Probing Mechanisms of Transcription Elongation Through Cell-to-Cell Variability of RNA Polymerase

Model-based characterization of the equilibrium dynamics of transcription initiation and promoter-proximal pausing in human cells

In metazoans, both transcription initiation and the escape of RNA polymerase (RNAP) from promoter-proximal pausing are key rate-limiting steps in gene expression. These processes play out at physically proximal sites on the DNA template and appear to influence one another through steric interactions. Here, we examine the dynamics of these processes using a combination of statistical modeling, simulation, and analysis of real nascent RNA sequencing data. We develop a simple probabilistic model that jointly describes the kinetics of transcription initiation, pause-escape, and elongation, and the generation of nascent RNA sequencing read counts under steady-state conditions. We then extend this initial model to allow for variability across cells in promoter-proximal pause site locations and steric hindrance of transcription initiation from paused RNAPs. In an extensive series of simulations, we show that this model enables accurate estimation of initiation and pause-escape rates. Furthermore, we show by simulation and analysis of real data that pause-escape is often strongly rate-limiting and that steric hindrance can dramatically reduce initiation rates. Our modeling framework is applicable to a variety of inference problems, and our software for estimation and simulation is freely available.

Regulation of the dynamic RNA Pol II elongation rate in Drosophila embryos

An increasing number of studies have shown the key role that RNA polymerase II (RNA Pol II) elongation plays in gene regulation. We systematically examine how various enhancers, promoters, and gene body composition influence the RNA Pol II elongation rate through a single-cell-resolution live imaging assay. By using reporter constructs containing 5' MS2 and 3' PP7 repeating stem loops, we quantify the rate of RNA Pol II elongation in live Drosophila embryos. We find that promoters and exonic gene lengths have no effect on elongation rate, while enhancers and the presence of long introns may significantly change how quickly RNA Pol II moves across a gene. Furthermore, we observe in multiple constructs that the RNA Pol II elongation rate accelerates after the transcriptional onset of nuclear cycle 14 in Drosophila embryos. Our study provides a single-cell view of various mechanisms that affect the dynamic RNA Pol II elongation rate, ultimately affecting the rate of mRNA production.

Stochastic modeling of the mRNA life process: A generalized master equation

The mRNA life cycle is a complex biochemical process, involving transcription initiation, elongation, termination, splicing, and degradation. Each of these molecular events is multistep and can create a memory. The effect of this molecular memory on gene expression is not clear, although there are many related yet scattered experimental reports. To address this important issue, we develop a general theoretical framework formulated as a master equation in the sense of queue theory, which can reduce to multiple previously studied gene models in limiting cases. This framework allows us to interpret experimental observations, extract kinetic parameters from experimental data, and identify how the mRNA kinetics vary under regulatory influences. Notably, it allows us to evaluate the influences of elongation processes on mature RNA distribution; e.g., we find that the non-exponential elongation time can induce the bimodal mRNA expression and there is an optimal elongation noise intensity such that the mature RNA noise achieves the lowest level. In a word, our framework can not only provide insight into complex mRNA life processes but also bridge a dialogue between theoretical studies and experimental data.

Deciphering a global source of non-genetic heterogeneity in cancer cells

Cell-to-cell variability within a clonal population, also known as non-genetic heterogeneity, has created significant challenges for intervening with diseases such as cancer. While non-genetic heterogeneity can arise from the variability in the expression of specific genes, it remains largely unclear whether and how clonal cells could be heterogeneous in the expression of the entire transcriptome. Here, we showed that gene transcriptional activity is globally modulated in individual cancer cells, leading to non-genetic heterogeneity in the global transcription rate. Such heterogeneity contributes to cell-to-cell variability in transcriptome size and displays both dynamic and static characteristics, with the global transcription rate temporally modulated in a cell-cycle-coupled manner and the time-averaged rate being distinct between cells and heritable across generations. Additional evidence indicated the role of ATP metabolism in this heterogeneity, and suggested its implication in intrinsic cancer drug tolerance. Collectively, our work shed light on the mode, mechanism, and implication of a global but often hidden source of non-genetic heterogeneity.

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.

The minimal intrinsic stochasticity of constitutively expressed eukaryotic genes is sub-Poissonian

Gene expression inherently gives rise to stochastic variation ("noise") in the production of gene products. Minimizing noise is crucial for ensuring reliable cellular functions. However, noise cannot be suppressed below a certain intrinsic limit. For constitutively expressed genes, this limit is typically assumed to be Poissonian noise, wherein the variance in mRNA numbers is equal to their mean. Here, we demonstrate that several cell division genes in fission yeast exhibit mRNA variances significantly below this limit. The reduced variance can be explained by a gene expression model incorporating multiple transcription and mRNA degradation steps. Notably, in this sub-Poissonian regime, distinct from Poissonian or super-Poissonian regimes, cytoplasmic noise is effectively suppressed through a higher mRNA export rate. Our findings redefine the lower limit of eukaryotic gene expression noise and uncover molecular requirements for achieving ultralow noise, which is expected to be important for vital cellular functions.

