Consequences of mRNA transport on stochastic variability in protein levels

Translation regulation by RNA stem-loops can reduce gene expression noise

BACKGROUND

Stochastic modelling plays a crucial role in comprehending the dynamics of intracellular events in various biochemical systems, including gene-expression models. Cell-to-cell variability arises from the stochasticity or noise in the levels of gene products such as messenger RNA (mRNA) and protein. The sources of noise can stem from different factors, including structural elements. Recent studies have revealed that the mRNA structure can be more intricate than previously assumed.

RESULTS

Here, we focus on the formation of stem-loops and present a reinterpretation of previous data, offering new insights. Our analysis demonstrates that stem-loops that restrict translation have the potential to reduce noise.

CONCLUSIONS

In conclusion, we investigate a structured/generalised version of a stochastic gene-expression model, wherein mRNA molecules can be found in one of their finite number of different states and transition between them. By characterising and deriving non-trivial analytical expressions for the steady-state protein distribution, we provide two specific examples which can be readily obtained from the structured/generalised model, showcasing the model's practical applicability.

Spectral neural approximations for models of transcriptional dynamics

The advent of high-throughput transcriptomics provides an opportunity to advance mechanistic understanding of transcriptional processes and their connections to cellular function at an unprecedented, genome-wide scale. These transcriptional systems, which involve discrete stochastic events, are naturally modeled using chemical master equations (CMEs), which can be solved for probability distributions to fit biophysical rates that govern system dynamics. While CME models have been used as standards in fluorescence transcriptomics for decades to analyze single-species RNA distributions, there are often no closed-form solutions to CMEs that model multiple species, such as nascent and mature RNA transcript counts. This has prevented the application of standard likelihood-based statistical methods for analyzing high-throughput, multi-species transcriptomic datasets using biophysical models. Inspired by recent work in machine learning to learn solutions to complex dynamical systems, we leverage neural networks and statistical understanding of system distributions to produce accurate approximations to a steady-state bivariate distribution for a model of the RNA life cycle that includes nascent and mature molecules. The steady-state distribution to this simple model has no closed-form solution and requires intensive numerical solving techniques: our approach reduces likelihood evaluation time by several orders of magnitude. We demonstrate two approaches, whereby solutions are approximated by 1) learning the weights of kernel distributions with constrained parameters or 2) learning both weights and scaling factors for parameters of kernel distributions. We show that our strategies, denoted by kernel weight regression and parameter-scaled kernel weight regression, respectively, enable broad exploration of parameter space and can be used in existing likelihood frameworks to infer transcriptional burst sizes, RNA splicing rates, and mRNA degradation rates from experimental transcriptomic data.

Biophysically interpretable inference of cell types from multimodal sequencing data

Multimodal, single-cell genomics technologies enable simultaneous measurement of multiple facets of DNA and RNA processing in the cell. This creates opportunities for transcriptome-wide, mechanistic studies of cellular processing in heterogeneous cell populations, such as regulation of cell fate by transcriptional stochasticity or tumor proliferation through aberrant splicing dynamics. However, current methods for determining cell types or 'clusters' in multimodal data often rely on ad hoc approaches to balance or integrate measurements, and assumptions ignoring inherent properties of the data. To enable interpretable and consistent cell cluster determination, we present meK-means (mechanistic K-means) which integrates modalities through a unifying model of transcription to learn underlying, shared biophysical states. With meK-means we can cluster cells with nascent and mature mRNA measurements, utilizing the causal, physical relationships between these modalities. This identifies shared transcription dynamics across cells, which induce the observed molecule counts, and provides an alternative definition for 'clusters' through the governing parameters of cellular processes.

Biophysical modeling with variational autoencoders for bimodal, single-cell RNA sequencing data

Here we present biVI, which combines the variational autoencoder framework of scVI with biophysical models describing the transcription and splicing kinetics of RNA molecules. We demonstrate on simulated and experimental single-cell RNA sequencing data that biVI retains the variational autoencoder's ability to capture cell type structure in a low-dimensional space while further enabling genome-wide exploration of the biophysical mechanisms, such as system burst sizes and degradation rates, that underlie observations.

Stochastic Modeling of Biophysical Responses to Perturbation

Recent advances in high-throughput, multi-condition experiments allow for genome-wide investigation of how perturbations affect transcription and translation in the cell across multiple biological entities or modalities, from chromatin and mRNA information to protein production and spatial morphology. This presents an unprecedented opportunity to unravel how the processes of DNA and RNA regulation direct cell fate determination and disease response. Most methods designed for analyzing large-scale perturbation data focus on the observational outcomes, e.g., expression; however, many potential transcriptional mechanisms, such as transcriptional bursting or splicing dynamics, can underlie these complex and noisy observations. In this analysis, we demonstrate how a stochastic biophysical modeling approach to interpreting high-throughout perturbation data enables deeper investigation of the 'how' behind such molecular measurements. Our approach takes advantage of modalities already present in data produced with current technologies, such as nascent and mature mRNA measurements, to illuminate transcriptional dynamics induced by perturbation, predict kinetic behaviors in new perturbation settings, and uncover novel populations of cells with distinct kinetic responses to perturbation.

