Stochastic Expression Research Articles

Contributions of mutation and selection to regulatory variation: lessons from the Saccharomyces cerevisiae TDH3 gene.

Heritable variation in gene expression is common within and among species and contributes to phenotypic diversity. Mutations affecting either cis- or trans-regulatory sequences controlling gene expression give rise to variation in gene expression, and natural selection acting on this variation causes some regulatory variants to persist in a population for longer than others. To understand how mutation and selection interact to produce the patterns of regulatory variation we see within and among species, my colleagues and I have been systematically determining the effects of new mutations on expression of the TDH3 gene in Saccharomyces cerevisiae and comparing them to the effects of polymorphisms segregating within this species. We have also investigated the molecular mechanisms by which regulatory variants act. Over the past decade, this work has revealed properties of cis- and trans-regulatory mutations including their relative frequency, effects, dominance, pleiotropy and fitness consequences. Comparing these mutational effects to the effects of polymorphisms in natural populations, we have inferred selection acting on expression level, expression noise and phenotypic plasticity. Here, I summarize this body of work and synthesize its findings to make inferences not readily discernible from the individual studies alone. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Interdisciplinary approaches to predicting evolutionary biology.

Interdisciplinary approaches to predicting evolutionary biology.

A tractable physical model for the yeast polarity predicts epistasis and fitness.

Accurate phenotype prediction based on genetic information has numerous societal applications, such as crop design or cellular factories. Epistasis, when biological components interact, complicates modelling phenotypes from genotypes. Here we show an approach to mitigate this complication for polarity establishment in budding yeast, where mechanistic information is abundant. We coarse-grain molecular interactions into a so-called mesotype, which we combine with gene expression noise into a physical cell cycle model. First, we show with computer simulations that the mesotype allows validation of the most current biochemical polarity models by quantitatively matching doubling times. Second, the mesotype elucidates epistasis emergence as exemplified by evaluating the predicted mutational effect of key polarity protein Bem1p when combined with known interactors or under different growth conditions. This example also illustrates how unlikely evolutionary trajectories can become more accessible. The tractability of our biophysically justifiable approach inspires a road-map towards bottom-up modelling complementary to statistical inferences. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Memory of stochastic single-cell apoptotic signaling promotes chemoresistance in neuroblastoma.

Gene expression noise is known to promote stochastic drug resistance through the elevated expression of individual genes in rare cancer cells. However, we now demonstrate that chemoresistant neuroblastoma cells emerge at a much higher frequency when the influence of noise is integrated across multiple components of an apoptotic signaling network. Using a JNK activity biosensor with longitudinal high-content and in vivo intravital imaging, we identify a population of stochastic, JNK-impaired, chemoresistant cells that exist because of noise within this signaling network. Furthermore, we reveal that the memory of this initially random state is retained following chemotherapy treatment across a series of in vitro, in vivo, and patient models. Using matched PDX models established at diagnosis and relapse from individual patients, we show that HDAC inhibitor priming cannot erase the memory of this resistant state within relapsed neuroblastomas but improves response in the first-line setting by restoring drug-induced JNK activity within the chemoresistant population of treatment-naïve tumors.

Effective bet-hedging through growth rate dependent stability

Microbes in the wild face highly variable and unpredictable environments and are naturally selected for their average growth rate across environments. Apart from using sensory regulatory systems to adapt in a targeted manner to changing environments, microbes employ bet-hedging strategies where cells in an isogenic population switch stochastically between alternative phenotypes. Yet, bet-hedging suffers from a fundamental trade-off: Increasing the phenotype-switching rate increases the rate at which maladapted cells explore alternative phenotypes but also increases the rate at which cells switch out of a well-adapted state. Consequently, it is currently believed that bet-hedging strategies are effective only when the number of possible phenotypes is limited and when environments last for sufficiently many generations. However, recent experimental results show that gene expression noise generally decreases with growth rate, suggesting that phenotype-switching rates may systematically decrease with growth rate. Such growth rate dependent stability (GRDS) causes cells to be more explorative when maladapted and more phenotypically stable when well-adapted, and we show that GRDS can almost completely overcome the trade-off that limits bet-hedging, allowing for effective adaptation even when environments are diverse and change rapidly. We further show that even a small decrease in switching rates of faster-growing phenotypes can substantially increase long-term fitness of bet-hedging strategies. Together, our results suggest that stochastic strategies may play an even bigger role for microbial adaptation than hitherto appreciated.

The role of RNA condensation in reducing gene expression noise.

