Stochastic expression dynamics of a transcription factor revealed by single-molecule noise analysis

Quantifying Landscape-Flux via Single-Cell Transcriptomics Uncovers the Underlying Mechanism of Cell Cycle

Recent developments in single-cell sequencing technology enable the acquisition of entire transcriptome data. Understanding the underlying mechanism and identifying the driving force of transcriptional regulation governing cell function directly from these data remains challenging. This study reconstructs a continuous vector field of the cell cycle based on discrete single-cell RNA velocity to quantify the single-cell global nonequilibrium dynamic landscape-flux. It reveals that large fluctuations disrupt the global landscape and genetic perturbations alter landscape-flux, thus identifying key genes in maintaining cell cycle dynamics and predicting associated functional effects. Additionally, it quantifies the fundamental energy cost of the cell cycle initiation and unveils that sustaining the cell cycle requires curl flux and dissipation to maintain the oscillatory phase coherence. This study enables the inference of the cell cycle gene regulatory networks directly from the single-cell transcriptomic data, including the feedback mechanisms and interaction intensity. This provides a golden opportunity to experimentally verify the landscape-flux theory and also obtain its associated quantifications. It also offers a unique framework for combining the landscape-flux theory and single-cell high-through sequencing experiments for understanding the underlying mechanisms of the cell cycle and can be extended to other nonequilibrium biological processes, such as differentiation development and disease pathogenesis.

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.

Double-edged role of resource competition in gene expression noise and control

Despite extensive investigation demonstrating that resource competition can significantly alter the deterministic behaviors of synthetic gene circuits, it remains unclear how resource competition contributes to the gene expression noise and how this noise can be controlled. Utilizing a two-gene circuit as a prototypical system, we uncover a surprising double-edged role of resource competition in gene expression noise: competition decreases noise through introducing a resource constraint but generates its own type of noise which we name as "resource competitive noise." Utilization of orthogonal resources enables retainment of the noise reduction conferred by resource constraint while removing the added resource competitive noise. The noise reduction effects are studied using three negative feedback types: negatively competitive regulation (NCR), local, and global controllers, each having four placement architectures in the protein biosynthesis pathway (mRNA or protein inhibition on transcription or translation). Our results show that both local and NCR controllers with mRNA-mediated inhibition are efficacious at reducing noise, with NCR controllers demonstrating a superior noise-reduction capability. We also find that combining feedback controllers with orthogonal resources can improve the local controllers. This work provides deep insights into the origin of stochasticity in gene circuits with resource competition and guidance for developing effective noise control strategies.

Next generation single-molecule techniques: Imaging, labeling, and manipulation in vitro and in cellulo

Owing to their unique abilities to manipulate, label, and image individual molecules in vitro and in cellulo, single-molecule techniques provide previously unattainable access to elementary biological processes. In imaging, single-molecule fluorescence resonance energy transfer (smFRET) and protein-induced fluorescence enhancement in vitro can report on conformational changes and molecular interactions, single-molecule pull-down (SiMPull) can capture and analyze the composition and function of native protein complexes, and single-molecule tracking (SMT) in live cells reveals cellular structures and dynamics. In labeling, the abilities to specifically label genomic loci, mRNA, and nascent polypeptides in cells have uncovered chromosome organization and dynamics, transcription and translation dynamics, and gene expression regulation. In manipulation, optical tweezers, integration of single-molecule fluorescence with force measurements, and single-molecule force probes in live cells have transformed our mechanistic understanding of diverse biological processes, ranging from protein folding, nucleic acids-protein interactions to cell surface receptor function.

Resolving the Rules of Robustness and Resilience in Biology Across Scales

Why do some biological systems and communities persist while others fail? Robustness, a system's stability, and resilience, the ability to return to a stable state, are key concepts that span multiple disciplines within and outside the biological sciences. Discovering and applying common rules that govern the robustness and resilience of biological systems is a critical step toward creating solutions for species survival in the face of climate change, as well as the for the ever-increasing need for food, health, and energy for human populations. We propose that network theory provides a framework for universal scalable mathematical models to describe robustness and resilience and the relationship between them, and hypothesize that resilience at lower organization levels contribute to robust systems. Insightful models of biological systems can be generated by quantifying the mechanisms of redundancy, diversity, and connectivity of networks, from biochemical processes to ecosystems. These models provide pathways towards understanding how evolvability can both contribute to and result from robustness and resilience under dynamic conditions. We now have an abundance of data from model and non-model systems and the technological and computational advances for studying complex systems. Several conceptual and policy advances will allow the research community to elucidate the rules of robustness and resilience. Conceptually, a common language and data structure that can be applied across levels of biological organization needs to be developed. Policy advances such as cross-disciplinary funding mechanisms, access to affordable computational capacity, and the integration of network theory and computer science within the standard biological science curriculum will provide the needed research environments. This new understanding of biological systems will allow us to derive ever more useful forecasts of biological behaviors and revolutionize the engineering of biological systems that can survive changing environments or disease, navigate the deepest oceans, or sustain life throughout the solar system.

