Effects of transcriptional pausing on gene expression dynamics

spotter: a single-nucleotide resolution stochastic simulation model of supercoiling-mediated transcription and translation in prokaryotes

Stochastic simulation models have played an important role in efforts to understand the mechanistic basis of prokaryotic transcription and translation. Despite the fundamental linkage of these processes in bacterial cells, however, most simulation models have been limited to representations of either transcription or translation. In addition, the available simulation models typically either attempt to recapitulate data from single-molecule experiments without considering cellular-scale high-throughput sequencing data or, conversely, seek to reproduce cellular-scale data without paying close attention to many of the mechanistic details. To address these limitations, we here present spotter (Simulation of Prokaryotic Operon Transcription & Translation Elongation Reactions), a flexible, user-friendly simulation model that offers highly-detailed combined representations of prokaryotic transcription, translation, and DNA supercoiling. In incorporating nascent transcript and ribosomal profiling sequencing data, spotter provides a critical bridge between data collected in single-molecule experiments and data collected at the cellular scale. Importantly, in addition to rapidly generating output that can be aggregated for comparison with next-generation sequencing and proteomics data, spotter produces residue-level positional information that can be used to visualize individual simulation trajectories in detail. We anticipate that spotter will be a useful tool in exploring the interplay of processes that are crucially linked in prokaryotes.

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.

Bayesian inference of polymerase dynamics over the exclusion process

Transcription is a complex phenomenon that permits the conversion of genetic information into phenotype by means of an enzyme called RNA polymerase, which erratically moves along and scans the DNA template. We perform Bayesian inference over a paradigmatic mechanistic model of non-equilibrium statistical physics, i.e. the asymmetric exclusion processes in the hydrodynamic limit, assuming a Gaussian process prior for the polymerase progression rate as a latent variable. Our framework allows us to infer the speed of polymerases during transcription given their spatial distribution, while avoiding the explicit inversion of the system's dynamics. The results, which show processing rates strongly varying with genomic position and minor role of traffic-like congestion, may have strong implications for the understanding of gene expression.

spotter : A single-nucleotide resolution stochastic simulation model of supercoiling-mediated transcription and translation in prokaryotes

Stochastic simulation models have played an important role in efforts to understand the mechanistic basis of prokaryotic transcription and translation. Despite the fundamental linkage of these processes in bacterial cells, however, most simulation models have been limited to representations of either transcription or translation. In addition, the available simulation models typically either attempt to recapitulate data from single-molecule experiments without considering cellular-scale high-throughput sequencing data or, conversely, seek to reproduce cellular-scale data without paying close attention to many of the mechanistic details. To address these limitations, we here present spotter (Simulation of Prokaryotic Operon Transcription & Translation Elongation Reactions), a flexible, user-friendly simulation model that offers highly-detailed combined representations of prokaryotic transcription, translation, and DNA supercoiling. In incorporating nascent transcript and ribosomal profiling sequencing data, spotter provides a critical bridge between data collected in single-molecule experiments and data collected at the cellular scale. Importantly, in addition to rapidly generating output that can be aggregated for comparison with next-generation sequencing and proteomics data, spotter produces residue-level positional information that can be used to visualize individual simulation trajectories in detail. We anticipate that spotter will be a useful tool in exploring the interplay of processes that are crucially linked in prokaryotes.

Timing RNA polymerase pausing with TV-PRO-seq

Transcription of many genes in metazoans is subject to polymerase pausing, which is the transient stop of transcriptionally engaged polymerases. This is known to mainly occur in promoter-proximal regions but it is not well understood. In particular, a genome-wide measurement of pausing times at high resolution has been lacking. We present here the time-variant precision nuclear run-on and sequencing (TV-PRO-seq) assay, an extension of the standard PRO-seq that allows us to estimate genome-wide pausing times at single-base resolution. Its application to human cells demonstrates that, proximal to promoters, polymerases pause more frequently but for shorter times than in other genomic regions. Comparison with single-cell gene expression data reveals that the polymerase pausing times are longer in highly expressed genes, while transcriptionally noisier genes have higher pausing frequencies and slightly longer pausing times. Analyses of histone modifications suggest that the marker H3K36me3 is related to the polymerase pausing.