Solving stochastic gene-expression models using queueing theory: A tutorial review

Stochastic models of gene expression are typically formulated using the chemical master equation, which can be solved exactly or approximately using a repertoire of analytical methods. Here, we provide a tutorial review of an alternative approach based on queueing theory that has rarely been used in the literature of gene expression. We discuss the interpretation of six types of infinite-server queues from the angle of stochastic single-cell biology and provide analytical expressions for the stationary and nonstationary distributions and/or moments of mRNA/protein numbers and bounds on the Fano factor. This approach may enable the solution of complex models that have hitherto evaded analytical solution.

Dissection and integration of bursty transcriptional dynamics for complex systems

RNA velocity estimation is a potentially powerful tool to reveal the directionality of transcriptional changes in single-cell RNA-sequencing data, but it lacks accuracy, absent advanced metabolic labeling techniques. We developed an approach, TopicVelo, that disentangles simultaneous, yet distinct, dynamics by using a probabilistic topic model, a highly interpretable form of latent space factorization, to infer cells and genes associated with individual processes, thereby capturing cellular pluripotency or multifaceted functionality. Focusing on process-associated cells and genes enables accurate estimation of process-specific velocities via a master equation for a transcriptional burst model accounting for intrinsic stochasticity. The method obtains a global transition matrix by leveraging cell topic weights to integrate process-specific signals. In challenging systems, this method accurately recovers complex transitions and terminal states, while our use of first-passage time analysis provides insights into transient transitions. These results expand the limits of RNA velocity, empowering future studies of cell fate and functional responses.

Exact solution of a three-stage model of stochastic gene expression including cell-cycle dynamics

The classical three-stage model of stochastic gene expression predicts the statistics of single cell mRNA and protein number fluctuations as a function of the rates of promoter switching, transcription, translation, degradation and dilution. While this model is easily simulated, its analytical solution remains an unsolved problem. Here we modify this model to explicitly include cell-cycle dynamics and then derive an exact solution for the time-dependent joint distribution of mRNA and protein numbers. We show large differences between this model and the classical model which captures cell-cycle effects implicitly via effective first-order dilution reactions. In particular we find that the Fano factor of protein numbers calculated from a population snapshot measurement are underestimated by the classical model whereas the correlation between mRNA and protein can be either over- or underestimated, depending on the timescales of mRNA degradation and promoter switching relative to the mean cell-cycle duration time.

Studying stochastic systems biology of the cell with single-cell genomics data

Recent experimental developments in genome-wide RNA quantification hold considerable promise for systems biology. However, rigorously probing the biology of living cells requires a unified mathematical framework that accounts for single-molecule biological stochasticity in the context of technical variation associated with genomics assays. We review models for a variety of RNA transcription processes, as well as the encapsulation and library construction steps of microfluidics-based single-cell RNA sequencing, and present a framework to integrate these phenomena by the manipulation of generating functions. Finally, we use simulated scenarios and biological data to illustrate the implications and applications of the approach.

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.

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.

Biophysically Interpretable Inference of Cell Types from Multimodal Sequencing Data

Multimodal, single-cell genomics technologies enable simultaneous capture of multiple facets of DNA and RNA processing in the cell. This creates opportunities for transcriptome-wide, mechanistic studies of cellular processing in heterogeneous cell types, with applications ranging from inferring kinetic differences between cells, to the role of stochasticity in driving heterogeneity. However, current methods for determining cell types or 'clusters' present in multimodal data often rely on ad hoc or independent treatment of modalities, and assumptions ignoring inherent properties of the count data. To enable interpretable and consistent cell cluster determination from multimodal data, we present meK-Means (mechanistic K-Means) which integrates modalities and learns underlying, shared biophysical states through a unifying model of transcription. In particular, we demonstrate how meK-Means can be used to cluster cells from unspliced and spliced mRNA count modalities. By utilizing the causal, physical relationships underlying these modalities, we identify shared transcriptional kinetics across cells, which induce the observed gene expression profiles, and provide an alternative definition for 'clusters' through the governing parameters of cellular processes.

Dissection and Integration of Bursty Transcriptional Dynamics for Complex Systems

RNA velocity estimation is a potentially powerful tool to reveal the directionality of transcriptional changes in single-cell RNA-seq data, but it lacks accuracy, absent advanced metabolic labeling techniques. We developed a novel approach, TopicVelo, that disentangles simultaneous, yet distinct, dynamics by using a probabilistic topic model, a highly interpretable form of latent space factorization, to infer cells and genes associated with individual processes, thereby capturing cellular pluripotency or multifaceted functionality. Focusing on process-associated cells and genes enables accurate estimation of process-specific velocities via a master equation for a transcriptional burst model accounting for intrinsic stochasticity. The method obtains a global transition matrix by leveraging cell topic weights to integrate process-specific signals. In challenging systems, this method accurately recovers complex transitions and terminal states, while our novel use of first-passage time analysis provides insights into transient transitions. These results expand the limits of RNA velocity, empowering future studies of cell fate and functional responses.