Collective polymerase dynamics emerge from DNA supercoiling during transcription

All biological processes ultimately come from physical interactions. The mechanical properties of DNA play a critical role in transcription. RNA polymerase can over or under twist DNA (referred to as DNA supercoiling) when it moves along a gene, resulting in mechanical stresses in DNA that impact its own motion and that of other polymerases. For example, when enough supercoiling accumulates, an isolated polymerase halts, and transcription stops. DNA supercoiling can also mediate nonlocal interactions between polymerases that shape gene expression fluctuations. Here, we construct a comprehensive model of transcription that captures how RNA polymerase motion changes the degree of DNA supercoiling, which in turn feeds back into the rate at which polymerases are recruited and move along the DNA. Surprisingly, our model predicts that a group of three or more polymerases move together at a constant velocity and sustain their motion (forming what we call a polymeton), whereas one or two polymerases would have halted. We further show that accounting for the impact of DNA supercoiling on both RNA polymerase recruitment and velocity recapitulates empirical observations of gene expression fluctuations. Finally, we propose a mechanical toggle switch whereby interactions between genes are mediated by DNA twisting as opposed to proteins. Understanding the mechanical regulation of gene expression provides new insights into how endogenous genes can interact and informs the design of new forms of engineered interactions.

Mean-field theory accurately captures the variation of copy number distributions across the mRNA life cycle

We consider a stochastic model where a gene switches between two states, an mRNA transcript is released in the active state, and subsequently it undergoes an arbitrary number of sequential unimolecular steps before being degraded. The reactions effectively describe various stages of the mRNA life cycle such as initiation, elongation, termination, splicing, export, and degradation. We construct a mean-field approach that leads to closed-form steady-state distributions for the number of transcript molecules at each stage of the mRNA life cycle. By comparison with stochastic simulations, we show that the approximation is highly accurate over all the parameter space, independent of the type of expression (constitutive or bursty) and of the shape of the distribution (unimodal, bimodal, and nearly bimodal). The theory predicts that in a population of identical cells, any bimodality is gradually washed away as the mRNA progresses through its life cycle.

Predictive landscapes hidden beneath biological cellular automata

To celebrate Hans Frauenfelder's achievements, we examine energy(-like) "landscapes" for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some biomolecular processes, including gene expression and, as Frauenfelder showed, protein folding. But energy-like landscapes and existing frameworks like statistical mechanics seem impractical for describing many living systems. Difficulties stem from living systems being high dimensional, nonlinear, and governed by many, tightly coupled constituents that are noisy. The predominant modeling approach is devising differential equations that are tailored to each living system. This ad hoc approach faces the notorious "parameter problem": models have numerous nonlinear, mathematical functions with unknown parameter values, even for describing just a few intracellular processes. One cannot measure many intracellular parameters or can only measure them as snapshots in time. Another modeling approach uses cellular automata to represent living systems as discrete dynamical systems with binary variables. Quantitative (Hamiltonian-based) rules can dictate cellular automata (e.g., Cellular Potts Model). But numerous biological features, in current practice, are qualitatively described rather than quantitatively (e.g., gene is (highly) expressed or not (highly) expressed). Cellular automata governed by verbal rules are useful representations for living systems and can mitigate the parameter problem. However, they can yield complex dynamics that are difficult to understand because the automata-governing rules are not quantitative and much of the existing mathematical tools and theorems apply to continuous but not discrete dynamical systems. Recent studies found ways to overcome this challenge. These studies either discovered or suggest an existence of predictive "landscapes" whose shapes are described by Lyapunov functions and yield "equations of motion" for a "pseudo-particle." The pseudo-particle represents the entire cellular lattice and moves on the landscape, thereby giving a low-dimensional representation of the cellular automata dynamics. We outline this promising modeling strategy.

Real-time single-cell characterization of the eukaryotic transcription cycle reveals correlations between RNA initiation, elongation, and cleavage

The eukaryotic transcription cycle consists of three main steps: initiation, elongation, and cleavage of the nascent RNA transcript. Although each of these steps can be regulated as well as coupled with each other, their in vivo dissection has remained challenging because available experimental readouts lack sufficient spatiotemporal resolution to separate the contributions from each of these steps. Here, we describe a novel application of Bayesian inference techniques to simultaneously infer the effective parameters of the transcription cycle in real time and at the single-cell level using a two-color MS2/PP7 reporter gene and the developing fruit fly embryo as a case study. Our method enables detailed investigations into cell-to-cell variability in transcription-cycle parameters as well as single-cell correlations between these parameters. These measurements, combined with theoretical modeling, suggest a substantial variability in the elongation rate of individual RNA polymerase molecules. We further illustrate the power of this technique by uncovering a novel mechanistic connection between RNA polymerase density and nascent RNA cleavage efficiency. Thus, our approach makes it possible to shed light on the regulatory mechanisms in play during each step of the transcription cycle in individual, living cells at high spatiotemporal resolution.

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.

A matter of time: Using dynamics and theory to uncover mechanisms of transcriptional bursting

Eukaryotic transcription generally occurs in bursts of activity lasting minutes to hours; however, state-of-the-art measurements have revealed that many of the molecular processes that underlie bursting, such as transcription factor binding to DNA, unfold on timescales of seconds. This temporal disconnect lies at the heart of a broader challenge in physical biology of predicting transcriptional outcomes and cellular decision-making from the dynamics of underlying molecular processes. Here, we review how new dynamical information about the processes underlying transcriptional control can be combined with theoretical models that predict not only averaged transcriptional dynamics, but also their variability, to formulate testable hypotheses about the molecular mechanisms underlying transcriptional bursting and control.