Regulatory activity revealed by dynamic correlations in gene expression noise

The interplay between metabolic stochasticity and cAMP-CRP regulation in single E. coli cells

The inherent stochasticity of metabolism raises a critical question for understanding homeostasis: are cellular processes regulated in response to internal fluctuations? Here, we show that, in E. coli cells under constant external conditions, catabolic enzyme expression continuously responds to metabolic fluctuations. The underlying regulatory feedback is enabled by the cyclic AMP (cAMP) and cAMP receptor protein (CRP) system, which controls catabolic enzyme expression based on metabolite concentrations. Using single-cell microscopy, genetic constructs in which this feedback is disabled, and mathematical modeling, we show how fluctuations circulate through the metabolic and genetic network at sub-cell-cycle timescales. Modeling identifies four noise propagation modes, including one specific to CRP regulation. Together, these modes correctly predict noise circulation at perturbed cAMP levels. The cAMP-CRP system may thus have evolved to control internal metabolic fluctuations in addition to external growth conditions. We conjecture that second messengers may more broadly function to achieve cellular homeostasis.

Systematic analysis and optimization of early warning signals for critical transitions using distribution data

Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.

Dynamic fluctuations in a bacterial metabolic network

The operation of the central metabolism is typically assumed to be deterministic, but dynamics and high connectivity of the metabolic network make it potentially prone to generating fluctuations. However, time-resolved measurements of metabolite levels in individual cells that are required to characterize such fluctuations remained a challenge, particularly in small bacterial cells. Here we use single-cell metabolite measurements based on Förster resonance energy transfer, combined with computer simulations, to explore the real-time dynamics of the metabolic network of Escherichia coli. We observe that steplike exposure of starved E. coli to glycolytic carbon sources elicits large periodic fluctuations in the intracellular concentration of pyruvate in individual cells. These fluctuations are consistent with predicted oscillatory dynamics of E. coli metabolic network, and they are primarily controlled by biochemical reactions around the pyruvate node. Our results further indicate that fluctuations in glycolysis propagate to other cellular processes, possibly leading to temporal heterogeneity of cellular states within a population.

Spatiotemporal feedforward between PKM2 tetramers and mTORC1 prompts mTORC1 activation

Most mammalian cells couple glucose availability to anabolic processes via the mTORC1 pathway. However, the mechanism by which fluctuations in glucose availability are rapidly translated into mTORC1 signals remains elusive. Here, we show that cells rapidly respond to changes in glucose availability through the spatial coupling of mTORC1 and tetramers of the key glycolytic enzyme pyruvate kinase M2 (PKM2) on lysosomal surfaces in the late G1/S phases. The lysosomal localization of PKM2 tetramers enables rapid increases in local ATP concentrations around lysosomes to activate mTORC1, while bypassing the need to elevate global ATP levels in the entire cell. In essence, this spatial coupling establishes a feedforward loop to enable mTORC1 to rapidly sense and respond to changes in glucose availability. We further demonstrate that this mechanism ensures robust cell proliferation upon fluctuating glucose availability. Thus, we present mechanistic insights into the rapid response of the mTORC1 pathway to changes in glucose availability. The underlying mechanism may be applicable to the control of other cellular processes.

Gene regulation by a protein translation factor at the single-cell level

Gene expression is inherently stochastic and pervasively regulated. While substantial work combining theory and experiments has been carried out to study how noise propagates through transcriptional regulations, the stochastic behavior of genes regulated at the level of translation is poorly understood. Here, we engineered a synthetic genetic system in which a target gene is down-regulated by a protein translation factor, which in turn is regulated transcriptionally. By monitoring both the expression of the regulator and the regulated gene at the single-cell level, we quantified the stochasticity of the system. We found that with a protein translation factor a tight repression can be achieved in single cells, noise propagation from gene to gene is buffered, and the regulated gene is sensitive in a nonlinear way to global perturbations in translation. A suitable mathematical model was instrumental to predict the transfer functions of the system. We also showed that a Gamma distribution parameterized with mesoscopic parameters, such as the mean expression and coefficient of variation, provides a deep analytical explanation about the system, displaying enough versatility to capture the cell-to-cell variability in genes regulated both transcriptionally and translationally. Overall, these results contribute to enlarge our understanding on stochastic gene expression, at the same time they provide design principles for synthetic biology.

In the cell, proteins can bind to DNA to regulate transcription as well as to RNA to regulate translation. However, cells have mainly evolved to exploit transcription factors as specific gene regulators, while translation factors have remained as global modulators of expression. Consequently, transcription regulation has attracted much attention over the last years to unveil design principles of genetic organization and to engineer synthetic circuits for cell reprogramming. In this work, the phage MS2 coat protein was exploited to regulate the expression of a green fluorescent protein at the level of translation. This synthetic system was instrumental to gain fundamental knowledge on stochasticity and regulation at an overlooked level within the genetic information flow.

Single-Cell Technologies to Study Phenotypic Heterogeneity and Bacterial Persisters

Antibiotic persistence is a phenomenon in which rare cells of a clonal bacterial population can survive antibiotic doses that kill their kin, even though the entire population is genetically susceptible. With antibiotic treatment failure on the rise, there is growing interest in understanding the molecular mechanisms underlying bacterial phenotypic heterogeneity and antibiotic persistence. However, elucidating these rare cell states can be technically challenging. The advent of single-cell techniques has enabled us to observe and quantitatively investigate individual cells in complex, phenotypically heterogeneous populations. In this review, we will discuss current technologies for studying persister phenotypes, including fluorescent tags and biosensors used to elucidate cellular processes; advances in flow cytometry, mass spectrometry, Raman spectroscopy, and microfluidics that contribute high-throughput and high-content information; and next-generation sequencing for powerful insights into genetic and transcriptomic programs. We will further discuss existing knowledge gaps, cutting-edge technologies that can address them, and how advances in single-cell microbiology can potentially improve infectious disease treatment outcomes.

