Dynamics of transcription driven by the tetA promoter, one event at a time, in live Escherichia coli cells

Transcription Attenuation in Synthetic Promoters in Nonoverlapping Tandem Formation

Closely spaced promoters are ubiquitous in prokaryotic and eukaryotic genomes. How their structure and dynamics relate remains unclear, particularly for tandem formations. To study their transcriptional interference, we engineered two pairs and one trio of synthetic promoters in nonoverlapping, tandem formation, in single-copy plasmids transformed into Escherichia coli cells. From in vivo measurements, we found that these promoters in tandem formation can have attenuated transcription rates. The attenuation strength can be widely fine-tuned by the promoters' positioning, natural regulatory mechanisms, and other factors, including the antibiotic rifampicin, which is known to hamper RNAP promoter escape. From this, and supported by in silico models, we concluded that the attenuation in these constructs emerges from premature terminations generated by collisions between RNAPs elongating from upstream promoters and RNAPs occupying downstream promoters. Moreover, we found that these collisions can cause one or both RNAPs to falloff. Finally, the broad spectrum of possible, externally regulated, attenuation strengths observed in our synthetic tandem promoters suggests that they could become useful as externally controllable regulators of future synthetic circuits.

Analysis of a detailed multi-stage model of stochastic gene expression using queueing theory and model reduction

We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA into protein. The processes in sub-cellular compartments are described by an arbitrary number of processing stages, thus accounting for a significantly finer molecular description of gene expression than conventional models such as the telegraph, two-stage and three-stage models of gene expression. We use two distinct tools, queueing theory and model reduction using the slow-scale linear-noise approximation, to derive exact or approximate analytic expressions for the moments or distributions of nuclear mRNA, cytoplasmic mRNA and protein fluctuations, as well as lower bounds for their Fano factors in steady-state conditions. We use these to study the phase diagram of the stochastic model; in particular we derive parametric conditions determining three types of transitions in the properties of mRNA fluctuations: from sub-Poissonian to super-Poissonian noise, from high noise in the nucleus to high noise in the cytoplasm, and from a monotonic increase to a monotonic decrease of the Fano factor with the number of processing stages. In contrast, protein fluctuations are always super-Poissonian and show weak dependence on the number of mRNA processing stages. Our results delineate the region of parameter space where conventional models give qualitatively incorrect results and provide insight into how the number of processing stages, e.g. the number of rate-limiting steps in initiation, splicing and mRNA degradation, shape stochastic gene expression by modulation of molecular memory.

Solving stochastic gene-expression models using queueing theory: A tutorial review

Stochastic models of gene expression are typically formulated using the chemical master equation, which can be solved exactly or approximately using a repertoire of analytical methods. Here, we provide a tutorial review of an alternative approach based on queueing theory that has rarely been used in the literature of gene expression. We discuss the interpretation of six types of infinite-server queues from the angle of stochastic single-cell biology and provide analytical expressions for the stationary and nonstationary distributions and/or moments of mRNA/protein numbers and bounds on the Fano factor. This approach may enable the solution of complex models that have hitherto evaded analytical solution.

Dynamical model of antibiotic responses linking expression of resistance genes to metabolism explains emergence of heterogeneity during drug exposures

Antibiotic responses in bacteria are highly dynamic and heterogeneous, with sudden exposure of bacterial colonies to high drug doses resulting in the coexistence of recovered and arrested cells. The dynamics of the response is determined by regulatory circuits controlling the expression of resistance genes, which are in turn modulated by the drug's action on cell growth and metabolism. Despite advances in understanding gene regulation at the molecular level, we still lack a framework to describe how feedback mechanisms resulting from the interdependence between expression of resistance and cell metabolism can amplify naturally occurring noise and create heterogeneity at the population level. To understand how this interplay affects cell survival upon exposure, we constructed a mathematical model of the dynamics of antibiotic responses that links metabolism and regulation of gene expression, based on the tetracycline resistancetetoperon inE. coli. We use this model to interpret measurements of growth and expression of resistance in microfluidic experiments, both in single cells and in biofilms. We also implemented a stochastic model of the drug response, to show that exposure to high drug levels results in large variations of recovery times and heterogeneity at the population level. We show that stochasticity is important to determine how nutrient quality affects cell survival during exposure to high drug concentrations. A quantitative description of how microbes respond to antibiotics in dynamical environments is crucial to understand population-level behaviors such as biofilms and pathogenesis.

