Regulatory activity revealed by dynamic correlations in gene expression noise

Feed-forward loops and diamond motifs lead to tunable transmission of information in the frequency domain

Using a Gaussian model, we study the transmission of time-varying biochemical signals through feed-forward motifs and diamond motifs. To this end, we compute the frequency dependence of the gain, the noise, as well as their ratio, the gain-to-noise ratio, which measures how reliably a network transmits signals at different frequencies. We find that both coherent and incoherent feed-forward motifs can either act as low-pass or high-pass filters for information: The frequency dependence of the gain-to-noise ratio increases or decreases with increasing frequency, respectively. Our analysis of diamond motifs reveals that cooperative activation of the output component can increase the gain-to-noise ratio. This means that from the perspective of information transmission, it can be beneficial to split the input signal in two and recombine the two propagated signals at the output. Cooperative activation can be implemented via the formation of homo- or heteromultimers that then bind and activate the output component or via the binding of individual molecules of the intermediate species to the output component.

Complex dynamics of transcription regulation

Transcription is a tightly regulated cellular function which can be triggered by endogenous (intrinsic) or exogenous (extrinsic) signals. The development of novel techniques to examine the dynamic behavior of transcription factors and the analysis of transcriptional activity at the single cell level with increased temporal resolution has revealed unexpected elements of stochasticity and dynamics of this process. Emerging research reveals a complex picture, wherein a wide range of time scales and temporal transcription patterns overlap to generate transcriptional programs. The challenge now is to develop a perspective that can guide us to common underlying mechanisms, and consolidate these findings. Here we review the recent literature on temporal dynamics and stochastic gene regulation patterns governed by intrinsic or extrinsic signals, utilizing the glucocorticoid receptor (GR)-mediated transcriptional model to illustrate commonality of these emerging concepts. This article is part of a Special Issue entitled: Chromatin in time and space.

Geometry-induced bursting dynamics in gene expression

In prokaryotes and eukaryotes, genes are transcribed stochastically according to various temporal patterns that range from simple first-order kinetics to marked bursts, resulting in temporal and cell-to-cell variations of mRNA and protein levels. Here, we consider the effect of the transport of regulatory molecules on the noise in gene expression by taking into account explicitly the dynamics of a finite number of transcription factors confined in the cell. We calculate analytically time-dependent correlation functions of mRNA levels for a wide range of transport mechanisms and find that in the limit of small-transcription-factor copy number, the results differ significantly from standard approaches, which ignore confinement. It is shown how such dynamical quantities, which can now be obtained experimentally, can be used to identify the underlying mechanisms of transcription. Of particular importance, it is demonstrated that the geometry of transcription-factor trajectories in the cellular environment plays a key role in transcription kinetics, and can intrinsically generate the observed various transcription patterns ranging from simple first-order kinetics to bursts.

Cellular noise regulons underlie fluctuations in Saccharomyces cerevisiae

Stochasticity is a hallmark of cellular processes, and different classes of genes show large differences in their cell-to-cell variability (noise). To decipher the sources and consequences of this noise, we systematically measured pairwise correlations between large numbers of genes, including those with high variability. We find that there is substantial pathway variability shared across similarly regulated genes. This induces quantitative correlations in the expression of functionally related genes such as those involved in the Msn2/4 stress response pathway, amino-acid biosynthesis, and mitochondrial maintenance. Bioinformatic analyses and genetic perturbations suggest that fluctuations in PKA and Tor signaling contribute to pathway-specific variability. Our results argue that a limited number of well-delineated "noise regulons" operate across a yeast cell and that such coordinated fluctuations enable a stochastic but coherent induction of functionally related genes. Finally, we show that pathway noise is a quantitative tool for exploring pathway features and regulatory relationships in un-stimulated systems.

Regulatory Snapshots: integrative mining of regulatory modules from expression time series and regulatory networks

Explaining regulatory mechanisms is crucial to understand complex cellular responses leading to system perturbations. Some strategies reverse engineer regulatory interactions from experimental data, while others identify functional regulatory units (modules) under the assumption that biological systems yield a modular organization. Most modular studies focus on network structure and static properties, ignoring that gene regulation is largely driven by stimulus-response behavior. Expression time series are key to gain insight into dynamics, but have been insufficiently explored by current methods, which often (1) apply generic algorithms unsuited for expression analysis over time, due to inability to maintain the chronology of events or incorporate time dependency; (2) ignore local patterns, abundant in most interesting cases of transcriptional activity; (3) neglect physical binding or lack automatic association of regulators, focusing mainly on expression patterns; or (4) limit the discovery to a predefined number of modules. We propose Regulatory Snapshots, an integrative mining approach to identify regulatory modules over time by combining transcriptional control with response, while overcoming the above challenges. Temporal biclustering is first used to reveal transcriptional modules composed of genes showing coherent expression profiles over time. Personalized ranking is then applied to prioritize prominent regulators targeting the modules at each time point using a network of documented regulatory associations and the expression data. Custom graphics are finally depicted to expose the regulatory activity in a module at consecutive time points (snapshots). Regulatory Snapshots successfully unraveled modules underlying yeast response to heat shock and human epithelial-to-mesenchymal transition, based on regulations documented in the YEASTRACT and JASPAR databases, respectively, and available expression data. Regulatory players involved in functionally enriched processes related to these biological events were identified. Ranking scores further suggested ability to discern the primary role of a gene (target or regulator). Prototype is available at: http://kdbio.inesc-id.pt/software/regulatorysnapshots.