Generation of Genetic Tools for Gauging Multiple-Gene Expression at the Single-Cell Level

Key microbial processes in many bacterial species are heterogeneously expressed in single cells of bacterial populations. However, the paucity of adequate molecular tools for live, real-time monitoring of multiple-gene expression at the single-cell level has limited the understanding of phenotypic heterogeneity. To investigate phenotypic heterogeneity in the ubiquitous opportunistic pathogen Pseudomonas aeruginosa, a genetic tool that allows gauging multiple-gene expression at the single-cell level has been generated. This tool, named pRGC, consists of a promoter-probe vector for transcriptional fusions that carries three reporter genes coding for the fluorescent proteins mCherry, green fluorescent protein (GFP), and cyan fluorescent protein (CFP). The pRGC vector has been characterized and validated via single-cell gene expression analysis of both constitutive and iron-regulated promoters, showing clear discrimination of the three fluorescence signals in single cells of a P. aeruginosa population without the need for image processing for spectral cross talk correction. In addition, two pRGC variants have been generated for either (i) integration of the reporter gene cassette into a single neutral site of P. aeruginosa chromosome that is suitable for long-term experiments in the absence of antibiotic selection or (ii) replication in bacterial genera other than Pseudomonas The easy-to-use genetic tools generated in this study will allow rapid and cost-effective investigation of multiple-gene expression in populations of environmental and pathogenic bacteria, hopefully advancing the understanding of microbial phenotypic heterogeneity.IMPORTANCE Within a bacterial population, single cells can differently express some genes, even though they are genetically identical and experience the same chemical and physical stimuli. This phenomenon, known as phenotypic heterogeneity, is mainly driven by gene expression noise and results in the emergence of bacterial subpopulations with distinct phenotypes. The analysis of gene expression at the single-cell level has shown that phenotypic heterogeneity is associated with key bacterial processes, including competence, sporulation, and persistence. In this study, new genetic tools have been generated that allow easy cloning of up to three promoters upstream of distinct fluorescent genes, making it possible to gauge multiple-gene expression at the single-cell level by fluorescence microscopy without the need for advanced image-processing procedures. A proof of concept has been provided by investigating iron uptake and iron storage gene expression in response to iron availability in P. aeruginosa.

Role of integrated noise in pathway-specific signal propagation in feed-forward loops

Cells impose optimal noise control mechanism in diverse situations to cope with distinct environmental cues. Sometimes, it is desirable for the cell to utilize fluctuations for noise-driven processes. In other cases, noise can be harmful to the cell to show optimal fitness. It is, therefore, important to unravel the noise propagation mechanism inside the cell. Such noise controlling mechanism is accomplished by using gene transcription regulatory networks. One such gene regulatory network is feed-forward loop, having three regulatory nodes S, X and Y. Here, we consider the most abundant type 1 of coherent and incoherent feed-forward loops with both OR and AND logic functions, forming four different architectures. In OR logic function, the functions representing S and X act additively for the regulation of Y, while in AND logic function, the same functions (S and X) act multiplicatively for the regulation of Y. Measurement of susceptibility of the signal at output Y is done using elasticity of each regulation in FFLs. Using susceptibility, we demonstrate the nature of pathway integration by which one-step and two-step pathways get overlapped. The integration type is competitive for motifs having OR gate, while it is noncompetitive for the same with AND gate. The pathway integration property explains the output noise behavior of the motifs properly but cannot infer about the mechanism by which the upstream noise propagates to output. To account this, the total output noise is decomposed, which results in integrated noise as an additional noise source along with pathway-specific noise components. The integrated noise is found to appear as a consequence of integration between the pathways and has different functional characteristics explaining noise amplification and noise attenuation property of coherent and incoherent feed-forward loops, respectively. The noise decomposition also quantifies the contribution of different noise sources toward total noise. Finally, the noise propagation is being tuned as a function of input signal noise and its time scale of fluctuations, which shows considerable intrinsic noise strength and relatively slow relaxation time scale causes a higher degree of noise propagation in FFLs.

Research progress and the biotechnological applications of multienzyme complex

The multienzyme complex system has become a research focus in synthetic biology due to its highly efficient overall catalytic ability and has been applied to various fields. Multienzyme complexes are formed by cascading complexes, which are multiple functionally related enzymes that continuously and efficiently catalyze the production of substrates. Compared with current mainstream microbial cell catalytic systems, in vitro multienzyme molecular machines have many advantages, such as fewer side reactions, a high product yield, a fast reaction speed, easy product separation, a tolerable toxic environment, and robust system operability, showing increasing competitiveness in the field of biomanufacturing. In this review, the research progress of multienzyme complexes in nature and multienzyme cascades in vivo or in vitro will be introduced, and the discovered enzyme cascades concerning scaffolding proteins will also be discussed. This review is expected to provide a more theoretical basis for the modification of multienzyme complexes and broaden their application in the field of synthetic biology. KEY POINTS: • The cascade reactions of some natural multienzyme complexes are reviewed. • The main approaches of constructing artificial multienzyme complexes are summarized. • The structure and application of cellulosomes are discussed and prospected.

Inferring the structures of signaling motifs from paired dynamic traces of single cells

Individual cells show variability in their signaling dynamics that often correlates with phenotypic responses, indicating that cell-to-cell variability is not merely noise but can have functional consequences. Based on this observation, we reasoned that cell-to-cell variability under the same treatment condition could be explained in part by a single signaling motif that maps different upstream signals into a corresponding set of downstream responses. If this assumption holds, then repeated measurements of upstream and downstream signaling dynamics in a population of cells could provide information about the underlying signaling motif for a given pathway, even when no prior knowledge of that motif exists. To test these two hypotheses, we developed a computer algorithm called MISC (Motif Inference from Single Cells) that infers the underlying signaling motif from paired time-series measurements from individual cells. When applied to measurements of transcription factor and reporter gene expression in the yeast stress response, MISC predicted signaling motifs that were consistent with previous mechanistic models of transcription. The ability to detect the underlying mechanism became less certain when a cell's upstream signal was randomly paired with another cell's downstream response, demonstrating how averaging time-series measurements across a population obscures information about the underlying signaling mechanism. In some cases, motif predictions improved as more cells were added to the analysis. These results provide evidence that mechanistic information about cellular signaling networks can be systematically extracted from the dynamical patterns of single cells.

Identification of FoxP circuits involved in locomotion and object fixation in Drosophila

The FoxP family of transcription factors is necessary for operant self-learning, an evolutionary conserved form of motor learning. The expression pattern, molecular function and mechanisms of action of the Drosophila FoxP orthologue remain to be elucidated. By editing the genomic locus of FoxP with CRISPR/Cas9, we find that the three different FoxP isoforms are expressed in neurons, but not in glia and that not all neurons express all isoforms. Furthermore, we detect FoxP expression in, e.g. the protocerebral bridge, the fan-shaped body and in motor neurons, but not in the mushroom bodies. Finally, we discover that FoxP expression during development, but not adulthood, is required for normal locomotion and landmark fixation in walking flies. While FoxP expression in the protocerebral bridge and motor neurons is involved in locomotion and landmark fixation, the FoxP gene can be excised from dorsal cluster neurons and mushroom-body Kenyon cells without affecting these behaviours.