From deterministic to fuzzy decision-making in artificial cells

Building autonomous artificial cells capable of homeostasis requires regulatory networks to gather information and make decisions that take time and cost energy. Decisions based on few molecules may be inaccurate but are cheap and fast. Realizing decision-making with a few molecules in artificial cells has remained a challenge. Here, we show decision-making by a bistable gene network in artificial cells with constant protein turnover. Reducing the number of gene copies from 10⁵ to about 10 per cell revealed a transition from deterministic and slow decision-making to a fuzzy and rapid regime dominated by small-number fluctuations. Gene regulation was observed at lower DNA and protein concentrations than necessary in equilibrium, suggesting rate enhancement by co-expressional localization. The high-copy regime was characterized by a sharp transition and hysteresis, whereas the low-copy limit showed strong fluctuations, state switching, and cellular individuality across the decision-making point. Our results demonstrate information processing with low-power consumption inside artificial cells.

Cell-state dynamics and therapeutic resistance in melanoma from the perspective of MITF and IFNγ pathways

Targeted therapy and immunotherapy have greatly improved the prognosis of patients with metastatic melanoma, but resistance to these therapeutic modalities limits the percentage of patients with long-lasting responses. Accumulating evidence indicates that a persisting subpopulation of melanoma cells contributes to resistance to targeted therapy or immunotherapy, even in patients who initially have a therapeutic response; however, the root mechanism of resistance remains elusive. To address this problem, we propose a new model, in which dynamic fluctuations of protein expression at the single-cell level and longitudinal reshaping of the cellular state at the cell-population level explain the whole process of therapeutic resistance development. Conceptually, we focused on two different pivotal signalling pathways (mediated by microphthalmia-associated transcription factor (MITF) and IFNγ) to construct the evolving trajectories of melanoma and described each of the cell states. Accordingly, the development of therapeutic resistance could be divided into three main phases: early survival of cell populations, reversal of senescence, and the establishment of new homeostatic states and development of irreversible resistance. On the basis of existing data, we propose future directions in both translational research and the design of therapeutic strategies that incorporate this emerging understanding of resistance.

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise

It is well known that the kinetics of an intracellular biochemical network is stochastic. This is due to intrinsic noise arising from the random timing of biochemical reactions in the network as well as due to extrinsic noise stemming from the interaction of unknown molecular components with the network and from the cell's changing environment. While there are many methods to study the effect of intrinsic noise on the system dynamics, few exist to study the influence of both types of noise. Here we show how one can extend the conventional linear-noise approximation to allow for the rapid evaluation of the molecule numbers statistics of a biochemical network influenced by intrinsic noise and by slow lognormally distributed extrinsic noise. The theory is applied to simple models of gene regulatory networks and its validity confirmed by comparison with exact stochastic simulations. In particular, we consider three important biological examples. First, we investigate how extrinsic noise modifies the dependence of the variance of the molecule number fluctuations on the rate constants. Second, we show how the mutual information between input and output of a network motif is affected by extrinsic noise. And third, we study the robustness of the ubiquitously found feed-forward loop motifs when subjected to extrinsic noise.

Single-Molecule Kinetics in Living Cells

In the past decades, advances in microscopy have made it possible to study the dynamics of individual biomolecules in vitro and resolve intramolecular kinetics that would otherwise be hidden in ensemble averages. More recently, single-molecule methods have been used to image, localize, and track individually labeled macromolecules in the cytoplasm of living cells, allowing investigations of intermolecular kinetics under physiologically relevant conditions. In this review, we illuminate the particular advantages of single-molecule techniques when studying kinetics in living cells and discuss solutions to specific challenges associated with these methods.

Cell fate potentials and switching kinetics uncovered in a classic bistable genetic switch

Bistable switches are common gene regulatory motifs directing two mutually exclusive cell fates. Theoretical studies suggest that bistable switches are sufficient to encode more than two cell fates without rewiring the circuitry due to the non-equilibrium, heterogeneous cellular environment. However, such a scenario has not been experimentally observed. Here by developing a new, dual single-molecule gene-expression reporting system, we find that for the two mutually repressing transcription factors CI and Cro in the classic bistable bacteriophage λ switch, there exist two new production states, in which neither CI nor Cro is produced, or both CI and Cro are produced. We construct the corresponding potential landscape and map the transition kinetics among the four production states. These findings uncover cell fate potentials beyond the classical picture of bistable switches, and open a new window to explore the genetic and environmental origins of the cell fate decision-making process in gene regulatory networks.

Simulating biological processes: stochastic physics from whole cells to colonies

The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a 'minimal cell'. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.

Temperature-dependence of the single-cell variability in the kinetics of transcription activation in Escherichia coli

From in vivo single-cell, single-RNA measurements of the activation times and subsequent steady-state active transcription kinetics of a single-copy Lac-ara-1 promoter in Escherichia coli, we characterize the intake kinetics of the inducer (IPTG) from the media, following temperature shifts. For this, for temperature shifts of various degrees, we obtain the distributions of transcription activation times as well as the distributions of intervals between consecutive RNA productions following activation in individual cells. We then propose a novel methodology that makes use of deconvolution techniques to extract the mean and the variability of the distribution of intake times. We find that cells, following shifts to low temperatures, have higher intake times, although, counter-intuitively, the cell-to-cell variability of these times is lower. We validate the results using a new methodology for direct estimation of mean intake times from measurements of activation times at various inducer concentrations. The results confirm that E. coli's inducer intake times from the environment are significantly higher following a shift to a sub-optimal temperature. Finally, we provide evidence that this is likely due to the emergence of additional rate-limiting steps in the intake process at low temperatures, explaining the reduced cell-to-cell variability in intake times.

