Theoretical Investigation of Transcriptional Bursting: A Multistate Approach

Transcriptional bursting dynamics in gene expression

Gene transcription is a stochastic process that occurs in all organisms. Transcriptional bursting, a critical molecular dynamics mechanism, creates significant heterogeneity in mRNA and protein levels. This heterogeneity drives cellular phenotypic diversity. Currently, the lack of a comprehensive quantitative model limits the research on transcriptional bursting. This review examines various gene expression models and compares their strengths and weaknesses to guide researchers in selecting the most suitable model for their research context. We also provide a detailed summary of the key metrics related to transcriptional bursting. We compared the temporal dynamics of transcriptional bursting across species and the molecular mechanisms influencing these bursts, and highlighted the spatiotemporal patterns of gene expression differences by utilizing metrics such as burst size and burst frequency. We summarized the strategies for modeling gene expression from both biostatistical and biochemical reaction network perspectives. Single-cell sequencing data and integrated multiomics approaches drive our exploration of cutting-edge trends in transcriptional bursting mechanisms. Moreover, we examined classical methods for parameter estimation that help capture dynamic parameters in gene expression data, assessing their merits and limitations to facilitate optimal parameter estimation. Our comprehensive summary and review of the current transcriptional burst dynamics theories provide deeper insights for promoting research on the nature of cell processes, cell fate determination, and cancer diagnosis.

Inferring transcriptional bursting kinetics from single-cell snapshot data using a generalized telegraph model

Gene expression has inherent stochasticity resulting from transcription's burst manners. Single-cell snapshot data can be exploited to rigorously infer transcriptional burst kinetics, using mathematical models as blueprints. The classical telegraph model (CTM) has been widely used to explain transcriptional bursting with Markovian assumptions. However, growing evidence suggests that the gene-state dwell times are generally non-exponential, as gene-state switching is a multi-step process in organisms. Therefore, interpretable non-Markovian mathematical models and efficient statistical inference methods are urgently required in investigating transcriptional burst kinetics. We develop an interpretable and tractable model, the generalized telegraph model (GTM), to characterize transcriptional bursting that allows arbitrary dwell-time distributions, rather than exponential distributions, to be incorporated into the ON and OFF switching process. Based on the GTM, we propose an inference method for transcriptional bursting kinetics using an approximate Bayesian computation framework. This method demonstrates an efficient and scalable estimation of burst frequency and burst size on synthetic data. Further, the application of inference to genome-wide data from mouse embryonic fibroblasts reveals that GTM would estimate lower burst frequency and higher burst size than those estimated by CTM. In conclusion, the GTM and the corresponding inference method are effective tools to infer dynamic transcriptional bursting from static single-cell snapshot data.

Gene expression model inference from snapshot RNA data using Bayesian non-parametrics

Gene expression models, which are key towards understanding cellular regulatory response, underlie observations of single-cell transcriptional dynamics. Although RNA expression data encode information on gene expression models, existing computational frameworks do not perform simultaneous Bayesian inference of gene expression models and parameters from such data. Rather, gene expression models-composed of gene states, their connectivities and associated parameters-are currently deduced by pre-specifying gene state numbers and connectivity before learning associated rate parameters. Here we propose a method to learn full distributions over gene states, state connectivities and associated rate parameters, simultaneously and self-consistently from single-molecule RNA counts. We propagate noise from fluctuating RNA counts over models by treating models themselves as random variables. We achieve this within a Bayesian non-parametric paradigm. We demonstrate our method on the Escherichia coli lacZ pathway and the Saccharomyces cerevisiae STL1 pathway, and verify its robustness on synthetic data.

Genome-wide inference reveals that feedback regulations constrain promoter-dependent transcriptional burst kinetics

Gene expression in mammalian cells is highly variable and episodic, resulting in a series of discontinuous bursts of mRNAs. A challenge is to understand how static promoter architecture and dynamic feedback regulations dictate bursting on a genome-wide scale. Although single-cell RNA sequencing (scRNA-seq) provides an opportunity to address this challenge, effective analytical methods are scarce. We developed an interpretable and scalable inference framework, which combined experimental data with a mechanistic model to infer transcriptional burst kinetics (sizes and frequencies) and feedback regulations. Applying this framework to scRNA-seq data generated from embryonic mouse fibroblast cells, we found Simpson's paradoxes, i.e. genome-wide burst kinetics exhibit different characteristics in two cases without and with distinguishing feedback regulations. We also showed that feedbacks differently modulate burst frequencies and sizes and conceal the effects of transcription start site distributions on burst kinetics. Notably, only in the presence of positive feedback, TATA genes are expressed with high burst frequencies and enhancer-promoter interactions mainly modulate burst frequencies. The developed inference method provided a flexible and efficient way to investigate transcriptional burst kinetics and the obtained results would be helpful for understanding cell development and fate decision.

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.

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.

What Is a Transcriptional Burst?

The idea that gene activity can be discontinuous will not surprise many biologists - many genes are restricted in when and where they can be expressed. Yet during the past 15 years, a collection of observations compiled under the umbrella term 'transcriptional bursting' has received considerable interest. Direct visualization of the dynamics of discontinuous transcription has expanded our understanding of basic transcriptional mechanisms and their regulation and provides a real-time readout of gene activity during the life of a cell. In this review, we try to reconcile the different views of the transcriptional process emerging from studies of bursting, and how this work contextualizes the relative importance of different regulatory inputs to normal dynamic ranges of gene activity.

A Mechanochemical Model of Transcriptional Bursting

Populations of genetically identical cells generally show a large variability in cell phenotypes, which is typically associated with the stochastic nature of gene expression processes. It is widely believed that a significant source of such randomness is transcriptional bursting, which is when periods of active production of RNA molecules alternate with periods of RNA degradation. However, the molecular mechanisms of such strong fluctuations remain unclear. Recent studies suggest that DNA supercoiling, which happens during transcription, might be directly related to the bursting behavior. Stimulated by these observations, we developed a stochastic mechanochemical model of supercoiling-induced transcriptional bursting in which the RNA synthesis leads to the buildup of torsion in DNA. This slows down the RNA production until it is bound by the enzyme gyrase to DNA, which releases the stress and allows for the RNA synthesis to restart with the original rate. Using a thermodynamically consistent coupling between mechanical and chemical processes, the dynamic properties of transcription are explicitly evaluated. In addition, a first-passage method to evaluate the dynamics of transcription is developed. Theoretical analysis shows that transcriptional bursting is observed when both the supercoiling and the mechanical stress release due to gyrase are present in the system. It is also found that the overall RNA production rate is not constant and depends on the number of previously synthesized RNA molecules. A comparison with experimental data on bacteria allows us to evaluate the energetic cost of supercoiling during transcription. It is argued that the relatively weak mechanochemical coupling might allow transcription to be regulated most effectively.