Using gene expression noise to understand gene regulation

Phenotypic variation is ubiquitous in biology and is often traceable to underlying genetic and environmental variation. However, even genetically identical cells in identical environments display variable phenotypes. Stochastic gene expression, or gene expression "noise," has been suggested as a major source of this variability, and its physiological consequences have been topics of intense research for the last decade. Several recent studies have measured variability in protein and messenger RNA levels, and they have discovered strong connections between noise and gene regulation mechanisms. When integrated with discrete stochastic models, measurements of cell-to-cell variability provide a sensitive "fingerprint" with which to explore fundamental questions of gene regulation. In this review, we highlight several studies that used gene expression variability to develop a quantitative understanding of the mechanisms and dynamics of gene regulation.

Adjusting phenotypes by noise control

Genetically identical cells can show phenotypic variability. This is often caused by stochastic events that originate from randomness in biochemical processes involving in gene expression and other extrinsic cellular processes. From an engineering perspective, there have been efforts focused on theory and experiments to control noise levels by perturbing and replacing gene network components. However, systematic methods for noise control are lacking mainly due to the intractable mathematical structure of noise propagation through reaction networks. Here, we provide a numerical analysis method by quantifying the parametric sensitivity of noise characteristics at the level of the linear noise approximation. Our analysis is readily applicable to various types of noise control and to different types of system; for example, we can orthogonally control the mean and noise levels and can control system dynamics such as noisy oscillations. As an illustration we applied our method to HIV and yeast gene expression systems and metabolic networks. The oscillatory signal control was applied to p53 oscillations from DNA damage. Furthermore, we showed that the efficiency of orthogonal control can be enhanced by applying extrinsic noise and feedback. Our noise control analysis can be applied to any stochastic model belonging to continuous time Markovian systems such as biological and chemical reaction systems, and even computer and social networks. We anticipate the proposed analysis to be a useful tool for designing and controlling synthetic gene networks.

Stochastic gene expression at the single cell level can lead to significant phenotypic variation at the population level. To obtain a desired phenotype, the noise levels of intracellular protein concentrations may need to be tuned and controlled. Noise levels often decrease in relative amount as the mean values increase. This implies that the noise levels can be passively controlled by changing the mean values. In an engineering perspective, the noise levels can be further controlled while the mean values can be simultaneously adjusted to desired values. Here, systematic schemes for such simultaneous control are described by identifying where and by how much the system needs to be perturbed. The schemes can be applied to the design process of a potential therapeutic HIV-drug that targets a certain set of reactions that are identified by the proposed analysis, to prevent stochastic transition to the lytic state. In some cases, the simultaneous control cannot be performed efficiently, when the noise levels strongly change with the mean values. This problem is shown to be resolved by applying extra noise and feedback.

Dynamics of protein noise can distinguish between alternate sources of gene-expression variability

Within individual cells, two molecular processes have been implicated as sources of noise in gene expression: (i) Poisson fluctuations in mRNA abundance arising from random birth and death of individual mRNA transcripts or (ii) promoter fluctuations arising from stochastic promoter transitions between different transcriptional states. Steady-state measurements of variance in protein levels are insufficient to discriminate between these two mechanisms, and mRNA single-molecule fluorescence in situ hybridization (smFISH) is challenging when cellular mRNA concentrations are high. Here, we present a perturbation method that discriminates mRNA birth/death fluctuations from promoter fluctuations by measuring transient changes in protein variance and that can operate in the regime of high molecular numbers. Conceptually, the method exploits the fact that transcriptional blockage results in more rapid increases in protein variability when mRNA birth/death fluctuations dominate over promoter fluctuations. We experimentally demonstrate the utility of this perturbation approach in the HIV-1 model system. Our results support promoter fluctuations as the primary noise source in HIV-1 expression. This study illustrates a relatively simple method that complements mRNA smFISH hybridization and can be used with existing GFP-tagged libraries to include or exclude alternate sources of noise in gene expression.

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 laboratory's 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.

Protein-level fluctuation correlation at the microcolony level and its application to the Vibrio harveyi quorum-sensing circuit

Gene expression is stochastic, and noise that arises from the stochastic nature of biochemical reactions propagates through active regulatory links. Thus, correlations in gene-expression noise can provide information about regulatory links. We present what to our knowledge is a new approach to measure and interpret such correlated fluctuations at the level of single microcolonies, which derive from single cells. We demonstrated this approach mathematically using stochastic modeling, and applied it to experimental time-lapse fluorescence microscopy data. Specifically, we investigated the relationships among LuxO, LuxR, and the small regulatory RNA qrr4 in the model quorum-sensing bacterium Vibrio harveyi. Our results show that LuxR positively regulates the qrr4 promoter. Under our conditions, we find that qrr regulation weakly depends on total LuxO levels and that LuxO autorepression is saturated. We also find evidence that the fluctuations in LuxO levels are dominated by intrinsic noise. We furthermore propose LuxO and LuxR interact at all autoinducer levels via an unknown mechanism. Of importance, our new method of evaluating correlations at the microcolony level is unaffected by partition noise at cell division. Moreover, the method is first-order accurate and requires less effort for data analysis than single-cell-based approaches. This new correlation approach can be applied to other systems to aid analysis of gene regulatory circuits.

