Stochastic Expression Research Articles

A dual fluorescence protein expression system detects cell cycle dependent protein noise

Inherently identical cells exhibit significant phenotypic variation. It can be essential for many biological processes and is known to arise from stochastic, ‘noisy’, gene expression that is determined by intrinsic and extrinsic components. It is now obvious that the noise varies as a function of inducer concentration. However, its fluctuation over the cell cycle is limited. Applying dual colour fluorescence protein reporter system, Cyan Fluorescent Protein (CFP) and Yellow fluorescent protein (YFP) tagged multi-copy plasmids, we determine variation of the noise components over the phases in lac promoter induced by Isopropyl β-D-1-thiogalactopyranoside (IPTG) and in presence of additional Magnesium, Mg2+ ion. We, also, estimate the how such system deviates from observations of single-copy plasmid. Found 25 % difference between multi-copy system and single-copy system clarifies that observed noise is considerable and estimates population behaviour during the cell cycle. We show that total variation in cells induced with IPTG is determined by higher extrinsic than intrinsic noise. It increases from Lag to Exponential phase and decreases from Retardation to Stationary phase. By observing slow and fast dividing cells, we show that 5 mM Mg2+ increases population homogeneity compared to 2.5 mM Mg2+ in the environment. The experimental data obtained using dual colour fluorescence protein reporter system demonstrates that protein expression noise, depending on intra cellular ionic concentration, is tightly controlled by phase of the cell.

Repurposing the mammalian RNA-binding protein Musashi-1 as an allosteric translation repressor in bacteria.

The RNA recognition motif (RRM) is the most common RNA-binding protein domain identified in nature. However, RRM-containing proteins are only prevalent in eukaryotic phyla, in which they play central regulatory roles. Here, we engineered an orthogonal post-transcriptional control system of gene expression in the bacterium Escherichia coli with the mammalian RNA-binding protein Musashi-1, which is a stem cell marker with neurodevelopmental role that contains two canonical RRMs. In the circuit, Musashi-1 is regulated transcriptionally and works as an allosteric translation repressor thanks to a specific interaction with the N-terminal coding region of a messenger RNA and its structural plasticity to respond to fatty acids. We fully characterized the genetic system at the population and single-cell levels showing a significant fold change in reporter expression, and the underlying molecular mechanism by assessing the in vitro binding kinetics and in vivo functionality of a series of RNA mutants. The dynamic response of the system was well recapitulated by a bottom-up mathematical model. Moreover, we applied the post-transcriptional mechanism engineered with Musashi-1 to specifically regulate a gene within an operon, implement combinatorial regulation, and reduce protein expression noise. This work illustrates how RRM-based regulation can be adapted to simple organisms, thereby adding a new regulatory layer in prokaryotes for translation control.

Repurposing the mammalian RNA-binding protein Musashi-1 as an allosteric translation repressor in bacteria

The RNA recognition motif (RRM) is the most common RNA-binding protein domain identified in nature. However, RRM-containing proteins are only prevalent in eukaryotic phyla, in which they play central regulatory roles. Here, we engineered an orthogonal post-transcriptional control system of gene expression in the bacterium Escherichia coli with the mammalian RNA-binding protein Musashi-1, which is a stem cell marker with neurodevelopmental role that contains two canonical RRMs. In the circuit, Musashi-1 is regulated transcriptionally and works as an allosteric translation repressor thanks to a specific interaction with the N-terminal coding region of a messenger RNA and its structural plasticity to respond to fatty acids. We fully characterized the genetic system at the population and single-cell levels showing a significant fold change in reporter expression, and the underlying molecular mechanism by assessing the in vitro binding kinetics and in vivo functionality of a series of RNA mutants. The dynamic response of the system was well recapitulated by a bottom-up mathematical model. Moreover, we applied the post-transcriptional mechanism engineered with Musashi-1 to specifically regulate a gene within an operon, implement combinatorial regulation, and reduce protein expression noise. This work illustrates how RRM-based regulation can be adapted to simple organisms, thereby adding a new regulatory layer in prokaryotes for translation control.