Dynamical model of antibiotic responses linking expression of resistance to metabolism explains emergence of heterogeneity during drug exposures

Antibiotic responses in bacteria are highly dynamic and heterogeneous, with sudden exposure of bacterial colonies to high drug doses resulting in the coexistence of recovered and arrested cells. The dynamics of the response is determined by regulatory circuits controlling the expression of resistance genes, which are in turn modulated by the drug's action on cell growth and metabolism. Despite advances in understanding gene regulation at the molecular level, we still lack a framework to describe how feedback mechanisms resulting from the interdependence between expression of resistance and cell metabolism can amplify naturally occurring noise and create heterogeneity at the population level. To understand how this interplay affects cell survival upon exposure, we constructed a mathematical model of the dynamics of antibiotic responses that links metabolism and regulation of gene expression, based on the tetracycline resistance tet operon in E. coli. We use this model to interpret measurements of growth and expression of resistance in microfluidic experiments, both in single cells and in biofilms. We also implemented a stochastic model of the drug response, to show that exposure to high drug levels results in large variations of recovery times and heterogeneity at the population level. We show that stochasticity is important to determine how nutrient quality affects cell survival during exposure to high drug concentrations. A quantitative description of how microbes respond to antibiotics in dynamical environments is crucial to understand population-level behaviors such as biofilms and pathogenesis.

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

Gene expression inherently gives rise to stochastic variation ("noise") in the production of gene products. Minimizing noise is crucial for ensuring reliable cellular functions. However, noise cannot be suppressed below a certain intrinsic limit. For constitutively expressed genes, this limit is typically assumed to be Poissonian noise, wherein the variance in mRNA numbers is equal to their mean. Here, we demonstrate that several cell division genes in fission yeast exhibit mRNA variances significantly below this limit. The reduced variance can be explained by a gene expression model incorporating multiple transcription and mRNA degradation steps. Notably, in this sub-Poissonian regime, distinct from Poissonian or super-Poissonian regimes, cytoplasmic noise is effectively suppressed through a higher mRNA export rate. Our findings redefine the lower limit of eukaryotic gene expression noise and uncover molecular requirements for achieving ultralow noise, which is expected to be important for vital cellular functions.

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.

Inference and uncertainty quantification of stochastic gene expression via synthetic models

Estimating uncertainty in model predictions is a central task in quantitative biology. Biological models at the single-cell level are intrinsically stochastic and nonlinear, creating formidable challenges for their statistical estimation which inevitably has to rely on approximations that trade accuracy for tractability. Despite intensive interest, a sweet spot in this trade-off has not been found yet. We propose a flexible procedure for uncertainty quantification in a wide class of reaction networks describing stochastic gene expression including those with feedback. The method is based on creating a tractable coarse-graining of the model that is learned from simulations, a synthetic model, to approximate the likelihood function. We demonstrate that synthetic models can substantially outperform state-of-the-art approaches on a number of non-trivial systems and datasets, yielding an accurate and computationally viable solution to uncertainty quantification in stochastic models of gene expression.

Nutrient Gradients Mediate Complex Colony-Level Antibiotic Responses in Structured Microbial Populations

Antibiotic treatments often fail to eliminate bacterial populations due to heterogeneity in how individual cells respond to the drug. In structured bacterial populations such as biofilms, bacterial metabolism and environmental transport processes lead to an emergent phenotypic structure and self-generated nutrient gradients toward the interior of the colony, which can affect cell growth, gene expression and susceptibility to the drug. Even in single cells, survival depends on a dynamic interplay between the drug's action and the expression of resistance genes. How expression of resistance is coordinated across populations in the presence of such spatiotemporal environmental coupling remains elusive. Using a custom microfluidic device, we observe the response of spatially extended microcolonies of tetracycline-resistant E. coli to precisely defined dynamic drug regimens. We find an intricate interplay between drug-induced changes in cell growth and growth-dependent expression of resistance genes, resulting in the redistribution of metabolites and the reorganization of growth patterns. This dynamic environmental feedback affects the regulation of drug resistance differently across the colony, generating dynamic phenotypic structures that maintain colony growth during exposure to high drug concentrations and increase population-level resistance to subsequent exposures. A mathematical model linking metabolism and the regulation of gene expression is able to capture the main features of spatiotemporal colony dynamics. Uncovering the fundamental principles that govern collective mechanisms of antibiotic resistance in spatially extended populations will allow the design of optimal drug regimens to counteract them.

Direct visualisation of drug-efflux in liveEscherichia colicells

Drug-efflux by pump proteins is one of the major mechanisms of antibiotic resistance in bacteria. Here, we use quantitative fluorescence microscopy to investigate the real-time dynamics of drug accumulation and efflux in live E. coli cells. We visualize simultaneously the intrinsically fluorescent protein-synthesis inhibitor tetracycline (Tc) and the fluorescently labelled Tc-specific efflux pump, TetA. We show that Tc penetrates the cells within minutes and accumulates to stable intracellular concentration after ∼20 min. The final level of drug accumulation reflects the balance between Tc-uptake by the cells and Tc-efflux by pump proteins. In wild-type Tc-sensitive cells, drug accumulation is significantly limited by the activity of the multidrug efflux pump, AcrAB-TolC. Tc-resistance wild-type cells carrying a plasmid-borne Tn10 transposon contain variable amounts of TetA protein, produced under steady-state repression by the TetR repressor. TetA content heterogeneity determines the cells’ initial ability to efflux Tc. Yet, efflux remains partial until the synthesis of additional TetA pumps allows for Tc-efflux activity to surpass Tc-uptake. Cells overproducing TetA no longer accumulate Tc and become resistant to high concentrations of the drug. This work uncovers the dynamic balance between drug entry, protein-synthesis inhibition, efflux-pump production, drug-efflux activity and drug-resistance levels.