Computation of steady-state probability distributions in stochastic models of cellular networks

Cellular processes are "noisy". In each cell, concentrations of molecules are subject to random fluctuations due to the small numbers of these molecules and to environmental perturbations. While noise varies with time, it is often measured at steady state, for example by flow cytometry. When interrogating aspects of a cellular network by such steady-state measurements of network components, a key need is to develop efficient methods to simulate and compute these distributions. We describe innovations in stochastic modeling coupled with approaches to this computational challenge: first, an approach to modeling intrinsic noise via solution of the chemical master equation, and second, a convolution technique to account for contributions of extrinsic noise. We show how these techniques can be combined in a streamlined procedure for evaluation of different sources of variability in a biochemical network. Evaluation and illustrations are given in analysis of two well-characterized synthetic gene circuits, as well as a signaling network underlying the mammalian cell cycle entry.

Dynamical consequences of bandpass feedback loops in a bacterial phosphorelay

Under conditions of nutrient limitation, Bacillus subtilis cells terminally differentiate into a dormant spore state. Progression to sporulation is controlled by a genetic circuit consisting of a phosphorelay embedded in multiple transcriptional feedback loops, which is used to activate the master regulator Spo0A by phosphorylation. These transcriptional regulatory interactions are "bandpass"-like, in the sense that activation occurs within a limited band of Spo0A∼P concentrations. Additionally, recent results show that the phosphorelay activation occurs in pulses, in a cell-cycle dependent fashion. However, the impact of these pulsed bandpass interactions on the circuit dynamics preceding sporulation remains unclear. In order to address this question, we measured key features of the bandpass interactions at the single-cell level and analyzed them in the context of a simple mathematical model. The model predicted the emergence of a delayed phase shift between the pulsing activity of the different sporulation genes, as well as the existence of a stable state, with elevated Spo0A activity but no sporulation, embedded within the dynamical structure of the system. To test the model, we used time-lapse fluorescence microscopy to measure dynamics of single cells initiating sporulation. We observed the delayed phase shift emerging during the progression to sporulation, while a re-engineering of the sporulation circuit revealed behavior resembling the predicted additional state. These results show that periodically-driven bandpass feedback loops can give rise to complex dynamics in the progression towards sporulation.

Frequency domain analysis reveals external periodic fluctuations can generate sustained p53 oscillation

p53 is a well-known tumor suppressor protein that regulates many pathways, such as ones involved in cell cycle and apoptosis. The p53 levels are known to oscillate without damping after DNA damage, which has been a focus of many recent studies. A negative feedback loop involving p53 and MDM2 has been reported to be responsible for this oscillatory behavior, but questions remain as how the dynamics of this loop alter in order to initiate and maintain the sustained or undamped p53 oscillation. Our frequency domain analysis suggests that the sustained p53 oscillation is not completely dictated by the negative feedback loop; instead, it is likely to be also modulated by periodic DNA repair-related fluctuations that are triggered by DNA damage. According to our analysis, the p53-MDM2 feedback mechanism exhibits adaptability in different cellular contexts. It normally filters noise and fluctuations exerted on p53, but upon DNA damage, it stops performing the filtering function so that DNA repair-related oscillatory signals can modulate the p53 oscillation. Furthermore, it is shown that the p53-MDM2 feedback loop increases its damping ratio allowing p53 to oscillate at a frequency more synchronized with the other cellular efforts to repair the damaged DNA, while suppressing its inherent oscillation-generating capability. Our analysis suggests that the overexpression of MDM2, observed in many types of cancer, can disrupt the operation of this adaptive mechanism by making it less responsive to the modulating signals after DNA damage occurs.

Measuring retroactivity from noise in gene regulatory networks

Synthetic gene regulatory networks show significant stochastic fluctuations in expression levels due to the low copy number of transcription factors. When a synthetic gene network is allowed to regulate a downstream network, the response time of the regulating transcription factors increases. This effect has been termed "retroactivity". In this article, we describe a method for estimating the retroactivity of a given system by measuring the stochastic noise in the transcription factor expression. We show that the noise in the output signal of the network can be affected significantly when the output is connected to a downstream module. More specifically, the output signal noise can show significantly longer correlations. We define retroactivity by the change in the correlation time. This measure of retroactivity corresponds well to the deterministic retroactivity described in another study. We provide an estimation method for measuring retroactivity from the gene expression noise by investigating its autocorrelation function. When retroactivity is defined using the decay (correlation) times from the gene expression autocorrelation functions, it is found not to depend on whether the module output is defined as either the free transcription factor or the total of the bound and free transcription factor. The frequency domain response, however, depends strongly on which output variable is considered. The proposed estimation method for measuring retroactivity, based on the gene expression noise, can serve as a practical method for characterizing interface conditions between two synthetic modules and eventually provide a step toward large-scale circuit design for synthetic biology.