In Vitro Screening of Various Bacterially Produced Double-Stranded RNAs for Silencing Cercospora cf. flagellaris Target Genes and Suppressing Cercosporin Production

Cercospora leaf blight (CLB), primarily caused by Cercospora cf. flagellaris, is one of the most important diseases of soybean (Glycine max) in Louisiana. The pathogen produces cercosporin, a nonspecific toxin and an important virulence factor. There are no commercial cultivars with CLB resistance, and the pathogen has developed substantial resistance to the frequently used fungicides. Consequently, alternative methods are needed to manage CLB. One possibility is the RNA interference-based topical application of double-stranded (ds)RNA. The present study addressed the two most critical steps for this novel approach to be practical: inexpensively producing large quantities of dsRNA and identifying the right target genes for silencing. A screening method was developed to compare the effectiveness of Escherichia coli-produced dsRNAs targeting five fungal genes involved in cercosporin production for silencing in liquid culture. As much as 151.6 mg of dsRNA-containing total nucleic acids (TNAs) was produced from 1 liter of E. coli Luria broth culture using the L4440 vector. All tested dsRNAs reduced cercosporin production. However, significant target gene suppression was only detected in the cultures treated with dsRNAs from Avr4 and CTB8. The most potent dsRNA was from Avr4, which reduced 50% of cercosporin production at an estimated TNA concentration of 10.4 µg/ml (half maximal effective concentration [EC₅₀]), and the least potent dsRNA was from HN-2, with an estimated EC₅₀ of 46.7 µg/ml TNA. The present study paves the road for managing CLB under field conditions using dsRNA. Additionally, this approach could be adapted to identify the best dsRNAs to manage other fungal diseases.

Statistics of Nascent and Mature RNA Fluctuations in a Stochastic Model of Transcriptional Initiation, Elongation, Pausing, and Termination

Recent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. We derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations on gene segments, as well as of total nascent RNA on a gene. We also obtain exact expressions for the first two moments of mature RNA fluctuations and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

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

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

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.

Bayesian inference on stochastic gene transcription from flow cytometry data

Motivation

Transcription in single cells is an inherently stochastic process as mRNA levels vary greatly between cells, even for genetically identical cells under the same experimental and environmental conditions. We present a stochastic two-state switch model for the population of mRNA molecules in single cells where genes stochastically alternate between a more active ON state and a less active OFF state. We prove that the stationary solution of such a model can be written as a mixture of a Poisson and a Poisson-beta probability distribution. This finding facilitates inference for single cell expression data, observed at a single time point, from flow cytometry experiments such as FACS or fluorescence in situ hybridization (FISH) as it allows one to sample directly from the equilibrium distribution of the mRNA population. We hence propose a Bayesian inferential methodology using a pseudo-marginal approach and a recent approximation to integrate over unobserved states associated with measurement error.

Results

We provide a general inferential framework which can be widely used to study transcription in single cells from the kind of data arising in flow cytometry experiments. The approach allows us to separate between the intrinsic stochasticity of the molecular dynamics and the measurement noise. The methodology is tested in simulation studies and results are obtained for experimental multiple single cell expression data from FISH flow cytometry experiments.

Availability and implementation

All analyses were implemented in R. Source code and the experimental data are available at https://github.com/SimoneTiberi/Bayesian-inference-on-stochastic-gene-transcription-from-flow-cytometry-data.

Supplementary information

Supplementary data are available at Bioinformatics online.

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

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

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.

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.

