A biophysical model of supercoiling dependent transcription predicts a structural aspect to gene regulation

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.

A spatially resolved stochastic model reveals the role of supercoiling in transcription regulation

In Escherichia coli, translocation of RNA polymerase (RNAP) during transcription introduces supercoiling to DNA, which influences the initiation and elongation behaviors of RNAP. To quantify the role of supercoiling in transcription regulation, we developed a spatially resolved supercoiling model of transcription. The integrated model describes how RNAP activity feeds back with the local DNA supercoiling and how this mechanochemical feedback controls transcription, subject to topoisomerase activities and stochastic topological domain formation. This model establishes that transcription-induced supercoiling mediates the cooperation of co-transcribing RNAP molecules in highly expressed genes, and this cooperation is achieved under moderate supercoiling diffusion and high topoisomerase unbinding rates. It predicts that a topological domain could serve as a transcription regulator, generating substantial transcriptional noise. It also shows the relative orientation of two closely arranged genes plays an important role in regulating their transcription. The model provides a quantitative platform for investigating how genome organization impacts transcription.

Selection for ancient periodic motifs that do not impart DNA bending

A ~10-11 bp periodicity in dinucleotides imparting DNA bending, with shorter periods found in organisms with positively-supercoiled DNA and longer periods found in organisms with negatively-supercoiled DNA, was previously suggested to assist in DNA compaction. However, when measured with more robust methods, variation in the observed periods between organisms with different growth temperatures is not consistent with that hypothesis. We demonstrate that dinucleotide periodicity does not arise solely by mutational biases but is under selection. We found variation between genomes in both the period and the suite of dinucleotides that are periodic. Whereas organisms with similar growth temperatures have highly variable periods, differences in periods increase with phylogenetic distance between organisms. In addition, while the suites of dinucleotides under selection for periodicity become more dissimilar among more distantly-related organisms, there is a core set of dinucleotides that are strongly periodic among genomes in all domains of life. Notably, this core set of periodic motifs are not involved in DNA bending. These data indicate that dinucleotide periodicity is an ancient genomic architecture which may play a role in shaping the evolution of genes and genomes.

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.

Complex Diffusion in Bacteria

Diffusion within bacteria is often thought of as a "simple" random process by which molecules collide and interact with each other. New research however shows that this is far from the truth. Here we shed light on the complexity and importance of diffusion in bacteria, illustrating the similarities and differences of diffusive behaviors of molecules within different compartments of bacterial cells. We first describe common methodologies used to probe diffusion and the associated models and analyses. We then discuss distinct diffusive behaviors of molecules within different bacterial cellular compartments, highlighting the influence of metabolism, size, crowding, charge, binding, and more. We also explicitly discuss where further research and a united understanding of what dictates diffusive behaviors across the different compartments of the cell are required, pointing out new research avenues to pursue.

Bacterial genome architecture shapes global transcriptional regulation by DNA supercoiling

DNA supercoiling acts as a global transcriptional regulator in bacteria, that plays an important role in adapting their expression programme to environmental changes, but for which no quantitative or even qualitative regulatory model is available. Here, we focus on spatial supercoiling heterogeneities caused by the transcription process itself, which strongly contribute to this regulation mode. We propose a new mechanistic modeling of the transcription-supercoiling dynamical coupling along a genome, which allows simulating and quantitatively reproducing in vitro and in vivo transcription assays, and highlights the role of genes' local orientation in their supercoiling sensitivity. Consistently with predictions, we show that chromosomal relaxation artificially induced by gyrase inhibitors selectively activates convergent genes in several enterobacteria, while conversely, an increase in DNA supercoiling naturally selected in a long-term evolution experiment with Escherichia coli favours divergent genes. Simulations show that these global expression responses to changes in DNA supercoiling result from fundamental mechanical constraints imposed by transcription, independently from more specific regulation of each promoter. These constraints underpin a significant and predictable contribution to the complex rules by which bacteria use DNA supercoiling as a global but fine-tuned transcriptional regulator.

How does supercoiling regulation on a battery of RNA polymerases impact on bacterial transcription bursting?