Using single-plant-omics in the field to link maize genes to functions and phenotypes

Most of our current knowledge on plant molecular biology is based on experiments in controlled laboratory environments. However, translating this knowledge from the laboratory to the field is often not straightforward, in part because field growth conditions are very different from laboratory conditions. Here, we test a new experimental design to unravel the molecular wiring of plants and study gene-phenotype relationships directly in the field. We molecularly profiled a set of individual maize plants of the same inbred background grown in the same field and used the resulting data to predict the phenotypes of individual plants and the function of maize genes. We show that the field transcriptomes of individual plants contain as much information on maize gene function as traditional laboratory-generated transcriptomes of pooled plant samples subject to controlled perturbations. Moreover, we show that field-generated transcriptome and metabolome data can be used to quantitatively predict individual plant phenotypes. Our results show that profiling individual plants in the field is a promising experimental design that could help narrow the lab-field gap.

Probing pluripotency gene regulatory networks with quantitative live cell imaging

Live cell imaging uniquely enables the measurement of dynamic events in single cells, but it has not been used often in the study of gene regulatory networks. Network components can be examined in relation to one another by quantitative live cell imaging of fluorescent protein reporter cell lines that simultaneously report on more than one network component. A series of dual-reporter cell lines would allow different combinations of network components to be examined in individual cells. Dynamical information about interacting network components in individual cells is critical to predictive modeling of gene regulatory networks, and such information is not accessible through omics and other end point techniques. Achieving this requires that gene-edited cell lines are appropriately designed and adequately characterized to assure the validity of the biological conclusions derived from the expression of the reporters. In this brief review we discuss what is known about the importance of dynamics to network modeling and review some recent advances in optical microscopy methods and image analysis approaches that are making the use of quantitative live cell imaging for network analysis possible. We also discuss how strategies for genetic engineering of reporter cell lines can influence the biological relevance of the data.

Engineered RNA-Interacting CRISPR Guide RNAs for Genetic Sensing and Diagnostics

CRISPR guide RNAs (gRNAs) can be programmed with relative ease to allow the genetic editing of nearly any DNA or RNA sequence. Here, we propose novel molecular architectures to achieve RNA-dependent modulation of CRISPR activity in response to specific RNA molecules. We designed and tested, in both living Escherichia coli cells and cell-free assays for rapid prototyping, cis-repressed RNA-interacting guide RNA (igRNA) that switch to their active state only upon interaction with small RNA fragments or long RNA transcripts, including pathogen-derived mRNAs of medical relevance such as the human immunodeficiency virus infectivity factor. The proposed CRISPR-igRNAs are fully customizable and easily adaptable to the majority if not all the available CRISPR-Cas variants to modulate a variety of genetic functions in response to specific cellular conditions, providing orthogonal activation and increased specificity. We thereby foresee a large scope of application for therapeutic, diagnostic, and biotech applications in both prokaryotic and eukaryotic systems.

A bacterial size law revealed by a coarse-grained model of cell physiology

Universal observations in Biology are sometimes described as “laws”. In E. coli, experimental studies performed over the past six decades have revealed major growth laws relating ribosomal mass fraction and cell size to the growth rate. Because they formalize complex emerging principles in biology, growth laws have been instrumental in shaping our understanding of bacterial physiology. Here, we discovered a novel size law that connects cell size to the inverse of the metabolic proteome mass fraction and the active fraction of ribosomes. We used a simple whole-cell coarse-grained model of cell physiology that combines the proteome allocation theory and the structural model of cell division. This integrated model captures all available experimental data connecting the cell proteome composition, ribosome activity, division size and growth rate in response to nutrient quality, antibiotic treatment and increased protein burden. Finally, a stochastic extension of the model explains non-trivial correlations observed in single cell experiments including the adder principle. This work provides a simple and robust theoretical framework for studying the fundamental principles of cell size determination in unicellular organisms.

Bacteria respond to environmental changes by adjusting their molecular composition, cell size and growth rate. This plasticity is thought to result from years of evolution and to be at least in part optimal for bacterial physiology. Over the past decades, quantitative studies of bacterial growth have revealed simple phenomenological relationships, called “growth laws”, which link cell size and cell composition to the growth rate. Simplified mathematical models of cell physiology are useful tools to gain quantitative understanding of the molecular mechanisms that underlie growth laws. For instance, these models helped explaining how optimal allocation of cellular resource to physiological processes and pathways governs the cell molecular composition in response to specific environmental conditions. In this study, we have extended and integrated existing mathematical models and used experimental data from several recent studies to understand the co-regulation of cell composition, cell size and the cellular growth rate. The model predictions uncovered a novel “size law” that links cell size to the levels of metabolic proteins and the fraction of active ribosomes present in the cell. This work provides a useful theoretical tool and a quantitative basis for understanding mechanistically bacterial physiology as a function of external conditions.

Partitioning stable and unstable expression level variation in cell populations: A theoretical framework and its application to the T cell receptor

Phenotypic variation in the copy number of gene products expressed by cells or tissues has been the focus of intense investigation. To what extent the observed differences in cellular expression levels are persistent or transient is an intriguing question. Here, we develop a quantitative framework that resolves the expression variation into stable and unstable components. The difference between the expression means in two cohorts isolated from any cell population is shown to converge to an asymptotic value, with a characteristic time, τ_T, that measures the timescale of the unstable dynamics. The asymptotic difference in the means, relative to the initial value, measures the stable proportion of the original population variance Rα2. Empowered by this insight, we analysed the T-cell receptor (TCR) expression variation in CD4 T cells. About 70% of TCR expression variance is stable in a diverse polyclonal population, while over 80% of the variance in an isogenic TCR transgenic population is volatile. In both populations the TCR levels fluctuate with a characteristic time of 32 hours. This systematic characterisation of the expression variation dynamics, relying on time series of cohorts’ means, can be combined with technologies that measure gene or protein expression in single cells or in bulk.

No two cells are identical. Even isogenic cells, living in the same environment and expressing the same set of genes display measurable differences or variation in the expression level of any of these genes. How much of the differences in expression levels are permanent and how much of these differences vanish in time has intrigued us for generations. We develop a theoretical framework based on a stochastic model and put it to work in the analysis of T cell receptor expression level in CD4 T cells. We show that T cell populations with genetically diverse receptors display stable variation in receptor expression but, surprisingly, we detect persistent differences in receptor levels among uniform transgenic T cells. The analysis, being based on the mean cohort expression levels logarithm, can be applied to techniques that measure expression at single-cell level and also to the myriad of genomics and proteomics techniques that measure expression in bulk populations.

