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

Transient power-law behaviour following induction distinguishes between competing models of stochastic gene expression

What features of transcription can be learnt by fitting mathematical models of gene expression to mRNA count data? Given a suite of models, fitting to data selects an optimal one, thus identifying a probable transcriptional mechanism. Whilst attractive, the utility of this methodology remains unclear. Here, we sample steady-state, single-cell mRNA count distributions from parameters in the physiological range, and show they cannot be used to confidently estimate the number of inactive gene states, i.e. the number of rate-limiting steps in transcriptional initiation. Distributions from over 99% of the parameter space generated using models with 2, 3, or 4 inactive states can be well fit by one with a single inactive state. However, we show that for many minutes following induction, eukaryotic cells show an increase in the mean mRNA count that obeys a power law whose exponent equals the sum of the number of states visited from the initial inactive to the active state and the number of rate-limiting post-transcriptional processing steps. Our study shows that estimation of the exponent from eukaryotic data can be sufficient to determine a lower bound on the total number of regulatory steps in transcription initiation, splicing, and nuclear export.

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.

A stochastic vs deterministic perspective on the timing of cellular events

Cells are the fundamental units of life, and like all life forms, they change over time. Changes in cell state are driven by molecular processes; of these many are initiated when molecule numbers reach and exceed specific thresholds, a characteristic that can be described as "digital cellular logic". Here we show how molecular and cellular noise profoundly influence the time to cross a critical threshold-the first-passage time-and map out scenarios in which stochastic dynamics result in shorter or longer average first-passage times compared to noise-less dynamics. We illustrate the dependence of the mean first-passage time on noise for a set of exemplar models of gene expression, auto-regulatory feedback control, and enzyme-mediated catalysis. Our theory provides intuitive insight into the origin of these effects and underscores two important insights: (i) deterministic predictions for cellular event timing can be highly inaccurate when molecule numbers are within the range known for many cells; (ii) molecular noise can significantly shift mean first-passage times, particularly within auto-regulatory genetic feedback circuits.

Cis-regulatory control of transcriptional timing and noise in response to estrogen

Cis-regulatory elements control transcription levels, temporal dynamics, and cell-cell variation or transcriptional noise. However, the combination of regulatory features that control these different attributes is not fully understood. Here, we used single-cell RNA-seq during an estrogen treatment time course and machine learning to identify predictors of expression timing and noise. We found that genes with multiple active enhancers exhibit faster temporal responses. We verified this finding by showing that manipulation of enhancer activity changes the temporal response of estrogen target genes. Analysis of transcriptional noise uncovered a relationship between promoter and enhancer activity, with active promoters associated with low noise and active enhancers linked to high noise. Finally, we observed that co-expression across single cells is an emergent property associated with chromatin looping, timing, and noise. Overall, our results indicate a fundamental tradeoff between a gene's ability to quickly respond to incoming signals and maintain low variation across cells.

Cis-regulatory control of transcriptional timing and noise in response to estrogen

Cis-regulatory elements control transcription levels, temporal dynamics, and cell-cell variation or transcriptional noise. However, the combination of regulatory features that control these different attributes is not fully understood. Here, we used single cell RNA-seq during an estrogen treatment time course and machine learning to identify predictors of expression timing and noise. We find that genes with multiple active enhancers exhibit faster temporal responses. We verified this finding by showing that manipulation of enhancer activity changes the temporal response of estrogen target genes. Analysis of transcriptional noise uncovered a relationship between promoter and enhancer activity, with active promoters associated with low noise and active enhancers linked to high noise. Finally, we observed that co-expression across single cells is an emergent property associated with chromatin looping, timing, and noise. Overall, our results indicate a fundamental tradeoff between a gene's ability to quickly respond to incoming signals and maintain low variation across cells.