Efficient and flexible implementation of Langevin simulation for gene burst production

Gene expression involves bursts of production of both mRNA and protein, and the fluctuations in their number are increased due to such bursts. The Langevin equation is an efficient and versatile means to simulate such number fluctuation. However, how to include these mRNA and protein bursts in the Langevin equation is not intuitively clear. In this work, we estimated the variance in burst production from a general gene expression model and introduced such variation in the Langevin equation. Our approach offers different Langevin expressions for either or both transcriptional and translational bursts considered and saves computer time by including many production events at once in a short burst time. The errors can be controlled to be rather precise (<2%) for the mean and <10% for the standard deviation of the steady-state distribution. Our scheme allows for high-quality stochastic simulations with the Langevin equation for gene expression, which is useful in analysis of biological networks.

A plasmid-based Escherichia coli gene expression system with cell-to-cell variation below the extrinsic noise limit

Experiments in synthetic biology and microbiology can benefit from protein expression systems with low cell-to-cell variability (noise) and expression levels precisely tunable across a useful dynamic range. Despite advances in understanding the molecular biology of microbial gene regulation, many experiments employ protein-expression systems exhibiting high noise and nearly all-or-none responses to induction. I present an expression system that incorporates elements known to reduce gene expression noise: negative autoregulation and bicistronic transcription. I show by stochastic simulation that while negative autoregulation can produce a more gradual response to induction, bicistronic expression of a repressor and gene of interest can be necessary to reduce noise below the extrinsic limit. I synthesized a plasmid-based system incorporating these principles and studied its properties in Escherichia coli cells, using flow cytometry and fluorescence microscopy to characterize induction dose-response, induction/repression kinetics and gene expression noise. By varying ribosome binding site strengths, expression levels from 55–10,740 molecules/cell were achieved with noise below the extrinsic limit. Individual strains are inducible across a dynamic range greater than 20-fold. Experimental comparison of different regulatory networks confirmed that bicistronic autoregulation reduces noise, and revealed unexpectedly high noise for a conventional expression system with a constitutively expressed transcriptional repressor. I suggest a hybrid, low-noise expression system to increase the dynamic range.

Rate-limiting steps in transcription dictate sensitivity to variability in cellular components

Cell-to-cell variability in cellular components generates cell-to-cell diversity in RNA and protein production dynamics. As these components are inherited, this should also cause lineage-to-lineage variability in these dynamics. We conjectured that these effects on transcription are promoter initiation kinetics dependent. To test this, first we used stochastic models to predict that variability in the numbers of molecules involved in upstream processes, such as the intake of inducers from the environment, acts only as a transient source of variability in RNA production numbers, while variability in the numbers of a molecular species controlling transcription of an active promoter acts as a constant source. Next, from single-cell, single-RNA level time-lapse microscopy of independent lineages of Escherichia coli cells, we demonstrate the existence of lineage-to-lineage variability in gene activation times and mean RNA production rates, and that these variabilities differ between promoters and inducers used. Finally, we provide evidence that this can be explained by differences in the kinetics of the rate-limiting steps in transcription between promoters and induction schemes. We conclude that cell-to-cell and consequent lineage-to-lineage variability in RNA and protein numbers are both promoter sequence-dependent and subject to regulation.

What's Luck Got to Do with It: Single Cells, Multiple Fates, and Biological Nondeterminism

The field of single-cell biology has morphed from a philosophical digression at its inception, to a playground for quantitative biologists, to a major area of biomedical research. The last several years have witnessed an explosion of new technologies, allowing us to apply even more of the modern molecular biology toolkit to single cells. Conceptual progress, however, has been comparatively slow. Here, we provide a framework for classifying both the origins of the differences between individual cells and the consequences of those differences. We discuss how the concept of "random" differences is context dependent, and propose that rigorous definitions of inputs and outputs may bring clarity to the discussion. We also categorize ways in which probabilistic behavior may influence cellular function, highlighting studies that point to exciting future directions in the field.

Resource Sharing Controls Gene Expression Bursting

Episodic gene expression, with periods of high expression separated by periods of no expression, is a pervasive biological phenomenon. This bursty pattern of expression draws from a finite reservoir of expression machinery in a highly time variant way, i.e., requiring no resources most of the time but drawing heavily on them during short intense bursts, that intimately links expression bursting and resource sharing. Yet, most recent investigations have focused on specific molecular mechanisms intrinsic to the bursty behavior of individual genes, while little is known about the interplay between resource sharing and global expression bursting behavior. Here, we confine Escherichia coli cell extract in both cell-sized microfluidic chambers and lipid-based vesicles to explore how resource sharing influences expression bursting. Interestingly, expression burst size, but not burst frequency, is highly sensitive to the size of the shared transcription and translation resource pools. The intriguing implication of these results is that expression bursts are more readily amplified than initiated, suggesting that burst formation occurs through positive feedback or cooperativity. When extrapolated to prokaryotic cells, these results suggest that large translational bursts may be correlated with large transcriptional bursts. This correlation is supported by recently reported transcription and translation bursting studies in E. coli. The results reported here demonstrate a strong intimate link between global expression burst patterns and resource sharing, and they suggest that bursting plays an important role in optimizing the use of limited, shared expression resources.

