RNAP. To quantify the role of supercoiling in transcription regulation, we developed a spatially resolved supercoiling model of transcription. The integrated model describes how RNAP activity feeds back with the local DNA supercoiling and how this mechanochemical feedback controls transcription, subject to topoisomerase activities and stochastic topological domain formation. This model establishes that transcription-induced supercoiling mediates the cooperation of co-transcribing RNAP molecules in highly expressed genes, and this cooperation is achieved under moderate supercoiling diffusion and high topoisomerase unbinding rates. It predicts that a topological domain could serve as a transcription regulator, generating substantial transcriptional noise. It also shows the relative orientation of two closely arranged genes plays an important role in regulating their transcription. The model provides a quantitative platform for investigating how genome organization impacts transcription.

Genetic, physiological, and cellular heterogeneities of bacterial pathogens in food matrices: Consequences for food safety

In complex food systems, bacteria live in heterogeneous microstructures, and the population displays phenotypic heterogeneities at the single-cell level. This review provides an overview of spatiotemporal drivers of phenotypic heterogeneity of bacterial pathogens in food matrices at three levels. The first level is the genotypic heterogeneity due to the possibility for various strains of a given species to contaminate food, each of them having specific genetic features. Then, physiological heterogeneities are induced within the same strain, due to specific microenvironments and heterogeneous adaptative responses to the food microstructure. The third level of phenotypic heterogeneity is related to cellular heterogeneity of the same strain in a specific microenvironment. Finally, we consider how these phenotypic heterogeneities at the single-cell level could be implemented in mathematical models to predict bacterial behavior and help ensure microbiological food safety.

Cohesin couples transcriptional bursting probabilities of inducible enhancers and promoters

Innate immune responses rely on inducible gene expression programmes which, in contrast to steady-state transcription, are highly dependent on cohesin. Here we address transcriptional parameters underlying this cohesin-dependence by single-molecule RNA-FISH and single-cell RNA-sequencing. We show that inducible innate immune genes are regulated predominantly by an increase in the probability of active transcription, and that probabilities of enhancer and promoter transcription are coordinated. Cohesin has no major impact on the fraction of transcribed inducible enhancers, or the number of mature mRNAs produced per transcribing cell. Cohesin is, however, required for coupling the probabilities of enhancer and promoter transcription. Enhancer-promoter coupling may not be explained by spatial proximity alone, and at the model locus Il12b can be disrupted by selective inhibition of the cohesinopathy-associated BET bromodomain BD2. Our data identify discrete steps in enhancer-mediated inducible gene expression that differ in cohesin-dependence, and suggest that cohesin and BD2 may act on shared pathways.

The role of Nucleic Acid Mimics (NAMs) on FISH-based techniques and applications for microbial detection

Fluorescent in situ hybridization (FISH) is a powerful tool that for more than 30 years has allowed to detect and quantify microorganisms as well as to study their spatial distribution in three-dimensional structured environments such as biofilms. Throughout these years, FISH has been improved in order to face some of its earlier limitations and to adapt to new research objectives. One of these improvements is related to the emergence of Nucleic Acid Mimics (NAMs), which are now employed as alternatives to the DNA and RNA probes that have been classically used in FISH. NAMs such as peptide and locked nucleic acids (PNA and LNA) have provided enhanced sensitivity and specificity to the FISH technique, as well as higher flexibility in terms of applications. In this review, we aim to cover the state-of-the-art of the different NAMs and explore their possible applications in FISH, providing a general overview of the technique advancement in the last decades.

