Dissecting the stochastic transcription initiation process in live Escherichia coli

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.

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.

The transcription factor network of E. coli steers global responses to shifts in RNAP concentration

The robustness and sensitivity of gene networks to environmental changes is critical for cell survival. How gene networks produce specific, chronologically ordered responses to genome-wide perturbations, while robustly maintaining homeostasis, remains an open question. We analysed if short- and mid-term genome-wide responses to shifts in RNA polymerase (RNAP) concentration are influenced by the known topology and logic of the transcription factor network (TFN) of Escherichia coli. We found that, at the gene cohort level, the magnitude of the single-gene, mid-term transcriptional responses to changes in RNAP concentration can be explained by the absolute difference between the gene's numbers of activating and repressing input transcription factors (TFs). Interestingly, this difference is strongly positively correlated with the number of input TFs of the gene. Meanwhile, short-term responses showed only weak influence from the TFN. Our results suggest that the global topological traits of the TFN of E. coli shape which gene cohorts respond to genome-wide stresses.

Using average transcription level to understand the regulation of stochastic gene activation

Gene activation is a random process, modelled as a framework of multiple rate-limiting steps listed sequentially, in parallel or in combination. Together with suitably assumed processes of gene inactivation, transcript birth and death, the step numbers and parameters in activation frameworks can be estimated by fitting single-cell transcription data. However, current algorithms require computing master equations that are tightly correlated with prior hypothetical frameworks of gene activation. We found that prior estimation of the framework can be facilitated by the traditional dynamical data of mRNA average level M(t), presenting discriminated dynamical features. Rigorous theory regarding M(t) profiles allows to confidently rule out the frameworks that fail to capture M(t) features and to test potential competent frameworks by fitting M(t) data. We implemented this procedure for a large number of mouse fibroblast genes under tumour necrosis factor induction and determined exactly the 'cross-talking n-state' framework; the cross-talk between the signalling and basal pathways is crucial to trigger the first peak of M(t), while the following damped gentle M(t) oscillation is regulated by the multi-step basal pathway. This framework can be used to fit sophisticated single-cell data and may facilitate a more accurate understanding of stochastic activation of mouse fibroblast genes.

Analytical kinetic model of native tandem promoters in E. coli

Closely spaced promoters in tandem formation are abundant in bacteria. We investigated the evolutionary conservation, biological functions, and the RNA and single-cell protein expression of genes regulated by tandem promoters in E. coli. We also studied the sequence (distance between transcription start sites ‘d_TSS’, pause sequences, and distances from oriC) and potential influence of the input transcription factors of these promoters. From this, we propose an analytical model of gene expression based on measured expression dynamics, where RNAP-promoter occupancy times and d_TSS are the key regulators of transcription interference due to TSS occlusion by RNAP at one of the promoters (when d_TSS ≤ 35 bp) and RNAP occupancy of the downstream promoter (when d_TSS > 35 bp). Occlusion and downstream promoter occupancy are modeled as linear functions of occupancy time, while the influence of d_TSS is implemented by a continuous step function, fit to in vivo data on mean single-cell protein numbers of 30 natural genes controlled by tandem promoters. The best-fitting step is at 35 bp, matching the length of DNA occupied by RNAP in the open complex formation. This model accurately predicts the squared coefficient of variation and skewness of the natural single-cell protein numbers as a function of d_TSS. Additional predictions suggest that promoters in tandem formation can cover a wide range of transcription dynamics within realistic intervals of parameter values. By accurately capturing the dynamics of these promoters, this model can be helpful to predict the dynamics of new promoters and contribute to the expansion of the repertoire of expression dynamics available to synthetic genetic constructs.

Tandem promoters are common in nature, but investigations on their dynamics have so far largely relied on synthetic constructs. Thus, their regulation and potentially unique dynamics remain unexplored. We first performed a comprehensive exploration of the conservation of genes regulated by these promoters in E. coli and the properties of their input transcription factors. We then measured protein and RNA levels expressed by 30 Escherichia coli tandem promoters, to establish an analytical model of the expression dynamics of genes controlled by such promoters. We show that start site occlusion and downstream RNAP occupancy can be realistically captured by a model with RNAP binding affinity, the time length of open complex formation, and the nucleotide distance between transcription start sites. This study contributes to a better understanding of the unique dynamics tandem promoters can bring to the dynamics of gene networks and will assist in their use in synthetic genetic circuits.

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.

Small binding-site clearance delays are not negligible in gene expression modeling

During the templated biopolymerization processes of transcription and translation, a macromolecular machine, either an RNA polymerase or a ribosome, binds to a specific site on the template. Due to the sizes of these enzymes, there is a waiting time before one clears the binding site and another can bind. These clearance delays are relatively short, and one might think that they could be neglected. However, in the case of transcription, these clearance delays are associated with conservation laws, resulting in surprisingly large effects on the bifurcation diagrams in models of gene expression networks. We study an example of this phenomenon in a model of a gene regulated by a non-coding RNA displaying bistability. Neglecting the binding-site clearance delays in this model can only be compensated for by making ad hoc, unphysical adjustments to the model's kinetic constants.