Effects of cell cycle noise on excitable gene circuits

We assess the impact of cell cycle noise on gene circuit dynamics. For bistable genetic switches and excitable circuits, we find that transitions between metastable states most likely occur just after cell division and that this concentration effect intensifies in the presence of transcriptional delay. We explain this concentration effect with a three-states stochastic model. For genetic oscillators, we quantify the temporal correlations between daughter cells induced by cell division. Temporal correlations must be captured properly in order to accurately quantify noise sources within gene networks.

Aspects of protein-DNA interactions: a review of quantitative thermodynamic theory for modelling synthetic circuits utilising LacI and CI repressors, IPTG and the reporter gene lacZ

Protein-DNA interactions are central to the control of gene expression across all forms of life. The development of approaches to rigorously model such interactions has often been hindered both by a lack of quantitative binding data and by the difficulty in accounting for parameters relevant to the intracellular situation, such as DNA looping and thermodynamic non-ideality. Here, we review these considerations by developing a thermodynamically based mathematical model that attempts to simulate the functioning of an Escherichia coli expression system incorporating two of the best characterised prokaryotic DNA binding proteins, Lac repressor and lambda CI repressor. The key aim was to reproduce experimentally observed reporter gene activities arising from the expression of either wild-type CI repressor or one of three positive-control CI mutants. The model considers the role of several potentially important, but sometimes neglected, biochemical features, including DNA looping, macromolecular crowding and non-specific binding, and allowed us to obtain association constants for the binding of CI and its variants to a specific operator sequence.

Mechanical slowing-down of cytoplasmic diffusion allows in vivo counting of proteins in individual cells

Many key regulatory proteins in bacteria are present in too low numbers to be detected with conventional methods, which poses a particular challenge for single-cell analyses because such proteins can contribute greatly to phenotypic heterogeneity. Here we develop a microfluidics-based platform that enables single-molecule counting of low-abundance proteins by mechanically slowing-down their diffusion within the cytoplasm of live Escherichia coli (E. coli) cells. Our technique also allows for automated microscopy at high throughput with minimal perturbation to native physiology, as well as viable enrichment/retrieval. We illustrate the method by analysing the control of the master regulator of the E. coli stress response, RpoS, by its adapter protein, SprE (RssB). Quantification of SprE numbers shows that though SprE is necessary for RpoS degradation, it is expressed at levels as low as 3–4 molecules per average cell cycle, and fluctuations in SprE are approximately Poisson distributed during exponential phase with no sign of bursting.

Several proteins are expressed at too low abundance in the Escherichia coli (E. coli) proteome to be detected by standard methods. Here, the authors create a microfluidics-based platform enabling single-molecule counting of low-abundance proteins by mechanically slowing-down their diffusion in live E. coli.

Noise propagation with interlinked feed-forward pathways

Functionally similar pathways are often seen in biological systems, forming feed-forward controls. The robustness in network motifs such as feed-forward loops (FFLs) has been reported previously. In this work, we studied noise propagation in a development network that has multiple interlinked FFLs. A FFL has the potential of asymmetric noise-filtering (i.e., it works at either the “ON” or the “OFF” state in the target gene). With multiple, interlinked FFLs, we show that the propagated noises are largely filtered regardless of the states in the input genes. The noise-filtering property of an interlinked FFL can be largely derived from that of the individual FFLs, and with interlinked FFLs, it is possible to filter noises in both “ON” and “OFF” states in the output. We demonstrated the noise filtering effect in the developmental regulatory network of Caenorhabditis elegans that controls the timing of distal tip cell (DTC) migration. The roles of positive feedback loops involving blmp-1 and the degradation regulation of DRE-1 also studied. Our analyses allow for better inference from network structures to noise-filtering properties, and provide insights into the mechanisms behind the precise DTC migration controls in space and time.

Measurement of gene regulation in individual cells reveals rapid switching between promoter states

In vivo mapping of transcription-factor binding to the transcriptional output of the regulated gene is hindered by probabilistic promoter occupancy, the presence of multiple gene copies, and cell-to-cell variability. We demonstrate how to overcome these obstacles in the lysogeny maintenance promoter of bacteriophage lambda, P(RM). We simultaneously measured the concentration of the lambda repressor CI and the number of messenger RNAs (mRNAs) from P(RM) in individual Escherichia coli cells, and used a theoretical model to identify the stochastic activity corresponding to different CI binding configurations. We found that switching between promoter configurations is faster than mRNA lifetime and that individual gene copies within the same cell act independently. The simultaneous quantification of transcription factor and promoter activity, followed by stochastic theoretical analysis, provides a tool that can be applied to other genetic circuits.