Collective Properties of a Transcription Initiation Model Under Varying Environment

The dynamics of gene transcription is tightly regulated in eukaryotes. Recent experiments have revealed various kinds of transcriptional dynamics, such as RNA polymerase II pausing, that involves regulation at the transcription initiation stage, and the choice of different regulation pattern is closely related to the physiological functions of the target gene. Here we consider a simplified model of transcription initiation, a process including the assembly of transcription complex and the pausing and releasing of the RNA polymerase II. Focusing on the collective behaviors of a population level, we explore the potential regulatory functions this model can offer. These functions include fast and synchronized response to environmental change, or long-term memory about the transcriptional status. As a proof of concept we also show that, by selecting different control mechanisms cells can adapt to different environments. These findings may help us better understand the design principles of transcriptional regulation.

The utility of simple mathematical models in understanding gene regulatory dynamics

In this review, we survey work that has been carried out in the attempts of biomathematicians to understand the dynamic behaviour of simple bacterial operons starting with the initial work of the 1960's. We concentrate on the simplest of situations, discussing both repressible and inducible systems and then turning to concrete examples related to the biology of the lactose and tryptophan operons. We conclude with a brief discussion of the role of both extrinsic noise and so-called intrinsic noise in the form of translational and/or transcriptional bursting.

Effects of elongation delay in transcription dynamics

In the transcription process, elongation delay is induced by the movement of RNA polymerases (RNAP) along the DNA sequence, and can result in changes in the transcription dynamics. This paper studies the transcription dynamics that involved the elongation delay and effects of cell division and DNA replication. The stochastic process of gene expression is modeled with delay chemical master equation with periodic coefficients, and is studied numerically through the stochastic simulation algorithm with delay. We show that the average transcription level approaches to a periodic dynamics over cell cycles at homeostasis, and the elongation delay can reduce the transcription level and increase the transcription noise. Moreover, the transcription elongation can induce bimodal distribution of mRNA levels that can be measured by the techniques of flow cytometry.

Uncovering the functional constraints underlying the genomic organization of the odorant-binding protein genes

Animal olfactory systems have a critical role for the survival and reproduction of individuals. In insects, the odorant-binding proteins (OBPs) are encoded by a moderately sized gene family, and mediate the first steps of the olfactory processing. Most OBPs are organized in clusters of a few paralogs, which are conserved over time. Currently, the biological mechanism explaining the close physical proximity among OBPs is not yet established. Here, we conducted a comprehensive study aiming to gain insights into the mechanisms underlying the OBP genomic organization. We found that the OBP clusters are embedded within large conserved arrangements. These organizations also include other non-OBP genes, which often encode proteins integral to plasma membrane. Moreover, the conservation degree of such large clusters is related to the following: 1) the promoter architecture of the confined genes, 2) a characteristic transcriptional environment, and 3) the chromatin conformation of the chromosomal region. Our results suggest that chromatin domains may restrict the location of OBP genes to regions having the appropriate transcriptional environment, leading to the OBP cluster structure. However, the appropriate transcriptional environment for OBP and the other neighbor genes is not dominated by reduced levels of expression noise. Indeed, the stochastic fluctuations in the OBP transcript abundance may have a critical role in the combinatorial nature of the olfactory coding process.

Heteroresistance at the single-cell level: adapting to antibiotic stress through a population-based strategy and growth-controlled interphenotypic coordination

Heteroresistance refers to phenotypic heterogeneity of microbial clonal populations under antibiotic stress, and it has been thought to be an allocation of a subset of “resistant” cells for surviving in higher concentrations of antibiotic. The assumption fits the so-called bet-hedging strategy, where a bacterial population “hedges” its “bet” on different phenotypes to be selected by unpredicted environment stresses. To test this hypothesis, we constructed a heteroresistance model by introducing a bla_CTX-M-14 gene (coding for a cephalosporin hydrolase) into a sensitive Escherichia coli strain. We confirmed heteroresistance in this clone and that a subset of the cells expressed more hydrolase and formed more colonies in the presence of ceftriaxone (exhibited stronger “resistance”). However, subsequent single-cell-level investigation by using a microfluidic device showed that a subset of cells with a distinguishable phenotype of slowed growth and intensified hydrolase expression emerged, and they were not positively selected but increased their proportion in the population with ascending antibiotic concentrations. Therefore, heteroresistance—the gradually decreased colony-forming capability in the presence of antibiotic—was a result of a decreased growth rate rather than of selection for resistant cells. Using a mock strain without the resistance gene, we further demonstrated the existence of two nested growth-centric feedback loops that control the expression of the hydrolase and maximize population growth in various antibiotic concentrations. In conclusion, phenotypic heterogeneity is a population-based strategy beneficial for bacterial survival and propagation through task allocation and interphenotypic collaboration, and the growth rate provides a critical control for the expression of stress-related genes and an essential mechanism in responding to environmental stresses.

