Origin and consequences of the relationship between protein mean and variance

Effect of genomic and cellular environments on gene expression noise

BACKGROUND

Individual cells from isogenic populations often display large cell-to-cell differences in gene expression. This "noise" in expression derives from several sources, including the genomic and cellular environment in which a gene resides. Large-scale maps of genomic environments have revealed the effects of epigenetic modifications and transcription factor occupancy on mean expression levels, but leveraging such maps to explain expression noise will require new methods to assay how expression noise changes at locations across the genome.

RESULTS

To address this gap, we present Single-cell Analysis of Reporter Gene Expression Noise and Transcriptome (SARGENT), a method that simultaneously measures the noisiness of reporter genes integrated throughout the genome and the global mRNA profiles of individual reporter-gene-containing cells. Using SARGENT, we perform the first comprehensive genome-wide survey of how genomic locations impact gene expression noise. We find that the mean and noise of expression correlate with different histone modifications. We quantify the intrinsic and extrinsic components of reporter gene noise and, using the associated mRNA profiles, assign the extrinsic component to differences between the CD24+ "stem-like" substate and the more "differentiated" substate. SARGENT also reveals the effects of transgene integrations on endogenous gene expression, which will help guide the search for "safe-harbor" loci.

CONCLUSIONS

Taken together, we show that SARGENT is a powerful tool to measure both the mean and noise of gene expression at locations across the genome and that the data generatd by SARGENT reveals important insights into the regulation of gene expression noise genome-wide.

Activation domains can decouple the mean and noise of gene expression

Regulatory mechanisms set a gene's average level of expression, but a gene's expression constantly fluctuates around that average. These stochastic fluctuations, or expression noise, play a role in cell-fate transitions, bet hedging in microbes, and the development of chemotherapeutic resistance in cancer. An outstanding question is what regulatory mechanisms contribute to noise. Here, we demonstrate that, for a fixed mean level of expression, strong activation domains (ADs) at low abundance produce high expression noise, while weak ADs at high abundance generate lower expression noise. We conclude that differences in noise can be explained by the interplay between a TF's nuclear concentration and the strength of its AD's effect on mean expression, without invoking differences between classes of ADs. These results raise the possibility of engineering gene expression noise independently of mean levels in synthetic biology contexts and provide a potential mechanism for natural selection to tune the noisiness of gene expression.

Exact distributions for stochastic gene expression models with arbitrary promoter architecture and translational bursting

Gene expression in individual cells is inherently variable and sporadic, leading to cell-to-cell variability in mRNA and protein levels. Recent single-cell and single-molecule experiments indicate that promoter architecture and translational bursting play significant roles in controlling gene expression noise and generating the phenotypic diversity that life exhibits. To quantitatively understand the impact of these factors, it is essential to construct an accurate mathematical description of stochastic gene expression and find the exact analytical results, which is a formidable task. Here, we develop a stochastic model of bursty gene expression, which considers the complex promoter architecture governing the variability in mRNA expression and a general distribution characterizing translational burst. We derive the analytical expression for the corresponding protein steady-state distribution and all moment statistics of protein counts. We show that the total protein noise can be decomposed into three parts: the low-copy noise of protein due to probabilistic individual birth and death events, the noise due to stochastic switching between promoter states, and the noise resulting from translational busting. The theoretical results derived provide quantitative insights into the biochemical mechanisms of stochastic gene expression.

Correlation between external regulators governs the mean-noise relationship in stochastic gene expression

Gene transcription in single cells is inherently a probabilistic process. The relationship between variance ($ \sigma^{2} $) and mean expression ($ \mu $) is of paramount importance for investigations into the evolutionary origins and consequences of noise in gene expression. It is often formulated as $ \log \left({{{\sigma}^{2}}}/{{{\mu}^{2}}}\; \right) = \beta\log\mu+\log\alpha $, where $ \beta $ is a key parameter since its sign determines the qualitative dependence of noise on mean. We reveal that the sign of $ \beta $ is controlled completely by external regulation, but independent of promoter structure. Specifically, it is negative if regulators as stochastic variables are independent but positive if they are correlated. The essential mechanism revealed here can well interpret diverse experimental phenomena underlying expression noise. Our results imply that external regulation rather than promoter sequence governs the mean-noise relationship.