Transcription closed and open complex formation coordinate expression of genes with a shared promoter region

Many genes are spaced closely, allowing coordination without explicit control through shared regulatory elements and molecular interactions. We study the dynamics of a stochastic model of a gene-pair in a head-to-head configuration, sharing promoter elements, which accounts for the rate-limiting steps in transcription initiation. We find that only in specific regions of the parameter space of the rate-limiting steps is orderly coexpression exhibited, suggesting that successful cooperation between closely spaced genes requires the coevolution of compatible rate-limiting step configuration. The model predictions are validated using in vivo single-cell, single-RNA measurements of the dynamics of pairs of genes sharing promoter elements. Our results suggest that, in E. coli, the kinetics of the rate-limiting steps in active transcription can play a central role in shaping the dynamics of gene-pairs sharing promoter elements.

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

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

A Post-translational Metabolic Switch Enables Complete Decoupling of Bacterial Growth from Biopolymer Production in Engineered Escherichia coli

Most of the current methods for controlling the formation rate of a key protein or enzyme in cell factories rely on the manipulation of target genes within the pathway. In this article, we present a novel synthetic system for post-translational regulation of protein levels, FENIX, which provides both independent control of the steady-state protein level and inducible accumulation of target proteins. The FENIX device is based on the constitutive, proteasome-dependent degradation of the target polypeptide by tagging with a short synthetic, hybrid NIa/SsrA amino acid sequence in the C-terminal domain. Protein production is triggered via addition of an orthogonal inducer ( i.e., 3-methylbenzoate) to the culture medium. The system was benchmarked in Escherichia coli by tagging two fluorescent proteins (GFP and mCherry), and further exploited to completely uncouple poly(3-hydroxybutyrate) (PHB) accumulation from bacterial growth. By tagging PhaA (3-ketoacyl-CoA thiolase, first step of the route), a dynamic metabolic switch at the acetyl-coenzyme A node was established in such a way that this metabolic precursor could be effectively redirected into PHB formation upon activation of the system. The engineered E. coli strain reached a very high specific rate of PHB accumulation (0.4 h^-1) with a polymer content of ca. 72% (w/w) in glucose cultures in a growth-independent mode. Thus, FENIX enables dynamic control of metabolic fluxes in bacterial cell factories by establishing post-translational synthetic switches in the pathway of interest.

Multiscale effects of heating and cooling on genes and gene networks

Fluctuating environments such as changes in ambient temperature represent a fundamental challenge to life. Cells must protect gene networks that protect them from such stresses, making it difficult to understand how temperature affects gene network function in general. Here, we focus on single genes and small synthetic network modules to reveal four key effects of nonoptimal temperatures at different biological scales: (i) a cell fate choice between arrest and resistance, (ii) slower growth rates, (iii) Arrhenius reaction rates, and (iv) protein structure changes. We develop a multiscale computational modeling framework that captures and predicts all of these effects. These findings promote our understanding of how temperature affects living systems and enables more robust cellular engineering for real-world applications.

Most organisms must cope with temperature changes. This involves genes and gene networks both as subjects and agents of cellular protection, creating difficulties in understanding. Here, we study how heating and cooling affect expression of single genes and synthetic gene circuits in Saccharomyces cerevisiae. We discovered that nonoptimal temperatures induce a cell fate choice between stress resistance and growth arrest. This creates dramatic gene expression bimodality in isogenic cell populations, as arrest abolishes gene expression. Multiscale models incorporating population dynamics, temperature-dependent growth rates, and Arrhenius scaling of reaction rates captured the effects of cooling, but not those of heating in resistant cells. Molecular-dynamics simulations revealed how heating alters the conformational dynamics of the TetR repressor, fully explaining the experimental observations. Overall, nonoptimal temperatures induce a cell fate decision and corrupt gene and gene network function in computationally predictable ways, which may aid future applications of engineered microbes in nonstandard temperatures.

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.