Heteroresistance is essentially phenotypic heterogeneity, where a population-based strategy is thought to be at work, being assumed to be variable cell-to-cell resistance to be selected under antibiotic stress. Exact mechanisms of heteroresistance and its roles in adaptation to antibiotic stress have yet to be fully understood at the molecular and single-cell levels. In our study, we have not been able to detect any apparent subset of “resistant” cells selected by antibiotics; on the contrary, cell populations differentiate into phenotypic subsets with variable growth statuses and hydrolase expression. The growth rate appears to be sensitive to stress intensity and plays a key role in controlling hydrolase expression at both the bulk population and single-cell levels. We have shown here, for the first time, that phenotypic heterogeneity can be beneficial to a growing bacterial population through task allocation and interphenotypic collaboration other than partitioning cells into different categories of selective advantage.

Transcriptome sequencing of Chinese and Caucasian population identifies ethnic-associated differential transcript abundance of heterogeneous nuclear ribonucleoprotein K (hnRNPK)

Gene expression variations (GEV) among different ethnic groups have been a subject matter for extensive study. Relatively less known is the extent of alternative splicing variations (ASV) in the context of ethnicity. We conducted a transcriptome sequencing study of 20 lymphoblastoid cell lines obtained from Caucasian and Han Chinese, and identified known genes that exhibit differential isoform abundance between the two ethnic groups. Among them hnRNPK, a co-factor of p53 (TP53), could be further replicated in a 39-sample cohort with TaqMan assay. Although within-population novel splice variants are common, inter-population novel splice variants are rare. We further analyzed 5.63 billion sequencing reads retrieved from the NCBI Sequence Read Archive and identified potential ethnic-specific transcribed regions.

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.

A three-component signalling system fine-tunes expression kinetics of HPPK responsible for folate synthesis by positive feedback loop during stress response of Xanthomonas campestris

During adaptation to environments, bacteria employ two-component signal transduction systems, which contain histidine kinases and response regulators, to sense and respond to exogenous and cellular stimuli in an accurate spatio-temporal manner. Although the protein phosphorylation process between histidine kinase and response regulator has been well documented, the molecular mechanism fine-tuning phosphorylation levels of response regulators is comparatively less studied. Here we combined genetic and biochemical approaches to reveal that a hybrid histidine kinase, SreS, is involved in the SreK-SreR phosphotransfer process to control salt stress response in the bacterium Xanthomonas campestris. The N-terminal receiver domain of SreS acts as a phosphate sink by competing with the response regulator SreR to accept the phosphoryl group from the latter's cognate histidine kinase SreK. This regulatory process is critical for bacterial survival because the dephosphorylated SreR protein participates in activating one of the tandem promoters (P2) at the 5' end of the sreK-sreR-sreS-hppK operon, and then modulates a transcriptional surge of the stress-responsive gene hppK, which is required for folic acid synthesis. Therefore, our study dissects the biochemical process of a positive feedback loop in which a 'three-component' signalling system fine-tunes expression kinetics of downstream genes.

Combinatorial control of gene expression

The complexity and diversity of eukaryotic organisms are a feat of nature's engineering. Pulling the strings of such an intricate machinery requires an even more masterful and crafty approach. Only the number and type of responses that they generate exceed the staggering proportions of environmental signals perceived and processed by eukaryotes. Hence, at first glance, the cell's sparse stockpile of controlling factors does not seem remotely adequate to carry out this response. The question as to how eukaryotes sense and respond to environmental cues has no single answer. It is an amalgamation, an interplay between several processes, pathways, and factors—a combinatorial control. A short description of some of the most important elements that operate this entire conglomerate is given in this paper.

