Bursting onto the scene? Exploring stochastic mRNA production in bacteria

Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions

Many imaging techniques for biological systems-like fixation of cells coupled with fluorescence microscopy-provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

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

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

Formation of synthetic RNA protein granules using engineered phage-coat-protein -RNA complexes

Liquid-solid transition, also known as gelation, is a specific form of phase separation in which molecules cross-link to form a highly interconnected compartment with solid - like dynamical properties. Here, we utilize RNA hairpin coat-protein binding sites to form synthetic RNA based gel-like granules via liquid-solid phase transition. We show both in-vitro and in-vivo that hairpin containing synthetic long non-coding RNA (slncRNA) molecules granulate into bright localized puncta. We further demonstrate that upon introduction of the coat-proteins, less-condensed gel-like granules form with the RNA creating an outer shell with the proteins mostly present inside the granule. Moreover, by tracking puncta fluorescence signals over time, we detected addition or shedding events of slncRNA-CP nucleoprotein complexes. Consequently, our granules constitute a genetically encoded storage compartment for protein and RNA with a programmable controlled release profile that is determined by the number of hairpins encoded into the RNA. Our findings have important implications for the potential regulatory role of naturally occurring granules and for the broader biotechnology field.

Molecular Origins of Transcriptional Heterogeneity in Diazotrophic Klebsiella oxytoca

Phenotypic heterogeneity in clonal bacterial batch cultures has been shown for a range of bacterial systems; however, the molecular origins of such heterogeneity and its magnitude are not well understood. Under conditions of extreme low-nitrogen stress in the model diazotroph Klebsiella oxytoca, we found remarkably high heterogeneity of nifHDK gene expression, which codes for the structural genes of nitrogenase, one key enzyme of the global nitrogen cycle. This heterogeneity limited the bulk observed nitrogen-fixing capacity of the population. Using dual-probe, single-cell RNA fluorescent in situ hybridization, we correlated nifHDK expression with that of nifLA and glnK-amtB, which code for the main upstream regulatory components. Through stochastic transcription models and mutual information analysis, we revealed likely molecular origins for heterogeneity in nitrogenase expression. In the wild type and regulatory variants, we found that nifHDK transcription was inherently bursty, but we established that noise propagation through signaling was also significant. The regulatory gene glnK had the highest discernible effect on nifHDK variance, while noise from factors outside the regulatory pathway were negligible. Understanding the basis of inherent heterogeneity of nitrogenase expression and its origins can inform biotechnology strategies seeking to enhance biological nitrogen fixation. Finally, we speculate on potential benefits of diazotrophic heterogeneity in natural soil environments. IMPORTANCE Nitrogen is an essential micronutrient for both plant and animal life and naturally exists in both reactive and inert chemical forms. Modern agriculture is heavily reliant on nitrogen that has been "fixed" into a reactive form via the energetically expensive Haber-Bosch process, with significant environmental consequences. Nitrogen-fixing bacteria provide an alternative source of fixed nitrogen for use in both biotechnological and agricultural settings, but this relies on a firm understanding of how the fixation process is regulated within individual bacterial cells. We examined the cell-to-cell variability in the nitrogen-fixing behavior of Klebsiella oxytoca, a free-living bacterium. The significance of our research is in identifying not only the presence of marked variability but also the specific mechanisms that give rise to it. This understanding gives insight into both the evolutionary advantages of variable behavior as well as strategies for biotechnological applications.

Inferring gene regulation dynamics from static snapshots of gene expression variability

Inferring functional relationships within complex networks from static snapshots of a subset of variables is a ubiquitous problem in science. For example, a key challenge of systems biology is to translate cellular heterogeneity data obtained from single-cell sequencing or flow-cytometry experiments into regulatory dynamics. We show how static population snapshots of covariability can be exploited to rigorously infer properties of gene expression dynamics when gene expression reporters probe their upstream dynamics on separate timescales. This can be experimentally exploited in dual-reporter experiments with fluorescent proteins of unequal maturation times, thus turning an experimental bug into an analysis feature. We derive correlation conditions that detect the presence of closed-loop feedback regulation in gene regulatory networks. Furthermore, we show how genes with cell-cycle-dependent transcription rates can be identified from the variability of coregulated fluorescent proteins. Similar correlation constraints might prove useful in other areas of science in which static correlation snapshots are used to infer causal connections between dynamically interacting components.

