A Mechanistic Model for Cooperative Behavior of Co-transcribing RNA Polymerases

RNA polymerase collisions and their role in transcription

RNA polymerases are the central enzymes of gene expression and function frequently in either a head-on or co-directional manner on the busy DNA track. Whether and how these collisions between RNA polymerases contribute to transcriptional regulation is mysterious. Increasing evidence from biochemical and single-molecule studies suggests that RNA polymerase collisions function as an important regulator to fine-tune transcription, rather than creating deleterious "traffic jams". This review summarizes the recent progress on elucidating the consequences of RNA polymerase collisions during transcription and highlights the significance of cooperation and coordination between RNA polymerases.

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.

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.

Women’s contribution in understanding how topoisomerases, supercoiling, and transcription control genome organization

One of the biggest paradoxes in biology is that human genome is roughly 2 m long, while the nucleus containing it is almost one million times smaller. To fit into the nucleus, DNA twists, bends and folds into several hierarchical levels of compaction. Still, DNA has to maintain a high degree of accessibility to be readily replicated and transcribed by proteins. How compaction and accessibility co-exist functionally in human cells is still a matter of debate. Here, we discuss how the torsional stress of the DNA helix acts as a buffer, regulating both chromatin compaction and accessibility. We will focus on chromatin supercoiling and on the emerging role of topoisomerases as pivotal regulators of genome organization. We will mainly highlight the major breakthrough studies led by women, with the intention of celebrating the work of this group that remains a minority within the scientific community.

DNA supercoiling-mediated collective behavior of co-transcribing RNA polymerases

Multiple RNA polymerases (RNAPs) transcribing a gene have been known to exhibit collective group behavior, causing the transcription elongation rate to increase with the rate of transcription initiation. Such behavior has long been believed to be driven by a physical interaction or ‘push’ between closely spaced RNAPs. However, recent studies have posited that RNAPs separated by longer distances may cooperate by modifying the DNA segment under transcription. Here, we present a theoretical model incorporating the mechanical coupling between RNAP translocation and the DNA torsional response. Using stochastic simulations, we demonstrate DNA supercoiling-mediated long-range cooperation between co-transcribing RNAPs. We find that inhibiting transcription initiation can slow down the already recruited RNAPs, in agreement with recent experimental observations, and predict that the average transcription elongation rate varies non-monotonically with the rate of transcription initiation. We further show that while RNAPs transcribing neighboring genes oriented in tandem can cooperate, those transcribing genes in divergent or convergent orientations can act antagonistically, and that such behavior holds over a large range of intergenic separations. Our model makes testable predictions, revealing how the mechanical interplay between RNAPs and the DNA they transcribe can govern transcriptional dynamics.

Density- and elongation speed-dependent error correction in RNA polymerization

Backtracking of RNA polymerase (RNAP) is an important pausing mechanism during DNA transcription that is part of the error correction process that enhances transcription fidelity. We model the backtracking mechanism of RNA polymerase, which usually happens when the polymerase tries to incorporate a noncognate or "mismatched" nucleotide triphosphate. Previous models have made simplifying assumptions such as neglecting the trailing polymerase behind the backtracking polymerase or assuming that the trailing polymerase is stationary. We derive exact analytic solutions of a stochastic model that includes locally interacting RNAPs by explicitly showing how a trailing RNAP influences the probability that an error is corrected or incorporated by the leading backtracking RNAP. We also provide two related methods for computing the mean times for error correction and incorporation given an initial local RNAP configuration. Using these results, we propose an effective interacting-RNAP lattice that can be readily simulated.

DNA Supercoiling Drives a Transition between Collective Modes of Gene Synthesis

Transcription of genes can be affected by both biochemical and mechanical factors. Recent experiments suggested that the mechanical stress associated with transcription-induced DNA supercoiling is responsible for the transition from cooperative to antagonistic group dynamics of RNA polymerases (RNAPs) upon promoter repression. To underpin the mechanism behind this drastic transition, we developed a continuum deterministic model for transcription under torsion. In our model, the speed of an RNAP is affected by the local DNA supercoiling, as well as two global factors: (i) the number of RNAPs on the gene affecting the torsional stress experienced by individual RNAPs and (ii) transcription factors blocking the diffusion of DNA supercoils. Our minimal model can successfully reproduce the experimental findings and helps elucidate the interplay of mechanical and biological factors in the collective dynamics of molecular machines involved in gene expression.