Transcription plays an essential role in gene expression. The transcription bursting in bacteria has been suggested to be regulated by positive supercoiling accumulation in front of a transcribing RNA polymerase (RNAP) together with gyrase binding on DNA to release the supercoiling. In this work, we study the supercoiling regulation in the case of a battery of RNAPs working together on DNA by constructing a multi-state quantitative model, which allows gradual and stepwise supercoiling accumulation and release in the RNAP transcription. We solved for transcription characteristics under the multi-state bursting model for a single RNAP transcription, and then simulated for a battery of RNAPs on DNA with T7 and Escherichia coli RNAP types of traffic, respectively, probing both the average and fluctuation impacts of the supercoiling regulation. Our studies show that due to the supercoiling accumulation and release, the number of RNAP molecules loaded onto the DNA vary significantly along time in the traffic condition. Though multiple RNAPs in transcription promote the mRNA production, they also enhance the supercoiling accumulation to suppress the production. In particular, the fluctuations of the mRNA transcripts become highly pronounced for a battery of RNAPs transcribing together under the supercoiling regulation, especially for a long process of transcription elongation. In such an elongation process, though a single RNAP can work at a high duty ratio, multiple RNAPs are hardly able to do so. Our multi-state model thus provides a systematical characterization of the quantitative features of the bacterial transcription bursting; it also supports improved physical examinations on top of this general modeling framework.

Bursting onto the scene? Exploring stochastic mRNA production in bacteria

Recent large-scale measurements of gene expression variability (or noise) in E. coli have led to the unexpected conclusion that the variability is in large part dictated by and increasing with the mean level of expression. Here we review the evidence for this apparent universal trend in variability, as well as for the related idea that transcription is fundamentally bursty. We examine recently proposed mechanisms for burstiness and universality and argue that they do not explain important features of observed data. Finally, we discuss potential limitations and pitfalls in the interpretation of experimental measurements of cell-to-cell variability.

Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise

This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable Lévy fluctuations. By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that via examining the mean first exit time (MFET) and the first escape probability (FEP), the asymmetric fluctuations, interacting with nonlinearity in the system, lead to peculiar likelihood for transcription. This includes, in the additive noise case, realizing higher likelihood of transcription for larger positive skewness (i.e., asymmetry) index β, causing a stochastic bifurcation at the non-Gaussianity index value α = 1 (i.e., it is a separating point or line for the likelihood for transcription), and achieving a turning point at the threshold value β≈-0.5 (i.e., beyond which the likelihood for transcription suddenly reversed for α values). The stochastic bifurcation and turning point phenomena do not occur in the symmetric noise case (β = 0). While in the multiplicative noise case, non-Gaussianity index value α = 1 is a separating point or line for both the MFET and the FEP. We also investigate the noise enhanced stability phenomenon. Additionally, we are able to specify the regions in the whole parameter space for the asymmetric noise, in which we attain desired likelihood for transcription. We have conducted a series of numerical experiments in "regulating" the likelihood of gene transcription by tuning asymmetric stable Lévy noise indexes. This work offers insights for possible ways of achieving gene regulation in experimental research.

Statistical mechanical model for a closed loop plectoneme with weak helix specific forces

We develop a statistical mechanical framework, based on a variational approximation, to describe closed loop plectonemes. This framework incorporates weak helix structure dependent forces into the determination of the free energy and average structure of a plectoneme. Notably, due to their chiral nature, helix structure dependent forces break the symmetry between left and right handed supercoiling. The theoretical approach, presented here, also provides a systematic way of enforcing the topological constraint of closed loop supercoiling in the variational approximation. At large plectoneme lengths, by considering correlation functions in an expansion in terms of the spatial mean twist density about its thermally averaged value, it can be argued that topological constraint may be approximated by replacing twist and writhe by their thermal averages. A Lagrange multiplier, containing the sum of average twist and writhe, can be added to the free energy to conveniently inforce this result. The average writhe can be calculated through the thermal average of the Gauss' integral in the variational approximation. Furthermore, this approach allows for a possible way to calculate finite size corrections due to the topological constraint. Using interaction energy terms from the mean-field Kornyshev-Leikin theory, for parameter values that correspond to weak helix dependent forces, we calculate the free energy, fluctuation magnitudes and mean geometric parameters for the plectoneme. We see a slight asymmetry, where interestingly, left handed supercoils have a looser structure than right handed ones, although with a lower free energy, unlike what the previous ground state calculations would suggest.