Feasibility of Gene Regulatory Network Inference Under Different Noise Conditions

One of the most difficult and pressing problems in computational cell biology is the inference of gene regulatory network structure from transcriptomic data. Although this topic has been widely studied for more than a decade, it is still unclear how well these methods work and how their performance differs under different conditions. We analyze the feasibility of network inference from mRNA abundance data using simulations of gene regulatory interactions, considering both intrinsic and extrinsic noise in the process of gene expression. We find that under conditions of only intrinsic noise in gene expression, the correlation between mRNA levels of genes in an activation relationship is quite low, suggesting that the task of network inference from transcriptomic data is very difficult under these conditions. By contrast, extrinsic noise affecting the process of gene expression, which could come from an upstream regulator, external stimulus, or change in the cell state, results in higher correlation between mRNA levels of these genes, potentially making the task of network inference from mRNA data more feasible. Lastly, we analyze the problem of false positives between genes that have no direct interaction but share a common upstream regulator, and explore a strategy for distinguishing between these false positives and true interactions based on noise profiles of mRNA expression levels.

Flagellar dynamics reveal fluctuations and kinetic limit in the Escherichia coli chemotaxis network

The Escherichia coli chemotaxis network, by which bacteria modulate their random run/tumble swimming pattern to navigate their environment, must cope with unavoidable number fluctuations (“noise”) in its molecular constituents like other signaling networks. The probability of clockwise (CW) flagellar rotation, or CW bias, is a measure of the chemotaxis network’s output, and its temporal fluctuations provide a proxy for network noise. Here we quantify fluctuations in the chemotaxis signaling network from the switching statistics of flagella, observed using time-resolved fluorescence microscopy of individual optically trapped E. coli cells. This approach allows noise to be quantified across the dynamic range of the network. Large CW bias fluctuations are revealed at steady state, which may play a critical role in driving flagellar switching and cell tumbling. When the network is stimulated chemically to higher activity, fluctuations dramatically decrease. A stochastic theoretical model, inspired by work on gene expression noise, points to CheY activation occurring in bursts, driving CW bias fluctuations. This model also shows that an intrinsic kinetic ceiling on network activity places an upper limit on activated CheY and CW bias, which when encountered suppresses network fluctuations. This limit may also prevent cells from tumbling unproductively in steep gradients.

Phase separation reduces cell-to-cell variability of transcriptional bursting

Gene expression is a stochastic and noisy process often occurring in "bursts". Experiments have shown that the compartmentalization of proteins by liquid-liquid phase separation is conducive to reducing the noise of gene expression. Therefore, an important goal is to explore the role of bursts in phase separation noise reduction processes. We propose a coupled model that includes phase separation and a two-state gene expression process. Using the timescale separation method, we obtain approximate solutions for the expectation, variance, and noise strength of the dilute phase. We find that a higher burst frequency weakens the ability of noise reduction by phase separation, but as the burst size increases, this ability first increases and then decreases. This study provides a deeper understanding of phase separation to reduce noise in the stochastic gene expression with burst kinetics.

Deep-learning-assisted Sort-Seq enables high-throughput profiling of gene expression characteristics with high precision.

Owing to the nondeterministic and nonlinear nature of gene expression, the steady-state intracellular protein abundance of a clonal population forms a distribution. The characteristics of this distribution, including expression strength and noise, are closely related to cellular behavior. However, quantitative description of these characteristics has so far relied on arrayed methods, which are time-consuming and labor-intensive. To address this issue, we propose a deep-learning-assisted Sort-Seq approach (dSort-Seq) in this work, enabling high-throughput profiling of expression properties with high precision. We demonstrated the validity of dSort-Seq for large-scale assaying of the dose-response relationships of biosensors. In addition, we comprehensively investigated the contribution of transcription and translation to noise production in Escherichia coli, from which we found that the expression noise is strongly coupled with the mean expression level. We also found that the transcriptional interference caused by overlapping RpoD-binding sites contributes to noise production, which suggested the existence of a simple and feasible noise control strategy in E. coli.

Effects of microRNA-mediated negative feedback on gene expression noise

MicroRNAs (miRNAs) are small noncoding RNAs that regulate gene expression post-transcriptionally in eukaryotes by binding with target mRNAs and preventing translation. miRNA-mediated feedback motifs are ubiquitous in various genetic networks that control cellular decision making. A key question is how such a feedback mechanism may affect gene expression noise. To answer this, we have developed a mathematical model to study the effects of a miRNA-dependent negative-feedback loop on mean expression and noise in target mRNAs. Combining analytics and simulations, we show the existence of an expression threshold demarcating repressed and expressed regimes in agreement with earlier studies. The steady-state mRNA distributions are bimodal near the threshold, where copy numbers of mRNAs and miRNAs exhibit enhanced anticorrelated fluctuations. Moreover, variation of negative-feedback strength shifts the threshold locations and modulates the noise profiles. Notably, the miRNA-mRNA binding affinity and feedback strength collectively shape the bimodality. We also compare our model with a direct auto-repression motif, where a gene produces its own repressor. Auto-repression fails to produce bimodal mRNA distributions as found in miRNA-based indirect repression, suggesting the crucial role of miRNAs in creating phenotypic diversity. Together, we demonstrate how miRNA-dependent negative feedback modifies the expression threshold and leads to a broader parameter regime of bimodality compared to the no-feedback case.