Diversity of bacterial small RNAs drives competitive strategies for a mutual chaperone

Hundreds of bacterial small RNAs (sRNAs) require the Hfq chaperone to regulate mRNA expression. Hfq is limiting, thus competition among sRNAs for binding to Hfq shapes the proteomes of individual cells. To understand how sRNAs compete for a common partner, we present a single-molecule fluorescence platform to simultaneously visualize binding and release of multiple sRNAs with Hfq. We show that RNA residents rarely dissociate on their own. Instead, clashes between residents and challengers on the same face of Hfq cause rapid exchange, whereas RNAs that recognize different surfaces may cohabit Hfq for several minutes before one RNA departs. The prevalence of these pathways depends on the structure of each RNA and how it interacts with Hfq. We propose that sRNA diversity creates many pairwise interactions with Hfq that allow for distinct biological outcomes: active exchange favors fast regulation whereas co-residence of dissimilar RNAs favors target co-recognition or target exclusion.

Riboswitch-inspired toehold riboregulators for gene regulation in Escherichia coli

Regulatory RNA molecules have been widely investigated as components for synthetic gene circuits, complementing the use of protein-based transcription factors. Among the potential advantages of RNA-based gene regulators are their comparatively simple design, sequence-programmability, orthogonality, and their relatively low metabolic burden. In this work, we developed a set of riboswitch-inspired riboregulators in Escherichia coli that combine the concept of toehold-mediated strand displacement (TMSD) with the switching principles of naturally occurring transcriptional and translational riboswitches. Specifically, for translational activation and repression, we sequestered anti-anti-RBS or anti-RBS sequences, respectively, inside the loop of a stable hairpin domain, which is equipped with a single-stranded toehold region at its 5' end and is followed by regulated sequences on its 3' side. A trigger RNA binding to the toehold region can invade the hairpin, inducing a structural rearrangement that results in translational activation or deactivation. We also demonstrate that TMSD can be applied in the context of transcriptional regulation by switching RNA secondary structure involved in Rho-dependent termination. Our designs expand the repertoire of available synthetic riboregulators by a set of RNA switches with no sequence limitation, which should prove useful for the development of robust genetic sensors and circuits.

Double-edged role of resource competition in gene expression noise and control

Despite extensive investigation demonstrating that resource competition can significantly alter the deterministic behaviors of synthetic gene circuits, it remains unclear how resource competition contributes to the gene expression noise and how this noise can be controlled. Utilizing a two-gene circuit as a prototypical system, we uncover a surprising double-edged role of resource competition in gene expression noise: competition decreases noise through introducing a resource constraint but generates its own type of noise which we name as "resource competitive noise." Utilization of orthogonal resources enables retainment of the noise reduction conferred by resource constraint while removing the added resource competitive noise. The noise reduction effects are studied using three negative feedback types: negatively competitive regulation (NCR), local, and global controllers, each having four placement architectures in the protein biosynthesis pathway (mRNA or protein inhibition on transcription or translation). Our results show that both local and NCR controllers with mRNA-mediated inhibition are efficacious at reducing noise, with NCR controllers demonstrating a superior noise-reduction capability. We also find that combining feedback controllers with orthogonal resources can improve the local controllers. This work provides deep insights into the origin of stochasticity in gene circuits with resource competition and guidance for developing effective noise control strategies.

Inference on the structure of gene regulatory networks

In this paper, we conduct theoretical analyses on inferring the structure of gene regulatory networks. Depending on the experimental method and data type, the inference problem is classified into 20 different scenarios. For each scenario, we discuss the problem that with enough data, under what assumptions, what can be inferred about the structure. For scenarios that have been covered in the literature, we provide a brief review. For scenarios that have not been covered in literature, if the structure can be inferred, we propose new mathematical inference methods and evaluate them on simulated data. Otherwise, we prove that the structure cannot be inferred.

Scalable inference of transcriptional kinetic parameters from MS2 time series data

MOTIVATION

The MS2-MCP (MS2 coat protein) live imaging system allows for visualization of transcription dynamics through the introduction of hairpin stem-loop sequences into a gene. A fluorescent signal at the site of nascent transcription in the nucleus quantifies mRNA production. Computational modelling can be used to infer the promoter states along with the kinetic parameters governing transcription, such as promoter switching frequency and polymerase loading rate. However, modelling of the fluorescent trace presents a challenge due its persistence; the observed fluorescence at a given time point depends on both current and previous promoter states. A compound state Hidden Markov Model (cpHMM) was recently introduced to allow inference of promoter activity from MS2-MCP data. However, the computational time for inference scales exponentially with gene length and the cpHMM is therefore not currently practical for application to many eukaryotic genes.

