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

Exact results for gene-expression models with general waiting-time distributions

Complex molecular details of transcriptional regulation can be coarse-grained by assuming that reaction waiting times for promoter-state transitions, the mRNA synthesis, and the mRNA degradation follow general distributions. However, how such a generalized two-state model is analytically solved is a long-standing issue. Here we first present analytical formulas of burst-size distributions for this model. Then, we derive an iterative equation for the mRNA moment-generating function, by which mRNA raw and binomial moments of any order can be conveniently calculated. The analytical results obtained in the special cases of phase-type waiting-time distributions not only provide insights into the mechanisms of complex transcriptional regulations but also bring conveniences for experimental data-based statistical inferences.

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.

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.

Stochastic dynamics and ribosome-RNAP interactions in transcription-translation coupling

Under certain cellular conditions, transcription and mRNA translation in prokaryotes appear to be "coupled," in which the formation of mRNA transcript and production of its associated protein are temporally correlated. Such transcription-translation coupling (TTC) has been evoked as a mechanism that speeds up the overall process, provides protection against premature termination, and/or regulates the timing of transcript and protein formation. What molecular mechanisms underlie ribosome-RNAP coupling and how they can perform these functions have not been explicitly modeled. We develop and analyze a continuous-time stochastic model that incorporates ribosome and RNAP elongation rates, initiation and termination rates, RNAP pausing, and direct ribosome and RNAP interactions (exclusion and binding). Our model predicts how distributions of delay times depend on these molecular features of transcription and translation. We also propose additional measures for TTC: a direct ribosome-RNAP binding probability and the fraction of time the translation-transcription process is "protected" from attack by transcription-terminating proteins. These metrics quantify different aspects of TTC and differentially depend on parameters of known molecular processes. We use our metrics to reveal how and when our model can exhibit either acceleration or deceleration of transcription, as well as protection from termination. Our detailed mechanistic model provides a basis for designing new experimental assays that can better elucidate the mechanisms of TTC.

Systematic analysis of the underlying genomic architecture for transcriptional-translational coupling in prokaryotes

Transcriptional-translational coupling is accepted to be a fundamental mechanism of gene expression in prokaryotes and therefore has been analyzed in detail. However, the underlying genomic architecture of the expression machinery has not been well investigated so far. In this study, we established a bioinformatics pipeline to systematically investigated >1800 bacterial genomes for the abundance of transcriptional and translational associated genes clustered in distinct gene cassettes. We identified three highly frequent cassettes containing transcriptional and translational genes, i.e. rplk-nusG (gene cassette 1; in 553 genomes), rpoA-rplQ-rpsD-rpsK-rpsM (gene cassette 2; in 656 genomes) and nusA-infB (gene cassette 3; in 877 genomes). Interestingly, each of the three cassettes harbors a gene (nusG, rpsD and nusA) encoding a protein which links transcription and translation in bacteria. The analyses suggest an enrichment of these cassettes in pathogenic bacterial phyla with >70% for cassette 3 (i.e. Neisseria, Salmonella and Escherichia) and >50% for cassette 1 (i.e. Treponema, Prevotella, Leptospira and Fusobacterium) and cassette 2 (i.e. Helicobacter, Campylobacter, Treponema and Prevotella). These insights form the basis to analyze the transcriptional regulatory mechanisms orchestrating transcriptional-translational coupling and might open novel avenues for future biotechnological approaches.

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.

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.

Advances in the technologies for studying consortia of bacteria and cyanobacteria/microalgae in wastewaters

The excessive generation and discharge of wastewaters have been serious concerns worldwide in the recent past. From an environmental friendly perspective, bacteria, cyanobacteria and microalgae, and the consortia have been largely considered for biological treatment of wastewaters. For efficient use of bacteria‒cyanobacteria/microalgae consortia in wastewater treatment, detailed knowledge on their structure, behavior and interaction is essential. In this direction, specific analytical tools and techniques play a significant role in studying these consortia. This review presents a critical perspective on physical, biochemical and molecular techniques such as microscopy, flow cytometry with cell sorting, nanoSIMS and omics approaches used for systematic investigations of the structure and function, particularly nutrient removal potential of bacteria‒cyanobacteria/microalgae consortia. In particular, the use of specific molecular techniques of genomics, transcriptomics, proteomics metabolomics and genetic engineering to develop more stable consortia of bacteria and cyanobacteria/microalgae with their improved biotechnological capabilities in wastewater treatment has been highlighted.

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.

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.

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.