Biomolecular condensates have been shown to play a fundamental role in localizing biochemistry in a cell. RNA is a common constituent with proteins and can determine biophysical properties. Functions of biomolecular condensates are varied including activating, inhibiting, and localizing reactions. Recently it has been proposed that condensates can buffer noise to diminish cell to cell variability. Here we introduce a phenomenological model in which phase separation of mRNAs into RNP droplets can regulate the abundance of the protein these mRNA encode and markedly decreases expression noise. We place particular emphasis on how this mechanism can facilitate efficient transcription by reducing noise even in the limit of infrequent bursts of transcription, by exploiting the physics of concentration dependent, deterministic phase separation threshold. We investigate two biologically relevant scenarios in which phase separation acts to either “buffer” noise by storing mRNA in inert droplets, or “filter” phase separated mRNAs by accelerating their decay, and quantify expression noise as a function of kinetic parameters. In either case the most efficient expression occurs when bursts produce mRNAs close to the phase separation threshold, which we find to be consistent with observations of a RNP-droplet forming cyclin in multinucleate Ashbya gossypii cells. We finally consider the contribution of noise in the phase separation threshold, and exhibit that protein copy number noise can be efficiently suppressed under modest assumptions on the magnitude and time scale of phase separation threshold fluctuations.

The effect of microRNA on protein variability and gene expression fidelity

Small regulatory RNA molecules such as microRNA modulate gene expression through inhibiting the translation of messenger RNA (mRNA). Such post-transcriptional regulation has been recently hypothesized to reduce the stochastic variability of gene expression around average levels. Here we quantify noise in stochastic gene expression models with and without such regulation. Our results suggest that silencing mRNA post-transcriptionally will always increase rather than decrease gene expression noise when the silencing of mRNA also increases its degradation as is expected for microRNA interactions with mRNA. In that regime we also find that silencing mRNA generally reduces the fidelity of signal transmission from deterministically varying upstream factors to protein levels. These findings suggest that microRNA binding to mRNA does not generically confer precision to protein expression.

Emergent Criticality in Coupled Boolean Networks.

Early embryonic development involves forming all specialized cells from a fluid-like mass of identical stem cells. The differentiation process consists of a series of symmetry-breaking events, starting from a high-symmetry state (stem cells) to a low-symmetry state (specialized cells). This scenario closely resembles phase transitions in statistical mechanics. To theoretically study this hypothesis, we model embryonic stem cell (ESC) populations through a coupled Boolean network (BN) model. The interaction is applied using a multilayer Ising model that considers paracrine and autocrine signaling, along with external interventions. It is demonstrated that cell-to-cell variability can be interpreted as a mixture of steady-state probability distributions. Simulations have revealed that such models can undergo a series of first- and second-order phase transitions as a function of the system parameters that describe gene expression noise and interaction strengths. These phase transitions result in spontaneous symmetry-breaking events that generate new types of cells characterized by various steady-state distributions. Coupled BNs have also been shown to self-organize in states that allow spontaneous cell differentiation.

The effect of microRNA on protein variability and gene expression fidelity

Small regulatory RNA molecules such as microRNA modulate gene expression through inhibiting the translation of messenger RNA (mRNA). Such posttranscriptional regulation has been recently hypothesized to reduce the stochastic variability of gene expression around average levels. Here, we quantify noise in stochastic gene expression models with and without such regulation. Our results suggest that silencing mRNA posttranscriptionally will always increase, rather than decrease, gene expression noise when the silencing of mRNA also increases its degradation, as is expected for microRNA interactions with mRNA. In that regime, we also find that silencing mRNA generally reduces the fidelity of signal transmission from deterministically varying upstream factors to protein levels. These findings suggest that microRNA binding to mRNA does not generically confer precision to protein expression.

Enhanced Transcriptional Strength of HIV-1 Subtype C Minimizes Gene Expression Noise and Confers Stability to the Viral Latent State.