Regulatory Dynamics Determine Cell Fate following Abrupt Antibiotic Exposure

Bacterial resistance mechanisms must cope with transient fast-changing conditions. These systems are often repressed in the absence of the drug, and it is unclear how their regulation can provide a quick response when challenged. Here, we focus on the tet operon, which provides resistance to tetracycline through efflux pump TetA. We show that, somewhat counterintuitively, prompt expression of the TetA repressor TetR is key for cellular survival upon abrupt drug exposure. Tracking individual cells upon exposure, we find that differences in the rate of TetR elevation result in three distinct cell fates: recovery (high rate), death due to excess TetA (intermediate rate), and death from the drug (low rate). A surge of TetR expression optimizes the response by allowing sensitive detection of both the initial rise and the later decline of intracellular drug, avoiding an undesirable overshoot in TetA expression. These results show how regulatory circuits of resistance genes have evolved for optimized dynamics.

Illuminating Messengers: An Update and Outlook on RNA Visualization in Bacteria

To be able to visualize the abundance and spatiotemporal features of RNAs in bacterial cells would permit obtaining a pivotal understanding of many mechanisms underlying bacterial cell biology. The first methods that allowed observing single mRNA molecules in individual cells were introduced by Bertrand et al. (1998) and Femino et al. (1998). Since then, a plethora of techniques to image RNA molecules with the aid of fluorescence microscopy has emerged. Many of these approaches are useful for the large eukaryotic cells but their adaptation to study RNA, specifically mRNA molecules, in bacterial cells progressed relatively slow. Here, an overview will be given of fluorescent techniques that can be used to reveal specific RNA molecules inside fixed and living single bacterial cells. It includes a critical evaluation of their caveats as well as potential solutions.

Application of an E. coli signal sequence as a versatile inclusion body tag

Background

Heterologous protein production in Escherichia coli often suffers from bottlenecks such as proteolytic degradation, complex purification procedures and toxicity towards the expression host. Production of proteins in an insoluble form in inclusion bodies (IBs) can alleviate these problems. Unfortunately, the propensity of heterologous proteins to form IBs is variable and difficult to predict. Hence, fusing the target protein to an aggregation prone polypeptide or IB-tag is a useful strategy to produce difficult-to-express proteins in an insoluble form.

Results

When screening for signal sequences that mediate optimal targeting of heterologous proteins to the periplasmic space of E. coli, we observed that fusion to the 39 amino acid signal sequence of E. coli TorA (ssTorA) did not promote targeting but rather directed high-level expression of the human proteins hEGF, Pla2 and IL-3 in IBs. Further analysis revealed that ssTorA even mediated IB formation of the highly soluble endogenous E. coli proteins TrxA and MBP. The ssTorA also induced aggregation when fused to the C-terminus of target proteins and appeared functional as IB-tag in E. coli K-12 as well as B strains. An additive effect on IB-formation was observed upon fusion of multiple ssTorA sequences in tandem, provoking almost complete aggregation of TrxA and MBP. The ssTorA-moiety was successfully used to produce the intrinsically unstable hEGF and the toxic fusion partner SymE, demonstrating its applicability as an IB-tag for difficult-to-express and toxic proteins.

Conclusions

We present proof-of-concept for the use of ssTorA as a small, versatile tag for robust E. coli-based expression of heterologous proteins in IBs.

Electronic supplementary material

The online version of this article (doi:10.1186/s12934-017-0662-4) contains supplementary material, which is available to authorized users.

Precision of Readout at the hunchback Gene: Analyzing Short Transcription Time Traces in Living Fly Embryos

The simultaneous expression of the hunchback gene in the numerous nuclei of the developing fly embryo gives us a unique opportunity to study how transcription is regulated in living organisms. A recently developed MS2-MCP technique for imaging nascent messenger RNA in living Drosophila embryos allows us to quantify the dynamics of the developmental transcription process. The initial measurement of the morphogens by the hunchback promoter takes place during very short cell cycles, not only giving each nucleus little time for a precise readout, but also resulting in short time traces of transcription. Additionally, the relationship between the measured signal and the promoter state depends on the molecular design of the reporting probe. We develop an analysis approach based on tailor made autocorrelation functions that overcomes the short trace problems and quantifies the dynamics of transcription initiation. Based on live imaging data, we identify signatures of bursty transcription initiation from the hunchback promoter. We show that the precision of the expression of the hunchback gene to measure its position along the anterior-posterior axis is low both at the boundary and in the anterior even at cycle 13, suggesting additional post-transcriptional averaging mechanisms to provide the precision observed in fixed embryos.

The fly embryo provides a natural laboratory to study the dynamics of transcription and its implications for the developing organism. Using live imaging experiments we investigate the nature of transcription regulation of the hunchback gene—the first to read out the maternal Bicoid gradient. While traditional time trace analysis methods based on OFF time distributions or autocorrelation functions fail for short signals, our tailored autocorrelation function overcomes these limitations revealing bursty dynamics that is reproducible between cell cycles and embryos. The inferred rates result in a lot of variability in the readout of nuclei sensing similar Bicoid concentrations, suggesting additional readout mechanisms than a one-to-one mapping of the input onto the output.