Studying stochastic systems biology of the cell with single-cell genomics data

Recent experimental developments in genome-wide RNA quantification hold considerable promise for systems biology. However, rigorously probing the biology of living cells requires a unified mathematical framework that accounts for single-molecule biological stochasticity in the context of technical variation associated with genomics assays. We review models for a variety of RNA transcription processes, as well as the encapsulation and library construction steps of microfluidics-based single-cell RNA sequencing, and present a framework to integrate these phenomena by the manipulation of generating functions. Finally, we use simulated scenarios and biological data to illustrate the implications and applications of the approach.

Analysis and design of single-cell experiments to harvest fluctuation information while rejecting measurement noise

Introduction: Despite continued technological improvements, measurement errors always reduce or distort the information that any real experiment can provide to quantify cellular dynamics. This problem is particularly serious for cell signaling studies to quantify heterogeneity in single-cell gene regulation, where important RNA and protein copy numbers are themselves subject to the inherently random fluctuations of biochemical reactions. Until now, it has not been clear how measurement noise should be managed in addition to other experiment design variables (e.g., sampling size, measurement times, or perturbation levels) to ensure that collected data will provide useful insights on signaling or gene expression mechanisms of interest. Methods: We propose a computational framework that takes explicit consideration of measurement errors to analyze single-cell observations, and we derive Fisher Information Matrix (FIM)-based criteria to quantify the information value of distorted experiments. Results and Discussion: We apply this framework to analyze multiple models in the context of simulated and experimental single-cell data for a reporter gene controlled by an HIV promoter. We show that the proposed approach quantitatively predicts how different types of measurement distortions affect the accuracy and precision of model identification, and we demonstrate that the effects of these distortions can be mitigated through explicit consideration during model inference. We conclude that this reformulation of the FIM could be used effectively to design single-cell experiments to optimally harvest fluctuation information while mitigating the effects of image distortion.

Biophysical modeling with variational autoencoders for bimodal, single-cell RNA sequencing data

We motivate and present biVI, which combines the variational autoencoder framework of scVI with biophysically motivated, bivariate models for nascent and mature RNA distributions. While previous approaches to integrate bimodal data via the variational autoencoder framework ignore the causal relationship between measurements, biVI models the biophysical processes that give rise to observations. We demonstrate through simulated benchmarking that biVI captures cell type structure in a low-dimensional space and accurately recapitulates parameter values and copy number distributions. On biological data, biVI provides a scalable route for identifying the biophysical mechanisms underlying gene expression. This analytical approach outlines a generalizable strategy for treating multimodal datasets generated by high-throughput, single-cell genomic assays.

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

Stochastic variation in gene products ("noise") is an inescapable by-product of gene expression. Noise must be minimized to allow for the reliable execution of cellular functions. However, noise cannot be suppressed beyond an intrinsic lower limit. For constitutively expressed genes, this limit is believed to be Poissonian, meaning that the variance in mRNA numbers cannot be lower than their mean. Here, we show that several cell division genes in fission yeast have mRNA variances significantly below this limit, which cannot be explained by the classical gene expression model for low-noise genes. Our analysis reveals that multiple steps in both transcription and mRNA degradation are essential to explain this sub-Poissonian variance. The sub-Poissonian regime differs qualitatively from previously characterized noise regimes, a hallmark being that cytoplasmic noise is reduced when the mRNA export rate increases. Our study re-defines the lower limit of eukaryotic gene expression noise and identifies molecular requirements for ultra-low noise which are expected to support essential cell functions.

Length biases in single-cell RNA sequencing of pre-mRNA

Single-cell RNA sequencing data can be modeled using Markov chains to yield genome-wide insights into transcriptional physics. However, quantitative inference with such data requires careful assessment of noise sources. We find that long pre-mRNA transcripts are over-represented in sequencing data. To explain this trend, we propose a length-based model of capture bias, which may produce false-positive observations. We solve this model and use it to find concordant parameter trends as well as systematic, mechanistically interpretable technical and biological differences in paired data sets.

Interpretable and tractable models of transcriptional noise for the rational design of single-molecule quantification experiments

The question of how cell-to-cell differences in transcription rate affect RNA count distributions is fundamental for understanding biological processes underlying transcription. Answering this question requires quantitative models that are both interpretable (describing concrete biophysical phenomena) and tractable (amenable to mathematical analysis). This enables the identification of experiments which best discriminate between competing hypotheses. As a proof of principle, we introduce a simple but flexible class of models involving a continuous stochastic transcription rate driving a discrete RNA transcription and splicing process, and compare and contrast two biologically plausible hypotheses about transcription rate variation. One assumes variation is due to DNA experiencing mechanical strain, while the other assumes it is due to regulator number fluctuations. We introduce a framework for numerically and analytically studying such models, and apply Bayesian model selection to identify candidate genes that show signatures of each model in single-cell transcriptomic data from mouse glutamatergic neurons.