Stochastic antagonism between two proteins governs a bacterial cell fate switch

Cell fate decision circuits must be variable enough for genetically identical cells to adopt a multitude of fates, yet ensure that these states are distinct, stably maintained, and coordinated with neighboring cells. A long-standing view is that this is achieved by regulatory networks involving self-stabilizing feedback loops that convert small differences into long-lived cell types. We combined regulatory mutants and in vivo reconstitution with theory for stochastic processes to show that the marquee features of a cell fate switch in Bacillus subtilis-discrete states, multigenerational inheritance, and timing of commitments-can instead be explained by simple stochastic competition between two constitutively produced proteins that form an inactive complex. Such antagonistic interactions are commonplace in cells and could provide powerful mechanisms for cell fate determination more broadly.

The role of fluctuations in determining cellular network thermodynamics

The steady state distributions of phenotypic responses within an isogenic population of cells result from both deterministic and stochastic characteristics of biochemical networks. A biochemical network can be characterized by a multidimensional potential landscape based on the distribution of responses and a diffusion matrix of the correlated dynamic fluctuations between N-numbers of intracellular network variables. In this work, we develop a thermodynamic description of biological networks at the level of microscopic interactions between network variables. The Boltzmann H-function defines the rate of free energy dissipation of a network system and provides a framework for determining the heat associated with the nonequilibrium steady state and its network components. The magnitudes of the landscape gradients and the dynamic correlated fluctuations of network variables are experimentally accessible. We describe the use of Fokker-Planck dynamics to calculate housekeeping heat from the experimental data by a method that we refer to as Thermo-FP. The method provides insight into the composition of the network and the relative thermodynamic contributions from network components. We surmise that these thermodynamic quantities allow determination of the relative importance of network components to overall network control. We conjecture that there is an upper limit to the rate of dissipative heat produced by a biological system that is associated with system size or modularity, and we show that the dissipative heat has a lower bound.

Ab initio scaling laws between noise and mean of gene expression

Gene expression is inherently noisy due to fluctuations occurring at the molecular level. From a top-down perspective, noise has been traditionally decomposed into an intrinsic component that scales inversely with the mean expression level and an extrinsic component that is constant in absence of regulatory changes. Here, we adopt a bottom-up approach to reveal that extrinsic noise, by itself, can follow the aforementioned decomposition, which entails that one component of it can be confounded with intrinsic noise. Analytical expressions of the noise-mean relationship were derived for different scenarios, which were in part supported by numerical simulations.

Stochastic transcriptional pulses orchestrate flagellar biosynthesis in Escherichia coli

The classic picture of flagellum biosynthesis in Escherichia coli, inferred from population measurements, depicts a deterministic program where promoters are sequentially up-regulated and are maintained steadily active throughout exponential growth. However, complex regulatory dynamics at the single-cell level can be masked by bulk measurements. Here, we discover that in individual E. coli cells, flagellar promoters are stochastically activated in pulses. These pulses are coordinated within specific classes of promoters and comprise "on" and "off" states, each of which can span multiple generations. We demonstrate that in this pulsing program, the regulatory logic of flagellar assembly dictates which promoters skip pulses. Surprisingly, pulses do not require specific transcriptional or translational regulation of the flagellar master regulator, FlhDC, but instead appears to be essentially governed by an autonomous posttranslational circuit. Our results suggest that even topologically simple transcriptional networks can generate unexpectedly rich temporal dynamics and phenotypic heterogeneities.

Corruption of the Pearson correlation coefficient by measurement error and its estimation, bias, and correction under different error models

Correlation coefficients are abundantly used in the life sciences. Their use can be limited to simple exploratory analysis or to construct association networks for visualization but they are also basic ingredients for sophisticated multivariate data analysis methods. It is therefore important to have reliable estimates for correlation coefficients. In modern life sciences, comprehensive measurement techniques are used to measure metabolites, proteins, gene-expressions and other types of data. All these measurement techniques have errors. Whereas in the old days, with simple measurements, the errors were also simple, that is not the case anymore. Errors are heterogeneous, non-constant and not independent. This hampers the quality of the estimated correlation coefficients seriously. We will discuss the different types of errors as present in modern comprehensive life science data and show with theory, simulations and real-life data how these affect the correlation coefficients. We will briefly discuss ways to improve the estimation of such coefficients.

Inferring reaction network structure from single-cell, multiplex data, using toric systems theory

The goal of many single-cell studies on eukaryotic cells is to gain insight into the biochemical reactions that control cell fate and state. In this paper we introduce the concept of Effective Stoichiometric Spaces (ESS) to guide the reconstruction of biochemical networks from multiplexed, fixed time-point, single-cell data. In contrast to methods based solely on statistical models of data, the ESS method leverages the power of the geometric theory of toric varieties to begin unraveling the structure of chemical reaction networks (CRN). This application of toric theory enables a data-driven mapping of covariance relationships in single-cell measurements into stoichiometric information, one in which each cell subpopulation has its associated ESS interpreted in terms of CRN theory. In the development of ESS we reframe certain aspects of the theory of CRN to better match data analysis. As an application of our approach we process cytomery- and image-based single-cell datasets and identify differences in cells treated with kinase inhibitors. Our approach is directly applicable to data acquired using readily accessible experimental methods such as Fluorescence Activated Cell Sorting (FACS) and multiplex immunofluorescence.

We introduce a new notion, which we call the effective stoichiometric space (ESS), that elucidates network structure from the covariances of single-cell multiplex data. The ESS approach differs from methods that are based on purely statistical models of data: it allows a completely new and data-driven translation of the theory of toric varieties in geometry and specifically their role in chemical reaction networks (CRN). In the process, we reframe certain aspects of the theory of CRN. As illustrations of our approach, we find stoichiometry in different single-cell datasets, and pinpoint dose-dependence of network perturbations in drug-treated cells.