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

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

Dissecting the in vivo dynamics of transcription locking due to positive supercoiling buildup

Positive supercoiling buildup (PSB) is a pervasive phenomenon in the transcriptional programs of Escherichia coli. After finding a range of Gyrase concentrations where the inverse of the transcription rate of a chromosome-integrated gene changes linearly with the inverse of Gyrase concentration, we apply a LineWeaver-Burk plot to dissect the expected in vivo transcription rate in absence of PSB. We validate the estimation by time-lapse microscopy of single-RNA production kinetics of the same gene when single-copy plasmid-borne, shown to be impervious to Gyrase inhibition. Next, we estimate the fraction of time in locked states and number of transcription events prior to locking, which we validate by measurements under Gyrase inhibition. Replacing the gene of interest by one with slower transcription rate decreases the fraction of time in locked states due to PSB. Finally, we combine data from both constructs to infer a range of possible transcription initiation locking kinetics in a chromosomal location, obtainable by tuning the transcription rate. We validate with measurements of transcription activity at different induction levels. This strategy for dissecting transcription initiation locking kinetics due to PSB can contribute to resolve the transcriptional programs of E. coli and in the engineering of synthetic genetic circuits.

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.

Estimating RNA numbers in single cells by RNA fluorescent tagging and flow cytometry

Estimating the statistics of single-cell RNA numbers has become a key source of information on gene expression dynamics. One of the most informative methods of in vivo single-RNA detection is MS2d-GFP tagging. So far, it requires microscopy and laborious semi-manual image analysis, which hampers the amount of collectable data. To overcome this limitation, we present a new methodology for quantifying the mean, standard deviation, and skewness of single-cell distributions of RNA numbers, from flow cytometry data on cells expressing RNA tagged with MS2d-GFP. The quantification method, based on scaling flow-cytometry data from microscopy single-cell data on integer-valued RNA numbers, is shown to readily produce precise, big data on in vivo single-cell distributions of RNA numbers and, thus, can assist in studies of transcription dynamics.

Diversity, versatility and complexity of bacterial gene regulation mechanisms: opportunities and drawbacks for applications in synthetic biology

Gene expression occurs in two essential steps: transcription and translation. In bacteria, the two processes are tightly coupled in time and space, and highly regulated. Tight regulation of gene expression is crucial. It limits wasteful consumption of resources and energy, prevents accumulation of potentially growth inhibiting reaction intermediates, and sustains the fitness and potential virulence of the organism in a fluctuating, competitive and frequently stressful environment. Since the onset of studies on regulation of enzyme synthesis, numerous distinct regulatory mechanisms modulating transcription and/or translation have been discovered. Mostly, various regulatory mechanisms operating at different levels in the flow of genetic information are used in combination to control and modulate the expression of a single gene or operon. Here, we provide an extensive overview of the very diverse and versatile bacterial gene regulatory mechanisms with major emphasis on their combined occurrence, intricate intertwinement and versatility. Furthermore, we discuss the potential of well-characterized basal expression and regulatory elements in synthetic biology applications, where they may ensure orthogonal, predictable and tunable expression of (heterologous) target genes and pathways, aiming at a minimal burden for the host.

Chromosome and plasmid-borne PLacO3O1 promoters differ in sensitivity to critically low temperatures

Temperature shifts trigger genome-wide changes in Escherichia coli's gene expression. We studied if chromosome integration impacts on a gene's sensitivity to these shifts, by comparing the single-RNA production kinetics of a PLacO3O1 promoter, when chromosomally-integrated and when single-copy plasmid-borne. At suboptimal temperatures their induction range, fold change, and response to decreasing temperatures are similar. At critically low temperatures, the chromosome-integrated promoter becomes weaker and noisier. Dissection of its initiation kinetics reveals longer lasting states preceding open complex formation, suggesting enhanced supercoiling buildup. Measurements with Gyrase and Topoisomerase I inhibitors suggest hindrance to escape supercoiling buildup at low temperatures. Consistently, similar phenomena occur in energy-depleted cells by DNP at 30 °C. Transient, critically-low temperatures have no long-term consequences, as raising temperature quickly restores transcription rates. We conclude that the chromosomally-integrated PLacO3O1 has higher sensitivity to low temperatures, due to longer-lasting super-coiled states. A lesser active, chromosome-integrated native lac is shown to be insensitive to Gyrase overexpression, even at critically low temperatures, indicating that the rate of escaping positive supercoiling buildup is temperature and transcription rate dependent. A genome-wide analysis supports this, since cold-shock genes exhibit atypical supercoiling-sensitivities. This phenomenon might partially explain the temperature-sensitivity of some transcriptional programs of E. coli.