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.

Exactly solvable models of stochastic gene expression

Stochastic models are key to understanding the intricate dynamics of gene expression. However, the simplest models that only account for active and inactive states of a gene fail to capture common observations in both prokaryotic and eukaryotic organisms. Here, we consider multistate models of gene expression that generalize the canonical Telegraph process and are capable of capturing the joint effects of transcription factors, heterochromatin state, and DNA accessibility (or, in prokaryotes, sigma-factor activity) on transcript abundance. We propose two approaches for solving classes of these generalized systems. The first approach offers a fresh perspective on a general class of multistate models and allows us to "decompose" more complicated systems into simpler processes, each of which can be solved analytically. This enables us to obtain a solution of any model from this class. Next, we develop an approximation method based on a power series expansion of the stationary distribution for an even broader class of multistate models of gene transcription. We further show that models from both classes cannot have a heavy-tailed distribution in the absence of extrinsic noise. The combination of analytical and computational solutions for these realistic gene expression models also holds the potential to design synthetic systems and control the behavior of naturally evolved gene expression systems in guiding cell-fate decisions.

Permutational analysis of Saccharomyces cerevisiae regulatory elements

Gene expression in Saccharomyces cerevisiae is regulated at multiple levels. Genomic and epigenomic mapping of transcription factors and chromatin factors has led to the delineation of various modular regulatory elements—enhancers (upstream activating sequences), core promoters, 5′ untranslated regions (5′ UTRs) and transcription terminators/3′ untranslated regions (3′ UTRs). However, only a few of these elements have been tested in combinations with other elements and the functional interactions between the different modular regulatory elements remain under explored. We describe a simple and rapid approach to build a combinatorial library of regulatory elements and have used this library to study 26 different enhancers, core promoters, 5′ UTRs and transcription terminators/3′ UTRs to estimate the contribution of individual regulatory parts in gene expression. Our combinatorial analysis shows that while enhancers initiate gene expression, core promoters modulate the levels of enhancer-mediated expression and can positively or negatively affect expression from even the strongest enhancers. Principal component analysis (PCA) indicates that enhancer and promoter function can be explained by a single principal component while UTR function involves multiple functional components. The PCA also highlights outliers and suggest differences in mechanisms of regulation by individual elements. Our data also identify numerous regulatory cassettes composed of different individual regulatory elements that exhibit equivalent gene expression levels. These data thus provide a catalog of elements that could in future be used in the design of synthetic regulatory circuits.

The route to transcription initiation determines the mode of transcriptional bursting in E. coli

Transcription is fundamentally noisy, leading to significant heterogeneity across bacterial populations. Noise is often attributed to burstiness, but the underlying mechanisms and their dependence on the mode of promotor regulation remain unclear. Here, we measure E. coli single cell mRNA levels for two stress responses that depend on bacterial sigma factors with different mode of transcription initiation (σ⁷⁰ and σ⁵⁴). By fitting a stochastic model to the observed mRNA distributions, we show that the transition from low to high expression of the σ⁷⁰-controlled stress response is regulated via the burst size, while that of the σ⁵⁴-controlled stress response is regulated via the burst frequency. Therefore, transcription initiation involving σ⁵⁴ differs from other bacterial systems, and yields bursting kinetics characteristic of eukaryotic systems.

Transcription noise in bacteria is often attributed to burstiness, but the mechanisms are unclear. Here, the authors show that the transition from low to high expression can be regulated via burst size or burst frequency, depending on the mode of transcription initiation determined by different sigma factors.

