Disentangling Intrinsic and Extrinsic Gene Expression Noise in Growing Cells

How do stochastic processes and genetic threshold effects explain incomplete penetrance and inform causal disease mechanisms?

Incomplete penetrance is the rule rather than the exception in Mendelian disease. In syndromic monogenic disorders, phenotypic variability can be viewed as the combination of incomplete penetrance for each of multiple independent clinical features. Within genetically identical individuals, such as isogenic model organisms, stochastic variation at molecular and cellular levels is the primary cause of incomplete penetrance according to a genetic threshold model. By defining specific probability distributions of causal biological readouts and genetic liability values, stochasticity and incomplete penetrance provide information about threshold values in biological systems. Ascertainment of threshold values has been achieved by simultaneous scoring of relatively simple phenotypes and quantitation of molecular readouts at the level of single cells. However, this is much more challenging for complex morphological phenotypes using experimental and reductionist approaches alone, where cause and effect are separated temporally and across multiple biological modes and scales. Here I consider how causal inference, which integrates observational data with high confidence causal models, might be used to quantify the relative contribution of different sources of stochastic variation to phenotypic diversity. Collectively, these approaches could inform disease mechanisms, improve predictions of clinical outcomes and prioritize gene therapy targets across modes and scales of gene function. This article is part of a discussion meeting issue 'Causes and consequences of stochastic processes in development and disease'.

Physiological stress drives the emergence of a Salmonella subpopulation through ribosomal RNA regulation

Bacteria undergo cycles of growth and starvation to which they must adapt swiftly. One important strategy for adjusting growth rates relies on ribosomal levels. Although high ribosomal levels are required for fast growth, their dynamics during starvation remain unclear. Here, we analyzed ribosomal RNA (rRNA) content of individual Salmonella cells by using fluorescence in situ hybridization (rRNA-FISH) and measured a dramatic decrease in rRNA numbers only in a subpopulation during nutrient limitation, resulting in a bimodal distribution of cells with high and low rRNA content. During nutritional upshifts, the two subpopulations were associated with distinct phenotypes. Using a transposon screen coupled with rRNA-FISH, we identified two mutants, DksA and RNase I, acting on rRNA transcription shutdown and degradation, which abolished the formation of the subpopulation with low rRNA content. Our work identifies a bacterial mechanism for regulation of ribosomal bimodality that may be beneficial for population survival during starvation.

Out-of-equilibrium gene expression fluctuations in the presence of extrinsic noise

Cell-to-cell variability in protein concentrations is strongly affected by extrinsic noise, especially for highly expressed genes. Extrinsic noise can be due to fluctuations of several possible cellular factors connected to cell physiology and to the level of key enzymes in the expression process. However, how to identify the predominant sources of extrinsic noise in a biological system is still an open question. This work considers a general stochastic model of gene expression with extrinsic noise represented as fluctuations of the different model rates, and focuses on the out-of-equilibrium expression dynamics. Combining analytical calculations with stochastic simulations, we characterize how extrinsic noise shapes the protein variability during gene activation or inactivation, depending on the prevailing source of extrinsic variability, on its intensity and timescale. In particular, we show that qualitatively different noise profiles can be identified depending on which are the fluctuating parameters. This indicates an experimentally accessible way to pinpoint the dominant sources of extrinsic noise using time-coarse experiments.

Implications of differential size-scaling of cell-cycle regulators on cell size homeostasis

Accurate timing of division and size homeostasis is crucial for cells. A potential mechanism for cells to decide the timing of division is the differential scaling of regulatory protein copy numbers with cell size. However, it remains unclear whether such a mechanism can lead to robust growth and division, and how the scaling behaviors of regulatory proteins influence the cell size distribution. Here we study a mathematical model combining gene expression and cell growth, in which the cell-cycle activators scale superlinearly with cell size while the inhibitors scale sublinearly. The cell divides once the ratio of their concentrations reaches a threshold value. We find that the cell can robustly grow and divide within a finite range of the threshold value with the cell size proportional to the ploidy. In a stochastic version of the model, the cell size at division is uncorrelated with that at birth. Also, the more differential the cell-size scaling of the cell-cycle regulators is, the narrower the cell-size distribution is. Intriguingly, our model with multiple regulators rationalizes the observation that after the deletion of a single regulator, the coefficient of variation of cell size remains roughly the same though the average cell size changes significantly. Our work reveals that the differential scaling of cell-cycle regulators provides a robust mechanism of cell size control.