A biophysical model of supercoiling dependent transcription predicts a structural aspect to gene regulation

Background

Transcription in Escherichia coli generates positive supercoiling in the DNA, which is relieved by the enzymatic activity of gyrase. Recently published experimental evidence suggests that transcription initiation and elongation are inhibited by the buildup of positive supercoiling. It has therefore been proposed that intermittent binding of gyrase plays a role in transcriptional bursting. Considering that transcription is one of the most fundamental cellular processes, it is desirable to be able to account for the buildup and release of positive supercoiling in models of transcription.

Results

Here we present a detailed biophysical model of gene expression that incorporates the effects of supercoiling due to transcription. By directly linking the amount of positive supercoiling to the rate of transcription, the model predicts that highly transcribed genes’ mRNA distributions should substantially deviate from Poisson distributions, with enhanced density at low mRNA copy numbers. Additionally, the model predicts a high degree of correlation between expression levels of genes inside the same supercoiling domain.

Conclusions

Our model, incorporating the supercoiling state of the gene, makes specific predictions that differ from previous models of gene expression. Genes in the same supercoiling domain influence the expression level of neighboring genes. Such structurally dependent regulation predicts correlations between genes in the same supercoiling domain. The topology of the chromosome therefore creates a higher level of gene regulation, which has broad implications for understanding the evolution and organization of bacterial genomes.

Electronic supplementary material

The online version of this article (doi:10.1186/s13628-016-0027-0) contains supplementary material, which is available to authorized users.

Macromolecular crowding creates heterogeneous environments of gene expression in picolitre droplets

Understanding the dynamics of complex enzymatic reactions in highly crowded small volumes is crucial for the development of synthetic minimal cells. Compartmentalized biochemical reactions in cell-sized containers exhibit a degree of randomness due to the small number of molecules involved. However, it is unknown how the physical environment contributes to the stochastic nature of multistep enzymatic processes. Here, we present a robust method to quantify gene expression noise in vitro using droplet microfluidics. We study the changes in stochasticity in the cell-free gene expression of two genes compartmentalized within droplets as a function of DNA copy number and macromolecular crowding. We find that decreased diffusion caused by a crowded environment leads to the spontaneous formation of heterogeneous microenvironments of mRNA as local production rates exceed the diffusion rates of macromolecules. This heterogeneity leads to a higher probability of the molecular machinery staying in the same microenvironment, directly increasing the system's stochasticity.

Sources of Variability in a Synthetic Gene Oscillator

Synthetic gene oscillators are small, engineered genetic circuits that produce periodic variations in target protein expression. Like other gene circuits, synthetic gene oscillators are noisy and exhibit fluctuations in amplitude and period. Understanding the origins of such variability is key to building predictive models that can guide the rational design of synthetic circuits. Here, we developed a method for determining the impact of different sources of noise in genetic oscillators by measuring the variability in oscillation amplitude and correlations between sister cells. We first used a combination of microfluidic devices and time-lapse fluorescence microscopy to track oscillations in cell lineages across many generations. We found that oscillation amplitude exhibited high cell-to-cell variability, while sister cells remained strongly correlated for many minutes after cell division. To understand how such variability arises, we constructed a computational model that identified the impact of various noise sources across the lineage of an initial cell. When each source of noise was appropriately tuned the model reproduced the experimentally observed amplitude variability and correlations, and accurately predicted outcomes under novel experimental conditions. Our combination of computational modeling and time-lapse data analysis provides a general way to examine the sources of variability in dynamic gene circuits.

Dynamics of simple gene-network motifs subject to extrinsic fluctuations

Cellular processes do not follow deterministic rules; even in identical environments genetically identical cells can make random choices leading to different phenotypes. This randomness originates from fluctuations present in the biomolecular interaction networks. Most previous work has been focused on the intrinsic noise (IN) of these networks. Yet, especially for high-copy-number biomolecules, extrinsic or environmental noise (EN) has been experimentally shown to dominate the variation. Here, we develop an analytical formalism that allows for calculation of the effect of EN on gene-expression motifs. We introduce a method for modeling bounded EN as an auxiliary species in the master equation. The method is fully generic and is not limited to systems with small EN magnitudes. We focus our study on motifs that can be viewed as the building blocks of genetic switches: a nonregulated gene, a self-inhibiting gene, and a self-promoting gene. The role of the EN properties (magnitude, correlation time, and distribution) on the statistics of interest are systematically investigated, and the effect of fluctuations in different reaction rates is compared. Due to its analytical nature, our formalism can be used to quantify the effect of EN on the dynamics of biochemical networks and can also be used to improve the interpretation of data from single-cell gene-expression experiments.

Biological Sources of Intrinsic and Extrinsic Noise in cI Expression of Lysogenic Phage Lambda

Genetically identical cells exposed to homogeneous environment can show remarkable phenotypic difference. To predict how phenotype is shaped, understanding of how each factor contributes is required. During gene expression processes, noise could arise either intrinsically in biochemical processes of gene expression or extrinsically from other cellular processes such as cell growth. In this work, important noise sources in gene expression of phage λ lysogen are quantified using models described by stochastic differential equations (SDEs). Results show that DNA looping has sophisticated impacts on gene expression noise: When DNA looping provides autorepression, like in wild type, it reduces noise in the system; When the autorepression is defected as it is in certain mutants, DNA looping increases expression noise. We also study how each gene operator affects the expression noise by changing the binding affinity between the gene and the transcription factor systematically. We find that the system shows extraordinarily large noise when the binding affinity is in certain range, which changes the system from monostable to bistable. In addition, we find that cell growth causes non-negligible noise, which increases with gene expression level. Quantification of noise and identification of new noise sources will provide deeper understanding on how stochasticity impacts phenotype.