RESULTS

We present a scalable implementation of the cpHMM for fast inference of promoter activity and transcriptional kinetic parameters. This new method can model genes of arbitrary length through the use of a time-adaptive truncated compound state space. The truncated state space provides a good approximation to the full state space by retaining the most likely set of states at each time during the forward pass of the algorithm. Testing on MS2-MCP fluorescent data collected from early Drosophila melanogaster embryos indicates that the method provides accurate inference of kinetic parameters within a computationally feasible timeframe. The inferred promoter traces generated by the model can also be used to infer single-cell transcriptional parameters.

AVAILABILITY AND IMPLEMENTATION

Python implementation is available at https://github.com/ManchesterBioinference/burstInfer, along with code to reproduce the examples presented here.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Kinetic characteristics of transcriptional bursting in a complex gene model with cyclic promoter structure

While transcription often occurs in a bursty manner, various possible regulations can lead to complex promoter patterns such as promoter cycles, giving rise to an important question: How do promoter kinetics shape transcriptional bursting kinetics? Here we introduce and analyze a general model of the promoter cycle consisting of multi-OFF states and multi-ON states, focusing on the effects of multi-ON mechanisms on transcriptional bursting kinetics. The derived analytical results indicate that burst size follows a mixed geometric distribution rather than a single geometric distribution assumed in previous studies, and ON and OFF times obey their own mixed exponential distributions. In addition, we find that the multi-ON mechanism can lead to bimodal burst-size distribution, antagonistic timing of ON and OFF, and diverse burst frequencies, each further contributing to cell-to-cell variability in the mRNA expression level. These results not only reveal essential features of transcriptional bursting kinetics patterns shaped by multi-state mechanisms but also can be used to the inferences of transcriptional bursting kinetics and promoter structure based on experimental data.

A Novel Approach for Calculating Exact Forms of mRNA Distribution in Single-Cell Measurements

Gene transcription is a stochastic process manifested by fluctuations in mRNA copy numbers in individual isogenic cells. Together with mathematical models of stochastic transcription, the massive mRNA distribution data that can be used to quantify fluctuations in mRNA levels can be fitted by Pm(t), which is the probability of producing m mRNA molecules at time t in a single cell. Tremendous efforts have been made to derive analytical forms of Pm(t), which rely on solving infinite arrays of the master equations of models. However, current approaches focus on the steady-state (t→∞) or require several parameters to be zero or infinity. Here, we present an approach for calculating Pm(t) with time, where all parameters are positive and finite. Our approach was successfully implemented for the classical two-state model and the widely used three-state model and may be further developed for different models with constant kinetic rates of transcription. Furthermore, the direct computations of Pm(t) for the two-state model and three-state model showed that the different regulations of gene activation can generate discriminated dynamical bimodal features of mRNA distribution under the same kinetic rates and similar steady-state mRNA distribution.

Heterogeneity is not always a source of noise: Stochastic gene expression in regulatory heterozygote

Zygosity of diploid genome (i.e., degree to which two parental alleles of a gene have varied genetic sequences) adds another dimension to stochastic gene expression. The allelic imbalance in chromatin accessibility or divergence in regulatory sequences leads to fitness effects but the quantitative aspects thereof are largely left unexplored. We investigate diploid gene expression systems with homozygous (the same) and heterozygous (varied) combination of alleles in cis-regulatory sequences, not in structural gene loci, and characterize the zygosity-associated stochastic fluctuations in protein abundance. An emerging feat of heterozygosity is its counterintuitive capacity for genetic noise control. Especially when the noise is dominantly contributed to by the fluctuations in duty cycle ("reliability") rather than in process speed ("productivity") of gene expression machinery, its interallelic discrepancy acts to reduce the gene expression noise. These findings offer a novel insight into the rich repertoire of balancing selection enriched in the regulatory elements of immune response genes.