Quantifying how post-transcriptional noise and gene copy number variation bias transcriptional parameter inference from mRNA distributions

Transcriptional rates are often estimated by fitting the distribution of mature mRNA numbers measured using smFISH (single molecule fluorescence in situ hybridization) with the distribution predicted by the telegraph model of gene expression, which defines two promoter states of activity and inactivity. However, fluctuations in mature mRNA numbers are strongly affected by processes downstream of transcription. In addition, the telegraph model assumes one gene copy but in experiments, cells may have two gene copies as cells replicate their genome during the cell cycle. While it is often presumed that post-transcriptional noise and gene copy number variation affect transcriptional parameter estimation, the size of the error introduced remains unclear. To address this issue, here we measure both mature and nascent mRNA distributions of GAL10 in yeast cells using smFISH and classify each cell according to its cell cycle phase. We infer transcriptional parameters from mature and nascent mRNA distributions, with and without accounting for cell cycle phase and compare the results to live-cell transcription measurements of the same gene. We find that: (i) correcting for cell cycle dynamics decreases the promoter switching rates and the initiation rate, and increases the fraction of time spent in the active state, as well as the burst size; (ii) additional correction for post-transcriptional noise leads to further increases in the burst size and to a large reduction in the errors in parameter estimation. Furthermore, we outline how to correctly adjust for measurement noise in smFISH due to uncertainty in transcription site localisation when introns cannot be labelled. Simulations with parameters estimated from nascent smFISH data, which is corrected for cell cycle phases and measurement noise, leads to autocorrelation functions that agree with those obtained from live-cell imaging.

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.

Analysis of a non-Markov transcription model with nuclear RNA export and RNA nuclear retention

Transcription involves gene activation, nuclear RNA export (NRE) and RNA nuclear retention (RNR). All these processes are multistep and biochemical. A multistep reaction process can create memories between reaction events, leading to non-Markovian kinetics. This raises an unsolved issue: how does molecular memory affect stochastic transcription in the case that NRE and RNR are simultaneously considered? To address this issue, we analyze a non-Markov model, which considers multistep activation, multistep NRE and multistep RNR can interpret many experimental phenomena. In order to solve this model, we introduce an effective transition rate for each reaction. These effective transition rates, which explicitly decode the effect of molecular memory, can transform the original non-Markov issue into an equivalent Markov one. Based on this technique, we derive analytical results, showing that molecular memory can significantly affect the nuclear and cytoplasmic mRNA mean and noise. In addition to the results providing insights into the role of molecular memory in gene expression, our modeling and analysis provide a paradigm for studying more complex stochastic transcription processes.

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.

Coloured noise induces phenotypic diversity with energy dissipation

Genes integrate many different sources of noise to adapt their survival strategy with energy costs, but how this noise impacts gene phenotype switching is not fully understood. Here, we refine a mechanistic model with multiplicative and additive coloured noise and analyse the influence of noise strength (NS) and autocorrelation time (AT) on gene phenotypic diversity. Different from white noise, we found that in the autocorrelation time-scale plane, increasing the multiplicative noise will broaden the bimodal region of the gene product, and additive noise will induce bimodal region drift from the lower level to the higher level, while the AT will promote this transition. Specifically, the effect of AT on gene expression is similar to a feedback loop; that is, the AT of multiplicative noise will elongate the mean first passage time (MFPT) from the low stable state to the high stable state, but it will reduce the MFPT from the high stable state to the low stable state, and the opposite is true for additive noise. Moreover, these transitions will violate the detailed equilibrium and then consume energy. By effective topology network reconstruction, we found that when the NS is small, the more obvious the bimodality is, the lower the energy dissipation; however, when the NS is large, it will consume more energy with a tendency for bimodality. The overall analysis implies that living organisms will utilize noise strength and its autocorrelation time for better survival in complex and fluctuating environments.

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.

Pathway dynamics can delineate the sources of transcriptional noise in gene expression

Single-cell expression profiling opens up new vistas on cellular processes. Extensive cell-to-cell variability at the transcriptomic and proteomic level has been one of the stand-out observations. Because most experimental analyses are destructive we only have access to snapshot data of cellular states. This loss of temporal information presents significant challenges for inferring dynamics, as well as causes of cell-to-cell variability. In particular, we typically cannot separate dynamic variability from within cells ('intrinsic noise') from variability across the population ('extrinsic noise'). Here, we make this non-identifiability mathematically precise, allowing us to identify new experimental set-ups that can assist in resolving this non-identifiability. We show that multiple generic reporters from the same biochemical pathways (e.g. mRNA and protein) can infer magnitudes of intrinsic and extrinsic transcriptional noise, identifying sources of heterogeneity. Stochastic simulations support our theory, and demonstrate that 'pathway-reporters' compare favourably to the well-known, but often difficult to implement, dual-reporter method.