Active Degradation Explains the Distribution of Nuclear Proteins during Cellular Senescence

The amount of cellular proteins is a crucial parameter that is known to vary between cells as a function of the replicative passages, and can be important during physiological aging. The process of protein degradation is known to be performed by a series of enzymatic reactions, ranging from an initial step of protein ubiquitination to their final fragmentation by the proteasome. In this paper we propose a stochastic dynamical model of nuclear proteins concentration resulting from a balance between a constant production of proteins and their degradation by a cooperative enzymatic reaction. The predictions of this model are compared with experimental data obtained by fluorescence measurements of the amount of nuclear proteins in murine tail fibroblast (MTF) undergoing cellular senescence. Our model provides a three-parameter stationary distribution that is in good agreement with the experimental data even during the transition to the senescent state, where the nuclear protein concentration changes abruptly. The estimation of three parameters (cooperativity, saturation threshold, and maximal velocity of the reaction), and their evolution during replicative passages shows that only the maximal velocity varies significantly. Based on our modeling we speculate the reduction of functionality of the protein degradation mechanism as a possible competitive inhibition of the proteasome.

Single molecule microscopy in 3D cell cultures and tissues

From the onset of the first microscopic visualization of single fluorescent molecules in living cells at the beginning of this century, to the present, almost routine application of single molecule microscopy, the method has well-proven its ability to contribute unmatched detailed insight into the heterogeneous and dynamic molecular world life is composed of. Except for investigations on bacteria and yeast, almost the entire story of success is based on studies on adherent mammalian 2D cell cultures. However, despite this continuous progress, the technique was not able to keep pace with the move of the cell biology community to adapt 3D cell culture models for basic research, regenerative medicine, or drug development and screening. In this review, we will summarize the progress, which only recently allowed for the application of single molecule microscopy to 3D cell systems and give an overview of the technical advances that led to it. While initially posing a challenge, we finally conclude that relevant 3D cell models will become an integral part of the on-going success of single molecule microscopy.

Noise decomposition of intracellular biochemical signaling networks using nonequivalent reporters

Experimental measurements of biochemical noise have primarily focused on sources of noise at the gene expression level due to limitations of existing noise decomposition techniques. Here, we introduce a mathematical framework that extends classical extrinsic-intrinsic noise analysis and enables mapping of noise within upstream signaling networks free of such restrictions. The framework applies to systems for which the responses of interest are linearly correlated on average, although the framework can be easily generalized to the nonlinear case. Interestingly, despite the high degree of complexity and nonlinearity of most mammalian signaling networks, three distinct tumor necrosis factor (TNF) signaling network branches displayed linearly correlated responses, in both wild-type and perturbed versions of the network, across multiple orders of magnitude of ligand concentration. Using the noise mapping analysis, we find that the c-Jun N-terminal kinase (JNK) pathway generates higher noise than the NF-κB pathway, whereas the activation of c-Jun adds a greater amount of noise than the activation of ATF-2. In addition, we find that the A20 protein can suppress noise in the activation of ATF-2 by separately inhibiting the TNF receptor complex and JNK pathway through a negative feedback mechanism. These results, easily scalable to larger and more complex networks, pave the way toward assessing how noise propagates through cellular signaling pathways and create a foundation on which we can further investigate the relationship between signaling system architecture and biological noise.

Contribution of RNA polymerase concentration variation to protein expression noise

Cell-to-cell variation in gene expression, or noise, is a general phenomenon observed within cell populations. Transcription is known to be the key stage of gene expression where noise is generated, however, how variation in RNA polymerase (RNAP) concentration contributes to gene expression noise is unclear. Here, we quantitatively investigate how variations in absolute amounts of RNAP molecules affect noise in the expression of two fluorescent protein reporters driven by identical promoters. We find that intrinsic noise is independent of variation in RNAP concentrations, whereas extrinsic noise, which is variation in gene expression due to varying cellular environments, scales linearly with variation in RNAP abundance. Specifically, the propagation of RNAP abundance variation to expressed protein noise is inversely proportional to the concentration of RNAP, which suggests that the change in noise that results from RNAP fluctuations is determined by the fraction of promoters that is not occupied by RNAP.

MCA: Multiresolution Correlation Analysis, a graphical tool for subpopulation identification in single-cell gene expression data

Background

Biological data often originate from samples containing mixtures of subpopulations, corresponding e.g. to distinct cellular phenotypes. However, identification of distinct subpopulations may be difficult if biological measurements yield distributions that are not easily separable.