Mechanical bounds to transcriptional noise

Over the past several decades it has been increasingly recognized that stochastic processes play a central role in transcription. Although many stochastic effects have been explained, the source of transcriptional bursting (one of the most well-known sources of stochasticity) has continued to evade understanding. Recent results have pointed to mechanical feedback as the source of transcriptional bursting, but a reconciliation of this perspective with preexisting views of transcriptional regulation is lacking. In this article, we present a simple phenomenological model that is able to incorporate the traditional view of gene expression within a framework with mechanical limits to transcription. By introducing a simple competition between mechanical arrest and relaxation copy number probability distributions collapse onto a shared universal curve under shifting and rescaling and a lower limit of intrinsic noise for any mean expression level is found.

DNA supercoiling is a fundamental regulatory principle in the control of bacterial gene expression

Although it has become routine to consider DNA in terms of its role as a carrier of genetic information, it is also an important contributor to the control of gene expression. This regulatory principle arises from its structural properties. DNA is maintained in an underwound state in most bacterial cells and this has important implications both for DNA storage in the nucleoid and for the expression of genetic information. Underwinding of the DNA through reduction in its linking number potentially imparts energy to the duplex that is available to drive DNA transactions, such as transcription, replication and recombination. The topological state of DNA also influences its affinity for some DNA binding proteins, especially in DNA sequences that have a high A + T base content. The underwinding of DNA by the ATP-dependent topoisomerase DNA gyrase creates a continuum between metabolic flux, DNA topology and gene expression that underpins the global response of the genome to changes in the intracellular and external environments. These connections describe a fundamental and generalised mechanism affecting global gene expression that underlies the specific control of transcription operating through conventional transcription factors. This mechanism also provides a basal level of control for genes acquired by horizontal DNA transfer, assisting microbial evolution, including the evolution of pathogenic bacteria.

Transitions in a genetic transcriptional regulatory system under Lévy motion

Based on a stochastic differential equation model for a single genetic regulatory system, we examine the dynamical effects of noisy fluctuations, arising in the synthesis reaction, on the evolution of the transcription factor activator in terms of its concentration. The fluctuations are modeled by Brownian motion and α-stable Lévy motion. Two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), are used to analyse the transitions from the low to high concentration states. A shorter MFET or higher FEP in the low concentration region facilitates such a transition. We have observed that higher noise intensities and larger jumps of the Lévy motion shortens the MFET and thus benefits transitions. The Lévy motion activates a transition from the low concentration region to the non-adjacent high concentration region, while Brownian motion can not induce this phenomenon. There are optimal proportions of Gaussian and non-Gaussian noises, which maximise the quantities MFET and FEP for each concentration, when the total sum of noise intensities are kept constant. Because a weaker stability indicates a higher transition probability, a new geometric concept is introduced to quantify the basin stability of the low concentration region, characterised by the escaping behaviour.

DNA supercoiling is a fundamental regulatory principle in the control of bacterial gene expression

Although it has become routine to consider DNA in terms of its role as a carrier of genetic information, it is also an important contributor to the control of gene expression. This regulatory principle arises from its structural properties. DNA is maintained in an underwound state in most bacterial cells and this has important implications both for DNA storage in the nucleoid and for the expression of genetic information. Underwinding of the DNA through reduction in its linking number potentially imparts energy to the duplex that is available to drive DNA transactions, such as transcription, replication and recombination. The topological state of DNA also influences its affinity for some DNA binding proteins, especially in DNA sequences that have a high A + T base content. The underwinding of DNA by the ATP-dependent topoisomerase DNA gyrase creates a continuum between metabolic flux, DNA topology and gene expression that underpins the global response of the genome to changes in the intracellular and external environments. These connections describe a fundamental and generalised mechanism affecting global gene expression that underlies the specific control of transcription operating through conventional transcription factors. This mechanism also provides a basal level of control for genes acquired by horizontal DNA transfer, assisting microbial evolution, including the evolution of pathogenic bacteria.