Quantifying and correcting bias in transcriptional parameter inference from single-cell data

The snapshot distribution of mRNA counts per cell can be measured using single-molecule fluorescence in situ hybridization or single-cell RNA sequencing. These distributions are often fit to the steady-state distribution of the two-state telegraph model to estimate the three transcriptional parameters for a gene of interest: mRNA synthesis rate, the switching on rate (the on state being the active transcriptional state), and the switching off rate. This model assumes no extrinsic noise, i.e., parameters do not vary between cells, and thus estimated parameters are to be understood as approximating the average values in a population. The accuracy of this approximation is currently unclear. Here, we develop a theory that explains the size and sign of estimation bias when inferring parameters from single-cell data using the standard telegraph model. We find specific bias signatures depending on the source of extrinsic noise (which parameter is most variable across cells) and the mode of transcriptional activity. If gene expression is not bursty then the population averages of all three parameters are overestimated if extrinsic noise is in the synthesis rate; underestimation occurs if extrinsic noise is in the switching on rate; both underestimation and overestimation can occur if extrinsic noise is in the switching off rate. We find that some estimated parameters tend to infinity as the size of extrinsic noise approaches a critical threshold. In contrast when gene expression is bursty, we find that in all cases the mean burst size (ratio of the synthesis rate to the switching off rate) is overestimated while the mean burst frequency (the switching on rate) is underestimated. We estimate the size of extrinsic noise from the covariance matrix of sequencing data and use this together with our theory to correct published estimates of transcriptional parameters for mammalian genes.

Modelling capture efficiency of single-cell RNA-sequencing data improves inference of transcriptome-wide burst kinetics

MOTIVATION

Gene expression is characterized by stochastic bursts of transcription that occur at brief and random periods of promoter activity. The kinetics of gene expression burstiness differs across the genome and is dependent on the promoter sequence, among other factors. Single-cell RNA sequencing (scRNA-seq) has made it possible to quantify the cell-to-cell variability in transcription at a global genome-wide level. However, scRNA-seq data are prone to technical variability, including low and variable capture efficiency of transcripts from individual cells.

RESULTS

Here, we propose a novel mathematical theory for the observed variability in scRNA-seq data. Our method captures burst kinetics and variability in both the cell size and capture efficiency, which allows us to propose several likelihood-based and simulation-based methods for the inference of burst kinetics from scRNA-seq data. Using both synthetic and real data, we show that the simulation-based methods provide an accurate, robust and flexible tool for inferring burst kinetics from scRNA-seq data. In particular, in a supervised manner, a simulation-based inference method based on neural networks proves to be accurate and useful when applied to both allele and nonallele-specific scRNA-seq data.

AVAILABILITY AND IMPLEMENTATION

The code for Neural Network and Approximate Bayesian Computation inference is available at https://github.com/WT215/nnRNA and https://github.com/WT215/Julia_ABC, respectively.

A Markovian arrival stream approach to stochastic gene expression in cells

We analyse a generalisation of the stochastic gene expression model studied recently in Fromion et al. (SIAM J Appl Math 73:195-211, 2013) and Robert (Probab Surv 16:277-332, 2019) that keeps track of the production of both mRNA and protein molecules, using techniques from the theory of point processes, as well as ideas from the theory of matrix-analytic methods. Here, both the activity of a gene and the creation of mRNA are modelled with an arbitrary Markovian Arrival Process governed by finitely many phases, and each mRNA molecule during its lifetime gives rise to protein molecules in accordance with a Poisson process. This modification is important, as Markovian Arrival Processes can be used to approximate many types of point processes on the nonnegative real line, meaning this framework allows us to further relax our assumptions on the overall process of transcription.

Long-Term Transcriptomic Changes and Cardiomyocyte Hyperpolyploidy after Lactose Intolerance in Neonatal Rats