Optimizing the hybridization chain reaction-fluorescence in situ hybridization (HCR-FISH) protocol for detection of microbes in sediments

Fluorescence in situ hybridization (FISH) is a canonical tool commonly used in environmental microbiology research to visualize targeted cells. However, the problems of low signal intensity and false-positive signals impede its widespread application. Alternatively, the signal intensity can be amplified by incorporating Hybridization Chain Reaction (HCR) with FISH, while the specificity can be improved through protocol modification and proper counterstaining. Here we optimized the HCR-FISH protocol for studying microbes in environmental samples, particularly marine sediments. Firstly, five sets of HCR initiator/amplifier pairs were tested on the laboratory-cultured bacterium Escherichia coli and the archaeon Methanococcoides methylutens, and two sets displayed high hybridization efficiency and specificity. Secondly, we tried to find the best combination of sample pretreatment methods and HCR-FISH protocol for environmental sample analysis with the aim of producing less false positive signals. Various detachment methods, extraction methods and formulas of hybridization buffer were tested using sediment samples. Thirdly, an image processing method was developed to enhance the DAPI signal of microbial cells against that of abiotic particles, providing a reliable reference for FISH imaging. In summary, our optimized HCR-FISH protocol showed promise to serve as an addendum to traditional FISH for research on environmental microbes.

Supplementary Information

The online version contains supplementary material available at 10.1007/s42995-021-00098-8.

Cis-Regulatory Logic Produces Gene-Expression Noise Describing Phenotypic Heterogeneity in Bacteria

Gene transcriptional process is random. It occurs in bursts and follows single-molecular kinetics. Intermittent bursts are measured based on their frequency and size. They influence temporal fluctuations in the abundance of total mRNA and proteins by generating distinct transcriptional variations referred to as “noise”. Noisy expression induces uncertainty because the association between transcriptional variation and the extent of gene expression fluctuation is ambiguous. The promoter architecture and remote interference of different cis-regulatory elements are the crucial determinants of noise, which is reflected in phenotypic heterogeneity. An alternative perspective considers that cellular parameters dictating genome-wide transcriptional kinetics follow a universal pattern. Research on noise and systematic perturbations of promoter sequences reinforces that both gene-specific and genome-wide regulation occur across species ranging from bacteria and yeast to animal cells. Thus, deciphering gene-expression noise is essential across different genomics applications. Amidst the mounting conflict, it is imperative to reconsider the scope, progression, and rational construction of diversified viewpoints underlying the origin of the noise. Here, we have established an indication connecting noise, gene expression variations, and bacterial phenotypic variability. This review will enhance the understanding of gene-expression noise in various scientific contexts and applications.

Pathway dynamics can delineate the sources of transcriptional noise in gene expression

Single-cell expression profiling opens up new vistas on cellular processes. Extensive cell-to-cell variability at the transcriptomic and proteomic level has been one of the stand-out observations. Because most experimental analyses are destructive we only have access to snapshot data of cellular states. This loss of temporal information presents significant challenges for inferring dynamics, as well as causes of cell-to-cell variability. In particular, we typically cannot separate dynamic variability from within cells ('intrinsic noise') from variability across the population ('extrinsic noise'). Here, we make this non-identifiability mathematically precise, allowing us to identify new experimental set-ups that can assist in resolving this non-identifiability. We show that multiple generic reporters from the same biochemical pathways (e.g. mRNA and protein) can infer magnitudes of intrinsic and extrinsic transcriptional noise, identifying sources of heterogeneity. Stochastic simulations support our theory, and demonstrate that 'pathway-reporters' compare favourably to the well-known, but often difficult to implement, dual-reporter method.