Temperature-Dependent Model of Multi-step Transcription Initiation in Escherichia coli Based on Live Single-Cell Measurements

Transcription kinetics is limited by its initiation steps, which differ between promoters and with intra- and extracellular conditions. Regulation of these steps allows tuning both the rate and stochasticity of RNA production. We used time-lapse, single-RNA microscopy measurements in live Escherichia coli to study how the rate-limiting steps in initiation of the P_lac/ara-1 promoter change with temperature and induction scheme. For this, we compared detailed stochastic models fit to the empirical data in maximum likelihood sense using statistical methods. Using this analysis, we found that temperature affects the rate limiting steps unequally, as nonlinear changes in the closed complex formation suffice to explain the differences in transcription dynamics between conditions. Meanwhile, a similar analysis of the P_tetA promoter revealed that it has a different rate limiting step configuration, with temperature regulating different steps. Finally, we used the derived models to explore a possible cause for why the identified steps are preferred as the main cause for behavior modifications with temperature: we find that transcription dynamics is either insensitive or responds reciprocally to changes in the other steps. Our results suggests that different promoters employ different rate limiting step patterns that control not only their rate and variability, but also their sensitivity to environmental changes.

Temperature affects the behavior of cells, such as their growth rate. However, it is not well understood how these changes result from the changes at the single molecule level. We observed the production of individual RNA molecules in live cells under a wide range of temperatures. This allowed us to determine not only how fast they are produced, but also how much variability there is in this process. Next, we fit a stochastic model to the data to identify which rate-limiting steps during RNA production are responsible for the observed differences between conditions. We found that genes differ in how their RNA production is limited by different steps and in how these are affected by the temperature, which explains why different genes respond differently to temperature fluctuations.

In silico analysis of division times of Escherichia coli populations as a function of the partitioning scheme of non-functional proteins

Recent evidence suggests that cells employ functionally asymmetric partitioning schemes in division to cope with aging. We explore various schemes in silico, with a stochastic model of Escherichia coli that includes gene expression, non-functional proteins generation, aggregation and polar retention, and molecule partitioning in division. The model is implemented in SGNS2, which allows stochastic, multi-delayed reactions within hierarchical, transient, interlinked compartments. After setting parameter values of non-functional proteins’ generation and effects that reproduce realistic intracellular and population dynamics, we investigate how the spatial organization of non-functional proteins affects mean division times of cell populations in lineages and, thus, mean cell numbers over time. We find that division times decrease for increasingly asymmetric partitioning. Also, increasing the clustering of non-functional proteins decreases division times. Increasing the bias in polar segregation further decreases division times, particularly if the bias favors the older pole and aggregates’ polar retention is robust. Finally, we show that the non-energy consuming retention of inherited non-functional proteins at the older pole via nucleoid occlusion is a source of functional asymmetries and, thus, is advantageous. Our results suggest that the mechanisms of intracellular organization of non-functional proteins, including clustering and polar retention, affect the vitality of E. coli populations.

Dissecting the stochastic transcription initiation process in live Escherichia coli

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

Characterizing rate limiting steps in transcription from RNA production times in live cells

MOTIVATION

Single-molecule measurements of live Escherichia coli transcription dynamics suggest that this process ranges from sub- to super-Poissonian, depending on the conditions and on the promoter. For its accurate quantification, we propose a model that accommodates all these settings, and statistical methods to estimate the model parameters and to select the relevant components.

RESULTS

The new methodology has improved accuracy and avoids overestimating the transcription rate due to finite measurement time, by exploiting unobserved data and by accounting for the effects of discrete sampling. First, we use Monte Carlo simulations of models based on measurements to show that the methods are reliable and offer substantial improvements over previous methods. Next, we apply the methods on measurements of transcription intervals of different promoters in live E. coli, and show that they produce significantly different results, both in low- and high-noise settings, and that, in the latter case, they even lead to qualitatively different results. Finally, we demonstrate that the methods can be generalized for other similar purposes, such as for estimating gene activation kinetics. In this case, the new methods allow quantifying the inducer uptake dynamics as opposed to just comparing them between cases, which was not previously possible. We expect this new methodology to be a valuable tool for functional analysis of cellular processes using single-molecule or single-event microscopy measurements in live cells.

