Peter S. Swain

Intrinsic and extrinsic contributions to stochasticity in gene expression

Gene expression is a stochastic, or “noisy,” process. This noise comes about in two ways. The inherent stochasticity of biochemical processes such as transcription and translation generates “intrinsic” noise. In addition, fluctuations in the amounts or states of other cellular components lead indirectly to variation in the expression of a particular gene and thus represent “extrinsic” noise. Here, we show how the total variation in the level of expression of a given gene can be decomposed into its intrinsic and extrinsic components. We demonstrate theoretically that simultaneous measurement of two identical genes per cell enables discrimination of these two types of noise. Analytic expressions for intrinsic noise are given for a model that involves all the major steps in transcription and translation. These expressions give the sensitivity to various parameters, quantify the deviation from Poisson statistics, and provide a way of fitting experiment. Transcription dominates the intrinsic noise when the average number of proteins made per mRNA transcript is greater than ≃2. Below this number, translational effects also become important. Gene replication and cell division, included in the model, cause protein numbers to tend to a limit cycle. We calculate a general form for the extrinsic noise and illustrate it with the particular case of a single fluctuating extrinsic variable—a repressor protein, which acts on the gene of interest. All results are confirmed by stochastic simulation using plausible parameters for Escherichia coli.

Analytical distributions for stochastic gene expression

Gene expression is significantly stochastic making modeling of genetic networks challenging. We present an approximation that allows the calculation of not only the mean and variance, but also the distribution of protein numbers. We assume that proteins decay substantially more slowly than their mRNA and confirm that many genes satisfy this relation by using high-throughput data from budding yeast. For a two-stage model of gene expression, with transcription and translation as first-order reactions, we calculate the protein distribution for all times greater than several mRNA lifetimes and thus qualitatively predict the distribution of times for protein levels to first cross an arbitrary threshold. If in addition the fluctuates between inactive and active states, we can find the steady-state protein distribution, which can be bimodal if fluctuations of the promoter are slow. We show that our assumptions imply that protein synthesis occurs in geometrically distributed bursts and allows mRNA to be eliminated from a master equation description. In general, we find that protein distributions are asymmetric and may be poorly characterized by their mean and variance. Through maximum likelihood methods, our expressions should therefore allow more quantitative comparisons with experimental data. More generally, we introduce a technique to derive a simpler, effective dynamics for a stochastic system by eliminating a fast variable.

Measuring single-cell gene expression dynamics in bacteria using fluorescence time-lapse microscopy

Quantitative single-cell time-lapse microscopy is a powerful method for analyzing gene circuit dynamics and heterogeneous cell behavior. We describe the application of this method to imaging bacteria by using an automated microscopy system. This protocol has been used to analyze sporulation and competence differentiation in Bacillus subtilis, and to quantify gene regulation and its fluctuations in individual Escherichia coli cells. The protocol involves seeding and growing bacteria on small agarose pads and imaging the resulting microcolonies. Images are then reviewed and analyzed using our laboratorys custom MATLAB analysis code, which segments and tracks cells in a frame-to-frame method. This process yields quantitative expression data on cell lineages, which can illustrate dynamic expression profiles and facilitate mathematical models of gene circuits. With fast-growing bacteria, such as E. coli or B. subtilis, image acquisition can be completed in 1 d, with an additional 1–2 d for progressing through the analysis procedure.

Colored extrinsic fluctuations and stochastic gene expression.

Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or ‘noise’, is predominantly generated by interactions of the system of interest with other stochastic systems in the cell or its environment. Such extrinsic fluctuations are nonspecific, affecting many system components, and have a substantial lifetime, comparable to the cell cycle (they are ‘colored’). Here, we extend the standard stochastic simulation algorithm to include extrinsic fluctuations. We show that these fluctuations affect mean protein numbers and intrinsic noise, can speed up typical network response times, and can explain trends in high‐throughput measurements of variation. If extrinsic fluctuations in two components of the network are correlated, they may combine constructively (amplifying each other) or destructively (attenuating each other). Consequently, we predict that incoherent feedforward loops attenuate stochasticity, while coherent feedforwards amplify it. Our results demonstrate that both the timescales of extrinsic fluctuations and their nonspecificity substantially affect the function and performance of biochemical networks.

Strategies for cellular decision-making

Stochasticity pervades life at the cellular level. Cells receive stochastic signals, perform detection and transduction with stochastic biochemistry, and grow and die in stochastic environments. Here we review progress in going from the molecular details to the information‐processing strategies cells use in their decision‐making. Such strategies are fundamentally influenced by stochasticity. We argue that the cellular decision‐making can only be probabilistic and occurs at three levels. First, cells must infer from noisy signals the probable current and anticipated future state of their environment. Second, they must weigh the costs and benefits of each potential response, given that future. Third, cells must decide in the presence of other, potentially competitive, decision‐makers. In this context, we discuss cooperative responses where some individuals can appear to sacrifice for the common good. We believe that decision‐making strategies will be conserved, with comparatively few strategies being implemented by different biochemical mechanisms in many organisms. Determining the strategy of a decision‐making network provides a potentially powerful coarse‐graining that links systems and evolutionary biology to understand biological design.