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.

Are gene loops the cause of transcriptional noise?

Expression levels of the same mRNA or protein vary significantly among the cells of an otherwise identical population. Such biological noise has great functional implications and is largely due to transcriptional bursting, the episodic production of mRNAs in short, intense bursts, interspersed by periods of transcriptional inactivity. Bursting has been demonstrated in a wide range of pro- and eukaryotic species, attesting to its universal importance. However, the mechanistic origins of bursting remain elusive. A different type of phenomenon, which has also been suggested to be widespread, is the physical interaction between the promoter and 3' end of a gene. Several functional roles have been proposed for such gene loops, including the facilitation of transcriptional reinitiation. Here, I discuss the most recent findings related to these subjects and argue that gene loops are a likely cause of transcriptional bursting and, thus, biological noise.

Cooperative RNA polymerase molecules behavior on a stochastic sequence-dependent model for transcription elongation

The transcription process is crucial to life and the enzyme RNA polymerase (RNAP) is the major component of the transcription machinery. The development of single-molecule techniques, such as magnetic and optical tweezers, atomic-force microscopy and single-molecule fluorescence, increased our understanding of the transcription process and complements traditional biochemical studies. Based on these studies, theoretical models have been proposed to explain and predict the kinetics of the RNAP during the polymerization, highlighting the results achieved by models based on the thermodynamic stability of the transcription elongation complex. However, experiments showed that if more than one RNAP initiates from the same promoter, the transcription behavior slightly changes and new phenomenona are observed. We proposed and implemented a theoretical model that considers collisions between RNAPs and predicts their cooperative behavior during multi-round transcription generalizing the Bai et al. stochastic sequence-dependent model. In our approach, collisions between elongating enzymes modify their transcription rate values. We performed the simulations in Mathematica® and compared the results of the single and the multiple-molecule transcription with experimental results and other theoretical models. Our multi-round approach can recover several expected behaviors, showing that the transcription process for the studied sequences can be accelerated up to 48% when collisions are allowed: the dwell times on pause sites are reduced as well as the distance that the RNAPs backtracked from backtracking sites.

Transcription elongation and tissue-specific somatic CAG instability

The expansion of CAG/CTG repeats is responsible for many diseases, including Huntington's disease (HD) and myotonic dystrophy 1. CAG/CTG expansions are unstable in selective somatic tissues, which accelerates disease progression. The mechanisms underlying repeat instability are complex, and it remains unclear whether chromatin structure and/or transcription contribute to somatic CAG/CTG instability in vivo. To address these issues, we investigated the relationship between CAG instability, chromatin structure, and transcription at the HD locus using the R6/1 and R6/2 HD transgenic mouse lines. These mice express a similar transgene, albeit integrated at a different site, and recapitulate HD tissue-specific instability. We show that instability rates are increased in R6/2 tissues as compared to R6/1 matched-samples. High transgene expression levels and chromatin accessibility correlated with the increased CAG instability of R6/2 mice. Transgene mRNA and H3K4 trimethylation at the HD locus were increased, whereas H3K9 dimethylation was reduced in R6/2 tissues relative to R6/1 matched-tissues. However, the levels of transgene expression and these specific histone marks were similar in the striatum and cerebellum, two tissues showing very different CAG instability levels, irrespective of mouse line. Interestingly, the levels of elongating RNA Pol II at the HD locus, but not the initiating form of RNA Pol II, were tissue-specific and correlated with CAG instability levels. Similarly, H3K36 trimethylation, a mark associated with transcription elongation, was specifically increased at the HD locus in the striatum and not in the cerebellum. Together, our data support the view that transcription modulates somatic CAG instability in vivo. More specifically, our results suggest for the first time that transcription elongation is regulated in a tissue-dependent manner, contributing to tissue-selective CAG instability.

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.