Coupling Between Production of Ribosomal RNA and Maturation: Just at the Beginning

Ribosomal RNA (rRNA) production represents the most active transcription in the cell. Synthesis of the large rRNA precursors (35S/47S in yeast/human) is achieved by up to hundreds of RNA polymerase I (Pol I) enzymes simultaneously transcribing a single rRNA gene. In this review, we present recent advances in understanding the coupling between rRNA production and nascent rRNA folding. Mapping of the distribution of Pol I along ribosomal DNA at nucleotide resolution, using either native elongating transcript sequencing (NET-Seq) or crosslinking and analysis of cDNAs (CRAC), revealed frequent Pol I pausing, and CRAC results revealed a direct coupling between pausing and nascent RNA folding. High density of Pol I per gene imposes topological constraints that establish a defined pattern of polymerase distribution along the gene, with a persistent spacing between transcribing enzymes. RNA folding during transcription directly acts as an anti-pausing mechanism, implying that proper folding of the nascent rRNA favors elongation in vivo. Defects in co-transcriptional folding of rRNA are likely to induce Pol I pausing. We propose that premature termination of transcription, at defined positions, can control rRNA production in vivo.

Understanding the molecular mechanisms of transcriptional bursting

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

Trade-offs among transcription elongation rate, number, and duration of ubiquitous pauses on highly transcribed bacterial genes

In this paper, we study the limitations imposed on the transcription process by the presence of short ubiquitous pauses and crowding. These effects are especially pronounced in highly transcribed genes such as ribosomal genes (rrn) in fast growing bacteria. Our model indicates that the quantity and duration of pauses reported for protein-coding genes is incompatible with the average elongation rate observed in rrn genes. When maximal elongation rate is high, pause-induced traffic jams occur, increasing promoter occlusion, thereby lowering the initiation rate. This lowers average transcription rate and increases average transcription time. Increasing maximal elongation rate in the model is insufficient to match the experimentally observed average elongation rate in rrn genes. This suggests that there may be rrn-specific modifications to RNAP, which then experience fewer pauses, or pauses of shorter duration than those in protein-coding genes. We identify model parameter triples (maximal elongation rate, mean pause duration time, number of pauses) which are compatible with experimentally observed elongation rates. Average transcription time and average transcription rate are the model outputs investigated as proxies for cell fitness. These fitness functions are optimized for different parameter choices, opening up a possibility of differential control of these aspects of the elongation process, with potential evolutionary consequences. As an example, a gene's average transcription time may be crucial to fitness when the surrounding medium is prone to abrupt changes. This paper demonstrates that a functional relationship among the model parameters can be estimated using a standard statistical analysis, and this functional relationship describes the various trade-offs that must be made in order for the gene to control the elongation process and achieve a desired average transcription time. It also demonstrates the robustness of the system when a range of maximal elongation rates can be balanced with transcriptional pause data in order to maintain a desired fitness.

Energetics of twisted DNA topologies

Our goal is to review the main theoretical models used to calculate free energy changes associated with common, torsion-induced conformational changes in DNA and provide the resulting equations hoping to facilitate quantitative analysis of both in vitro and in vivo studies. This review begins with a summary of work regarding the energy change of the negative supercoiling-induced B- to L-DNA transition, followed by a discussion of the energetics associated with the transition to Z-form DNA. Finally, it describes the energy changes associated with the formation of DNA curls and plectonemes, which can regulate DNA-protein interactions and promote cross talk between distant DNA elements, respectively. The salient formulas and parameters for each scenario are summarized in table format to facilitate comparison and provide a concise, user-friendly resource.