Uncovering the effect of RNA polymerase steric interactions on gene expression noise: Analytical distributions of nascent and mature RNA numbers.

The telegraph model is the standard model of stochastic gene expression, which can be solved exactly to obtain the distribution of mature RNA numbers per cell. A modification of this model also leads to an analytical distribution of nascent RNA numbers. These solutions are routinely used for the analysis of single-cell data, including the inference of transcriptional parameters. However, these models neglect important mechanistic features of transcription elongation, such as the stochastic movement of RNA polymerases and their steric (excluded-volume) interactions. Here we construct a model of gene expression describing promoter switching between inactive and active states, binding of RNA polymerases in the active state, their stochastic movement including steric interactions along the gene, and their unbinding leading to a mature transcript that subsequently decays. We derive the steady-state distributions of the nascent and mature RNA numbers in two important limiting cases: constitutive expression and slow promoter switching. We show that RNA fluctuations are suppressed by steric interactions between RNA polymerases, and that this suppression can in some instances even lead to sub-Poissonian fluctuations; these effects are most pronounced for nascent RNA and less prominent for mature RNA, since the latter is not a direct sensor of transcription. We find a relationship between the parameters of our microscopic mechanistic model and those of the standard models that ensures excellent consistency in their prediction of the first and second RNA number moments over vast regions of parameter space, encompassing slow, intermediate, and rapid promoter switching, provided the RNA number distributions are Poissonian or super-Poissonian. Furthermore, we identify the limitations of inference from mature RNA data, specifically showing that it cannot differentiate between highly distinct RNA polymerase traffic patterns on a gene.

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

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

The σB alternative sigma factor circuit modulates noise to generate different types of pulsing dynamics.

Single-cell approaches are revealing a high degree of heterogeneity, or noise, in gene expression in isogenic bacteria. How gene circuits modulate this noise in gene expression to generate robust output dynamics is unclear. Here we use the Bacillus subtilis alternative sigma factor σB as a model system for understanding the role of noise in generating circuit output dynamics. σB controls the general stress response in B. subtilis and is activated by a range of energy and environmental stresses. Recent single-cell studies have revealed that the circuit can generate two distinct outputs, stochastic pulsing and a single pulse response, but the conditions under which each response is generated are under debate. We implement a stochastic mathematical model of the σB circuit to investigate this and find that the system's core circuit can generate both response types. This is despite one response (stochastic pulsing) being stochastic in nature, and the other (single response pulse) being deterministic. We demonstrate that the main determinant for whichever response is generated is the degree with which the input pathway activates the core circuit, although the noise properties of the input pathway also biases the system towards one or the other type of output. Thus, our work shows how stochastic modelling can reveal the mechanisms behind non-intuitive gene circuit output dynamics.

Obtaining Stable Predicted Distributions of Response Times and Decision Outcomes for the Circular Diffusion Model

The circular diffusion model represents continuous outcome decision making as evidence accumulation by a two-dimensional Wiener process with drift on the interior of a disk, whose radius represents the decision criterion for the task. The hitting point on the circumference of the disk represents the decision outcome and the hitting time represents the decision time. The Girsanov change-of-measure theorem applied to the first-passage time distribution for the Euclidean distance Bessel process yields an explicit expression for the joint distribution of decision outcomes and decision times for the model. A problem with the expression for the joint distribution obtained in this way is that the change-of-measure calculation magnifies numerical noise in the series expression for the Bessel process, which can make the expression unstable at small times when the drift rate or decision criterion is large. We introduce a new method that uses an asymptotic approximation to characterize the Bessel process at short times and the series expression for the large times. The resulting expressions are stable across all parts of the parameter space likely to be of interest in experiments, which greatly simplifies the task of fitting the model to data. The new method applies to the spherical and hyperspherical generalizations of the model and to versions of it in which the drift rates are normally distributed across trials with independent or correlated components.

Noise Minimization in Cell-Free Gene Expression.