Interplay of Cellular mRNA, miRNA and Viral miRNA during Infection of a Cell

The understanding of the kinetics of gene expression in cells infected by viruses is currently limited. As a rule, the corresponding models do not take viral microRNAs (miRNAs) into account. Such RNAs are, however, operative during the replication of some viruses, including, e.g., herpesvirus. To clarify the kinetics of this category (with emphasis on the information available for herpesvirus), I introduce a generic model describing the transient interplay of cellular mRNA, protein, miRNA and viral miRNA. In the absence of viral miRNA, the cellular miRNA is considered to suppress the populations of mRNA and protein due to association with mRNA and subsequent degradation. During infection, the viral miRNA suppresses the population of cellular miRNA and via this pathway makes the mRNA and protein populations larger. This effect becomes appreciable with the progress of intracellular viral replication. Using biologically reasonable parameters, I investigate the corresponding mean-field kinetics and show the scale of the effect of viral miRNAs on cellular miRNA and mRNA. The scale of fluctuations of the populations of these species is illustrated as well by employing Monte Carlo simulations.

Mechanisms of cellular mRNA transcript homeostasis

For most genes, mRNA transcript abundance scales with cell size to ensure a constant concentration. Scaling of mRNA synthesis rates with cell size plays an important role, with regulation of the activity and abundance of RNA polymerase II (Pol II) now emerging as a key point of control. However, there is also considerable evidence for feedback mechanisms that kinetically couple the rates of mRNA synthesis, nuclear export, and degradation to allow cells to compensate for changes in one by adjusting the others. Researchers are beginning to integrate results from these different fields to reveal the mechanisms underlying transcript homeostasis. This will be crucial for moving beyond our current understanding of relative gene expression towards an appreciation of how absolute transcript levels are linked to other aspects of the cellular phenotype.

Multiple timescales in bacterial growth homeostasis

In balanced exponential growth, bacteria maintain many properties statistically stable for a long time: cell size, cell cycle time, and more. As these are strongly coupled variables, it is not a-priori obvious which are directly regulated and which are stabilized through interactions. Here, we address this problem by separating timescales in bacterial single-cell dynamics. Disentangling homeostatic set points from fluctuations around them reveals that some variables, such as growth-rate, cell size and cycle time, are "sloppy" with highly volatile set points. Quantifying the relative contribution of environmental and internal sources, we find that sloppiness is primarily driven by the environment. Other variables such as fold-change define "stiff" combinations of coupled variables with robust set points. These results are manifested geometrically as a control manifold in the space of variables: set points span a wide range of values within the manifold, whereas out-of-manifold deviations are constrained. Our work offers a generalizable data-driven approach for identifying control variables in a multidimensional system.

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.

Challenges of analysing stochastic gene expression in bacteria using single-cell time-lapse experiments

Stochastic gene expression causes phenotypic heterogeneity in a population of genetically identical bacterial cells. Such non-genetic heterogeneity can have important consequences for the population fitness, and therefore cells implement regulation strategies to either suppress or exploit such heterogeneity to adapt to their circumstances. By employing time-lapse microscopy of single cells, the fluctuation dynamics of gene expression may be analysed, and their regulatory mechanisms thus deciphered. However, a careful consideration of the experimental design and data-analysis is needed to produce useful data for deriving meaningful insights from them. In the present paper, the individual steps and challenges involved in a time-lapse experiment are discussed, and a rigorous framework for designing, performing, and extracting single-cell gene expression dynamics data from such experiments is outlined.