Long-Range Supercoiling-Mediated RNA Polymerase Cooperation in Transcription

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

Coupled Transcription-Translation in Prokaryotes: An Old Couple With New Surprises

Coupled transcription-translation (CTT) is a hallmark of prokaryotic gene expression. CTT occurs when ribosomes associate with and initiate translation of mRNAs whose transcription has not yet concluded, therefore forming "RNAP.mRNA.ribosome" complexes. CTT is a well-documented phenomenon that is involved in important gene regulation processes, such as attenuation and operon polarity. Despite the progress in our understanding of the cellular signals that coordinate CTT, certain aspects of its molecular architecture remain controversial. Additionally, new information on the spatial segregation between the transcriptional and the translational machineries in certain species, and on the capability of certain mRNAs to localize translation-independently, questions the unanimous occurrence of CTT. Furthermore, studies where transcription and translation were artificially uncoupled showed that transcription elongation can proceed in a translation-independent manner. Here, we review studies supporting the occurrence of CTT and findings questioning its extent, as well as discuss mechanisms that may explain both coupling and uncoupling, e.g., chromosome relocation and the involvement of cis- or trans-acting elements, such as small RNAs and RNA-binding proteins. These mechanisms impact RNA localization, stability, and translation. Understanding the two options by which genes can be expressed and their consequences should shed light on a new layer of control of bacterial transcripts fate.

Current-density relation in the exclusion process with dynamic obstacles

We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of obstacles that dynamically bind and unbind from the lattice. The model is motivated by biological processes such as transcription in the presence of DNA-binding proteins. Similar models have been studied before using the mean-field approximation, but the exact relation between the particle current and density remains elusive. Here, we first show using extensive Monte Carlo simulations that the current-density relation in this model assumes a quasiparabolic form similar to that of the ordinary TASEP without obstacles. We then attempt to explain this relation using exact calculations in the limit of low and high density of particles. Our results suggest that the symmetric, quasiparabolic current-density relation arises through a nontrivial cancellation of higher-order terms, similarly as in the standard TASEP.

Nascent Transcript Folding Plays a Major Role in Determining RNA Polymerase Elongation Rates

Transcription elongation rates influence RNA processing, but sequence-specific regulation is poorly understood. We addressed this in vivo, analyzing RNAPI in S. cerevisiae. Mapping RNAPI by Miller chromatin spreads or UV crosslinking revealed 5' enrichment and strikingly uneven local polymerase occupancy along the rDNA, indicating substantial variation in transcription speed. Two features of the nascent transcript correlated with RNAPI distribution: folding energy and GC content in the transcription bubble. In vitro experiments confirmed that strong RNA structures close to the polymerase promote forward translocation and limit backtracking, whereas high GC in the transcription bubble slows elongation. A mathematical model for RNAPI elongation confirmed the importance of nascent RNA folding in transcription. RNAPI from S. pombe was similarly sensitive to transcript folding, as were S. cerevisiae RNAPII and RNAPIII. For RNAPII, unstructured RNA, which favors slowed elongation, was associated with faster cotranscriptional splicing and proximal splice site use, indicating regulatory significance for transcript folding.

Long-Distance Cooperative and Antagonistic RNA Polymerase Dynamics via DNA Supercoiling

Genes are often transcribed by multiple RNA polymerases (RNAPs) at densities that can vary widely across genes and environmental conditions. Here, we provide in vitro and in vivo evidence for a built-in mechanism by which co-transcribing RNAPs display either collaborative or antagonistic dynamics over long distances (>2 kb) through transcription-induced DNA supercoiling. In Escherichia coli, when the promoter is active, co-transcribing RNAPs translocate faster than a single RNAP, but their average speed is not altered by large variations in promoter strength and thus RNAP density. Environmentally induced promoter repression reduces the elongation efficiency of already-loaded RNAPs, causing premature termination and quick synthesis arrest of no-longer-needed proteins. This negative effect appears independent of RNAP convoy formation and is abrogated by topoisomerase I activity. Antagonistic dynamics can also occur between RNAPs from divergently transcribed gene pairs. Our findings may be broadly applicable given that transcription on topologically constrained DNA is the norm across organisms.

Stationary RNA polymerase fluctuations during transcription elongation

We study fluctuation effects of nonsteric molecular interactions between RNA polymerase (RNAP) motors that move simultaneously on the same DNA track during transcription elongation. Based on a stochastic model that allows for the exact analytical computation of the stationary distribution of RNAPs as a function of their density, interaction strength, nucleoside triphosphate concentration, and rate of pyrophosphate release we predict an almost geometric headway distribution of subsequent RNAP transcribing on the same DNA segment. The localization length which characterizes the decay of the headway distribution depends directly only the average density of RNAP and the interaction strength, but not on specific single-RNAP properties. Density correlations are predicted to decay exponentially with the distance (in units of DNA base pairs), with a correlation length that is significantly shorter than the localization length.