Detecting sequence dependent transcriptional pauses from RNA and protein number time series

BACKGROUND

Evidence suggests that in prokaryotes sequence-dependent transcriptional pauses affect the dynamics of transcription and translation, as well as of small genetic circuits. So far, a few pause-prone sequences have been identified from in vitro measurements of transcription elongation kinetics.

RESULTS

Using a stochastic model of gene expression at the nucleotide and codon levels with realistic parameter values, we investigate three different but related questions and present statistical methods for their analysis. First, we show that information from in vivo RNA and protein temporal numbers is sufficient to discriminate between models with and without a pause site in their coding sequence. Second, we demonstrate that it is possible to separate a large variety of models from each other with pauses of various durations and locations in the template by means of a hierarchical clustering and a random forest classifier. Third, we introduce an approximate likelihood function that allows to estimate the location of a pause site.

CONCLUSIONS

This method can aid in detecting unknown pause-prone sequences from temporal measurements of RNA and protein numbers at a genome-wide scale and thus elucidate possible roles that these sequences play in the dynamics of genetic networks and phenotype.

Transcriptional interference by RNA polymerase pausing and dislodgement of transcription factors

Transcriptional interference is the in cis suppression of one transcriptional process by another. Mathematical modeling shows that promoter occlusion by elongating RNA polymerases cannot produce strong interference. Interference may instead be generated by (1) dislodgement of slow-to-assemble pre-initiation complexes and transcription factors and (2) prolonged occlusion by paused RNA polymerases.

Evolving kinetics of gene expression in stochastic environments

Recent studies have shown that the in vivo dynamics of RNA numbers in bacteria is regulated, to a great extent, by the kinetics of rate limiting steps in transcription. Strong evidence suggests that the kinetics of these steps is sequence dependent. We investigate the selective advantages of rate limiting steps of differing kinetics. For that, we model the kinetics of expression of a gene responsible for promoting cell division at the expense of resources in the environment in individual cells of a population. We model mutations that affect the kinetics of the rate limiting steps and selective pressure in various environmental conditions. Depletion of resources leads to cell death. We find that small changes in the evolutionary constraints can favor widely different noise levels in RNA and protein numbers. Increasing the cost in nutrients for division favors noisier expression. The results provide a better understanding of why different genes differ in the kinetics of production of RNA and proteins.

A systems view of the protein expression process

Many biological processes are regulated by changing the concentration and activity of proteins. The presence of a protein at a given subcellular location at a given time with a certain conformation is the result of an apparently sequential process. The rate of protein formation is influenced by chromatin state, and the rates of transcription, translation, and degradation. There is an exquisite control system where each stage of the process is controlled both by seemingly unregulated proteins as well as through feedbacks mediated by RNA and protein products. Here we review the biological facts and mathematical models for each stage of the protein production process. We conclude that advances in experimental techniques leading to a detailed description of the process have not been matched by mathematical models that represent the details of the process and facilitate analysis. Such an exercise is the first step towards development of a framework for a systems biology analysis of the protein production process.

ELECTRONIC SUPPLEMENTARY MATERIAL

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In vivo kinetics of transcription initiation of the lar promoter in Escherichia coli. Evidence for a sequential mechanism with two rate-limiting steps

BACKGROUND

In Escherichia coli the mean and cell-to-cell diversity in RNA numbers of different genes vary widely. This is likely due to different kinetics of transcription initiation, a complex process with multiple rate-limiting steps that affect RNA production.

RESULTS

We measured the in vivo kinetics of production of individual RNA molecules under the control of the lar promoter in E. coli. From the analysis of the distributions of intervals between transcription events in the regimes of weak and medium induction, we find that the process of transcription initiation of this promoter involves a sequential mechanism with two main rate-limiting steps, each lasting hundreds of seconds. Both steps become faster with increasing induction by IPTG and Arabinose.

CONCLUSIONS

The two rate-limiting steps in initiation are found to be important regulators of the dynamics of RNA production under the control of the lar promoter in the regimes of weak and medium induction. Variability in the intervals between consecutive RNA productions is much lower than if there was only one rate-limiting step with a duration following an exponential distribution. The methodology proposed here to analyze the in vivo dynamics of transcription may be applicable at a genome-wide scale and provide valuable insight into the dynamics of prokaryotic genetic networks.