Results

We present Multiresolution Correlation Analysis (MCA), a method for visually identifying subpopulations based on the local pairwise correlation between covariates, without needing to define an a priori interaction scale. We demonstrate that MCA facilitates the identification of differentially regulated subpopulations in simulated data from a small gene regulatory network, followed by application to previously published single-cell qPCR data from mouse embryonic stem cells. We show that MCA recovers previously identified subpopulations, provides additional insight into the underlying correlation structure, reveals potentially spurious compartmentalizations, and provides insight into novel subpopulations.

Conclusions

MCA is a useful method for the identification of subpopulations in low-dimensional expression data, as emerging from qPCR or FACS measurements. With MCA it is possible to investigate the robustness of covariate correlations with respect subpopulations, graphically identify outliers, and identify factors contributing to differential regulation between pairs of covariates. MCA thus provides a framework for investigation of expression correlations for genes of interests and biological hypothesis generation.

The embryo as a laboratory: quantifying transcription in Drosophila

Transcriptional regulation of gene expression is fundamental to most cellular processes, including determination of cellular fates. Quantitative studies of transcription in cultured cells have led to significant advances in identifying mechanisms underlying transcriptional control. Recent progress allowed implementation of these same quantitative methods in multicellular organisms to ask how transcriptional regulation unfolds both in vivo and at the single molecule level in the context of embryonic development. Here we review some of these advances in early Drosophila development, which bring the embryo on par with its single celled counterparts. In particular, we discuss progress in methods to measure mRNA and protein distributions in fixed and living embryos, and we highlight some initial applications that lead to fundamental new insights about molecular transcription processes. We end with an outlook on how to further exploit the unique advantages that come with investigating transcriptional control in the multicellular context of development.

Revisiting bistability in the lysis/lysogeny circuit of bacteriophage lambda

The lysis/lysogeny switch of bacteriophage lambda serves as a paradigm for binary cell fate decision, long-term maintenance of cellular state and stimulus-triggered switching between states. In the literature, the system is often referred to as “bistable.” However, it remains unclear whether this term provides an accurate description or is instead a misnomer. Here we address this question directly. We first quantify transcriptional regulation governing lysogenic maintenance using a single-cell fluorescence reporter. We then use the single-cell data to derive a stochastic theoretical model for the underlying regulatory network. We use the model to predict the steady states of the system and then validate these predictions experimentally. Specifically, a regime of bistability, and the resulting hysteretic behavior, are observed. Beyond the steady states, the theoretical model successfully predicts the kinetics of switching from lysogeny to lysis. Our results show how the physics-inspired concept of bistability can be reliably used to describe cellular phenotype, and how an experimentally-calibrated theoretical model can have accurate predictive power for cell-state switching.

Stochastic holin expression can account for lysis time variation in the bacteriophage λ

The inherent stochastic nature of biochemical processes can drive differences in gene expression between otherwise identical cells. While cell-to-cell variability in gene expression has received much attention, randomness in timing of events has been less studied. We investigate event timing at the single-cell level in a simple system, the lytic pathway of the bacterial virus phage λ. In individual cells, lysis occurs on average at 65 min, with an s.d. of 3.5 min. Interestingly, mutations in the lysis protein, holin, alter both the lysis time (LT) mean and variance. In our analysis, LT is formulated as the first-passage time (FPT) for cellular holin levels to cross a critical threshold. Exact analytical formulae for the FPT moments are derived for stochastic gene expression models. These formulae reveal how holin transcription and translation efficiencies independently modulate the LT mean and variation. Analytical expressions for the LT moments are used to evaluate previously published single-cell LT data for λ phages with mutations in the holin sequence or its promoter. Our results show that stochastic holin expression is sufficient to account for the intercellular LT differences in both wild-type phages, and phage variants where holin transcription and the threshold for lysis have been experimentally altered. Finally, our analysis reveals regulatory motifs that enhance the robustness of lysis timing to cellular noise.

On the dephasing of genetic oscillators

The digital nature of genes combined with the associated low copy numbers of proteins regulating them is a significant source of stochasticity, which affects the phase of biochemical oscillations. We show that unlike ordinary chemical oscillators, the dichotomic molecular noise of gene state switching in gene oscillators affects the stochastic dephasing in a way that may not always be captured by phenomenological limit cycle-based models. Through simulations of a realistic model of the NFκB/IκB network, we also illustrate the dephasing phenomena that are important for reconciling single-cell and population-based experiments on gene oscillators.

How reliable is the linear noise approximation of gene regulatory networks?

Background

The linear noise approximation (LNA) is commonly used to predict how noise is regulated and exploited at the cellular level. These predictions are exact for reaction networks composed exclusively of first order reactions or for networks involving bimolecular reactions and large numbers of molecules. It is however well known that gene regulation involves bimolecular interactions with molecule numbers as small as a single copy of a particular gene. It is therefore questionable how reliable are the LNA predictions for these systems.

Results

We implement in the software package intrinsic Noise Analyzer (iNA), a system size expansion based method which calculates the mean concentrations and the variances of the fluctuations to an order of accuracy higher than the LNA. We then use iNA to explore the parametric dependence of the Fano factors and of the coefficients of variation of the mRNA and protein fluctuations in models of genetic networks involving nonlinear protein degradation, post-transcriptional, post-translational and negative feedback regulation. We find that the LNA can significantly underestimate the amplitude and period of noise-induced oscillations in genetic oscillators. We also identify cases where the LNA predicts that noise levels can be optimized by tuning a bimolecular rate constant whereas our method shows that no such regulation is possible. All our results are confirmed by stochastic simulations.