AVAILABILITY AND IMPLEMENTATION

Source code is available under Mozilla Public License at http://www.cs.tut.fi/%7Ehakkin22/censored/

CONTACT

andre.ribeiro@tut.fi or andre.sanchesribeiro@tut.fi

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Phase-dependent dynamics of the lac promoter under nutrient stress

To survive, a bacterial population must sense nutrient availability and adjust its growth phase accordingly. Few studies have quantitatively analyzed the single-cell behavior of stress and growth phase-related transcriptional changes in Escherichia coli. To investigate the dynamic changes in transcription during different growth phases and starvation, we analyzed the single-cell transcriptional dynamics of the E. coli lac promoter. Cells were grown under different starvation conditions, including glucose, magnesium, phosphate and thiamine limitations, and transcription dynamics was quantified using a single RNA detection method at different phases. Differences in gene expression over conditions and phases indicate that stochasticity in transcription dynamics is directly connected to cell phase and availability of nutrients. Except for glucose, the pattern of transcription dynamics under all starvation conditions appears to be similar. Transcriptional bursts were more prominent in lag and stationary phase cells starved for energy sources. Identical behavior was observed in exponential phase cells starved for phosphate and thiamine. Noise measurements under all nutrient exhaustion conditions indicate that intrinsic noise is higher than extrinsic noise. Our results, obtained in a relA1 mutational background, which led to suboptimal production of ppGpp, suggest that the single-cell transcriptional changes we observed were largely ppGpp-independent. Taken together, we propose that, under different starvation conditions, cells are able to decrease the trend in cell-to-cell variability in transcription as a common means of adaptation.

Estimation of kinetic parameters of transcription from temporal single-RNA measurements

Gene expression dynamics in prokaryotes is largely controlled by the multi-step process of transcription initiation whose kinetics is subject to regulation. Since the number and duration of these steps cannot be currently measured in vivo, we propose a novel method for estimating them from time series of RNA numbers in individual cells. We demonstrate the method's applicability on measurements of fluorescence-tagged RNA molecules in Escherichia coli cells, and compare with a previous method. We show that the results of the two methods agree for equal data. We also show that, when incorporating additional data, the new method produces significantly different estimates, which are in closer agreement with qPCR measurements. Unlike the previous method, the new method requires no preprocessing of the RNA numbers, using maximal information from the RNA time series. In addition, it can use data outside of the observed RNA productions. Overall, the new method characterizes the transcription initiation process with enhanced detail.

Kinetics of the cellular intake of a gene expression inducer at high concentrations

From in vivo single-event measurements of the transient and steady-state transcription activity of a single-copy lac-ara-1 promoter in Escherichia coli, we characterize the intake kinetics of its inducer (IPTG) from the media. We show that the empirical data are well-fit by a model of intake assuming a bilayer membrane, with the passage through the second layer being rate-limiting, coupled to a stochastic, sub-Poissonian, multi-step transcription process. Using this model, we show that for a wide range of extracellular inducer levels (up to 1.25 mM) the intake process is diffusive-like, suggesting unsaturated membrane permeability. Inducer molecules travel from the periplasm to the cytoplasm in, on average, 31.7 minutes, strongly affecting cells' response time. The novel methodology followed here should aid the study of cellular intake mechanisms at the single-event level.

Dynamic competition between transcription initiation and repression: Role of nonequilibrium steps in cell-to-cell heterogeneity

Transcriptional repression may cause transcriptional noise by a competition between repressor and RNA polymerase binding. Although promoter activity is often governed by a single limiting step, we argue here that the size of the noise strongly depends on whether this step is the initial equilibrium binding or one of the subsequent unidirectional steps. Overall, we show that nonequilibrium steps of transcription initiation systematically increase the cell-to-cell heterogeneity in bacterial populations. In particular, this allows also weak promoters to give substantial transcriptional noise.

Estimation of GFP-tagged RNA numbers from temporal fluorescence intensity data

MOTIVATION

MS2-GFP-tagging of RNA is currently the only method to measure intervals between consecutive transcription events in live cells. For this, new transcripts must be accurately detected from intensity time traces.

RESULTS

We present a novel method for automatically estimating RNA numbers and production intervals from temporal data of cell fluorescence intensities that reduces uncertainty by exploiting temporal information. We also derive a robust variant, more resistant to outliers caused e.g. by RNAs moving out of focus. Using Monte Carlo simulations, we show that the quantification of RNA numbers and production intervals is generally improved compared with previous methods. Finally, we analyze data from live Escherichia coli and show statistically significant differences to previous methods. The new methods can be used to quantify numbers and production intervals of any fluorescent probes, which are present in low copy numbers, are brighter than the cell background and degrade slowly.

AVAILABILITY

Source code is available under Mozilla Public License at http://www.cs.tut.fi/%7ehakkin22/jumpdet/.

In vivo kinetics of segregation and polar retention of MS2-GFP-RNA complexes in Escherichia coli

The cytoplasm of Escherichia coli is a crowded, heterogeneous environment. From single cell live imaging, we investigated the spatial kinetics and heterogeneities of synthetic RNA-protein complexes. First, although their known tendency to accumulate at the cell poles does not appear to introduce asymmetries between older and newer cell poles within a cell lifetime, these emerge with cell divisions. This suggests strong polar retention of the complexes, which we verified in their history of positions and mean escape time from the poles. Next, we show that the polar retention relies on anisotropies in the displacement distribution in the region between midcell and poles, whereas the speed is homogeneous along the major cell axis. Afterward, we establish that these regions are at the border of the nucleoid and shift outward with cell growth, due to the nucleoid's replication. Overall, the spatiotemporal kinetics of the complexes, which is robust to suboptimal temperatures, suggests that nucleoid occlusion is a source of dynamic heterogeneities of macromolecules in E. coli that ultimately generate phenotypic differences between sister cells.