Effect of promoter architecture on the cell-to-cell variability in gene expression

According to recent experimental evidence, promoter architecture, defined by the number, strength and regulatory role of the operators that control transcription, plays a major role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effort that addresses the question of how changes in promoter architecture affect variability in gene expression in a systematic rather than case-by-case fashion. In this article we make such a systematic investigation, based on a microscopic model of gene regulation that incorporates stochastic effects. In particular, we show how operator strength and operator multiplicity affect this variability. We examine different modes of transcription factor binding to complex promoters (cooperative, independent, simultaneous) and how each of these affects the level of variability in transcriptional output from cell-to-cell. We propose that direct comparison between in vivo single-cell experiments and theoretical predictions for the moments of the probability distribution of mRNA number per cell can be used to test kinetic models of gene regulation. The emphasis of the discussion is on prokaryotic gene regulation, but our analysis can be extended to eukaryotic cells as well.

Origins of regulated cell-to-cell variability

Single-cell measurements and lineage-tracing experiments are revealing that phenotypic cell-to-cell variability is often the result of deterministic processes, despite the existence of intrinsic noise in molecular networks. In most cases, this determinism represents largely uncharacterized molecular regulatory mechanisms, which places the study of cell-to-cell variability in the realm of molecular cell biology. Further research in the field will be important to advance quantitative cell biology because it will provide new insights into the mechanisms by which cells coordinate their intracellular activities in the spatiotemporal context of the multicellular environment.

Defining cooperativity in gene regulation locally through intrinsic noise

Regulatory networks in cells may comprise a variety of types of molecular interactions. The most basic are pairwise interactions, in which one species controls the behaviour of another (e.g. a transcription factor activates or represses a gene). Higher-order interactions, while more subtle, may be important for determining the function of networks. Here, the authors systematically expand a simple master equation model for a gene to derive an approach for robustly assessing the cooperativity (effective copy number) with which a transcription factor acts. The essential idea is that moments of a joint distribution of protein copy numbers determine the Hill coefficient of a cis-regulatory input function without non-linear fitting. The authors show that this method prescribes a definition of cooperativity that is meaningful even in highly complex situations in which the regulation does not conform to a simple Hill function. To illustrate the utility of the method, the authors measure the cooperativity of the transcription factor CI in simulations of phage- and show how the cooperativity accurately reflects the behaviour of the system. The authors numerically assess the effects of deviations from ideality, as well as possible sources of error. The relationship to other definitions of cooperativity and issues for experimentally realising the procedure are discussed.

Using noisy gene expression mediated by engineered adenovirus to probe signaling dynamics in mammalian cells

Perturbations from environmental, genetic, and pharmacological sources can generate heterogeneous biological responses, even in genetically identical cells. Although these differences have important consequences on cell physiology and survival, they are often subsumed in measurements that average over the population. Here, we describe in detail how variability in adenoviral-mediated gene expression provides an effective means to map dose responses of signaling pathways. Cell-cell variability is inherent in gene delivery methods used in cell biology, which makes this approach adaptable to many existing experimental systems. We also discuss strategies to quantify biologically relevant inputs and outputs.

Fan-out in gene regulatory networks

Background

In synthetic biology, gene regulatory circuits are often constructed by combining smaller circuit components. Connections between components are achieved by transcription factors acting on promoters. If the individual components behave as true modules and certain module interface conditions are satisfied, the function of the composite circuits can in principle be predicted.

Results

In this paper, we investigate one of the interface conditions: fan-out. We quantify the fan-out, a concept widely used in electrical engineering, to indicate the maximum number of the downstream inputs that an upstream output transcription factor can regulate. The fan-out is shown to be closely related to retroactivity studied by Del Vecchio, et al. An efficient operational method for measuring the fan-out is proposed and shown to be applied to various types of module interfaces. The fan-out is also shown to be enhanced by self-inhibitory regulation on the output. The potential role of an inhibitory regulation is discussed.

Conclusions

The proposed estimation method for fan-out not only provides an experimentally efficient way for quantifying the level of modularity in gene regulatory circuits but also helps characterize and design module interfaces, enabling the modular construction of gene circuits.

Generation of double-labeled reporter cell lines for studying co-dynamics of endogenous proteins in individual human cells

Understanding the dynamic relationship between components of a system or pathway at the individual cell level is a current challenge. To address this, we developed an approach that allows simultaneous tracking of several endogenous proteins of choice within individual living human cells. The approach is based on fluorescent tagging of proteins at their native locus by directed gene targeting. A fluorescent tag-encoding DNA is introduced as a new exon into the intronic region of the gene of interest, resulting in expression of a full-length fluorescently tagged protein. We used this approach to establish human cell lines simultaneously expressing two components of a major antioxidant defense system, thioredoxin 1 (Trx) and thioredoxin reductase 1 (TrxR1), labeled with CFP and YFP, respectively. We find that the distributions of both proteins between nuclear and cytoplasmic compartments were highly variable between cells. However, the two proteins did not vary independently of each other: protein levels of Trx and TrxR1 in both the whole cell and the nucleus were substantially correlated. We further find that in response to a stress-inducing drug (CPT), both Trx and TrxR1 accumulated in the nuclei in a manner that was highly temporally correlated. This accumulation considerably reduced cell-to-cell variability in nuclear content of both proteins, suggesting a uniform response of the thioredoxin system to stress. These results indicate that Trx and TrxR1 act in concert in response to stress in regard to both time course and variability. Thus, our approach provides an efficient tool for studying dynamic relationship between components of systems of interest at a single-cell level.