The scaffold protein Ste5 directly controls a switch-like mating decision in yeast

Evolution has resulted in numerous innovations that allow organisms to increase their fitness by choosing particular mating partners, including secondary sexual characteristics, behavioural patterns, chemical attractants and corresponding sensory mechanisms. The haploid yeast Saccharomyces cerevisiae selects mating partners by interpreting the concentration gradient of pheromone secreted by potential mates through a network of mitogen-activated protein kinase (MAPK) signalling proteins. The mating decision in yeast is an all-or-none, or switch-like, response that allows cells to filter weak pheromone signals, thus avoiding inappropriate commitment to mating by responding only at or above critical concentrations when a mate is sufficiently close. The molecular mechanisms that govern the switch-like mating decision are poorly understood. Here we show that the switching mechanism arises from competition between the MAPK Fus3 and a phosphatase Ptc1 for control of the phosphorylation state of four sites on the scaffold protein Ste5. This competition results in a switch-like dissociation of Fus3 from Ste5 that is necessary to generate the switch-like mating response. Thus, the decision to mate is made at an early stage in the pheromone pathway and occurs rapidly, perhaps to prevent the loss of the potential mate to competitors. We argue that the architecture of the Fus3–Ste5–Ptc1 circuit generates a novel ultrasensitivity mechanism, which is robust to variations in the concentrations of these proteins. This robustness helps assure that mating can occur despite stochastic or genetic variation between individuals. The role of Ste5 as a direct modulator of a cell-fate decision expands the functional repertoire of scaffold proteins beyond providing specificity and efficiency of information processing. Similar mechanisms may govern cellular decisions in higher organisms and be disrupted in cancer.

The stochastic nature of biochemical networks

Cell behaviour and the cellular environment are stochastic. Phenotypes vary across isogenic populations and in individual cells over time. Here we will argue that to understand the abilities of cells we need to understand their stochastic nature. New experimental techniques allow gene expression to be followed in single cells over time and reveal stochastic bursts of both mRNA and protein synthesis in many different types of organisms. Stochasticity has been shown to be exploited by bacteria and viruses to decide between different behaviours. In fluctuating environments, cells that respond stochastically can out-compete those that sense environmental changes, and stochasticity may even have contributed to chromosomal gene order. We will focus on advances in modelling stochasticity, in understanding its effects on evolution and cellular design, and on means by which it may be exploited in biotechnology and medicine.

Mechanistic links between cellular trade-offs, gene expression, and growth.

Significance Cells have finite resources. Committing resources to one task therefore reduces the amount of resources available to others. These trade-offs are often overlooked but potentially modify all cellular processes. Building a mathematical cell model that respects such trade-offs and describes the mechanisms of protein synthesis and how cells extract resources from their environment, we quantitatively recover the typical behavior of an individual growing cell and of a population of cells. As trade-offs are experienced by all cells and because growth largely determines cellular fitness, a predictive understanding of how biochemical processes affect others and affect growth is important for diverse applications, such as the use of microbes for biotechnology, the inhibition of antibiotic resistance, and the growth of cancers. Intracellular processes rarely work in isolation but continually interact with the rest of the cell. In microbes, for example, we now know that gene expression across the whole genome typically changes with growth rate. The mechanisms driving such global regulation, however, are not well understood. Here we consider three trade-offs that, because of limitations in levels of cellular energy, free ribosomes, and proteins, are faced by all living cells and we construct a mechanistic model that comprises these trade-offs. Our model couples gene expression with growth rate and growth rate with a growing population of cells. We show that the model recovers Monod’s law for the growth of microbes and two other empirical relationships connecting growth rate to the mass fraction of ribosomes. Further, we can explain growth-related effects in dosage compensation by paralogs and predict host–circuit interactions in synthetic biology. Simulating competitions between strains, we find that the regulation of metabolic pathways may have evolved not to match expression of enzymes to levels of extracellular substrates in changing environments but rather to balance a trade-off between exploiting one type of nutrient over another. Although coarse-grained, the trade-offs that the model embodies are fundamental, and, as such, our modeling framework has potentially wide application, including in both biotechnology and medicine.

Accurate prediction of gene feedback circuit behavior from component properties.

A basic assumption underlying synthetic biology is that analysis of genetic circuit elements, such as regulatory proteins and promoters, can be used to understand and predict the behavior of circuits containing those elements. To test this assumption, we used time‐lapse fluorescence microscopy to quantitatively analyze two autoregulatory negative feedback circuits. By measuring the gene regulation functions of the corresponding repressor–promoter interactions, we accurately predicted the expression level of the autoregulatory feedback loops, in molecular units. This demonstration that quantitative characterization of regulatory elements can predict the behavior of genetic circuits supports a fundamental requirement of synthetic biology.

Identifying sources of variation and the flow of information in biochemical networks

To understand how cells control and exploit biochemical fluctuations, we must identify the sources of stochasticity, quantify their effects, and distinguish informative variation from confounding “noise.” We present an analysis that allows fluctuations of biochemical networks to be decomposed into multiple components, gives conditions for the design of experimental reporters to measure all components, and provides a technique to predict the magnitude of these components from models. Further, we identify a particular component of variation that can be used to quantify the efficacy of information flow through a biochemical network. By applying our approach to osmosensing in yeast, we can predict the probability of the different osmotic conditions experienced by wild-type yeast and show that the majority of variation can be informational if we include variation generated in response to the cellular environment. Our results are fundamental to quantifying sources of variation and thus are a means to understand biological “design.”