In vivo transcription kinetics of a synthetic gene uninvolved in stress-response pathways in stressed Escherichia coli cells

The fast adaptation of Escherichia coli to stressful environments includes the regulation of gene expression rates, mainly of transcription, by specific and global stress-response mechanisms. To study the effects of mechanisms acting on a global level, we observed with single molecule sensitivity the effects of mild acidic shift and oxidative stress on the in vivo transcription dynamics of a probe gene encoding an RNA target for MS2d-GFP, under the control of a synthetic promoter. After showing that this promoter is uninvolved in fast stress-response pathways, we compared its kinetics of transcript production under stress and in optimal conditions. We find that, following the application of either stress, the mean rates of transcription activation and of subsequent RNA production of the probe gene are reduced, particularly under oxidative stress. Meanwhile, the noise in RNA production decreases under oxidative stress, but not under acidic shift. From distributions of intervals between consecutive RNA productions, we infer that the number and duration of the rate-limiting steps in transcription initiation change, following the application of stress. These changes differ in the two stress conditions and are consistent with the changes in noise in RNA production. Overall, our measurements of the transcription initiation kinetics of the probe gene indicate that, following sub-lethal stresses, there are stress-specific changes in the dynamics of transcription initiation of the probe gene that affect its mean rate and noise of transcript production. Given the non-involvement of the probe gene in stress-response pathways, we suggest that these changes are caused by global response mechanisms of E. coli to stress.

Formation of DNA:RNA hybrid G-quadruplexes of two G-quartet layers in transcription: expansion of the prevalence and diversity of G-quadruplexes in genomes

G-quadruplexes are implicated in important cellular processes. Previous studies mostly focused on intramolecular G-quadruplexes of three or more G-quartets. Those composed of two G-quartets were only shown to form in single-stranded oligonucleotides. On the basis of electrophoresis, DMS footprinting, fluorescence labeling, and photo-cross-linking, we detected the formation of DNA:RNA hybrid G-quadruplexes (HQs) of two G-quartets during the transcription of DNA duplexes. These HQs have a lifetime on the minute scale and are stabilized by a stabilizing ligand. They are far shorter-lived than the HQs of three G-quartets, which last for hours. The occurrence of putative formation motifs of such HQs shows a transcription-dependent strand-biased selection, thus supporting their formation and function in genomes. They are present in almost all human genes in large amounts. We speculate that the two-G-quartet HQs may be a distinct type of G-quadruplexes that may play a role in timely responsive processes and for purposes of fine-tuning.

Effects of multimerization on the temporal variability of protein complex abundance

We explore whether the process of multimerization can be used as a means to regulate noise in the abundance of functional protein complexes. Additionally, we analyze how this process affects the mean level of these functional units, response time of a gene, and temporal correlation between the numbers of expressed proteins and of the functional multimers. We show that, although multimerization increases noise by reducing the mean number of functional complexes it can reduce noise in comparison with a monomer, when abundance of the functional proteins are comparable. Alternatively, reduction in noise occurs if both monomeric and multimeric forms of the protein are functional. Moreover, we find that multimerization either increases the response time to external signals or decreases the correlation between number of functional complexes and protein production kinetics. Finally, we show that the results are in agreement with recent genome-wide assessments of cell-to-cell variability in protein numbers and of multimerization in essential and non-essential genes in Escherichia coli, and that the effects of multimerization are tangible at the level of genetic circuits.

Bistability in a stochastic RNA-mediated gene network

Small regulatory RNAs (srRNAs) are important regulators of gene expression in eukaryotes and prokaryotes. A common motif containing srRNA is a bistable two-gene motif where one gene codes for a transcription factor (TF) which represses the transcription of the second gene, whose transcript is a srRNA which targets the first gene's transcript. Here, we investigate the properties of this motif in a stochastic model which takes the low copy numbers of the RNA components into account. First, we examine the conditions for stability of the two "noisy attractors." We find that for realistic low copy numbers, extreme, but within realistic intervals, mutual repression strengths are required to compensate for the variability of the RNA numbers and thus, achieve long-term bistability. Second, the promoter initiation kinetics is found to strongly influence the bistability of the switch. Super-Poissonian RNA production disrupts the ability of the srRNA to silence its target, though sub-Poissonian RNA production does not rule out the need for strong mutual repression. Finally, we show that asymmetry between the two interactions forming the switch allows an external input to induce the transition from "high srRNA" to "'high TF" more easily (i.e., with a shorter input) than in the opposite direction. We hypothesize that this asymmetric switching property allows these circuits to be more sensitive to one external input, without sacrificing the stability of one of the noisy attractors.