Correlated fluctuations carry signatures of gene regulatory network dynamics

The dynamics of transcriptional control involve small numbers of molecules and result in significant fluctuations in protein and mRNA concentrations. The correlations between these intrinsic fluctuations then offer, via the fluctuation dissipation relation, the possibility of capturing the system's response to external perturbations, and hence the nature of the regulatory activity itself. We show that for simple regulatory networks of activators and repressors, the correlated fluctuations between molecular species show distinct characteristics for changes in regulatory mechanism and for changes to the topology of causal influence. Here, we do a stochastic analysis and derive time-dependent correlation functions between molecular species of regulatory networks and present analytical and numerical results on peaks and delays in correlations between proteins within networks. Upon using these values of peaks and delays as a two-dimensional feature space, we find that different regulatory mechanisms separate into distinct clusters. This indicates that experimentally observable pairwise correlations can distinguish between gene regulatory networks.

Functional roles for noise in genetic circuits

The genetic circuits that regulate cellular functions are subject to stochastic fluctuations, or 'noise', in the levels of their components. Noise, far from just a nuisance, has begun to be appreciated for its essential role in key cellular activities. Noise functions in both microbial and eukaryotic cells, in multicellular development, and in evolution. It enables coordination of gene expression across large regulons, as well as probabilistic differentiation strategies that function across cell populations. At the longest timescales, noise may facilitate evolutionary transitions. Here we review examples and emerging principles that connect noise, the architecture of the gene circuits in which it is present, and the biological functions it enables. We further indicate some of the important challenges and opportunities going forward.

Linear control theory for gene network modeling

Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain) and linear state-space (time domain) can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.

Trade-offs and noise tolerance in signal detection by genetic circuits

Genetic circuits can implement elaborated tasks of amplitude or frequency signal detection. What type of constraints could circuits experience in the performance of these tasks, and how are they affected by molecular noise? Here, we consider a simple detection process–a signal acting on a two-component module–to analyze these issues. We show that the presence of a feedback interaction in the detection module imposes a trade-off on amplitude and frequency detection, whose intensity depends on feedback strength. A direct interaction between the signal and the output species, in a type of feed-forward loop architecture, greatly modifies these trade-offs. Indeed, we observe that coherent feed-forward loops can act simultaneously as good frequency and amplitude noise-tolerant detectors. Alternatively, incoherent feed-forward loop structures can work as high-pass filters improving high frequency detection, and reaching noise tolerance by means of noise filtering. Analysis of experimental data from several specific coherent and incoherent feed-forward loops shows that these properties can be realized in a natural context. Overall, our results emphasize the limits imposed by circuit structure on its characteristic stimulus response, the functional plasticity of coherent feed-forward loops, and the seemingly paradoxical advantage of improving signal detection with noisy circuit components.

A synthetic three-color scaffold for monitoring genetic regulation and noise

Background

Current methods for analyzing the dynamics of natural regulatory networks, and quantifying synthetic circuit function, are limited by the lack of well-characterized genetic measurement tools. Fluorescent reporters have been used to measure dynamic gene expression, but recent attempts to monitor multiple genes simultaneously in single cells have not focused on independent, isolated measurements. Multiple reporters can be used to observe interactions between natural genes, or to facilitate the 'debugging' of biologically engineered genetic networks. Using three distinguishable reporter genes in a single cell can reveal information not obtainable from only one or two reporters. One application of multiple reporters is the use of genetic noise to reveal regulatory connections between genes. Experiments in both natural and synthetic systems would benefit from a well-characterized platform for expressing multiple reporter genes and synthetic network components.

Results

We describe such a plasmid-based platform for the design and optimization of synthetic gene networks, and for analysis of endogenous gene networks. This network scaffold consists of three distinguishable fluorescent reporter genes controlled by inducible promoters, with conveniently placed restriction sites to make modifications straightforward. We quantitatively characterize the scaffold in Escherichia coli with single-cell fluorescence imaging and time-lapse microscopy. The three spectrally distinct reporters allow independent monitoring of genetic regulation and analysis of genetic noise. As a novel application of this tool we show that the presence of genetic noise can reveal transcriptional co-regulation due to a hidden factor, and can distinguish constitutive from regulated gene expression.

Conclusion

We have constructed a general chassis where three promoters from natural genes or components of synthetic networks can be easily inserted and independently monitored on a single construct using optimized fluorescent protein reporters. We have quantitatively characterized the baseline behavior of the chassis so that it can be used to measure dynamic gene regulation and noise. Overall, the system will be useful both for analyzing natural genetic networks and assembling synthetic ones.