Cis-Acting Relaxases Guarantee Independent Mobilization of MOBQ 4 Plasmids

Plasmids are key vehicles of horizontal gene transfer and contribute greatly to bacterial genome plasticity. In this work, we studied a group of plasmids from enterobacteria that encode phylogenetically related mobilization functions that populate the previously non-described MOB_Q4 relaxase family. These plasmids encode two transfer genes: mobA coding for the MOB_Q4 relaxase; and mobC, which is non-essential but enhances the plasmid mobilization frequency. The origin of transfer is located between these two divergently transcribed mob genes. We found that MPF_I conjugative plasmids were the most efficient helpers for MOB_Q4 conjugative dissemination among clinically relevant enterobacteria. While highly similar in their mobilization module, two sub-groups with unrelated replicons (Rep_3 and ColE2) can be distinguished in this plasmid family. These subgroups can stably coexist (are compatible) and transfer independently, despite origin-of-transfer cross-recognition by their relaxases. Specific discrimination among their highly similar oriT sequences is guaranteed by the preferential cis activity of the MOB_Q4 relaxases. Such a strategy would be biologically relevant in a scenario of co-residence of non-divergent elements to favor self-dissemination.

Heterogeneity in efflux pump expression predisposes antibiotic-resistant cells to mutation

Antibiotic resistance is often the result of mutations that block drug activity; however, bacteria also evade antibiotics by transiently expressing genes such as multidrug efflux pumps. A crucial question is whether transient resistance can promote permanent genetic changes. Previous studies have established that antibiotic treatment can select tolerant cells that then mutate to achieve permanent resistance. Whether these mutations result from antibiotic stress or preexist within the population is unclear. To address this question, we focused on the multidrug pump AcrAB-TolC. Using time-lapse microscopy, we found that cells with higher acrAB expression have lower expression of the DNA mismatch repair gene mutS, lower growth rates, and higher mutation frequencies. Thus, transient antibiotic resistance from elevated acrAB expression can promote spontaneous mutations within single cells.

Temporal order and precision of complex stress responses in individual bacteria

Sudden stress often triggers diverse, temporally structured gene expression responses in microbes, but it is largely unknown how variable in time such responses are and if genes respond in the same temporal order in every single cell. Here, we quantified timing variability of individual promoters responding to sublethal antibiotic stress using fluorescent reporters, microfluidics, and time-lapse microscopy. We identified lower and upper bounds that put definite constraints on timing variability, which varies strongly among promoters and conditions. Timing variability can be interpreted using results from statistical kinetics, which enable us to estimate the number of rate-limiting molecular steps underlying different responses. We found that just a few critical steps control some responses while others rely on dozens of steps. To probe connections between different stress responses, we then tracked the temporal order and response time correlations of promoter pairs in individual cells. Our results support that, when bacteria are exposed to the antibiotic nitrofurantoin, the ensuing oxidative stress and SOS responses are part of the same causal chain of molecular events. In contrast, under trimethoprim, the acid stress response and the SOS response are part of different chains of events running in parallel. Our approach reveals fundamental constraints on gene expression timing and provides new insights into the molecular events that underlie the timing of stress responses.

DynamicME: dynamic simulation and refinement of integrated models of metabolism and protein expression

BACKGROUND

Genome-scale models of metabolism and macromolecular expression (ME models) enable systems-level computation of proteome allocation coupled to metabolic phenotype.

RESULTS

We develop DynamicME, an algorithm enabling time-course simulation of cell metabolism and protein expression. DynamicME correctly predicted the substrate utilization hierarchy on a mixed carbon substrate medium. We also found good agreement between predicted and measured time-course expression profiles. ME models involve considerably more parameters than metabolic models (M models). We thus generate an ensemble of models (each model having its rate constants perturbed), and then analyze the models by identifying archetypal time-course metabolite concentration profiles. Furthermore, we use a metaheuristic optimization method to calibrate ME model parameters using time-course measurements such as from a (fed-) batch culture. Finally, we show that constraints on protein concentration dynamics ("inertia") alter the metabolic response to environmental fluctuations, including increased substrate-level phosphorylation and lowered oxidative phosphorylation.

CONCLUSIONS

Overall, DynamicME provides a novel method for understanding proteome allocation and metabolism under complex and transient environments, and to utilize time-course cell culture data for model-based interpretation or model refinement.

Analysis of Cell Lineage Trees by Exact Bayesian Inference Identifies Negative Autoregulation of Nanog in Mouse Embryonic Stem Cells

Many cellular effectors of pluripotency are dynamically regulated. In principle, regulatory mechanisms can be inferred from single-cell observations of effector activity across time. However, rigorous inference techniques suitable for noisy, incomplete, and heterogeneous data are lacking. Here, we introduce stochastic inference on lineage trees (STILT), an algorithm capable of identifying stochastic models that accurately describe the quantitative behavior of cell fate markers observed using time-lapse microscopy data collected from proliferating cell populations. STILT performs exact Bayesian parameter inference and stochastic model selection using a particle-filter-based algorithm. We use STILT to investigate the autoregulation of Nanog, a heterogeneously expressed core pluripotency factor, in mouse embryonic stem cells. STILT rejects the possibility of positive Nanog autoregulation with high confidence; instead, model predictions indicate weak negative feedback. We use STILT for rational experimental design and validate model predictions using novel experimental data. STILT is available for download as an open source framework from http://www.imsb.ethz.ch/research/claassen/Software/stilt---stochastic-inference-on-lineage-trees.html.

Using time-lapse fluorescence microscopy to study gene regulation

Time-lapse fluorescence microscopy is a powerful tool to study gene regulation. By probing fluorescent signals in single cells over extended period of time, this method can be used to study the dynamics, noise, movement, memory, inheritance, and coordination, of gene expression during cell growth, development, and differentiation. In combination with a flow-cell device, it can also measure gene regulation by external stimuli. Due to the single cell nature and the spatial/temporal capacity, this method can often provide information that is hard to get using other methods. Here, we review the standard experimental procedures and new technical developments in this field.

Active degradation of MarA controls coordination of its downstream targets

Several key transcription factors have unusually short half-lives compared to other cellular proteins. Here, we explore the utility of active degradation in shaping how the multiple antibiotic resistance activator MarA coordinates its downstream targets. MarA controls a variety of stress response genes in Escherichia coli. We modify its half-life either by knocking down the protease that targets it via CRISPRi or by engineering MarA to protect it from degradation. Our experimental and analytical results indicate that active degradation can impact both the rate of coordination and the maximum coordination that downstream genes can achieve. In the context of multi-gene regulation, trade-offs between these properties show that perfect information fidelity and instantaneous coordination cannot coexist.