Dynamics of a genetic toggle switch at the nucleotide and codon levels

We study the dynamics of a model stochastic two-gene switch at the nucleotide and codon levels. First, we show that its stability, the mean lifetime of the noisy attractors, differs from that of a model where transcription and translation elongation are modeled as single-step delayed events, indicating the need of detailed models to study the dynamics of switches. Next, we vary the coupling between the two genes by varying the affinity of repressor proteins to the promoters and measure the mutual information between the two proteins times series. We find that there is a degree of coupling that maximizes information propagation between the two genes. This is explained by the effects of the coupling on mean and entropy of RNA and protein numbers of each gene, as well as correlation, 2-tuple entropy between the two proteins numbers, and, finally, the stability of the noisy attractors. We also find that increasing the rate of translation initiation increases the correlation between RNA and protein numbers and between the two proteins, due to increased stability of the noisy attractors. Increasing the rate of transcription or decreasing RNA degradation causes opposite effects to the correlation between RNA and proteins of each gene and the stability of the noisy attractors. Finally, we add a sequence-dependent transcription pause site and show that both its probability of occurrence, as well as its mean time length, affects the dynamics of the switch, further demonstrating the dependence of the dynamics of this circuit on sequence level events.

Transcriptional regulation: effects of promoter proximal pausing on speed, synchrony and reliability

Recent whole genome polymerase binding assays in the Drosophila embryo have shown that a substantial proportion of uninduced genes have pre-assembled RNA polymerase-II transcription initiation complex (PIC) bound to their promoters. These constitute a subset of promoter proximally paused genes for which mRNA elongation instead of promoter access is regulated. This difference can be described as a rearrangement of the regulatory topology to control the downstream transcriptional process of elongation rather than the upstream transcriptional initiation event. It has been shown experimentally that genes with the former mode of regulation tend to induce faster and more synchronously, and that promoter-proximal pausing is observed mainly in metazoans, in accord with a posited impact on synchrony. However, it has not been shown whether or not it is the change in the regulated step per se that is causal. We investigate this question by proposing and analyzing a continuous-time Markov chain model of PIC assembly regulated at one of two steps: initial polymerase association with DNA, or release from a paused, transcribing state. Our analysis demonstrates that, over a wide range of physical parameters, increased speed and synchrony are functional consequences of elongation control. Further, we make new predictions about the effect of elongation regulation on the consistent control of total transcript number between cells. We also identify which elements in the transcription induction pathway are most sensitive to molecular noise and thus possibly the most evolutionarily constrained. Our methods produce symbolic expressions for quantities of interest with reasonable computational effort and they can be used to explore the interplay between interaction topology and molecular noise in a broader class of biochemical networks. We provide general-purpose code implementing these methods.

Gene activation is an inherently random process because numerous diffusing proteins and DNA must first interact by random association before transcription can begin. For many genes the necessary protein–DNA associations only begin after activation, but it has recently been noted that a large class of genes in multicellular organisms can assemble the initiation complex of proteins on the core promoter prior to activation. For these genes, activation merely releases polymerase from the preassembled complex to transcribe the gene. It has been proposed on the basis of experiments that such a mechanism, while possibly costly, increases both the speed and the synchrony of the process of gene transcription. We study a realistic model of gene transcription, and show that this conclusion holds for all but a tiny fraction of the space of physical rate parameters that govern the process. The improved control of cell-to-cell variations afforded by regulation through a paused polymerase may help multicellular organisms achieve the high degree of coordination required for development. Our approach has also generated tools with which one can study the effects of analogous changes in other molecular networks and determine the relative importance of various molecular binding rates to particular system properties.