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

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

The precision of the symmetry in Z-ring placement in Escherichia coli is hampered at critical temperatures

Cell division in Escherichia coli is morphologically symmetric due to, among other things, the ability of these cells to place the Z-ring at midcell. Studies have reported that, at sub-optimal temperatures, this symmetry decreases at the single-cell level, but the causes remain unclear. Using fluorescence microscopy, we observe FtsZ-GFP and DAPI-stained nucleoids to assess the robustness of the symmetry of Z-ring formation and positioning in individual cells under sub-optimal and critical temperatures. We find the Z-ring formation and positioning to be robust at sub-optimal temperatures, as the Z-ring's mean width, density and displacement from midcell maintain similar levels of correlation to one another as at optimal temperatures. However, at critical temperatures, the Z-ring displacement from midcell is greatly increased. We present evidence showing that this is due to enhanced distance between the replicated nucleoids and, thus, reduced Z-ring density, which explains the weaker precision in setting a morphologically symmetric division site. This also occurs in rich media and is cumulative, i.e. combining richer media and critically high temperatures enhances the asymmetries in division, which is evidence that the causes are biophysical. To further support this, we show that the effects are reversible, i.e. shifting cells from optimal to critical, and then to optimal again, reduces and then enhances the symmetry in Z-ring positioning, respectively, as the width and density of the Z-ring return to normal values. Overall, our findings show that the Z-ring positioning in E. coli is a robust biophysical process under sub-optimal temperatures, and that critical temperatures cause significant asymmetries in division.

Temperature-dependence of the single-cell variability in the kinetics of transcription activation in Escherichia coli

From in vivo single-cell, single-RNA measurements of the activation times and subsequent steady-state active transcription kinetics of a single-copy Lac-ara-1 promoter in Escherichia coli, we characterize the intake kinetics of the inducer (IPTG) from the media, following temperature shifts. For this, for temperature shifts of various degrees, we obtain the distributions of transcription activation times as well as the distributions of intervals between consecutive RNA productions following activation in individual cells. We then propose a novel methodology that makes use of deconvolution techniques to extract the mean and the variability of the distribution of intake times. We find that cells, following shifts to low temperatures, have higher intake times, although, counter-intuitively, the cell-to-cell variability of these times is lower. We validate the results using a new methodology for direct estimation of mean intake times from measurements of activation times at various inducer concentrations. The results confirm that E. coli's inducer intake times from the environment are significantly higher following a shift to a sub-optimal temperature. Finally, we provide evidence that this is likely due to the emergence of additional rate-limiting steps in the intake process at low temperatures, explaining the reduced cell-to-cell variability in intake times.

Rate-limiting steps in transcription dictate sensitivity to variability in cellular components

Cell-to-cell variability in cellular components generates cell-to-cell diversity in RNA and protein production dynamics. As these components are inherited, this should also cause lineage-to-lineage variability in these dynamics. We conjectured that these effects on transcription are promoter initiation kinetics dependent. To test this, first we used stochastic models to predict that variability in the numbers of molecules involved in upstream processes, such as the intake of inducers from the environment, acts only as a transient source of variability in RNA production numbers, while variability in the numbers of a molecular species controlling transcription of an active promoter acts as a constant source. Next, from single-cell, single-RNA level time-lapse microscopy of independent lineages of Escherichia coli cells, we demonstrate the existence of lineage-to-lineage variability in gene activation times and mean RNA production rates, and that these variabilities differ between promoters and inducers used. Finally, we provide evidence that this can be explained by differences in the kinetics of the rate-limiting steps in transcription between promoters and induction schemes. We conclude that cell-to-cell and consequent lineage-to-lineage variability in RNA and protein numbers are both promoter sequence-dependent and subject to regulation.

Polar Localization of the Serine Chemoreceptor of Escherichia coli Is Nucleoid Exclusion-Dependent

We studied whether nucleoid exclusion contributes to the segregation and retention of Tsr chemoreceptor clusters at the cell poles. Using live time-lapse, single-cell microscopy measurements, we show that the single-cell spatial distributions of Tsr clusters have heterogeneities and asymmetries that are consistent with nucleoid exclusion and cannot be explained by the diffusion-and-capture mechanism supported by Tol-Pal complexes at the poles. Also, in cells subjected to ampicillin, which enhances relative nucleoid lengths, Tsr clusters locate relatively closer to the cell extremities, whereas in anucleated cells (deletion mutants for mukB), the Tsr clusters are closer to midcell. In addition, we find that the fraction of Tsr clusters at the poles is smaller in deletion mutants for Tol-Pal than in wild-type cells, although it is still larger than would be expected by chance. Also in deletion mutants, the distribution of Tsr clusters differs widely between cells with relatively small and large nucleoids, in a manner consistent with nucleoid exclusion from midcell. This comparison further showed that diffusion-and-capture by Tol-Pal complexes and nucleoid exclusion from the midcell have complementary effects. Subsequently, we subjected deletion mutants to suboptimal temperatures that are known to enhance cytoplasm viscosity, which hampers nucleoid exclusion effects. As the temperature was lowered, the fraction of clusters at the poles decreased linearly. Finally, a stochastic model including nucleoid exclusion at midcell and diffusion-and-capture due to Tol-Pal at the poles is shown to exhibit a cluster dynamics that is consistent with the empirical data. We conclude that nucleoid exclusion also contributes to the preference of Tsr clusters for polar localization.

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.