Sources, propagation and consequences of stochasticity in cellular growth

Growth impacts a range of phenotypic responses. Identifying the sources of growth variation and their propagation across the cellular machinery can thus unravel mechanisms that underpin cell decisions. We present a stochastic cell model linking gene expression, metabolism and replication to predict growth dynamics in single bacterial cells. Alongside we provide a theory to analyse stochastic chemical reactions coupled with cell divisions, enabling efficient parameter estimation, sensitivity analysis and hypothesis testing. The cell model recovers population-averaged data on growth-dependence of bacterial physiology and how growth variations in single cells change across conditions. We identify processes responsible for this variation and reconstruct the propagation of initial fluctuations to growth and other processes. Finally, we study drug-nutrient interactions and find that antibiotics can both enhance and suppress growth heterogeneity. Our results provide a predictive framework to integrate heterogeneous data and draw testable predictions with implications for antibiotic tolerance, evolutionary and synthetic biology.

The drivers of growth rate variability in bacteria are yet unknown. Here, the authors present a theory to predict the growth dynamics of individual cells and use a stochastic cell model integrating metabolism, gene expression and replication to identify the processes that underlie growth variation.

Precision in a rush: Trade-offs between reproducibility and steepness of the hunchback expression pattern

Fly development amazes us by the precision and reproducibility of gene expression, especially since the initial expression patterns are established during very short nuclear cycles. Recent live imaging of hunchback promoter dynamics shows a stable steep binary expression pattern established within the three minute interphase of nuclear cycle 11. Considering expression models of different complexity, we explore the trade-off between the ability of a regulatory system to produce a steep boundary and minimize expression variability between different nuclei. We show how a limited readout time imposed by short developmental cycles affects the gene’s ability to read positional information along the embryo’s anterior posterior axis and express reliably. Comparing our theoretical results to real-time monitoring of the hunchback transcription dynamics in live flies, we discuss possible regulatory strategies, suggesting an important role for additional binding sites, gradients or non-equilibrium binding and modified transcription factor search strategies.

Despite very limited time, organisms develop in reproducible ways. In the early stages of fly development the information about maternal signals is read out in a few minutes to produce steep and precise gene expression patterns. Motivated by recent live imaging experiments in fly embryos, we explore the consequences of the trade-off between a rushed but reproducible readout and a steep expression pattern on the regulatory modules of gene expression. We show that the current view of one anterior gradient morphogen binding to six binding sites is quantitatively inconsistent with the experimental data given the short readout time, suggesting other regulatory features.

Noise propagation in an integrated model of bacterial gene expression and growth

In bacterial cells, gene expression, metabolism, and growth are highly interdependent and tightly coordinated. As a result, stochastic fluctuations in expression levels and instantaneous growth rate show intricate cross-correlations. These correlations are shaped by feedback loops, trade-offs and constraints acting at the cellular level; therefore a quantitative understanding requires an integrated approach. To that end, we here present a mathematical model describing a cell that contains multiple proteins that are each expressed stochastically and jointly limit the growth rate. Conversely, metabolism and growth affect protein synthesis and dilution. Thus, expression noise originating in one gene propagates to metabolism, growth, and the expression of all other genes. Nevertheless, under a small-noise approximation many statistical quantities can be calculated analytically. We identify several routes of noise propagation, illustrate their origins and scaling, and establish important connections between noise propagation and the field of metabolic control analysis. We then present a many-protein model containing >1000 proteins parameterized by previously measured abundance data and demonstrate that the predicted cross-correlations between gene expression and growth rate are in broad agreement with published measurements.

A systematic study of the determinants of protein abundance memory in cell lineage

Proteins are essential players of life activities. Intracellular protein levels directly affect cellular functions and cell fate. Upon cell division, the proteins in the mother cell are inherited by the daughters. However, what factors and by how much they affect this epigenetic inheritance of protein abundance remains unclear. Using both computational and experimental approaches, we systematically investigated this problem. We derived an analytical expression for the dependence of protein inheritance on various factors and showed that it agreed with numerical simulations of protein production and experimental results. Our work provides a framework for quantitative studies of protein inheritance and for the potential application of protein memory manipulation.

Detection of network motifs using three-way ANOVA

Motivation

Gene regulatory networks (GRN) can be determined via various experimental techniques, and also by computational methods, which infer networks from gene expression data. However, these techniques treat interactions separately such that interdependencies of interactions forming meaningful subnetworks are typically not considered.

Methods

For the investigation of network properties and for the classification of different (sub-)networks based on gene expression data, we consider biological network motifs consisting of three genes and up to three interactions, e.g. the cascade chain (CSC), feed-forward loop (FFL), and dense-overlapping regulon (DOR). We examine several conventional methods for the inference of network motifs, which typically consider each interaction individually. In addition, we propose a new method based on three-way ANOVA (ANalysis Of VAriance) (3WA) that analyzes entire subnetworks at once. To demonstrate the advantages of such a more holistic perspective, we compare the ability of 3WA and other methods to detect and categorize network motifs on large real and artificial datasets.

Results

We find that conventional methods perform much better on artificial data (AUC up to 80%), than on real E. coli expression datasets (AUC 50% corresponding to random guessing). To explain this observation, we examine several important properties that differ between datasets and analyze predicted motifs in detail. We find that in case of real networks our new 3WA method outperforms (AUC 70% in E. coli) previous methods by exploiting the interdependencies in the full motif structure. Because of important differences between current artificial datasets and real measurements, the construction and testing of motif detection methods should focus on real data.

LlamaTags: A Versatile Tool to Image Transcription Factor Dynamics in Live Embryos

Embryonic cell fates are defined by transcription factors that are rapidly deployed, yet attempts to visualize these factors in vivo often fail because of slow fluorescent protein maturation. Here, we pioneer a protein tag, LlamaTag, which circumvents this maturation limit by binding mature fluorescent proteins, making it possible to visualize transcription factor concentration dynamics in live embryos. Implementing this approach in the fruit fly Drosophila melanogaster, we discovered stochastic bursts in the concentration of transcription factors that are correlated with bursts in transcription. We further used LlamaTags to show that the concentration of protein in a given nucleus heavily depends on transcription of that gene in neighboring nuclei; we speculate that this inter-nuclear signaling is an important mechanism for coordinating gene expression to delineate straight and sharp boundaries of gene expression. Thus, LlamaTags now make it possible to visualize the flow of information along the central dogma in live embryos.

Early-warning signals of critical transition: Effect of extrinsic noise

Complex dynamical systems often have tipping points and exhibit catastrophic regime shift. Despite the notorious difficulty of predicting such transitions, accumulating studies have suggested the existence of generic early-warning signals (EWSs) preceding upcoming transitions. However, previous theories and models were based on the effect of the intrinsic noise (IN) when a system is approaching a critical point, and did not consider the pervasive environmental fluctuations or the extrinsic noise (EN). Here, we extend previous theory to investigate how the interplay of EN and IN affects EWSs. Stochastic simulations of model systems subject to both IN and EN have verified our theory and demonstrated that EN can dramatically alter and diminish the EWS. This effect is stronger with increasing amplitude and correlation time scale of the EN. In the presence of EN, the EWS can fail to predict or even give a false alarm of critical transitions.