Understanding the molecular mechanisms of transcriptional bursting

In recent years, it has been experimentally established that transcription, a fundamental biological process that involves the synthesis of messenger RNA molecules from DNA templates, does not proceed continuously as was expected. Rather, it exhibits a distinct dynamic behavior of alternating between productive phases when RNA molecules are actively synthesized and inactive phases when there is no RNA production at all. The bimodal transcriptional dynamics is now confirmed to be present in most living systems. This phenomenon is known as transcriptional bursting and it attracts significant amounts of attention from researchers in different fields. However, despite multiple experimental and theoretical investigations, the microscopic origin and biological functions of the transcriptional bursting remain unclear. Here we discuss the recent developments in uncovering the underlying molecular mechanisms of transcriptional bursting and our current understanding of them. Our analysis presents a physicochemical view of the processes that govern transcriptional bursting in living cells.

Approximating gene transcription dynamics using steady-state formulas

Understanding how genes in a single cell respond to dynamically changing signals has been a central question in stochastic gene transcription research. Recent studies have generated massive steady-state or snapshot mRNA distribution data of individual cells, and inferred a large spectrum of kinetic transcription parameters under varying conditions. However, there have been few algorithms to convert these static data into the temporal variation of kinetic rates. Real-time imaging has been developed to monitor stochastic transcription processes at the single-cell level, but the immense technicality has prevented its application to most endogenous loci in mammalian cells. In this article, we introduced a stochastic gene transcription model with variable kinetic rates induced by unstable cellular conditions. We approximated the transcription dynamics using easily obtained steady-state formulas in the model. We tested the approximation against experimental data in both prokaryotic and eukaryotic cells and further solidified the conditions that guarantee the robustness of the method. The method can be easily implemented to provide convenient tools for quantifying dynamic kinetics and mechanisms underlying the widespread static transcription data, and may shed a light on circumventing the limitation of current bursting data on transcriptional real-time imaging.

Spatial transcriptomics of planktonic and sessile bacterial populations at single-cell resolution

Capturing the heterogeneous phenotypes of microbial populations at relevant spatiotemporal scales is highly challenging. Here, we present par-seqFISH (parallel sequential fluorescence in situ hybridization), a transcriptome-imaging approach that records gene expression and spatial context within microscale assemblies at a single-cell and molecule resolution. We applied this approach to the opportunistic pathogen Pseudomonas aeruginosa, analyzing about 600,000 individuals across dozens of conditions in planktonic and biofilm cultures. We identified numerous metabolic- and virulence-related transcriptional states that emerged dynamically during planktonic growth, as well as highly spatially resolved metabolic heterogeneity in sessile populations. Our data reveal that distinct physiological states can coexist within the same biofilm just several micrometers away, underscoring the importance of the microenvironment. Our results illustrate the complex dynamics of microbial populations and present a new way of studying them at high resolution.

RNA imaging in bacteria

The spatiotemporal regulation of gene expression plays an essential role in many biological processes. Recently, several imaging-based RNA labeling and detection methods, both in fixed and live cells, were developed and now enable the study of transcript abundance, localization and dynamics. Here, we review the main single-cell techniques for RNA visualization with fluorescence microscopy and describe their applications in bacteria.

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.

TNF stimulation primarily modulates transcriptional burst size of NF-κB-regulated genes

Cell-to-cell heterogeneity is a feature of the tumor necrosis factor (TNF)-stimulated inflammatory response mediated by the transcription factor NF-κB, motivating an exploration of the underlying sources of this noise. Here, we combined single-transcript measurements with computational models to study transcriptional noise at six NF-κB-regulated inflammatory genes. In the basal state, NF-κB-target genes displayed an inverse correlation between mean and noise characteristic of transcriptional bursting. By analyzing transcript distributions with a bursting model, we found that TNF primarily activated transcription by increasing burst size while maintaining burst frequency for gene promoters with relatively high basal histone 3 acetylation (AcH3) that marks open chromatin environments. For promoters with lower basal AcH3 or when AcH3 was decreased with a small molecule drug, the contribution of burst frequency to TNF activation increased. Finally, we used a mathematical model to show that TNF positive feedback amplified gene expression noise resulting from burst size-mediated transcription, leading to a subset of cells with high TNF protein expression. Our results reveal potential sources of noise underlying intercellular heterogeneity in the TNF-mediated inflammatory response.