Fourier analysis and systems identification of the p53 feedback loop

A key circuit in the response of cells to damage is the p53-mdm2 feedback loop. This circuit shows sustained, noisy oscillations in individual human cells following DNA breaks. Here, we apply an engineering approach known as systems identification to quantify the in vivo interactions in the circuit on the basis of accurate measurements of its power spectrum. We obtained oscillation time courses of p53 and Mdm2 protein levels from several hundred cells and analyzed their Fourier spectra. We find characteristic spectra with distinct low-frequency components that are well-described by a third-order linear model with white noise. The model identifies the sign and strength of the known interactions, including a negative feedback loop between p53 and its upstream regulator. It also implies that noise can trigger and maintain the oscillations. The model also captures the power spectra of p53 dynamics without DNA damage. Parameters such as noise amplitudes and protein lifetimes are estimated. This approach employs natural biological noise as a diagnostic that stimulates the system at many frequencies at once. It seems to be a useful way to find the in vivo design of circuits and may be applied to other systems by monitoring their power spectrum in individual cells.

Biological role of noise encoded in a genetic network motif

Genetic circuits that regulate distinct cellular processes can differ in their wiring pattern of interactions (architecture) and susceptibility to stochastic fluctuations (noise). Whether the link between circuit architecture and noise is of biological importance remains, however, poorly understood. To investigate this problem, we performed a computational study of gene expression noise for all possible circuit architectures of feed-forward loop (FFL) motifs. Results revealed that FFL architectures fall into two categories depending on whether their ON (stimulated) or OFF (unstimulated) steady states exhibit noise. To explore the biological importance of this difference in noise behavior, we analyzed 858 documented FFLs in Escherichia coli that were divided into 39 functional categories. The majority of FFLs were found to regulate two subsets of functional categories. Interestingly, these two functional categories associated with FFLs of opposite noise behaviors. This opposite noise preference revealed two noise-based strategies to cope with environmental constraints where cellular responses are either initiated or terminated stochastically to allow probabilistic sampling of alternative states. FFLs may thus be selected for their architecture-dependent noise behavior, revealing a biological role for noise that is encoded in gene circuit architectures.

Dissecting variability in responses to cancer chemotherapy through systems pharmacology

Variability in patient responses to even the most potent and targeted therapeutics is now the primary challenge facing drug discovery and patient care, particularly in oncology and immune therapy. Variability with respect to mechanisms of induced resistance is observed both in drug-naive patients and among those who are initially responsive. Genomics has developed powerful tools for systematic interrogation of disease genotype and transcriptional states (particularly in cancer) and for correlation of these measures with parameters of disease such as histological diagnosis and outcome. In contrast, mechanistic preclinical studies remain relatively narrowly focused, leading to many apparent contradictions and poor understanding of the determinants of response. We describe the emergence of a systems pharmacology approach that is mechanistic, quantitative, probabilistic, and postgenomic and promises to do for mechanistic pharmacology what genomics is doing for correlative studies. We focus on studies in cell lines (which currently dominate mechanism-oriented analysis), but our arguments are equally valid for real tumors studied in short-term culture as xenografts and, perhaps some time in the future, in humans.

A model for improving microbial biofuel production using a synthetic feedback loop

Cells use feedback to implement a diverse range of regulatory functions. Building synthetic feedback control systems may yield insight into the roles that feedback can play in regulation since it can be introduced independently of native regulation, and alternative control architectures can be compared. We propose a model for microbial biofuel production where a synthetic control system is used to increase cell viability and biofuel yields. Although microbes can be engineered to produce biofuels, the fuels are often toxic to cell growth, creating a negative feedback loop that limits biofuel production. These toxic effects may be mitigated by expressing efflux pumps that export biofuel from the cell. We developed a model for cell growth and biofuel production and used it to compare several genetic control strategies for their ability to improve biofuel yields. We show that controlling efflux pump expression directly with a biofuel-responsive promoter is a straightforward way of improving biofuel production. In addition, a feed forward loop controller is shown to be versatile at dealing with uncertainty in biofuel production rates.

Statecharts for gene network modeling

State diagrams (stategraphs) are suitable for describing the behavior of dynamic systems. However, when they are used to model large and complex systems, determining the states and transitions among them can be overwhelming, due to their flat, unstratified structure. In this article, we present the use of statecharts as a novel way of modeling complex gene networks. Statecharts extend conventional state diagrams with features such as nested hierarchy, recursion, and concurrency. These features are commonly utilized in engineering for designing complex systems and can enable us to model complex gene networks in an efficient and systematic way. We modeled five key gene network motifs, simple regulation, autoregulation, feed-forward loop, single-input module, and dense overlapping regulon, using statecharts. Specifically, utilizing nested hierarchy and recursion, we were able to model a complex interlocked feed-forward loop network in a highly structured way, demonstrating the potential of our approach for modeling large and complex gene networks.

On the spontaneous stochastic dynamics of a single gene: complexity of the molecular interplay at the promoter

BACKGROUND

Gene promoters can be in various epigenetic states and undergo interactions with many molecules in a highly transient, probabilistic and combinatorial way, resulting in a complex global dynamics as observed experimentally. However, models of stochastic gene expression commonly consider promoter activity as a two-state on/off system. We consider here a model of single-gene stochastic expression that can represent arbitrary prokaryotic or eukaryotic promoters, based on the combinatorial interplay between molecules and epigenetic factors, including energy-dependent remodeling and enzymatic activities.