Biochemical reactions that involve small numbers of molecules are accompanied by a degree of inherent randomness that results in noisy reaction outcomes. In synthetic biology, the ability to minimize noise particularly during the reconstitution of future synthetic protocells is an outstanding challenge to secure robust and reproducible behavior. Here we show that by encapsulation of a bacterial cell-free gene expression system in water-in-oil droplets, in vitro-synthesized MazF reduces cell-free gene expression noise >2-fold. With stochastic simulations we identify that this noise minimization acts through both increased degradation and the autoregulatory feedback of MazF. Specifically, we find that the expression of MazF enhances the degradation rate of mRNA up to 18-fold in a sequence-dependent manner. This sequence specificity of MazF would allow targeted noise control, making it ideal to integrate into synthetic gene networks. Therefore, including MazF production in synthetic biology can significantly minimize gene expression noise, impacting future design principles of more complex cell-free gene circuits.

Serum Response Factor Reduces Gene Expression Noise and Confers Cell State Stability.

The role of serum response factor (Srf), a central mediator of actin dynamics and mechanical signaling, in cell identity regulation is debated to be either a stabilizer or a destabilizer. We investigated the role of Srf in cell fate stability using mouse pluripotent stem cells. Despite the fact that serum-containing cultures yield heterogeneous gene expression, deletion of Srf in mouse pluripotent stem cells leads to further exacerbated cell state heterogeneity. The exaggerated heterogeneity is detectible not only as increased lineage priming but also as the developmentally earlier 2C-like cell state. Thus, pluripotent cells explore more variety of cellular states in both directions of development surrounding naïve pluripotency, a behavior that is constrained by Srf. These results support that Srf functions as a cell state stabilizer, providing rationale for its functional modulation in cell fate intervention and engineering.

VarID2 quantifies gene expression noise dynamics and unveils functional heterogeneity of ageing hematopoietic stem cells

Variability of gene expression due to stochasticity of transcription or variation of extrinsic signals, termed biological noise, is a potential driving force of cellular differentiation. Utilizing single-cell RNA-sequencing, we develop VarID2 for the quantification of biological noise at single-cell resolution. VarID2 reveals enhanced nuclear versus cytoplasmic noise, and distinct regulatory modes stratified by correlation between noise, expression, and chromatin accessibility. Noise levels are minimal in murine hematopoietic stem cells (HSCs) and increase during differentiation and ageing. Differential noise identifies myeloid-biased Dlk1+ long-term HSCs in aged mice with enhanced quiescence and self-renewal capacity. VarID2 reveals noise dynamics invisible to conventional single-cell transcriptome analysis.

Phenotype switching of the mutation rate facilitates adaptive evolution.

The mutation rate plays an important role in adaptive evolution. It can be modified by mutator and anti-mutator alleles. Recent empirical evidence hints that the mutation rate may vary among genetically identical individuals: evidence from bacteria suggests that the mutation rate can be affected by expression noise of a DNA repair protein and potentially also by translation errors in various proteins. Importantly, this non-genetic variation may be heritable via a transgenerational epigenetic mode of inheritance, giving rise to a mutator phenotype that is independent from mutator alleles. Here, we investigate mathematically how the rate of adaptive evolution is affected by the rate of mutation rate phenotype switching. We model an asexual population with two mutation rate phenotypes, non-mutator and mutator. An offspring may switch from its parental phenotype to the other phenotype. We find that switching rates that correspond to so-far empirically described non-genetic systems of inheritance of the mutation rate lead to higher rates of adaptation on both artificial and natural fitness landscapes. These switching rates can maintain within the same individuals both a mutator phenotype and intermediary mutations, a combination that facilitates adaptation. Moreover, non-genetic inheritance increases the proportion of mutators in the population, which in turn increases the probability of hitchhiking of the mutator phenotype with adaptive mutations. This in turns facilitates the acquisition of additional adaptive mutations. Our results rationalize recently observed noise in the expression of proteins that affect the mutation rate and suggest that non-genetic inheritance of this phenotype may facilitate evolutionary adaptive processes.

MATTE: a pipeline of transcriptome module alignment for anti-noise phenotype-gene-related analysis.

