Stochastic simulation and statistical inference platform for visualization and estimation of transcriptional kinetics

Global transcription regulation revealed from dynamical correlations in time-resolved single-cell RNA sequencing

Single-cell transcriptomics reveals significant variations in transcriptional activity across cells. Yet, it remains challenging to identify mechanisms of transcription dynamics from static snapshots. It is thus still unknown what drives global transcription dynamics in single cells. We present a stochastic model of gene expression with cell size- and cell cycle-dependent rates in growing and dividing cells that harnesses temporal dimensions of single-cell RNA sequencing through metabolic labeling protocols and cel lcycle reporters. We develop a parallel and highly scalable approximate Bayesian computation method that corrects for technical variation and accurately quantifies absolute burst frequency, burst size, and degradation rate along the cell cycle at a transcriptome-wide scale. Using Bayesian model selection, we reveal scaling between transcription rates and cell size and unveil waves of gene regulation across the cell cycle-dependent transcriptome. Our study shows that stochastic modeling of dynamical correlations identifies global mechanisms of transcription regulation. A record of this paper's transparent peer review process is included in the supplemental information.

Assessing Markovian and Delay Models for Single-Nucleus RNA Sequencing

The serial nature of reactions involved in the RNA life-cycle motivates the incorporation of delays in models of transcriptional dynamics. The models couple a transcriptional process to a fairly general set of delayed monomolecular reactions with no feedback. We provide numerical strategies for calculating the RNA copy number distributions induced by these models, and solve several systems with splicing, degradation, and catalysis. An analysis of single-cell and single-nucleus RNA sequencing data using these models reveals that the kinetics of nuclear export do not appear to require invocation of a non-Markovian waiting time.

Bayesian analysis dissects kinetic modulation during non-stationary gene expression

Labelling of nascent stem loops with fluorescent proteins has fostered the visualization of transcription in living cells. Quantitative analysis of recorded fluorescence traces can shed light on kinetic transcription parameters and regulatory mechanisms. However, existing methods typically focus on steady state dynamics. Here, we combine a stochastic process transcription model with a hierarchical Bayesian method to infer global as well locally shared parameters for groups of cells and recover unobserved quantities such as initiation times and polymerase loading of the gene. We apply our approach to the cyclic response of the yeast CUP1 locus to heavy metal stress. Within the previously described slow cycle of transcriptional activity on the scale of minutes, we discover fast time-modulated bursting on the scale of seconds. Model comparison suggests that slow oscillations of transcriptional output are regulated by the amplitude of the bursts. Several polymerases may initiate during a burst.

Synergising single-cell resolution and 4sU labelling boosts inference of transcriptional bursting

Despite the recent rise of RNA-seq datasets combining single-cell (sc) resolution with 4-thiouridine (4sU) labelling, analytical methods exploiting their power to dissect transcriptional bursting are lacking. Here, we present a mathematical model and Bayesian inference implementation to facilitate genome-wide joint parameter estimation and confidence quantification (R package: burstMCMC). We demonstrate that, unlike conventional scRNA-seq, 4sU scRNA-seq resolves temporal parameters and furthermore boosts inference of dimensionless parameters via a synergy between single-cell resolution and 4sU labelling. We apply our method to published 4sU scRNA-seq data and linked with ChIP-seq data, we uncover previously obscured associations between different parameters and histone modifications.

RNA velocity unraveled

We perform a thorough analysis of RNA velocity methods, with a view towards understanding the suitability of the various assumptions underlying popular implementations. In addition to providing a self-contained exposition of the underlying mathematics, we undertake simulations and perform controlled experiments on biological datasets to assess workflow sensitivity to parameter choices and underlying biology. Finally, we argue for a more rigorous approach to RNA velocity, and present a framework for Markovian analysis that points to directions for improvement and mitigation of current problems.

Modeling bursty transcription and splicing with the chemical master equation

Splicing cascades that alter gene products posttranscriptionally also affect expression dynamics. We study a class of processes and associated distributions that emerge from models of bursty promoters coupled to directed acyclic graphs of splicing. These solutions provide full time-dependent joint distributions for an arbitrary number of species with general noise behaviors and transient phenomena, offering qualitative and quantitative insights about how splicing can regulate expression dynamics. Finally, we derive a set of quantitative constraints on the minimum complexity necessary to reproduce gene coexpression patterns using synchronized burst models. We validate these findings by analyzing long-read sequencing data, where we find evidence of expression patterns largely consistent with these constraints.

Altering transcription factor binding reveals comprehensive transcriptional kinetics of a basic gene

Transcription is a vital process activated by transcription factor (TF) binding. The active gene releases a burst of transcripts before turning inactive again. While the basic course of transcription is well understood, it is unclear how binding of a TF affects the frequency, duration and size of a transcriptional burst. We systematically varied the residence time and concentration of a synthetic TF and characterized the transcription of a synthetic reporter gene by combining single molecule imaging, single molecule RNA-FISH, live transcript visualisation and analysis with a novel algorithm, Burst Inference from mRNA Distributions (BIRD). For this well-defined system, we found that TF binding solely affected burst frequency and variations in TF residence time had a stronger influence than variations in concentration. This enabled us to device a model of gene transcription, in which TF binding triggers multiple successive steps before the gene transits to the active state and actual mRNA synthesis is decoupled from TF presence. We quantified all transition times of the TF and the gene, including the TF search time and the delay between TF binding and the onset of transcription. Our quantitative measurements and analysis revealed detailed kinetic insight, which may serve as basis for a bottom-up understanding of gene regulation.

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.

Special function methods for bursty models of transcription

We explore a Markov model used in the analysis of gene expression, involving the bursty production of pre-mRNA, its conversion to mature mRNA, and its consequent degradation. We demonstrate that the integration used to compute the solution of the stochastic system can be approximated by the evaluation of special functions. Furthermore, the form of the special function solution generalizes to a broader class of burst distributions. In light of the broader goal of biophysical parameter inference from transcriptomics data, we apply the method to simulated data, demonstrating effective control of precision and runtime. Finally, we propose and validate a non-Bayesian approach for parameter estimation based on the characteristic function of the target joint distribution of pre-mRNA and mRNA.