MicroRNA Based Feedforward Control of Intrinsic Gene Expression Noise

Intrinsic noise, which arises in gene expression at low copy numbers, can be controlled by diverse regulatory motifs, including feedforward loops. Here, we study an example of a feedforward control system based on the interaction between an mRNA molecule and an antagonistic microRNA molecule encoded by the same gene, aiming to quantify the variability (or noise) in molecular copy numbers. Using linear noise approximation, we show that the mRNA noise is sub-Poissonian in case of non-bursty transcription, and exhibits a nonmonotonic response both to the species natural lifetime ratio and to the strength of the antagonistic interaction. Additionally, we use the Chemical Reaction Network Theory to prove that the mRNA copy number distribution is Poissonian in the absence of spontaneous mRNA decay channel. In case of transcriptional bursts, we show that feedforward control can attenuate the super-Poissonian gene-expression noise that is due to bursting, and that the effect is more considerable at the protein than at the mRNA level. Our results indicate that the strong coupling between mRNA and microRNA in the sense of burst stoichiometry and also of timing of production events renders the microRNA based feedforward motif an effective mechanism for the control of gene expression noise.

Buffering noise: KAT2A modular contributions to stabilization of transcription and cell identity in cancer and development

KAT2A is a histone acetyltransferase recently identified as a vulnerability in at least some forms of Acute Myeloid Leukemia (AML). Its loss or inhibition prompts leukemia stem cells out of self-renewal and into differentiation with ultimate exhaustion of the leukemia pool. We have recently linked the Kat2a requirement in AML to control of transcriptional noise, reflecting an evolutionary-conserved role of Kat2a in promoting burst-like promoter activity and stabilizing gene expression. We suggest that through this role, Kat2a contributes to preservation of cell identity. KAT2A exerts its acetyltransferase activity in the context of two macromolecular complexes, Spt-Ada-Gcn5-Acetyltransferase (SAGA) and Ada-Two-A-Containing (ATAC), but the specific contribution of each complex to stabilization of gene expression is currently unknown. By reviewing specific gene targets and requirements of the two complexes in cancer and development, we suggest that SAGA regulates lineage-specific programs, and ATAC maintains biosynthetic activity through control of ribosomal protein and translation-associated genes, on which cells may be differentially dependent. While our data suggest that KAT2A-mediated regulation of transcriptional noise in AML may be exerted through ATAC, we discuss potential caveats and probe general vs. complex-specific contributions of KAT2A to transcriptional stability, with implications for control and perturbation of cell identity.

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.

Mixture distributions in a stochastic gene expression model with delayed feedback: a WKB approximation approach

Noise in gene expression can be substantively affected by the presence of production delay. Here we consider a mathematical model with bursty production of protein, a one-step production delay (the passage of which activates the protein), and feedback in the frequency of bursts. We specifically focus on examining the steady-state behaviour of the model in the slow-activation (i.e. large-delay) regime. Using a formal asymptotic approach, we derive an autonomous ordinary differential equation for the inactive protein that applies in the slow-activation regime. If the differential equation is monostable, the steady-state distribution of the inactive (active) protein is approximated by a single Gaussian (Poisson) mode located at the globally stable fixed point of the differential equation. If the differential equation is bistable (due to cooperative positive feedback), the steady-state distribution of the inactive (active) protein is approximated by a mixture of Gaussian (Poisson) modes located at the stable fixed points; the weights of the modes are determined from a WKB approximation to the stationary distribution. The asymptotic results are compared to numerical solutions of the chemical master equation.

Enhancement of gene expression noise from transcription factor binding to genomic decoy sites

The genome contains several high-affinity non-functional binding sites for transcription factors (TFs) creating a hidden and unexplored layer of gene regulation. We investigate the role of such “decoy sites” in controlling noise (random fluctuations) in the level of a TF that is synthesized in stochastic bursts. Prior studies have assumed that decoy-bound TFs are protected from degradation, and in this case decoys function to buffer noise. Relaxing this assumption to consider arbitrary degradation rates for both bound/unbound TF states, we find rich noise behaviors. For low-affinity decoys, noise in the level of unbound TF always monotonically decreases to the Poisson limit with increasing decoy numbers. In contrast, for high-affinity decoys, noise levels first increase with increasing decoy numbers, before decreasing back to the Poisson limit. Interestingly, while protection of bound TFs from degradation slows the time-scale of fluctuations in the unbound TF levels, the decay of bound TFs leads to faster fluctuations and smaller noise propagation to downstream target proteins. In summary, our analysis reveals stochastic dynamics emerging from nonspecific binding of TFs and highlights the dual role of decoys as attenuators or amplifiers of gene expression noise depending on their binding affinity and stability of the bound TF.