Many cardiovascular diseases originate from growth retardation, inflammation, and malnutrition during early postnatal development. The nature of this phenomenon is not completely understood. Here we aimed to verify the hypothesis that systemic inflammation triggered by neonatal lactose intolerance (NLI) may exert long-term pathologic effects on cardiac developmental programs and cardiomyocyte transcriptome regulation. Using the rat model of NLI triggered by lactase overloading with lactose and the methods of cytophotometry, image analysis, and mRNA-seq, we evaluated cardiomyocyte ploidy, signs of DNA damage, and NLI-associated long-term transcriptomic changes of genes and gene modules that differed qualitatively (i.e., were switched on or switched off) in the experiment vs. the control. Our data indicated that NLI triggers the long-term animal growth retardation, cardiomyocyte hyperpolyploidy, and extensive transcriptomic rearrangements. Many of these rearrangements are known as manifestations of heart pathologies, including DNA and telomere instability, inflammation, fibrosis, and reactivation of fetal gene program. Moreover, bioinformatic analysis identified possible causes of these pathologic traits, including the impaired signaling via thyroid hormone, calcium, and glutathione. We also found transcriptomic manifestations of increased cardiomyocyte polyploidy, such as the induction of gene modules related to open chromatin, e.g., "negative regulation of chromosome organization", "transcription" and "ribosome biogenesis". These findings suggest that ploidy-related epigenetic alterations acquired in the neonatal period permanently rewire gene regulatory networks and alter cardiomyocyte transcriptome. Here we provided first evidence indicating that NLI can be an important trigger of developmental programming of adult cardiovascular disease. The obtained results can help to develop preventive strategies for reducing the NLI-associated adverse effects of inflammation on the developing cardiovascular system.

Coupling gene expression dynamics to cell size dynamics and cell cycle events: Exact and approximate solutions of the extended telegraph model

The standard model describing the fluctuations of mRNA numbers in single cells is the telegraph model which includes synthesis and degradation of mRNA, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by the cell cycle phase, cellular growth and division, and other crucial aspects of cellular biology. Here, we derive the analytical time-dependent solution of an extended telegraph model that explicitly considers the doubling of gene copy numbers upon DNA replication, dependence of the mRNA synthesis rate on cellular volume, gene dosage compensation, partitioning of molecules during cell division, cell-cycle duration variability, and cell-size control strategies. Based on the time-dependent solution, we obtain the analytical distributions of transcript numbers for lineage and population measurements in steady-state growth and also find a linear relation between the Fano factor of mRNA fluctuations and cell volume fluctuations. We show that generally the lineage and population distributions in steady-state growth cannot be accurately approximated by the steady-state solution of extrinsic noise models, i.e. a telegraph model with parameters drawn from probability distributions. This is because the mRNA lifetime is often not small enough compared to the cell cycle duration to erase the memory of division and replication. Accurate approximations are possible when this memory is weak, e.g. for genes with bursty expression and for which there is sufficient gene dosage compensation when replication occurs.

Allelic correlation is a marker of trade-offs between barriers to transmission of expression variability and signal responsiveness in genetic networks

Genetic networks should respond to signals but prevent the transmission of spontaneous fluctuations. Limited data from mammalian cells suggest that noise transmission is uncommon, but systematic claims about noise transmission have been limited by the inability to directly measure it. Here, we build a mathematical framework modeling allelic correlation and noise transmission, showing that allelic correlation and noise transmission correspond across model parameters and network architectures. Limiting noise transmission comes with the trade-off of being unresponsive to signals, and within responsive regimes, there is a further trade-off between response time and basal noise transmission. Analysis of allele-specific single-cell RNA-sequencing data revealed that genes encoding upstream factors in signaling pathways and cell-type-specific factors have higher allelic correlation than downstream factors, suggesting they are more subject to regulation. Overall, our findings suggest that some noise transmission must result from signal responsiveness, but it can be minimized by trading off for a slower response. A record of this paper's transparent peer review process is included in the supplemental information.

Transcriptional noise adjusted for expression levels reveals genes with high transcriptional noise that are highly expressed, functionally related, and co-regulated in yeast

Understanding the relationship between variability in single-cell and non-single-cell gene expression studies will aid in understanding the role of and mechanisms that lead to variability in biological systems. Studies on the variation of gene expression levels in yeast normally focus on single cells and use the coefficient of variance (CV) as a measure of noise. The CV is typically negatively correlated with gene expression levels, so most of the studies using yeast find that genes with high transcriptional noise are lowly expressed. We find adjusting noise for expression levels using linear/natural log polynomial, and local fits and analyzing many non-single-cell RNA-seq sets identifies genes with high median transcriptional noise that are different than those that have high median CVs. Interestingly, these genes are heavily regulated by transcription factors that are related to variability and stochastic processes based on single-cell studies, including Msn2p, Msn4p, Hsf1p, and Crz1p but are not associated with genes with high median CVs based on non-single-cell gene expression data. In addition, adjusting noise for expression levels in a single-cell RNA-seq data set adds value by finding genes that have noisy gene expression levels and their associated transcription factors that are not found to be associated with genes with high CVs in the single-cell expression data or a comparable non-single-cell gene expression data. Lastly, S. cerevisiae genes with noisy expression tend to have orthologs with noisy gene expression in C. albicans, indicating transcriptional noise is evolutionarily conserved.