A phenotype may be associated with multiple genes that interact with each other in the form of a gene module or network. How to identify these relationships is one important aspect of comparative transcriptomics. However, it is still a challenge to align gene modules associated with different phenotypes. Although several studies attempted to address this issue in different aspects, a general framework is still needed. In this study, we introduce Module Alignment of TranscripTomE (MATTE), a novel approach to analyze transcriptomics data and identify differences in a modular manner. MATTE assumes that gene interactions modulate a phenotype and models phenotype differences as gene location changes. Specifically, we first represented genes by a relative differential expression to reduce the influence of noise in omics data. Meanwhile, clustering and aligning are combined to depict gene differences in a modular way robustly. The results show that MATTE outperformed state-of-the-art methods in identifying differentially expressed genes under noise in gene expression. In particular, MATTE could also deal with single-cell ribonucleic acid-seq data to extract the best cell-type marker genes compared to other methods. Additionally, we demonstrate how MATTE supports the discovery of biologically significant genes and modules, and facilitates downstream analyses to gain insight into breast cancer. The source code of MATTE and case analysis are available at https://github.com/zjupgx/MATTE.

MaxCal can infer models from coupled stochastic trajectories of gene expression and cell division

Gene expression is inherently noisy due to small numbers of proteins and nucleic acids inside a cell. Likewise, cell division is stochastic, particularly when tracking at the level of a single cell. The two can be coupled when gene expression affects the rate of cell division. Single-cell time-lapse experiments can measure both fluctuations by simultaneously recording protein levels inside a cell and its stochastic division. These information-rich noisy trajectory data sets can be harnessed to learn about the underlying molecular and cellular details that are often not known a priori. A critical question is: How can we infer a model given data where fluctuations at two levels—gene expression and cell division—are intricately convoluted? We show the principle of maximum caliber (MaxCal)—integrated within a Bayesian framework—can be used to infer several cellular and molecular details (division rates, protein production, and degradation rates) from these coupled stochastic trajectories (CSTs). We demonstrate this proof of concept using synthetic data generated from a known model. An additional challenge in data analysis is that trajectories are often not in protein numbers, but in noisy fluorescence that depends on protein number in a probabilistic manner. We again show that MaxCal can infer important molecular and cellular rates even when data are in fluorescence, another example of CST with three confounding factors—gene expression noise, cell division noise, and fluorescence distortion—all coupled. Our approach will provide guidance to build models in synthetic biology experiments as well as general biological systems where examples of CSTs are abundant.

An alternative interpretation for tailing in survival curves for bacteria exposed to germicidal radiation.

It has been proposed that transient and reversible phenotypic changes could modify the response of bacteria to germicidal radiation, eventually leading to tailing in the survival curves. If this were the case, changes in susceptibility to radiation would reflect variations in gene expression and should only occur in cells in which gene expression is active. To obtain experimental evidence supporting the involvement of phenotypic changes in the origin of tailing, we studied changes in the susceptibility to radiation of cells able to survive high fluences, using split irradiations. Stationary phase cells of Enterobacter cloacae and Deinococcus radiodurans, in which gene expression is active, and spores of Bacillus subtilis, which are dormant cells without active gene expression, were used as microbial models. While cells of E. cloacae and D. radiodurans became susceptible after surviving exposures to high fluences, tolerant spores exhibited unchanged response to radiation. The results can be interpreted assuming that noise in gene expression modifies bacterial susceptibility to radiation, and tailing is the result of intrinsic phenomena of bacterial physiology rather than a technical artifact. For either theoretical or practical purposes, deviations from simple exponential decay kinetics should be considered in estimations of the effects of germicidal radiation at high fluences.

Being noisy in a crowd: Differential selective pressure on gene expression noise in model gene regulatory networks.

Expression noise, the variability of the amount of gene product among isogenic cells grown in identical conditions, originates from the inherent stochasticity of diffusion and binding of the molecular players involved in transcription and translation. It has been shown that expression noise is an evolvable trait and that central genes exhibit less noise than peripheral genes in gene networks. A possible explanation for this pattern is increased selective pressure on central genes since they propagate their noise to downstream targets, leading to noise amplification. To test this hypothesis, we developed a new gene regulatory network model with inheritable stochastic gene expression and simulated the evolution of gene-specific expression noise under constraint at the network level. Stabilizing selection was imposed on the expression level of all genes in the network and rounds of mutation, selection, replication and recombination were performed. We observed that local network features affect both the probability to respond to selection, and the strength of the selective pressure acting on individual genes. In particular, the reduction of gene-specific expression noise as a response to stabilizing selection on the gene expression level is higher in genes with higher centrality metrics. Furthermore, global topological structures such as network diameter, centralization and average degree affect the average expression variance and average selective pressure acting on constituent genes. Our results demonstrate that selection at the network level leads to differential selective pressure at the gene level, and local and global network characteristics are an essential component of gene-specific expression noise evolution.