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

The process of transcription initiation and elongation are primary points of control in the regulation of gene expression. Although biochemical studies have uncovered the mechanisms involved in controlling transcription at each step, how these mechanisms manifest in vivo at the level of individual genes is still unclear. Recent experimental advances have enabled single-cell measurements of RNA polymerase (RNAP) molecules engaged in the process of transcribing a gene of interest. In this article, we use Gillespie simulations to show that measurements of cell-to-cell variability of RNAP numbers and interpolymerase distances can reveal the prevailing mode of regulation of a given gene. Mechanisms of regulation at each step, from initiation to elongation dynamics, produce qualitatively distinct signatures, which can further be used to discern between them. Most intriguingly, depending on the initiation kinetics, stochastic elongation can either enhance or suppress cell-to-cell variability at the RNAP level. To demonstrate the value of this framework, we analyze RNAP number distribution data for ribosomal genes in Saccharomyces cerevisiae from three previously published studies and show that this approach provides crucial mechanistic insights into the transcriptional regulation of these genes.

Coupled membrane transporters reduce noise

Molecular systems are inherently probabilistic and operate in a noisy environment, yet, despite all these uncertainties, molecular functions are surprisingly reliable and robust. The principles used by natural systems to deal with noise are still not well understood, especially in a nonhomogeneous environment where molecules can diffuse across different compartments. In this paper we show that membrane transport mechanisms have very effective properties of noise reduction. In particular, we show that active transport mechanisms (those that can transport against a gradient of concentration by using energy or by means of the concentration gradient of other substances), such as symporters and antiporters, have surprising efficiency in noise reduction, which outperforms passive diffusion mechanisms and are well below Poisson levels. We link our results to the coupled transport of potassium, sodium, and glucose to show that the noise in internal glucose level can be greatly reduced. Our results show that compartmentalization can be a highly effective mechanism of noise reduction and suggests that membrane transport could give this extra benefit, contributing to the emergence of complex compartmentalization in eukaryotes.

Decoding the grammar of transcriptional regulation from RNA polymerase measurements: models and their applications

The genomic revolution has indubitably brought about a paradigm shift in the field of molecular biology, wherein we can sequence, write and re-write genomes. In spite of achieving such feats, we still lack a quantitative understanding of how cells integrate environmental and intra-cellular signals at the promoter and accordingly regulate the production of messenger RNAs. This current state of affairs is being redressed by recent experimental breakthroughs which enable the counting of RNA polymerase molecules (or the corresponding nascent RNAs) engaged in the process of transcribing a gene at the single-cell level. Theorists, in conjunction, have sought to unravel the grammar of transcriptional regulation by harnessing the various statistical properties of these measurements. In this review, we focus on the recent progress in developing falsifiable models of transcription that aim to connect the molecular mechanisms of transcription to single-cell polymerase measurements. We discuss studies where the application of such models to the experimental data have led to novel mechanistic insights into the process of transcriptional regulation. Such interplay between theory and experiments will likely contribute towards the exciting journey of unfurling the governing principles of transcriptional regulation ranging from bacteria to higher organisms.

Modulation of first-passage time for gene expression via asymmetric cell division

How to balance the size of exponentially growing cells has always been a focus of biologists. Recent experiments have uncovered that the cell is divided into two daughter cells only when the level of time-keeper protein reaches a fixed threshold and cell division in prokaryote is not completely symmetric. The timing of cell division is essentially random because gene expression is stochastic, but cells seen to manage to have precise timing of cell division events. Although the inter-cellular variability of gene expression has attracted much attention, the randomness of event timing has been rarely studied. In our analysis, the timing of cell division is formulated as the first-passage time (denoted by FPT) for time-keeper protein’s level to cross a critical threshold firstly, we derive exact analytical formulae for the mean and noise of FPT based on stochastic gene expression model with asymmetric cell division. The results of numerical simulation show that the regulatory factors (division rate, newborn cell size, exponential growth rate and threshold) have significant influence on the mean and noise of FPT. We also show that both the increase of division rate and newborn cell size could reduce the mean of FPT and increase the noise of FPT, the larger the exponential growth rate is, the smaller the mean and noise of FPT will be; and the larger the threshold value is, the higher the mean of FPT is and the lower the noise is. In addition, compared with symmetric division, asymmetric division can reduce the mean of FPT and improve the noise of FPT. In summary, our results provide insight into the relationship between regulatory factors and FPT and reveal that asymmetric division is an effective mechanism to shorten the mean of FPT.

Post-Transcriptional Noise Control

Recent evidence indicates that transcriptional bursts are intrinsically amplified by messenger RNA cytoplasmic processing to generate large stochastic fluctuations in protein levels. These fluctuations can be exploited by cells to enable probabilistic bet-hedging decisions. But large fluctuations in gene expression can also destabilize cell-fate commitment. Thus, it is unclear if cells temporally switch from high to low noise, and what mechanisms enable this switch. Here, the discovery of a post-transcriptional mechanism that attenuates noise in HIV is reviewed. Early in its life cycle, HIV amplifies transcriptional fluctuations to probabilistically select alternate fates, whereas at late times, HIV utilizes a post-transcriptional feedback mechanism to commit to a specific fate. Reanalyzing various reported post-transcriptional negative feedback architectures reveals that they attenuate noise more efficiently than classic transcriptional autorepression, leading to the derivation of an assay to detect post-transcriptional motifs. It is hypothesized that coupling transcriptional and post-transcriptional autoregulation enables efficient temporal noise control to benefit developmental bet-hedging decisions.