Visualizing the intercity correlation of PM2.5 time series in the Beijing-Tianjin-Hebei region using ground-based air quality monitoring data

The Beijing-Tianjin-Hebei area faces a severe fine particulate matter (PM_2.5) problem. To date, considerable progress has been made toward understanding the PM_2.5 problem, including spatial-temporal characterization, driving factors, and health effects. However, little research has been done on the dynamic interactions and relationships between PM_2.5 concentrations in different cities in this area. To address the research gap, this study discovered a phenomenon of time-lagged intercity correlations of PM_2.5 time series and proposed a visualization framework based on this phenomenon to visualize the interaction in PM_2.5 concentrations between cities. The visualizations produced using the framework show that there are significant time-lagged correlations between the PM_2.5 time series in different cities in this area. The visualizations also show that the correlations are more significant in colder months and between cities that are closer, and that there are seasonal changes in the temporal order of the correlated PM_2.5 time series. Further analysis suggests that the time-lagged intercity correlations of PM_2.5 time series are most likely due to synoptic meteorological variations. We argue that the visualizations demonstrate the interactions of air pollution between cities in the Beijing-Tianjin-Hebei area and the significant effect of synoptic meteorological conditions on PM_2.5 pollution. The visualization framework could help determine the pathway of regional transportation of air pollution and may also be useful in delineating the area of interaction of PM_2.5 pollution for impact analysis.

Complexity of Biochemical and Genetic Responses Reduced Using Simple Theoretical Models

Living systems are known to behave in a complex and sometimes unpredictable manner. Humans, for a very long time, have been intrigued by nature, and have attempted to understand biological processes and mechanisms using numerous experimental and mathematical techniques. In this chapter, we will look at simple theoretical models, using both linear and nonlinear differential equations, that realistically capture complex biochemical and genetic responses of living cells. Even for cases where cellular behaviors are stochastic, as for single-cell responses, randomness added to well-defined deterministic models has elegantly been shown to be useful. The data collectively present evidence for further exploration of the self-organizing rules and laws of living matter.

Systematic characterization of maturation time of fluorescent proteins in living cells

The slow maturation time of fluorescent proteins (FPs) limits the temporal accuracy of measurements of rapid processes such as gene expression dynamics and effectively reduces fluorescence signal in growing cells. We used high-precision time-lapse microscopy to characterize the maturation kinetics of 50 FPs that span the visible spectrum at two different temperatures in Escherichia coli cells. We identified fast-maturing FPs from this set that yielded the highest signal-to-noise ratio and temporal resolution in individual growing cells.

Micro-patterned agarose gel devices for single-cell high-throughput microscopy of E. coli cells

High-throughput microscopy of bacterial cells elucidated fundamental cellular processes including cellular heterogeneity and cell division homeostasis. Polydimethylsiloxane (PDMS)-based microfluidic devices provide advantages including precise positioning of cells and throughput, however device fabrication is time-consuming and requires specialised skills. Agarose pads are a popular alternative, however cells often clump together, which hinders single cell quantitation. Here, we imprint agarose pads with micro-patterned ‘capsules’, to trap individual cells and ‘lines’, to direct cellular growth outwards in a straight line. We implement this micro-patterning into multi-pad devices called CapsuleHotel and LineHotel for high-throughput imaging. CapsuleHotel provides ~65,000 capsule structures per mm² that isolate individual Escherichia coli cells. In contrast, LineHotel provides ~300 line structures per mm that direct growth of micro-colonies. With CapsuleHotel, a quantitative single cell dataset of ~10,000 cells across 24 samples can be acquired and analysed in under 1 hour. LineHotel allows tracking growth of > 10 micro-colonies across 24 samples simultaneously for up to 4 generations. These easy-to-use devices can be provided in kit format, and will accelerate discoveries in diverse fields ranging from microbiology to systems and synthetic biology.

Information-theoretic analysis of the directional influence between cellular processes

Inferring the directionality of interactions between cellular processes is a major challenge in systems biology. Time-lagged correlations allow to discriminate between alternative models, but they still rely on assumed underlying interactions. Here, we use the transfer entropy (TE), an information-theoretic quantity that quantifies the directional influence between fluctuating variables in a model-free way. We present a theoretical approach to compute the transfer entropy, even when the noise has an extrinsic component or in the presence of feedback. We re-analyze the experimental data from Kiviet et al. (2014) where fluctuations in gene expression of metabolic enzymes and growth rate have been measured in single cells of E. coli. We confirm the formerly detected modes between growth and gene expression, while prescribing more stringent conditions on the structure of noise sources. We furthermore point out practical requirements in terms of length of time series and sampling time which must be satisfied in order to infer optimally transfer entropy from times series of fluctuations.

The Role of Chromatin Density in Cell Population Heterogeneity during Stem Cell Differentiation

We incorporate three-dimensional (3D) conformation of chromosome (Hi-C) and single-cell RNA sequencing data together with discrete stochastic simulation, to explore the role of chromatin reorganization in determining gene expression heterogeneity during development. While previous research has emphasized the importance of chromatin architecture on activation and suppression of certain regulatory genes and gene networks, our study demonstrates how chromatin remodeling can dictate gene expression distribution by folding into distinct topological domains. We hypothesize that the local DNA density during differentiation accentuate transcriptional bursting due to the crowding effect of chromatin. This phenomenon yields a heterogeneous cell population, thereby increasing the potential of differentiation of the stem cells.

Regime shifts driven by dynamic correlations in gene expression noise

Gene expression is a noisy process that leads to regime shifts between alternative steady states among individual living cells, inducing phenotypic variability. The effects of white noise on the regime shift in bistable systems have been well characterized, however little is known about such effects of colored noise (noise with nonzero correlation time). Here, we show that noise correlation time, by considering a genetic circuit of autoactivation, can have a significant effect on the regime shift between distinct phenotypic states in gene expression. We demonstrate this theoretically, using stochastic potential, stationary probability density function, and first-passage time based on the Fokker-Planck description, where the Ornstein-Uhlenbeck process is used to model colored noise. We find that an increase in noise correlation time in the degradation rate can induce a regime shift from a low to a high protein concentration state and enhance the bistable regime, while an increase in noise correlation time in the basal rate retains the bimodal distribution. We then show how cross-correlated colored noises in basal and degradation rates can induce regime shifts from a low to a high protein concentration state, but reduce the bistable regime. We also validate these results through direct numerical simulations of the stochastic differential equation. In gene expression understanding the causes of regime shift to a harmful phenotype could improve early therapeutic intervention in complex human diseases.