Dynamic insights on transcription initiation and RNA processing during bacterial adaptation

Transcription initiation and RNA processing govern gene expression and enable bacterial adaptation by reshaping the RNA landscape. The aim of this study was to simultaneously observe these two fundamental processes in a transcriptome responding to an environmental signal. A controlled σ^E system in E. coli was coupled to our previously described tagRNA-seq method to yield process kinetics information. Changes in transcription initiation frequencies (TIF) and RNA processing frequencies (PF) were followed using 5' RNA tags. Changes in TIF showed a binary increased/decreased pattern that alternated between transcriptionally activated and repressed promoters, providing the bacterial population with transcriptional oscillation. PF variation fell into three categories of cleavage activity: (i) constant and independent of RNA levels, (ii) increased once RNA has accumulated, and (iii) positively correlated to changes in TIF. This work provides a comprehensive and dynamic view of major events leading to transcriptomic reshaping during bacterial adaptation. It unveils an interplay between transcription initiation and the activity of specific RNA cleavage sites. This study utilized a well-known genetic system to analyze fundamental processes and can serve as a blueprint for comprehensive studies that exploit the RNA metabolism to decipher and understand bacterial gene expression control.

Extrinsic Noise and Heavy-Tailed Laws in Gene Expression

Noise in gene expression is one of the hallmarks of life at the molecular scale. Here we derive analytical solutions to a set of models describing the molecular mechanisms underlying transcription of DNA into RNA. Our ansatz allows us to incorporate the effects of extrinsic noise-encompassing factors external to the transcription of the individual gene-and discuss the ramifications for heterogeneity in gene product abundance that has been widely observed in single cell data. Crucially, we are able to show that heavy-tailed distributions of RNA copy numbers cannot result from the intrinsic stochasticity in gene expression alone, but must instead reflect extrinsic sources of variability.

Phenotypic heterogeneity of microbial populations under nutrient limitation

Phenotypic heterogeneity is a phenomenon in which genetically identical individuals have different characteristics. This behavior can also be found in bacteria, even if they grow as monospecies in well-mixed environments such as bioreactors. Here it is discussed how phenotypic heterogeneity is generated by internal factors and how it is promoted under nutrient-limited growth conditions. A better understanding of the molecular levels that control phenotypic heterogeneity could improve biotechnological production processes.

Analytical Expressions and Physics for Single-Cell mRNA Distributions of the lac Operon of E. coli

Mechanistic models of stochastic gene expression are of considerable interest, but their complexity often precludes tractable analytical expressions for messenger RNA (mRNA) and protein distributions. The lac operon of Escherichia coli is a model system with regulatory elements such as multiple operators and DNA looping that are shared by many operons. Although this system is complex, intuition suggests that fast DNA looping may simplify it by causing the repressor-bound states of the operon to equilibrate rapidly, thus ensuring that the subsequent dynamics are governed by slow transitions between the repressor-free and the equilibrated repressor-bound states. Here, we show that this intuition is correct by applying singular perturbation theory to a mechanistic model of lac transcription with the scaled time constant of DNA looping as the perturbation parameter. We find that at steady state, the repressor-bound states satisfy detailed balance and are dominated by the looped states; moreover, the interaction between the repressor-free and the equilibrated repressor-bound states is described by an extension of the Peccoud-Ycart two-state model in which both (repressor-free and repressor-bound) states support transcription. The solution of this extended two-state model reveals that the steady-state mRNA distribution is a mixture of the Poisson and negative hypergeometric distributions, which reflects mRNAs obtained by transcription from the repressor-bound and repressor-free states. Finally, we show that the physics revealed by perturbation theory makes it easy to derive the extended two-state model equations for complex regulatory architectures.

Single-Molecule Kinetics in Living Cells

In the past decades, advances in microscopy have made it possible to study the dynamics of individual biomolecules in vitro and resolve intramolecular kinetics that would otherwise be hidden in ensemble averages. More recently, single-molecule methods have been used to image, localize, and track individually labeled macromolecules in the cytoplasm of living cells, allowing investigations of intermolecular kinetics under physiologically relevant conditions. In this review, we illuminate the particular advantages of single-molecule techniques when studying kinetics in living cells and discuss solutions to specific challenges associated with these methods.