Distribution of Initiation Times Reveals Mechanisms of Transcriptional Regulation in Single Cells

Transcription is the dominant point of control of gene expression. Biochemical studies have revealed key molecular components of transcription and their interactions, but the dynamics of transcription initiation in cells is still poorly understood. This state of affairs is being remedied with experiments that observe transcriptional dynamics in single cells using fluorescent reporters. Quantitative information about transcription initiation dynamics can also be extracted from experiments that use electron micrographs of RNA polymerases caught in the act of transcribing a gene (Miller spreads). Inspired by these data, we analyze a general stochastic model of transcription initiation and elongation and compute the distribution of transcription initiation times. We show that different mechanisms of initiation leave distinct signatures in the distribution of initiation times that can be compared to experiments. We analyze published data from micrographs of RNA polymerases transcribing ribosomal RNA genes in Escherichia coli and compare the observed distributions of interpolymerase distances with the predictions from previously hypothesized mechanisms for the regulation of these genes. Our analysis demonstrates the potential of measuring the distribution of time intervals between initiation events as a probe for dissecting mechanisms of transcription initiation in live cells.

Cytoplasmic Amplification of Transcriptional Noise Generates Substantial Cell-to-Cell Variability

Transcription is an episodic process characterized by probabilistic bursts, but how the transcriptional noise from these bursts is modulated by cellular physiology remains unclear. Using simulations and single-molecule RNA counting, we examined how cellular processes influence cell-to-cell variability (noise). The results show that RNA noise is higher in the cytoplasm than the nucleus in ∼85% of genes across diverse promoters, genomic loci, and cell types (human and mouse). Measurements show further amplification of RNA noise in the cytoplasm, fitting a model of biphasic mRNA conversion between translation- and degradation-competent states. This multi-state translation-degradation of mRNA also causes substantial noise amplification in protein levels, ultimately accounting for ∼74% of intrinsic protein variability in cell populations. Overall, the results demonstrate how noise from transcriptional bursts is intrinsically amplified by mRNA processing, leading to a large super-Poissonian variability in protein levels.

Nascent RNA kinetics: Transient and steady state behavior of models of transcription

Regulation of transcription is a vital process in cells, but mechanistic details of this regulation still remain elusive. The dominant approach to unravel the dynamics of transcriptional regulation is to first develop mathematical models of transcription and then experimentally test the predictions these models make for the distribution of mRNA and protein molecules at the individual cell level. However, these measurements are affected by a multitude of downstream processes which make it difficult to interpret the measurements. Recent experimental advancements allow for counting the nascent mRNA number of a gene as a function of time at the single-cell level. These measurements closely reflect the dynamics of transcription. In this paper, we consider a general mechanism of transcription with stochastic initiation and deterministic elongation and probe its impact on the temporal behavior of nascent RNA levels. Using techniques from queueing theory, we derive exact analytical expressions for the mean and variance of the nascent RNA distribution as functions of time. We apply these analytical results to obtain the mean and variance of nascent RNA distribution for specific models of transcription. These models of initiation exhibit qualitatively distinct transient behaviors for both the mean and variance which further allows us to discriminate between them. Stochastic simulations confirm these results. Overall the analytical results presented here provide the necessary tools to connect mechanisms of transcription initiation to single-cell measurements of nascent RNA.

Single molecule approaches for studying gene regulation in metabolic tissues

Gene expression in metabolic tissues can be regulated at multiple levels, ranging from the control of promoter accessibilities, transcription rates, mRNA degradation rates and mRNA localization. Modulating these processes can differentially affect important performance criteria of cells. These include precision, cellular economy, rapid response and maintenance of DNA integrity. In this review we will describe how distinct strategies of gene regulation impact the trade-offs between the cells' performance criteria. We will highlight tools based on single molecule visualization of transcripts that can be used to measure promoter states, transcription rates and mRNA degradation rates in intact tissues. These approaches revealed surprising recurrent patterns in mammalian tissues, that include transcriptional bursting, nuclear retention of mRNA, and coordination of mRNA lifetimes to facilitate rapid adaptation to changing metabolic inputs. The ability to characterize gene expression at the single molecule level can uncover the design principles of gene regulation in metabolic tissues such as the liver and the pancreas.