Stochastic sequence-level model of coupled transcription and translation in prokaryotes

Background

In prokaryotes, transcription and translation are dynamically coupled, as the latter starts before the former is complete. Also, from one transcript, several translation events occur in parallel. To study how events in transcription elongation affect translation elongation and fluctuations in protein levels, we propose a delayed stochastic model of prokaryotic transcription and translation at the nucleotide and codon level that includes the promoter open complex formation and alternative pathways to elongation, namely pausing, arrests, editing, pyrophosphorolysis, RNA polymerase traffic, and premature termination. Stepwise translation can start after the ribosome binding site is formed and accounts for variable codon translation rates, ribosome traffic, back-translocation, drop-off, and trans-translation.

Results

First, we show that the model accurately matches measurements of sequence-dependent translation elongation dynamics. Next, we characterize the degree of coupling between fluctuations in RNA and protein levels, and its dependence on the rates of transcription and translation initiation. Finally, modeling sequence-specific transcriptional pauses, we find that these affect protein noise levels.

Conclusions

For parameter values within realistic intervals, transcription and translation are found to be tightly coupled in Escherichia coli, as the noise in protein levels is mostly determined by the underlying noise in RNA levels. Sequence-dependent events in transcription elongation, e.g. pauses, are found to cause tangible effects in the degree of fluctuations in protein levels.

Single-molecule studies of transcription: from one RNA polymerase at a time to the gene expression profile of a cell

Single-molecule techniques have emerged as powerful tools for deciphering mechanistic details of transcription and have yielded discoveries that would otherwise have been impossible to make through the use of more traditional biochemical and/or biophysical techniques. Here, we provide a brief overview of single-molecule techniques most commonly used for studying RNA polymerase and transcription. We then present specific examples of single-molecule studies that have contributed to our understanding of key mechanistic details for each different stage of the transcription cycle. Finally, we discuss emerging single-molecule approaches and future directions, including efforts to study transcription at the single-molecule level in living cells.

The role of physiological heterogeneity in microbial population behavior

As the ability to analyze individual cells in microbial populations expands, it is becoming apparent that isogenic microbial populations contain substantial cell-to-cell differences in physiological parameters such as growth rate, resistance to stress and regulatory circuit output. Subpopulations exist that are manyfold different in these parameters from the population average, and these differences arise by stochastic processes. Such differences can dramatically affect the response of cells to perturbations, especially stress, which in turn dictates overall population response. Defining the role of cell-to-cell heterogeneity in population behavior is important for understanding population-based research problems, including those involving infecting populations, normal flora and bacterial populations in water and soils. Emerging technological breakthroughs are poised to transform single-cell analysis and are critical for the next phase of insights into physiological heterogeneity in the near future. These include technologies for multiparameter analysis of live cells, with downstream processing and analysis.

A comparative analysis of synthetic genetic oscillators

Synthetic biology is a rapidly expanding discipline at the interface between engineering and biology. Much research in this area has focused on gene regulatory networks that function as biological switches and oscillators. Here we review the state of the art in the design and construction of oscillators, comparing the features of each of the main networks published to date, the models used for in silico design and validation and, where available, relevant experimental data. Trends are apparent in the ways that network topology constrains oscillator characteristics and dynamics. Also, noise and time delay within the network can both have constructive and destructive roles in generating oscillations, and stochastic coherence is commonplace. This review can be used to inform future work to design and implement new types of synthetic oscillators or to incorporate existing oscillators into new designs.

Dynamical effects of transcriptional pause-prone sites

We study how long pause-prone sites, commonly sequence-dependent, affect transcription and RNA temporal levels in a delayed stochastic model of transcription at the single nucleotide level. We vary pause propensity, duration and the probability of premature termination of elongation at the pause site. We also study the effects of multiple pause sites. We show that pause sites can be used to fine-tune noise strength and burst size distribution of RNA levels. Varying pause rate and duration alone affects bursting but noise is not significantly affected. Noise strength can be changed by varying both parameters and, even more pronouncedly, by varying the probability of premature termination. Adding multiple pause sites amplifies the increase in noise and bursting. This regulatory mechanism of noise and bursting, being evolvable, may partially explain how different genes exhibit a wide spectrum of different behaviors. The results might assist the engineering of genes with a desired degree of noise.