RESULTS

We show that, considering the mere molecular interplay at the promoter, a single-gene can demonstrate an elaborate spontaneous stochastic activity (eg. multi-periodic multi-relaxation dynamics), similar to what is known to occur at the gene-network level. Characterizing this generic model with indicators of dynamic and steady-state properties (including power spectra and distributions), we reveal the potential activity of any promoter and its influence on gene expression. In particular, we can reproduce, based on biologically relevant mechanisms, the strongly periodic patterns of promoter occupancy by transcription factors (TF) and chromatin remodeling as observed experimentally on eukaryotic promoters. Moreover, we link several of its characteristics to properties of the underlying biochemical system. The model can also be used to identify behaviors of interest (eg. stochasticity induced by high TF concentration) on minimal systems and to test their relevance in larger and more realistic systems. We finally show that TF concentrations can regulate many aspects of the stochastic activity with a considerable flexibility and complexity.

CONCLUSIONS

This tight promoter-mediated control of stochasticity may constitute a powerful asset for the cell. Remarkably, a strongly periodic activity that demonstrates a complex TF concentration-dependent control is obtained when molecular interactions have typical characteristics observed on eukaryotic promoters (high mobility, functional redundancy, many alternate states/pathways). We also show that this regime results in a direct and indirect energetic cost. Finally, this model can constitute a framework for unifying various experimental approaches. Collectively, our results show that a gene - the basic building block of complex regulatory networks - can itself demonstrate a significantly complex behavior.

Machine vision for digital microfluidics

Machine vision is widely used in an industrial environment today. It can perform various tasks, such as inspecting and controlling production processes, that may require humanlike intelligence. The importance of imaging technology for biological research or medical diagnosis is greater than ever. For example, fluorescent reporter imaging enables scientists to study the dynamics of gene networks with high spatial and temporal resolution. Such high-throughput imaging is increasingly demanding the use of machine vision for real-time analysis and control. Digital microfluidics is a relatively new technology with expectations of becoming a true lab-on-a-chip platform. Utilizing digital microfluidics, only small amounts of biological samples are required and the experimental procedures can be automatically controlled. There is a strong need for the development of a digital microfluidics system integrated with machine vision for innovative biological research today. In this paper, we show how machine vision can be applied to digital microfluidics by demonstrating two applications: machine vision-based measurement of the kinetics of biomolecular interactions and machine vision-based droplet motion control. It is expected that digital microfluidics-based machine vision system will add intelligence and automation to high-throughput biological imaging in the future.

Network inference and network response identification: moving genome-scale data to the next level of biological discovery

The escalating amount of genome-scale data demands a pragmatic stance from the research community. How can we utilize this deluge of information to better understand biology, cure diseases, or engage cells in bioremediation or biomaterial production for various purposes? A research pipeline moving new sequence, expression and binding data towards practical end goals seems to be necessary. While most individual researchers are not motivated by such well-articulated pragmatic end goals, the scientific community has already self-organized itself to successfully convert genomic data into fundamentally new biological knowledge and practical applications. Here we review two important steps in this workflow: network inference and network response identification, applied to transcriptional regulatory networks. Among network inference methods, we concentrate on relevance networks due to their conceptual simplicity. We classify and discuss network response identification approaches as either data-centric or network-centric. Finally, we conclude with an outlook on what is still missing from these approaches and what may be ahead on the road to biological discovery.

Computational limits to binary genes

We analyse the trade-off between the speed with which a gene can propagate information, the noise of its output and its metabolic cost. Our main finding is that for any given level of metabolic cost there is an optimal trade-off between noise and processing speed. Any system with a non-vanishing leak expression rate is suboptimal, i.e. it will exhibit higher noise and/or slower speed than leak-free systems with the same metabolic cost. We also show that there is an optimal Hill coefficient h which minimizes noise and metabolic cost at fixed speeds, and an optimal threshold K which minimizes noise.

Listening to the noise: random fluctuations reveal gene network parameters

The cellular environment is abuzz with noise originating from the inherent random motion of reacting molecules in the living cell. In this noisy environment, clonal cell populations show cell-to-cell variability that can manifest significant phenotypic differences. Noise-induced stochastic fluctuations in cellular constituents can be measured and their statistics quantified. We show that these random fluctuations carry within them valuable information about the underlying genetic network. Far from being a nuisance, the ever-present cellular noise acts as a rich source of excitation that, when processed through a gene network, carries its distinctive fingerprint that encodes a wealth of information about that network. We show that in some cases the analysis of these random fluctuations enables the full identification of network parameters, including those that may otherwise be difficult to measure. This establishes a potentially powerful approach for the identification of gene networks and offers a new window into the workings of these networks.