A Modeling Framework for Generation of Positional and Temporal Simulations of Transcriptional Regulation

We present a modeling framework aimed at capturing both the positional and temporal behavior of transcriptional regulatory proteins in eukaryotic cells. There is growing evidence that transcriptional regulation is the complex behavior that emerges not solely from the individual components, but rather from their collective behavior, including competition and cooperation. Our framework describes individual regulatory components using generic action oriented descriptions of their biochemical interactions with a DNA sequence. All the possible actions are based on the current state of factors bound to the DNA. We developed a rule builder to automatically generate the complete set of biochemical interaction rules for any given DNA sequence. Off-the-shelf stochastic simulation engines can model the behavior of a system of rules and the resulting changes in the configuration of bound factors can be visualized. We compared our model to experimental data at well-studied loci in yeast, confirming that our model captures both the positional and temporal behavior of transcriptional regulation.

Effects of cooperation between translating ribosome and RNA polymerase on termination efficiency of the Rho-independent terminator

An experimental system was designed to measure in vivo termination efficiency (TE) of the Rho-independent terminator and position–function relations were quantified for the terminator tR2 in Escherichia coli. The terminator function was almost completely repressed when tR2 was located several base pairs downstream from the gene, and TE gradually increased to maximum values with the increasing distance between the gene and terminator. This TE–distance relation reflected a stochastic coupling of the ribosome and RNA polymerase (RNAP). Terminators located in the first 100 bp of the coding region can function efficiently. However, functional repression was observed when the terminator was located in the latter part of the coding region, and the degree of repression was determined by transcriptional and translational dynamics. These results may help to elucidate mechanisms of Rho-independent termination and reveal genomic locations of terminators and functions of the sequence that precedes terminators. These observations may have important applications in synthetic biology.

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.

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.

Quasi-cellular systems: stochastic simulation analysis at nanoscale range

BACKGROUND

The wet-lab synthesis of the simplest forms of life (minimal cells) is a challenging aspect in modern synthetic biology. Quasi-cellular systems able to produce proteins directly from DNA can be obtained by encapsulating the cell-free transcription/translation system PURESYSTEM(PS) in liposomes. It is possible to detect the intra-vesicle protein production using DNA encoding for GFP and monitoring the fluorescence emission over time. The entrapment of solutes in small-volume liposomes is a fundamental open problem. Stochastic simulation is a valuable tool in the study of biochemical reaction at nanoscale range. QDC (Quick Direct-Method Controlled), a stochastic simulation software based on the well-known Gillespie's SSA algorithm, was used. A suitable model formally describing the PS reactions network was developed, to predict, from inner species concentrations (very difficult to measure in small-volumes), the resulting fluorescence signal (experimentally observable).

RESULTS

Thanks to suitable features specific of QDC, we successfully formalized the dynamical coupling between the transcription and translation processes that occurs in the real PS, thus bypassing the concurrent-only environment of Gillespie's algorithm. Simulations were firstly performed for large liposomes (2.67µm of diameter) entrapping the PS to synthetize GFP. By varying the initial concentrations of the three main classes of molecules involved in the PS (DNA, enzymes, consumables), we were able to stochastically simulate the time-course of GFP-production. The sigmoid fit of the GFP-production curves allowed us to extract three quantitative parameters which are significantly dependent on the various initial states. Then we extended this study for small-volume liposomes (575 nm of diameter), where it is more complex to infer the intra-vesicle composition, due to the expected anomalous entrapment phenomena. We identified almost two extreme states that are forecasted to give rise to significantly different experimental observables.

CONCLUSIONS

The present work is the first one describing in the detail the stochastic behavior of the PS. Thanks to our results, an experimental approach is now possible, aimed at recording the GFP production kinetics in very small micro-emulsion droplets or liposomes, and inferring, by using the simulation as a reverse-engineering procedure, the internal solutes distribution, and shed light on the still unknown forces driving the entrapment phenomenon.

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.

Effects of codon sequence on the dynamics of genetic networks

In prokaryotes, the rate at which codons are translated varies from one codon to the next. Using a stochastic model of transcription and translation at the nucleotide and codon levels, we investigate the effects of the codon sequence on the dynamics of protein numbers. For sequences generated according to the codon frequencies in Escherichia coli, we find that mean protein numbers at near equilibrium differ with the codon sequence, due to the mean codon translation efficiencies, in particular of the codons at the ribosome binding site region. We find close agreement between these predictions and measurements of protein expression levels as a function of the codon sequence. Next, we investigate the effects of short codon sequences at the start/end of the RNA sequence with linearly increasing/decreasing translation efficiencies, known as slow ramps. The ramps affect the mean, but not the fluctuations, in proteins numbers by affecting the rate of translation initiation. Finally, we show that slow ramps affect the dynamics of small genetic circuits, namely, switches and clocks. In switches, ramps affect the frequency of switching and bias the robustness of the noisy attractors. In repressilators, ramps alter the robustness of periodicity. We conclude that codon sequences affect the dynamics of gene expression and genetic circuits and, thus, are likely to be under selection regarding both mean codon frequency as well as spatial arrangement along the sequence.

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.

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.