Protein Adsorption Loss─The Bottleneck of Single-Cell Proteomics

Single-cell proteomics is a promising field to provide direct yet comprehensive molecular insights into cellular functions without averaging effects. Here, we address a grand technical challenge impeding the maturation of single-cell proteomics─protein adsorption loss (PAL). Even though widely known, there is currently no quantitation on how profoundly and selectively PAL has affected single-cell proteomics. Therefore, the mitigations to this challenge have been generic, and their efficacy was only evaluated by the size of the resolved proteome with no specificity on individual proteins. We use the existing knowledge of PAL, protein expression, and the typical surface area used in single-cell proteomics to discuss the severity of protein loss. We also summarize the current solutions to this challenge and briefly review the available methods to characterize the physical and chemical properties of protein surface adsorption. By citing successful strategies in single-cell genomics for measurement errors in individual transcripts, we pinpoint the urgency to benchmark PAL at the proteome scale with individual protein resolution. Finally, orthogonal single-cell proteomic techniques that have the potential to cross validate PAL are proposed. We hope these efforts can promote the fruition of single-cell proteomics in the near future.

The chemical Langevin equation for biochemical systems in dynamic environments

Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly stem from the interplay of the network with many other - and mostly unknown - fluctuating processes, as well as with various random signals arising from the extracellular world; these sources contribute extrinsic noise. Here we provide a computational simulation method to probe the stochastic dynamics of biochemical systems subject to both intrinsic and extrinsic noise. We develop an extrinsic chemical Langevin equation-a physically motivated extension of the chemical Langevin equation- to model intrinsically noisy reaction networks embedded in a stochastically fluctuating environment. The extrinsic CLE is a continuous approximation to the Chemical Master Equation (CME) with time-varying propensities. In our approach, noise is incorporated at the level of the CME, and can account for the full dynamics of the exogenous noise process, irrespective of timescales and their mismatches. We show that our method accurately captures the first two moments of the stationary probability density when compared with exact stochastic simulation methods, while reducing the computational runtime by several orders of magnitude. Our approach provides a method that is practical, computationally efficient and physically accurate to study systems that are simultaneously subject to a variety of noise sources.

Identifying cell-to-cell variability in internalization using flow cytometry

Biological heterogeneity is a primary contributor to the variation observed in experiments that probe dynamical processes, such as the internalization of material by cells. Given that internalization is a critical process by which many therapeutics and viruses reach their intracellular site of action, quantifying cell-to-cell variability in internalization is of high biological interest. Yet, it is common for studies of internalization to neglect cell-to-cell variability. We develop a simple mathematical model of internalization that captures the dynamical behaviour, cell-to-cell variation, and extrinsic noise introduced by flow cytometry. We calibrate our model through a novel distribution-matching approximate Bayesian computation algorithm to flow cytometry data of internalization of anti-transferrin receptor antibody in a human B-cell lymphoblastoid cell line. This approach provides information relating to the region of the parameter space, and consequentially the nature of cell-to-cell variability, that produces model realizations consistent with the experimental data. Given that our approach is agnostic to sample size and signal-to-noise ratio, our modelling framework is broadly applicable to identify biological variability in single-cell data from internalization assays and similar experiments that probe cellular dynamical processes.