Environment Tunes Propagation of Cell-to-Cell Variation in the Human Macrophage Gene Network

Cell-to-cell variation in gene expression and the propagation of such variation (PoV or "noise propagation") from one gene to another in the gene network, as reflected by gene-gene correlation across single cells, are commonly observed in single-cell transcriptomic studies and can shape the phenotypic diversity of cell populations. While gene network "rewiring" is known to accompany cellular adaptation to different environments, how PoV changes between environments and its underlying regulatory mechanisms are less understood. Here, we systematically explored context-dependent PoV among genes in human macrophages, utilizing different cytokines as natural perturbations of multiple molecular parameters that may influence PoV. Our single-cell, epigenomic, computational, and stochastic simulation analyses reveal that environmental adaptation can tune PoV to potentially shape cellular heterogeneity by changing parameters such as the degree of phosphorylation and transcription factor-chromatin interactions. This quantitative tuning of PoV may be a widespread, yet underexplored, property of cellular adaptation to distinct environments.

Determining the Limitations and Benefits of Noise in Gene Regulation and Signal Transduction through Single Cell, Microscopy-Based Analysis

Stochastic fluctuations, termed "noise," in the level of biological molecules can greatly impact cellular functions. While biological noise can sometimes be detrimental, recent studies have provided an increasing number of examples in which biological noise can be functionally beneficial. Rather than provide an exhaustive review of the growing literature in this field, in this review, we focus on single-cell studies based on quantitative microscopy that have generated a deeper understanding of the sources, characteristics, limitations, and benefits of biological noise. Specifically, we highlight studies showing how noise can help coordinate the expression of multiple downstream target genes, impact the channel capacity of signaling networks, and interact synergistically with oscillatory dynamics to enhance the sensitivity of signal processing. We conclude with a discussion of current challenges and future opportunities.

Customized Regulation of Diverse Stress Response Genes by the Multiple Antibiotic Resistance Activator MarA

Stress response networks frequently have a single upstream regulator that controls many downstream genes. However, the downstream targets are often diverse, therefore it remains unclear how their expression is specialized when under the command of a common regulator. To address this, we focused on a stress response network where the multiple antibiotic resistance activator MarA from Escherichia coli regulates diverse targets ranging from small RNAs to efflux pumps. Using single-cell experiments and computational modeling, we showed that each downstream gene studied has distinct activation, noise, and information transmission properties. Critically, our results demonstrate that understanding biological context is essential; we found examples where strong activation only occurs outside physiologically relevant ranges of MarA and others where noise is high at wild type MarA levels and decreases as MarA reaches its physiological limit. These results demonstrate how a single regulatory protein can maintain specificity while orchestrating the response of many downstream genes.

Bacteria can sense and respond to stress in their environment. This process is often coordinated by a master regulator that turns on or off many downstream genes, allowing the cell to survive the stress. However, individual genes encode products that are diverse and optimal expression for each gene may differ. Here, we focus on how expression of diverse downstream genes is optimized by targets of the multiple antibiotic resistance activator MarA. Using single-cell experiments and computational modeling we show that downstream genes process MarA signals differently, with unique activation, noise, and information transmission properties. We find that each downstream gene’s response depends critically on the level of the input MarA. Furthermore, by swapping parts of the regulatory elements of genes we were able to create novel responses. This suggests that these properties can be readily tuned by evolution. Our findings show how a network with diverse downstream genes can be used to process the same command to achieve many distinct outputs, which work together to coordinate the response to stress.

Frequency doubling in the cyanobacterial circadian clock

Organisms use circadian clocks to generate 24‐h rhythms in gene expression. However, the clock can interact with other pathways to generate shorter period oscillations. It remains unclear how these different frequencies are generated. Here, we examine this problem by studying the coupling of the clock to the alternative sigma factor sigC in the cyanobacterium Synechococcus elongatus. Using single‐cell microscopy, we find that psbAI, a key photosynthesis gene regulated by both sigC and the clock, is activated with two peaks of gene expression every circadian cycle under constant low light. This two‐peak oscillation is dependent on sigC, without which psbAI rhythms revert to one oscillatory peak per day. We also observe two circadian peaks of elongation rate, which are dependent on sigC, suggesting a role for the frequency doubling in modulating growth. We propose that the two‐peak rhythm in psbAI expression is generated by an incoherent feedforward loop between the clock, sigC and psbAI. Modelling and experiments suggest that this could be a general network motif to allow frequency doubling of outputs.

Precision of Readout at the hunchback Gene: Analyzing Short Transcription Time Traces in Living Fly Embryos

The simultaneous expression of the hunchback gene in the numerous nuclei of the developing fly embryo gives us a unique opportunity to study how transcription is regulated in living organisms. A recently developed MS2-MCP technique for imaging nascent messenger RNA in living Drosophila embryos allows us to quantify the dynamics of the developmental transcription process. The initial measurement of the morphogens by the hunchback promoter takes place during very short cell cycles, not only giving each nucleus little time for a precise readout, but also resulting in short time traces of transcription. Additionally, the relationship between the measured signal and the promoter state depends on the molecular design of the reporting probe. We develop an analysis approach based on tailor made autocorrelation functions that overcomes the short trace problems and quantifies the dynamics of transcription initiation. Based on live imaging data, we identify signatures of bursty transcription initiation from the hunchback promoter. We show that the precision of the expression of the hunchback gene to measure its position along the anterior-posterior axis is low both at the boundary and in the anterior even at cycle 13, suggesting additional post-transcriptional averaging mechanisms to provide the precision observed in fixed embryos.

The fly embryo provides a natural laboratory to study the dynamics of transcription and its implications for the developing organism. Using live imaging experiments we investigate the nature of transcription regulation of the hunchback gene—the first to read out the maternal Bicoid gradient. While traditional time trace analysis methods based on OFF time distributions or autocorrelation functions fail for short signals, our tailored autocorrelation function overcomes these limitations revealing bursty dynamics that is reproducible between cell cycles and embryos. The inferred rates result in a lot of variability in the readout of nuclei sensing similar Bicoid concentrations, suggesting additional readout mechanisms than a one-to-one mapping of the input onto the output.