Elucidating effects of reaction rates on dynamics of the lac circuit in Escherichia coli

Gene expression is regulated by a complex transcriptional network. It is of interest to quantify uncertainty of not knowing accurately reaction rates of underlying biochemical reactions, and to understand how they affect gene expression. Assuming a kinetic model of the lac circuit in Escherichia coli, regardless of how many reactions are involved in transcription regulation, transcription rate is shown to be the most important parameter affecting steady state production of mRNA and protein in the cell. In particular, doubling the transcription rate approximately doubles the number of mRNA synthesized at steady state for any rates of transcription inhibition and activation. On the other hand, increasing the rate of transcription inhibition by 10% reduces the average steady state count of mRNA by about 7%, whereas changes in the rate of transcription activation appear to have no such effect. Furthermore, for wide range of reaction rates in the kinetic model of the lac genetic switch considered, protein production was observed to always reach a maximum before the degradation reduces its count to zero, and this maximum was found to be always at least 27 protein molecules. Such value appears to be a fundamental structural property of genetic circuits making it very robust against changes in the internal and external conditions.

Fitness effects of altering gene expression noise in Saccharomyces cerevisiae

Gene expression noise is an evolvable property of biological systems that describes differences in expression among genetically identical cells in the same environment. Prior work has shown that expression noise is heritable and can be shaped by selection, but the impact of variation in expression noise on organismal fitness has proven difficult to measure. Here, we quantify the fitness effects of altering expression noise for the TDH3 gene in Saccharomyces cerevisiae. We show that increases in expression noise can be deleterious or beneficial depending on the difference between the average expression level of a genotype and the expression level maximizing fitness. We also show that a simple model relating single-cell expression levels to population growth produces patterns consistent with our empirical data. We use this model to explore a broad range of average expression levels and expression noise, providing additional insight into the fitness effects of variation in expression noise.

A microRNA feedback loop regulates global microRNA abundance during aging

Expression levels of many microRNAs (miRNAs) change during aging, notably declining globally in a number of organisms and tissues across taxa. However, little is known about the mechanisms or the biological relevance for this change. We investigated the network of genes that controls miRNA transcription and processing during C. elegans aging. We found that miRNA biogenesis genes are highly networked with transcription factors and aging-associated miRNAs. In particular, miR-71, known to influence life span and itself up-regulated during aging, represses alg-1/Argonaute expression post-transcriptionally during aging. Increased ALG-1 abundance in mir-71 loss-of-function mutants led to globally increased miRNA expression. Interestingly, these mutants demonstrated widespread mRNA expression dysregulation and diminished levels of variability both in gene expression and in overall life span. Thus, the progressive molecular decline often thought to be the result of accumulated damage over an organism's life may be partially explained by a miRNA-directed mechanism of age-associated decline.

Decomposition and tunability of expression noise in the presence of coupled feedbacks

Expression noise results in cell-to-cell variability in expression levels, and feedback regulation may complicate the tracing of sources of this noise. Using a representative model of gene expression with feedbacks, we analytically show that the expression noise (or the total noise) is decomposed into three parts: feedback-dependent promoter noise determined by a continuous approximation, birth-death noise determined by a simple Poisson process, and correlation noise induced by feedbacks. We clarify confused relationships between feedback and noise in previous studies, by showing that feedback-regulated noisy sources have different contributions to the total noise in different cases of promoter switching (it is an essential reason resulting in confusions). More importantly, we find that there is a tradeoff between response time and expression noise. In addition, we show that in contrast to single feedbacks, coupled positive and negative feedbacks can perform better in tuning expression noise, controlling expression levels, and maintaining response time. The overall analysis implies that living organisms would utilize coupled positive and negative feedbacks for better survival in complex and fluctuating environments.