Stochastic fluctuations in gene expression emanating from the HIV-1 long terminal repeat (LTR), amplified by the Tat positive feedback circuit, determine the choice between viral infection fates: active transcription (ON) or transcriptional silence (OFF). The emergence of several transcription factor binding site (TFBS) variant strains in HIV-1 subtype C (HIV-1C), especially those containing the duplication of the NF-κB motif, mandates the evaluation of the effect of enhanced transcriptional strength on gene expression noise and its influence on viral fate selection switch. Using a panel of subgenomic LTR-variant strains containing different copy numbers of the NF-κB motif (ranging from 0 to 4), we used flow cytometry, mRNA quantification, and pharmacological perturbations to demonstrate an inverse correlation between promoter strength and gene expression noise in Jurkat T cells and primary CD4+ T cells. The inverse correlation is consistent in clonal cell populations at constant intracellular concentrations of Tat and when NF-κB levels were regulated pharmacologically. Further, we show that strong LTRs containing at least two copies of the NF-κB motif in the enhancer establish a more stable latent state and demonstrate more rapid latency reversal than weak LTRs containing fewer motifs. We also demonstrate a cooperative binding of NF-κB to the motif cluster in HIV-1C LTRs containing two, three, or four NF-κB motifs (Hill coefficient [H] = 2.61, 3.56, and 3.75, respectively). The present work alludes to a possible evolution of the HIV-1C LTR toward gaining transcriptional strength associated with attenuated gene expression noise with implications for viral latency. IMPORTANCE Over the past two consecutive decades, HIV-1 subtype C (HIV-1C) has been undergoing directional evolution toward augmenting the transcriptional strength of the long terminal repeat (LTR) by adding more copies of the existing transcription factor binding site (TFBS) by sequence duplication. Additionally, the duplicated elements are genetically diverse, suggesting broader-range signal receptivity by variant LTRs. The HIV-1 promoter is inherently noisy, and the stochastic fluctuations in gene expression of variant LTRs may influence the active transcription (ON)/transcriptional silence (OFF) latency decisions. The evolving NF-κB motif variations of HIV-1C offer a powerful opportunity to examine how the transcriptional strength of the LTR might influence gene expression noise. Our work here shows that the augmented transcriptional strength of the HIV-1C LTR leads to concomitantly reduced gene expression noise, consequently leading to stabler latency maintenance and rapid latency reversal. The present work offers a novel lead toward appreciating the molecular mechanisms governing HIV-1 latency.

Transcription factor binding process is the primary driver of noise in gene expression.

Noise in expression of individual genes gives rise to variations in activity of cellular pathways and generates heterogeneity in cellular phenotypes. Phenotypic heterogeneity has important implications for antibiotic persistence, mutation penetrance, cancer growth and therapy resistance. Specific molecular features such as the presence of the TATA box sequence and the promoter nucleosome occupancy have been associated with noise. However, the relative importance of these features in noise regulation is unclear and how well these features can predict noise has not yet been assessed. Here through an integrated statistical model of gene expression noise in yeast we found that the number of regulating transcription factors (TFs) of a gene was a key predictor of noise, whereas presence of the TATA box and the promoter nucleosome occupancy had poor predictive power. With an increase in the number of regulatory TFs, there was a rise in the number of cooperatively binding TFs. In addition, an increased number of regulatory TFs meant more overlaps in TF binding sites, resulting in competition between TFs for binding to the same region of the promoter. Through modeling of TF binding to promoter and application of stochastic simulations, we demonstrated that competition and cooperation among TFs could increase noise. Thus, our work uncovers a process of noise regulation that arises out of the dynamics of gene regulation and is not dependent on any specific transcription factor or specific promoter sequence.

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.

Large-scale analysis and computer modeling reveal hidden regularities behind variability of cell division patterns in Arabidopsis thaliana embryogenesis.

Noise plays a major role in cellular processes and in the development of tissues and organs. Several studies have examined the origin, the integration or the accommodation of noise in gene expression, cell growth and elaboration of organ shape. By contrast, much less is known about variability in cell division plane positioning, its origin and links with cell geometry, and its impact on tissue organization. Taking advantage of the first-stereotyped-then-variable division patterns in the embryo of the model plant Arabidopsis thaliana, we combined 3D imaging and quantitative cell shape and cell lineage analysis together with mathematical and computer modeling to perform a large-scale, systematic analysis of variability in division plane orientation. Our results reveal that, paradoxically, variability in cell division patterns of Arabidopsis embryos is accompanied by a progressive reduction of heterogeneity in cell shape topology. The paradox is solved by showing that variability operates within a reduced repertoire of possible division plane orientations that is related to cell geometry. We show that in several domains of the embryo, a recently proposed geometrical division rule recapitulates observed variable patterns, suggesting that variable patterns emerge from deterministic principles operating in a variable geometrical context. Our work highlights the importance of emerging patterns in the plant embryo under iterated division principles, but also reveal domains where deviations between rule predictions and experimental observations point to additional regulatory mechanisms.

Nonstop mRNAs generate a ground state of mitochondrial gene expression noise.