Cell Fate Decisions Within the Vascular Cambium-Initiating Wood and Bast Formation

Precise coordination of cell fate decisions is a hallmark of multicellular organisms. Especially in tissues with non-stereotypic anatomies, dynamic communication between developing cells is vital for ensuring functional tissue organization. Radial plant growth is driven by a plant stem cell niche known as vascular cambium, usually strictly producing secondary xylem (wood) inward and secondary phloem (bast) outward, two important structures serving as much-needed CO₂ depositories and building materials. Because of its bidirectional nature and its developmental plasticity, the vascular cambium serves as an instructive paradigm for investigating principles of tissue patterning. Although genes and hormones involved in xylem and phloem formation have been identified, we have a yet incomplete picture of the initial steps of cell fate transitions of stem cell daughters into xylem and phloem progenitors. In this mini-review perspective, we describe two possible scenarios of cell fate decisions based on the current knowledge about gene regulatory networks and how cellular environments are established. In addition, we point out further possible research directions.

New horizons in the stormy sea of multimodal single-cell data integration

While measurements of RNA expression have dominated the world of single-cell analyses, new single-cell techniques increasingly allow collection of different data modalities, measuring different molecules, structural connections, and intermolecular interactions. Integrating the resulting multimodal single-cell datasets is a new bioinformatics challenge. Equally important, it is a new experimental design challenge for the bench scientist, who is not only choosing from a myriad of techniques for each data modality but also faces new challenges in experimental design. The ultimate goal is to design, execute, and analyze multimodal single-cell experiments that are more than just descriptive but enable the learning of new causal and mechanistic biology. This objective requires strict consideration of the goals behind the analysis, which might range from mapping the heterogeneity of a cellular population to assembling system-wide causal networks that can further our understanding of cellular functions and eventually lead to models of tissues and organs. We review steps and challenges toward this goal. Single-cell transcriptomics is now a mature technology, and methods to measure proteins, lipids, small-molecule metabolites, and other molecular phenotypes at the single-cell level are rapidly developing. Integrating these single-cell readouts so that each cell has measurements of multiple types of data, e.g., transcriptomes, proteomes, and metabolomes, is expected to allow identification of highly specific cellular subpopulations and to provide the basis for inferring causal biological mechanisms.

Lack of evidence for increased transcriptional noise in aged tissues

Aging is often associated with a loss of cell type identity that results in an increase in transcriptional noise in aged tissues. If this phenomenon reflects a fundamental property of aging remains an open question. Transcriptional changes at the cellular level are best detected by single-cell RNA sequencing (scRNAseq). However, the diverse computational methods used for the quantification of age-related loss of cellular identity have prevented reaching meaningful conclusions by direct comparison of existing scRNAseq datasets. To address these issues we created Decibel, a Python toolkit that implements side-to-side four commonly used methods for the quantification of age-related transcriptional noise in scRNAseq data. Additionally, we developed Scallop, a novel computational method for the quantification of membership of single cells to their assigned cell type cluster. Cells with a greater Scallop membership score are transcriptionally more stable. Application of these computational tools to seven aging datasets showed large variability between tissues and datasets, suggesting that increased transcriptional noise is not a universal hallmark of aging. To understand the source of apparent loss of cell type identity associated with aging, we analyzed cell type-specific changes in transcriptional noise and the changes in cell type composition of the mammalian lung. No robust pattern of cell type-specific transcriptional noise alteration was found across aging lung datasets. In contrast, age-associated changes in cell type composition of the lung were consistently found, particularly of immune cells. These results suggest that claims of increased transcriptional noise of aged tissues should be reformulated.

Forecasting cellular states: from descriptive to predictive biology via single-cell multiomics

As the single cell field races to characterize each cell type, state, and behavior, the complexity of the computational analysis approaches the complexity of the biological systems. Single cell and imaging technologies now enable unprecedented measurements of state transitions in biological systems, providing high-throughput data that capture tens-of-thousands of measurements on hundreds-of-thousands of samples. Thus, the definition of cell type and state is evolving to encompass the broad range of biological questions now attainable. To answer these questions requires the development of computational tools for integrated multi-omics analysis. Merged with mathematical models, these algorithms will be able to forecast future states of biological systems, going from statistical inferences of phenotypes to time course predictions of the biological systems with dynamic maps analogous to weather systems. Thus, systems biology for forecasting biological system dynamics from multi-omic data represents the future of cell biology empowering a new generation of technology-driven predictive medicine.