A modified consumer inkjet for spatiotemporal control of gene expression

This paper presents a low-cost inkjet dosing system capable of continuous, two-dimensional spatiotemporal regulation of gene expression via delivery of diffusible regulators to a custom-mounted gel culture of E. coli. A consumer-grade, inkjet printer was adapted for chemical printing; E. coli cultures were grown on 750 microm thick agar embedded in micro-wells machined into commercial compact discs. Spatio-temporal regulation of the lac operon was demonstrated via the printing of patterns of lactose and glucose directly into the cultures; X-Gal blue patterns were used for visual feedback. We demonstrate how the bistable nature of the lac operon's feedback, when perturbed by patterning lactose (inducer) and glucose (inhibitor), can lead to coordination of cell expression patterns across a field in ways that mimic motifs seen in developmental biology. Examples of this include sharp boundaries and the generation of traveling waves of mRNA expression. To our knowledge, this is the first demonstration of reaction-diffusion effects in the well-studied lac operon. A finite element reaction-diffusion model of the lac operon is also presented which predicts pattern formation with good fidelity.

Geometric characteristics of dynamic correlations for combinatorial regulation in gene expression noise

Knowing which mode of combinatorial regulation (typically, AND or OR logic operation) that a gene employs is important for determining its function in regulatory networks. Here, we introduce a dynamic cross-correlation function between the output of a gene and its upstream regulator concentrations for signatures of combinatorial regulation in gene expression noise. We find that such a correlation function with respect to the correlation time near the peak close to the point of the zero correlation time is always upward convex in the case of AND logic whereas is always downward convex in the case of OR logic, whichever sources of noise (intrinsic or extrinsic or both). In turn, this fact implies a means for inferring regulatory synergies from available experimental data. The extensions and applications are discussed.

Noisy cell growth rate leads to fluctuating protein concentration in bacteria

The present study discusses a prime cause of fluctuating protein concentrations, which play a significant role in generating phenotypic diversity in bacteria. A genetic circuit integrated in a bacterial genome was used to evaluate the cell-to-cell variation in protein concentration. A simple dynamic model, comprising terms for synthesis and dilution, was used to elucidate the contributions of distinct noises to the fluctuation in cell protein concentration. Experimental and theoretical results demonstrated that noise in the rate of increase in cell volume (cell growth rate) serves as a source of extrinsic noise that accounts for dozens of percent of the total noise, whereas intrinsic noise in protein synthesis makes only a moderate contribution to the fluctuation in protein concentration. This suggests that such external noise in the cell growth rate has a global effect on cellular components, resulting in a large fluctuation in protein concentration in bacterial cells.

Decoding biological principles using gene circuits

A major flavor of synthetic biology is the creation of artificial gene circuits to perform user-defined tasks. One aspect of this area is to realize ever-increasingly more complicated circuit behavior. Such efforts have led to the identification and evaluation of design strategies that enable robust control of dynamics in single cells and in cell populations. On the other hand, there is increasing emphasis on using artificial systems programmed by simple circuits to explore fundamental biological questions of broad significance.

Using movies to analyse gene circuit dynamics in single cells

Many bacterial systems rely on dynamic genetic circuits to control crucial biological processes. A major goal of systems biology is to understand these behaviours in terms of individual genes and their interactions. However, traditional techniques based on population averages 'wash out' crucial dynamics that are either unsynchronized between cells or are driven by fluctuations, or 'noise', in cellular components. Recently, the combination of time-lapse microscopy, quantitative image analysis and fluorescent protein reporters has enabled direct observation of multiple cellular components over time in individual cells. In conjunction with mathematical modelling, these techniques are now providing powerful insights into genetic circuit behaviour in diverse microbial systems.

Emergent genome-wide control in wildtype and genetically mutated lipopolysaccarides-stimulated macrophages

Large-scale gene expression studies have mainly focused on highly expressed and 'discriminatory' genes to decipher key regulatory processes. Biological responses are consequence of the concerted action of gene regulatory network, thus, limiting our attention to genes having the most significant variations is insufficient for a thorough understanding of emergent whole genome response. Here we comprehensively analyzed the temporal oligonucleotide microarray data of lipopolysaccharide (LPS) stimulated macrophages in 4 genotypes; wildtype, Myeloid Differentiation factor 88 (MyD88) knockout (KO), TIR-domain-containing adapter-inducing interferon-beta (TRIF) KO and MyD88/TRIF double KO (DKO). Pearson correlations computed on the whole genome expression between different genotypes are extremely high (>0.98), indicating a strong co-regulation of the entire expression network. Further correlation analyses reveal genome-wide response is biphasic, i) acute-stochastic mode consisting of small number of sharply induced immune-related genes and ii) collective mode consisting of majority of weakly induced genes of diverse cellular processes which collectively adjust their expression level. Notably, temporal correlations of a small number of randomly selected genes from collective mode show scalability. Furthermore, in collective mode, the transition from large scatter in expression distributions for single ORFs to smooth linear lines emerges as an organizing principle when grouping of 50 ORFs and above. With this emergent behavior, the role of MyD88, TRIF and novel MyD88, TRIF-independent processes for gene induction can be linearly superposed to decipher quantitative whole genome differential control of transcriptional and mRNA decay machineries. Our work demonstrates genome-wide co-regulated responses subsequent to specific innate immune stimulus which have been largely neglected.