A stop codon within the mRNA facilitates coordinated termination of protein synthesis, releasing the nascent polypeptide from the ribosome. This essential step in gene expression is impeded with transcripts lacking a stop codon, generating nonstop ribosome complexes. Here, we use deep sequencing to investigate sources of nonstop mRNAs generated from the human mitochondrial genome. We identify diverse types of nonstop mRNAs on mitochondrial ribosomes that are resistant to translation termination by canonical release factors. Failure to resolve these aberrations by the mitochondrial release factor in rescue (MTRFR) imparts a negative regulatory effect on protein synthesis that is associated with human disease. Our findings reveal a source of underlying noise in mitochondrial gene expression and the importance of responsive ribosome quality control mechanisms for cell fitness and human health.

Genome-Wide Analysis of Gene Expression Noise Brought About by Transcriptional Regulation in Pseudomonas aeruginosa.

The part of expression noise that is brought about by transcriptional regulation (represented here as NTR) is an important criterion for estimating the regulatory mode of a gene. However, characterization of NTR is an under-explored area, and there is little knowledge regarding the genome-wide NTR in the model pathogen Pseudomonas aeruginosa. Here, with a library of dual-color transcriptional reporters, we estimated the NTR for over 90% of the promoters in P. aeruginosa. Most promoters exhibit low NTR, while 42 and 115 promoters with high NTR were screened out in the exponential and the stationary growth phases, respectively. Specifically, a rearrangement of NTR was found in promoters involved in amino acid metabolism when bacteria enter the exponential phase. In addition, during the stationary phase, high NTR was found in a wide range of iron-related promoters involving siderophore synthesis and heme uptake, ExsA-regulated promoters involving bacterial virulence, and FleQ-regulated promoters involving biofilm development. We also found a large-scale negative dependence of transcriptional regulation between high-NTR promoters belonging to different functional categories. Our findings offer a global view of transcriptional heterogeneity in P. aeruginosa. IMPORTANCE The phenotypic diversity of Pseudomonas aeruginosa is frequently observed in research, suggesting that bacteria adopt strategies such as bet-hedging to survive ever-changing environments. Gene expression noise (GEN) is the major source of phenotypic diversity. Large GEN from transcriptional regulation (represented as NTR) represent an evolutionary necessity to maintain the copy number diversity of certain proteins in the population. Here, we provide a system-wide view of NTR in P. aeruginosa under nutrient-rich and stressed conditions. High NTR was found in genes involved in flagella biosynthesis and amino acid metabolism under both conditions. Specially, iron acquisition genes exhibited high NTR in the stressed condition, suggesting a great diversity of iron physiology in P. aeruginosa. We further revealed a global negative dependence of transcriptional regulation between those high-NTR genes under the stressed condition, suggesting a mutually exclusive relationship between different bacterial survival strategies.

Analysis of MicroRNA Regulation and Gene Expression Variability in Single Cell Data.

MicroRNAs (miRNAs) regulate gene expression by binding to mRNAs, and thus reduce target gene expression levels and expression variability, also known as ‘noise’. Single-cell RNA sequencing (scRNA-seq) technology has been used to study miRNA and mRNA expression in single cells. To evaluate scRNA-seq as a tool for investigating miRNA regulation, we analyzed datasets with both mRNA and miRNA expression in single-cell format. We found that miRNAs slightly reduce the expression noise of target genes; however, this effect is easily masked by strong technical noise from scRNA-seq. We suggest improvements aimed at reducing technical noise, which can be implemented in experimental design and computational analysis prior to running scRNA-seq. Our study provides useful guidelines for experiments that evaluate the effect of miRNAs on mRNA expression from scRNA-seq.

Mother-Fetus Immune Cross-Talk Coordinates "Extrinsic"/"Intrinsic" Embryo Gene Expression Noise and Growth Stability.

Developmental instability (DI) is thought to be inversely related to a capacity of an organism to buffer its development against random genetic and environmental perturbations. DI is represented by a trait’s inter- and intra-individual variabilities. The inter-individual variability (inversely referred to as canalization) indicates the capability of organisms to reproduce a trait from individual to individual. The intra-individual variability reflects an organism’s capability to stabilize a trait internally under the same conditions, and, for symmetric traits, it is expressed as fluctuating asymmetry (FA). When representing a trait as a random variable conditioned on environmental fluctuations, it is clear that, in statistical terms, the DI partitions into “extrinsic” (canalization) and “intrinsic” (FA) components of a trait’s variance/noise. We established a simple statistical framework to dissect both parts of a symmetric trait variance/noise using a PCA (principal component analysis) projection of the left/right measurements on eigenvectors followed by GAMLSS (generalized additive models for location scale and shape) modeling of eigenvalues. The first eigenvalue represents “extrinsic” and the second—“intrinsic” DI components. We applied this framework to investigate the impact of mother–fetus major histocompatibility complex (MHC)-mediated immune cross-talk on gene expression noise and developmental stability. We showed that “intrinsic” gene noise for the entire transcriptional landscape could be estimated from a small subset of randomly selected genes. Using a diagnostic set of genes, we found that allogeneic MHC combinations tended to decrease “extrinsic” and “intrinsic” gene noise in C57BL/6J embryos developing in the surrogate NOD-SCID and BALB/c mothers. The “intrinsic” gene noise was negatively correlated with growth (embryonic mass) and the levels of placental growth factor (PLGF), but not vascular endothelial growth factor (VEGF). However, it was positively associated with phenotypic growth instability and noise in PLGF. In mammals, the mother–fetus MHC interaction plays a significant role in development, contributing to the fitness of the offspring. Our results demonstrate that a positive impact of distant MHC combinations on embryonic growth could be mediated by the reduction of “intrinsic” gene noise followed by the developmental stabilization of growth.