Intracellular mRNA transport and localized translation

Fine-tuning cellular physiology in response to intracellular and environmental cues requires precise temporal and spatial control of gene expression. High-resolution imaging technologies to detect mRNAs and their translation state have revealed that all living organisms localize mRNAs in subcellular compartments and create translation hotspots, enabling cells to tune gene expression locally. Therefore, mRNA localization is a conserved and integral part of gene expression regulation from prokaryotic to eukaryotic cells. In this Review, we discuss the mechanisms of mRNA transport and local mRNA translation across the kingdoms of life and at organellar, subcellular and multicellular resolution. We also discuss the properties of messenger ribonucleoprotein and higher order RNA granules and how they may influence mRNA transport and local protein synthesis. Finally, we summarize the technological developments that allow us to study mRNA localization and local translation through the simultaneous detection of mRNAs and proteins in single cells, mRNA and nascent protein single-molecule imaging, and bulk RNA and protein detection methods.

Altering transcription factor binding reveals comprehensive transcriptional kinetics of a basic gene

Transcription is a vital process activated by transcription factor (TF) binding. The active gene releases a burst of transcripts before turning inactive again. While the basic course of transcription is well understood, it is unclear how binding of a TF affects the frequency, duration and size of a transcriptional burst. We systematically varied the residence time and concentration of a synthetic TF and characterized the transcription of a synthetic reporter gene by combining single molecule imaging, single molecule RNA-FISH, live transcript visualisation and analysis with a novel algorithm, Burst Inference from mRNA Distributions (BIRD). For this well-defined system, we found that TF binding solely affected burst frequency and variations in TF residence time had a stronger influence than variations in concentration. This enabled us to device a model of gene transcription, in which TF binding triggers multiple successive steps before the gene transits to the active state and actual mRNA synthesis is decoupled from TF presence. We quantified all transition times of the TF and the gene, including the TF search time and the delay between TF binding and the onset of transcription. Our quantitative measurements and analysis revealed detailed kinetic insight, which may serve as basis for a bottom-up understanding of gene regulation.

Visualization of Gene Reciprocity among Lactic Acid Bacteria in Yogurt by RNase H-Assisted Rolling Circle Amplification-Fluorescence In Situ Hybridization

Recently, we developed an in situ mRNA detection method termed RNase H-assisted rolling circle amplification-fluorescence in situ hybridization (RHa-RCA-FISH), which can detect even short mRNA in a bacterial cell. However, because this FISH method is sensitive to the sample condition, it is necessary to find a suitable cell permeabilization and collection protocol. Here, we demonstrate its further applicability for detecting intrinsic mRNA expression using lactic acid bacteria (LAB) as a model consortium. Our results show that this method can visualize functional gene expression in LAB cells and can be used for monitoring the temporal transition of gene expression. In addition, we also confirmed that data obtained from bulk analyses such as RNA-seq or microarray do not always correspond to gene expression in individual cells. RHa-RCA-FISH will be a powerful tool to compensate for insufficient data from metatranscriptome analyses while clarifying the carriers of function in microbial consortia. By extending this technique to capture spatiotemporal microbial gene expression at the single-cell level, it will be able to characterize microbial interactions in phytoplankton-bacteria interactions.