Conclusion

The software iNA allows the investigation of parameter regimes where the LNA fares well and where it does not. We have shown that the parametric dependence of the coefficients of variation and Fano factors for common gene regulatory networks is better described by including terms of higher order than LNA in the system size expansion. This analysis is considerably faster than stochastic simulations due to the extensive ensemble averaging needed to obtain statistically meaningful results. Hence iNA is well suited for performing computationally efficient and quantitative studies of intrinsic noise in gene regulatory networks.

Transcription-factor-mediated DNA looping probed by high-resolution, single-molecule imaging in live E. coli cells

DNA looping mediated by transcription factors plays critical roles in prokaryotic gene regulation. The "genetic switch" of bacteriophage λ determines whether a prophage stays incorporated in the E. coli chromosome or enters the lytic cycle of phage propagation and cell lysis. Past studies have shown that long-range DNA interactions between the operator sequences O(R) and O(L) (separated by 2.3 kb), mediated by the λ repressor CI (accession number P03034), play key roles in regulating the λ switch. In vitro, it was demonstrated that DNA segments harboring the operator sequences formed loops in the presence of CI, but CI-mediated DNA looping has not been directly visualized in vivo, hindering a deep understanding of the corresponding dynamics in realistic cellular environments. We report a high-resolution, single-molecule imaging method to probe CI-mediated DNA looping in live E. coli cells. We labeled two DNA loci with differently colored fluorescent fusion proteins and tracked their separations in real time with ∼40 nm accuracy, enabling the first direct analysis of transcription-factor-mediated DNA looping in live cells. Combining looping measurements with measurements of CI expression levels in different operator mutants, we show quantitatively that DNA looping activates transcription and enhances repression. Further, we estimated the upper bound of the rate of conformational change from the unlooped to the looped state, and discuss how chromosome compaction may impact looping kinetics. Our results provide insights into transcription-factor-mediated DNA looping in a variety of operator and CI mutant backgrounds in vivo, and our methodology can be applied to a broad range of questions regarding chromosome conformations in prokaryotes and higher organisms.

Single-molecule imaging of gene regulation in vivo using cotranslational activation by Cleavage (CoTrAC)

We describe a fluorescence microscopy method, Co-Translational Activation by Cleavage (CoTrAC) to image the production of protein molecules in live cells with single-molecule precision without perturbing the protein's functionality. This method makes it possible to count the numbers of protein molecules produced in one cell during sequential, five-minute time windows. It requires a fluorescence microscope with laser excitation power density of ~0.5 to 1 kW/cm(2), which is sufficiently sensitive to detect single fluorescent protein molecules in live cells. The fluorescent reporter used in this method consists of three parts: a membrane targeting sequence, a fast-maturing, yellow fluorescent protein and a protease recognition sequence. The reporter is translationally fused to the N-terminus of a protein of interest. Cells are grown on a temperature-controlled microscope stage. Every five minutes, fluorescent molecules within cells are imaged (and later counted by analyzing fluorescence images) and subsequently photobleached so that only newly translated proteins are counted in the next measurement. Fluorescence images resulting from this method can be analyzed by detecting fluorescent spots in each image, assigning them to individual cells and then assigning cells to cell lineages. The number of proteins produced within a time window in a given cell is calculated by dividing the integrated fluorescence intensity of spots by the average intensity of single fluorescent molecules. We used this method to measure expression levels in the range of 0-45 molecules in single 5 min time windows. This method enabled us to measure noise in the expression of the λ repressor CI, and has many other potential applications in systems biology.

Single-molecule methods for studying gene regulation in vivo

The recent emergence of new experimental tools employing sensitive fluorescence detection in vivo has made it possible to visualize various aspects of gene regulation at the single-molecule level in the native, intracellular context. In this review, we will first describe general considerations for in vivo, single-molecule fluorescence detection of DNA, mRNA, and protein molecules involved in gene regulation. We will then give an overview of the rapidly evolving suite of molecular tools available for observing gene regulation in vivo and discuss new insights they have brought into gene regulation.

Dynamic mechanism for the transcription apparatus orchestrating reliable responses to activators

The transcription apparatus (TA) is a huge molecular machine. It detects the time-varying concentrations of transcriptional activators and initiates mRNA transcripts at appropriate rates. Based on the general structural organizations of the TA, we propose how the TA dynamically orchestrates transcriptional responses. The activators rapidly cycle in and out of a clamp-like space temporarily formed between the enhancer and the Mediator, with the concentration of activators encoded as their temporal occupancy rate (R_TOR) within the space. The entry of activators into this space induces allostery in the Mediator, resulting in a facilitated circumstance for transcriptional reinitiation. The reinitiation rate is much larger than the cycling rate of activators, thereby R_TOR guiding the amount of transcripts. Based on this mechanism, stochastic simulations can qualitatively reproduce and interpret multiple features of gene expression, e.g., transcriptional bursting is not mere noise as traditionally believed, but rather the basis of reliable transcriptional responses.