Noise in a Metabolic Pathway Leads to Persister Formation in Mycobacterium tuberculosis.

ABSTRACTTuberculosis is difficult to treat due to dormant cells formed in response to immune stress and stochastically formed persisters, both of which are tolerant of antibiotics. Bactericidal antibiotics kill by corrupting their energy-dependent targets. We reasoned that stochastic variation, or noise, in the expression of an energy-generating component will produce rare persister cells. In sorted M. tuberculosis cells grown on acetate, there is considerable cell-to-cell variation in the level of mRNA coding for AckA, the acetate kinase. Quenching the noise by overexpressing ackA sharply decreases persisters, showing that it acts as the main persister gene under these conditions. This demonstrates that a low energy mechanism is responsible for the formation of M. tuberculosis persisters. Entrance into a low-energy state driven by noise in expression of energy-producing enzymes is likely a general mechanism by which bacteria produce persisters.IMPORTANCE M. tuberculosis infection requires the administration of multiple antibiotics for a prolonged period of time. Treatment difficulty is generally attributed to M. tuberculosis entrance into a nonreplicative, antibiotic-tolerant state. M. tuberculosis enters this nonreplicative state in response to immune stress. However, a small population of cells enter a nonreplicative, multidrug-tolerant state under normal growth conditions, absent any stress. These cells are termed persisters. The mechanisms by which persisters enter a nonreplicative state are largely unknown. Here, we show that, as with other bacteria, M. tuberculosis persisters are low-energy cells formed stochastically during normal growth. Additionally, we identify the natural variation in the expression of energy producing genes as a source of the stochastic entrance of M. tuberculosis into the low-energy persister state. These findings have important implications for understanding the heterogeneous nature of M. tuberculosis infection and will aid in designing better treatment regimens against this important human pathogen.

NoisET: Noise Learning and Expansion Detection of T-Cell Receptors.

High-throughput sequencing of T- and B-cell receptors makes it possible to track immune repertoires across time, in different tissues, in acute and chronic diseases and in healthy individuals. However, quantitative comparison between repertoires is confounded by variability in the read count of each receptor clonotype due to sampling, library preparation, and expression noise. We review methods for accounting for both biological and experimental noise and present an easy-to-use python package NoisET that implements and generalizes a previously developed Bayesian method. It can be used to learn experimental noise models for repertoire sequencing from replicates, and to detect responding clones following a stimulus. We test the package on different repertoire sequencing technologies and data sets. We review how such approaches have been used to identify responding clonotypes in vaccination and disease data. Availability: NoisET is freely available to use with source code at github.com/statbiophys/NoisET.

Rhythmicity is linked to expression cost at the protein level but to expression precision at the mRNA level.

Many genes have nycthemeral rhythms of expression, i.e. a 24-hours periodic variation, at either mRNA or protein level or both, and most rhythmic genes are tissue-specific. Here, we investigate and discuss the evolutionary origins of rhythms in gene expression. Our results suggest that rhythmicity of protein expression could have been favored by selection to minimize costs. Trends are consistent in bacteria, plants and animals, and are also supported by tissue-specific patterns in mouse. Unlike for protein level, cost cannot explain rhythm at the RNA level. We suggest that instead it allows to periodically reduce expression noise. Noise control had the strongest support in mouse, with limited evidence in other species. We have also found that genes under stronger purifying selection are rhythmically expressed at the mRNA level, and we propose that this is because they are noise sensitive genes. Finally, the adaptive role of rhythmic expression is supported by rhythmic genes being highly expressed yet tissue-specific. This provides a good evolutionary explanation for the observation that nycthemeral rhythms are often tissue-specific.