Effects of rate-limiting steps in transcription initiation on genetic filter motifs

The behavior of genetic motifs is determined not only by the gene-gene interactions, but also by the expression patterns of the constituent genes. Live single-molecule measurements have provided evidence that transcription initiation is a sequential process, whose kinetics plays a key role in the dynamics of mRNA and protein numbers. The extent to which it affects the behavior of cellular motifs is unknown. Here, we examine how the kinetics of transcription initiation affects the behavior of motifs performing filtering in amplitude and frequency domain. We find that the performance of each filter is degraded as transcript levels are lowered. This effect can be reduced by having a transcription process with more steps. In addition, we show that the kinetics of the stepwise transcription initiation process affects features such as filter cutoffs. These results constitute an assessment of the range of behaviors of genetic motifs as a function of the kinetics of transcription initiation, and thus will aid in tuning of synthetic motifs to attain specific characteristics without affecting their protein products.

Kinetics of gene expression in bacteria — From models to measurements, and back again

Dennis Salahub has contributed to several scientific areas. Likely, one of the lesser known contributions is the one on the study of the kinetics of gene expression in prokaryotes, which resulted in a delayed stochastic model of transcription and translation dynamics in bacteria. The model has become the basis for modeling stochastic genetic circuits and has provided a framework for interpreting recent measurements of transcripts production dynamics in live cells, one event at a time. Here, we review the contributions by Salahub and colleagues to the modeling strategies of gene expression as a multi-delayed stochastic process. Next, we describe recent findings, which build upon this work and provide experimental validation of the models. Finally, we discuss potential future developments in this field of research.

In vivo single-molecule kinetics of activation and subsequent activity of the arabinose promoter

Using a single-RNA detection technique in live Escherichia coli cells, we measure, for each cell, the waiting time for the production of the first RNA under the control of P_BAD promoter after induction by arabinose, and subsequent intervals between transcription events. We find that the kinetics of the arabinose intake system affect mean and diversity in RNA numbers, long after induction. We observed the same effect on P_lac/ara-1 promoter, which is inducible by arabinose or by IPTG. Importantly, the distribution of waiting times of P_lac/ara-1 is indistinguishable from that of P_BAD, if and only if induced by arabinose alone. Finally, RNA production under the control of P_BAD is found to be a sub-Poissonian process. We conclude that inducer-dependent waiting times affect mean and cell-to-cell diversity in RNA numbers long after induction, suggesting that intake mechanisms have non-negligible effects on the phenotypic diversity of cell populations in natural, fluctuating environments.

Effects of gene length on the dynamics of gene expression

In Escherichia coli, the nucleotide length of a gene is bound to affect its expression dynamics. From simulations of a stochastic model of gene expression at the nucleotide and codon levels we show that, within realistic parameter values, the nucleotide length affects RNA and protein mean levels, as well as the expected transient time for RNA and protein numbers to change, following a signal. Fluctuations in RNA and protein numbers are found to be minimized for a small range of lengths, which matches the means of the distributions of lengths found in E. coli of both essential and non-essential genes. The variance of the length distribution for essential genes is found to be smaller than for non-essential genes, implying that these distributions are far from random. Finally, gene lengths are shown to affect the kinetics of a genetic switch, namely, the correlation between temporal proteins numbers, the stability of the two noisy attractors of the switch, and how biased is the choice of noisy attractor. The stability increases with gene length due to increased 'memory' about the previous states of the switch. We argue that, by affecting the dynamics of gene expression and of genetic circuits, gene lengths are subject to selection.

SGNS2: a compartmentalized stochastic chemical kinetics simulator for dynamic cell populations

MOTIVATION

Cell growth and division affect the kinetics of internal cellular processes and the phenotype diversity of cell populations. Since the effects are complex, e.g. different cellular components are partitioned differently in cell division, to account for them in silico, one needs to simulate these processes in great detail.

RESULTS

We present SGNS2, a simulator of chemical reaction systems according to the Stochastic Simulation Algorithm with multi-delayed reactions within hierarchical, interlinked compartments which can be created, destroyed and divided at runtime. In division, molecules are randomly segregated into the daughter cells following a specified distribution corresponding to one of several partitioning schemes, applicable on a per-molecule-type basis. We exemplify its use with six models including a stochastic model of the disposal mechanism of unwanted protein aggregates in Escherichia coli, a model of phenotypic diversity in populations with different levels of synchrony, a model of a bacteriophage's infection of a cell population and a model of prokaryotic gene expression at the nucleotide and codon levels.

AVAILABILITY

SGNS2, instructions and examples available at www.cs.tut.fi/~lloydpri/sgns2/ (open source under New BSD license).

CONTACT

jason.lloyd-price@tut.fi.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.