Comparison of bias and resolvability in single-cell and single-transcript methods

Single-cell and single-transcript measurement methods have elevated our ability to understand and engineer biological systems. However, defining and comparing performance between methods remains a challenge, in part due to the confounding effects of experimental variability. Here, we propose a generalizable framework for performing multiple methods in parallel using split samples, so that experimental variability is shared between methods. We demonstrate the utility of this framework by performing 12 different methods in parallel to measure the same underlying reference system for cellular response. We compare method performance using quantitative evaluations of bias and resolvability. We attribute differences in method performance to steps along the measurement process such as sample preparation, signal detection, and choice of measurand. Finally, we demonstrate how this framework can be used to benchmark different methods for single-transcript detection. The framework we present here provides a practical way to compare performance of any methods.

Correlation between external regulators governs the mean-noise relationship in stochastic gene expression

Gene transcription in single cells is inherently a probabilistic process. The relationship between variance ($ \sigma^{2} $) and mean expression ($ \mu $) is of paramount importance for investigations into the evolutionary origins and consequences of noise in gene expression. It is often formulated as $ \log \left({{{\sigma}^{2}}}/{{{\mu}^{2}}}\; \right) = \beta\log\mu+\log\alpha $, where $ \beta $ is a key parameter since its sign determines the qualitative dependence of noise on mean. We reveal that the sign of $ \beta $ is controlled completely by external regulation, but independent of promoter structure. Specifically, it is negative if regulators as stochastic variables are independent but positive if they are correlated. The essential mechanism revealed here can well interpret diverse experimental phenomena underlying expression noise. Our results imply that external regulation rather than promoter sequence governs the mean-noise relationship.

Neural network aided approximation and parameter inference of non-Markovian models of gene expression

Non-Markovian models of stochastic biochemical kinetics often incorporate explicit time delays to effectively model large numbers of intermediate biochemical processes. Analysis and simulation of these models, as well as the inference of their parameters from data, are fraught with difficulties because the dynamics depends on the system's history. Here we use an artificial neural network to approximate the time-dependent distributions of non-Markovian models by the solutions of much simpler time-inhomogeneous Markovian models; the approximation does not increase the dimensionality of the model and simultaneously leads to inference of the kinetic parameters. The training of the neural network uses a relatively small set of noisy measurements generated by experimental data or stochastic simulations of the non-Markovian model. We show using a variety of models, where the delays stem from transcriptional processes and feedback control, that the Markovian models learnt by the neural network accurately reflect the stochastic dynamics across parameter space.

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.

Long-Range Supercoiling-Mediated RNA Polymerase Cooperation in Transcription

It is widely believed that DNA supercoiling plays an important role in the regulation of transcriptional dynamics. Recent studies show that it could affect transcription not only through the buildup and relaxation of torsional strain on DNA strands but also via effective long-range supercoiling-mediated interactions between RNA polymerase (RNAP) molecules. Here, we present a theoretical study that quantitatively analyzes the effect of long-range RNAP cooperation in transcription dynamics. Our minimal chemical-kinetic model assumes that one or two RNAP molecules can simultaneously participate in the transcription, and it takes into account their binding to and dissociation from DNA. It also explicitly accounts for competition between the supercoiling buildup that reduces the RNA elongation speed and gyrase binding that rescues the RNA synthesis. The full analytical solution of the model accompanied by Monte Carlo computer simulations predicts that the system should exhibit transcriptional bursting dynamics, in agreement with experimental observations. The analysis also revealed that when there are two polymerases participating in the elongation rather than one, the transcription process becomes much more efficient since the level of stochastic noise decreases while more RNA transcripts are produced. Our theoretical investigation clarifies molecular aspects of the supercoiling-mediated RNAP cooperativity during transcription.

Single-cell measurement of plasmid copy number and promoter activity

Accurate measurements of promoter activities are crucial for predictably building genetic systems. Here we report a method to simultaneously count plasmid DNA, RNA transcripts, and protein expression in single living bacteria. From these data, the activity of a promoter in units of RNAP/s can be inferred. This work facilitates the reporting of promoters in absolute units, the variability in their activity across a population, and their quantitative toll on cellular resources, all of which provide critical insights for cellular engineering.