A mechanistic stochastic framework for regulating bacterial cell division

How exponentially growing cells maintain size homeostasis is an important fundamental problem. Recent single-cell studies in prokaryotes have uncovered the adder principle, where cells add a fixed size (volume) from birth to division, irrespective of their size at birth. To mechanistically explain the adder principle, we consider a timekeeper protein that begins to get stochastically expressed after cell birth at a rate proportional to the volume. Cell-division time is formulated as the first-passage time for protein copy numbers to hit a fixed threshold. Consistent with data, the model predicts that the noise in division timing increases with size at birth. Intriguingly, our results show that the distribution of the volume added between successive cell-division events is independent of the newborn cell size. This was dramatically seen in experimental studies, where histograms of the added volume corresponding to different newborn sizes collapsed on top of each other. The model provides further insights consistent with experimental observations: the distribution of the added volume when scaled by its mean becomes invariant of the growth rate. In summary, our simple yet elegant model explains key experimental findings and suggests a mechanism for regulating both the mean and fluctuations in cell-division timing for controlling size.

Control of Transcript Variability in Single Mammalian Cells

A central question in biology is whether variability between genetically identical cells exposed to the same culture conditions is largely stochastic or deterministic. Using image-based transcriptomics in millions of single human cells, we find that while variability of cytoplasmic transcript abundance is large, it is for most genes minimally stochastic and can be predicted with multivariate models of the phenotypic state and population context of single cells. Computational multiplexing of these predictive signatures across hundreds of genes revealed a complex regulatory system that controls the observed variability of transcript abundance between individual cells. Mathematical modeling and experimental validation show that nuclear retention and transport of transcripts between the nucleus and the cytoplasm is central to buffering stochastic transcriptional fluctuations in mammalian gene expression. Our work indicates that cellular compartmentalization confines transcriptional noise to the nucleus, thereby preventing it from interfering with the control of single-cell transcript abundance in the cytoplasm.

Single-cell states versus single-cell atlases - two classes of heterogeneity that differ in meaning and method

Recent advances have created new opportunities to dissect cellular heterogeneity at the omics level. The enthusiasm for deep single-cell profiling has obscured a discussion of different types of heterogeneity and the most-appropriate techniques for studying each type. Here, I distinguish heterogeneity in regulation from heterogeneity in lineage. Snapshots of lineage heterogeneity provide a cell atlas that catalogs cellular diversity within complex tissues. Profiles of regulatory heterogeneity seek to interrogate one lineage deeply to capture an ensemble of single-cell states. Single-cell atlases require molecular signatures from many cells at a throughput afforded by mass cytometry-based, microfluidic-based, and microencapsulation-based methods. Single-cell states are more dependent on time, microenvironment, and low-abundance transcripts, emphasizing in situ methods that stress depth of profiling and quantitative accuracy.

Nuclear Retention of mRNA in Mammalian Tissues

mRNA is thought to predominantly reside in the cytoplasm, where it is translated and eventually degraded. Although nuclear retention of mRNA has a regulatory potential, it is considered extremely rare in mammals. Here, to explore the extent of mRNA retention in metabolic tissues, we combine deep sequencing of nuclear and cytoplasmic RNA fractions with single-molecule transcript imaging in mouse beta cells, liver, and gut. We identify a wide range of protein-coding genes for which the levels of spliced polyadenylated mRNA are higher in the nucleus than in the cytoplasm. These include genes such as the transcription factor ChREBP, Nlrp6, Glucokinase, and Glucagon receptor. We demonstrate that nuclear retention of mRNA can efficiently buffer cytoplasmic transcript levels from noise that emanates from transcriptional bursts. Our study challenges the view that transcripts predominantly reside in the cytoplasm and reveals a role of the nucleus in dampening gene expression noise.

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Genome-wide catalog of nuclear and cytoplasmic mRNA in mouse tissues

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Spliced, polyadenylated mRNA is retained in the nucleus for many protein-coding genes

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Retained genes include ChREBP and liver Nlrp6, co-localized with nuclear speckles

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Nuclear retention of mRNA reduces cytoplasmic gene expression noise

Deciphering Transcriptional Dynamics In Vivo by Counting Nascent RNA Molecules

Deciphering how the regulatory DNA sequence of a gene dictates its expression in response to intra and extracellular cues is one of the leading challenges in modern genomics. The development of novel single-cell sequencing and imaging techniques, as well as a better exploitation of currently available single-molecule imaging techniques, provides an avenue to interrogate the process of transcription and its dynamics in cells by quantifying the number of RNA polymerases engaged in the transcription of a gene (or equivalently the number of nascent RNAs) at a given moment in time. In this paper, we propose that measurements of the cell-to-cell variability in the number of nascent RNAs provide a mostly unexplored method for deciphering mechanisms of transcription initiation in cells. We propose a simple kinetic model of transcription initiation and elongation from which we calculate nascent RNA copy-number fluctuations. To demonstrate the usefulness of this approach, we test our theory against published nascent RNA data for twelve constitutively expressed yeast genes. Rather than transcription being initiated through a single rate limiting step, as it had been previously proposed, our single-cell analysis reveals the presence of at least two rate limiting steps. Surprisingly, half of the genes analyzed have nearly identical rates of transcription initiation, suggesting a common mechanism. Our analytical framework can be used to extract quantitative information about dynamics of transcription from single-cell sequencing data, as well as from single-molecule imaging and electron micrographs of fixed cells, and provides the mathematical means to exploit the quantitative power of these technologies.