Noise in transcription negative feedback loops: simulation and experimental analysis

Robustness of signal transduction pathways

Signal transduction pathways transduce information about the outside of the cell to the nucleus, regulating gene expression and cell fate. To reliably inform the cell about its surroundings, information transfer has to be robust against typical perturbation that a cell experiences. Robustness of several mammalian signaling pathways has been studied recently by quantitative experimentation and using mathematical modeling. Here, we review these studies, and describe the emerging concepts of robustness and the underlying mechanisms.

Multicellular computing using conjugation for wiring

Recent efforts in synthetic biology have focussed on the implementation of logical functions within living cells. One aim is to facilitate both internal "re-programming" and external control of cells, with potential applications in a wide range of domains. However, fundamental limitations on the degree to which single cells may be re-engineered have led to a growth of interest in multicellular systems, in which a "computation" is distributed over a number of different cell types, in a manner analogous to modern computer networks. Within this model, individual cell type perform specific sub-tasks, the results of which are then communicated to other cell types for further processing. The manner in which outputs are communicated is therefore of great significance to the overall success of such a scheme. Previous experiments in distributed cellular computation have used global communication schemes, such as quorum sensing (QS), to implement the "wiring" between cell types. While useful, this method lacks specificity, and limits the amount of information that may be transferred at any one time. We propose an alternative scheme, based on specific cell-cell conjugation. This mechanism allows for the direct transfer of genetic information between bacteria, via circular DNA strands known as plasmids. We design a multi-cellular population that is able to compute, in a distributed fashion, a Boolean XOR function. Through this, we describe a general scheme for distributed logic that works by mixing different strains in a single population; this constitutes an important advantage of our novel approach. Importantly, the amount of genetic information exchanged through conjugation is significantly higher than the amount possible through QS-based communication. We provide full computational modelling and simulation results, using deterministic, stochastic and spatially-explicit methods. These simulations explore the behaviour of one possible conjugation-wired cellular computing system under different conditions, and provide baseline information for future laboratory implementations.

Synthetic mammalian transgene negative autoregulation

Biological networks contain overrepresented small-scale topologies, typically called motifs. A frequently appearing motif is the transcriptional negative-feedback loop, where a gene product represses its own transcription. Here, using synthetic circuits stably integrated in human kidney cells, we study the effect of negative-feedback regulation on cell-wide (extrinsic) and gene-specific (intrinsic) sources of uncertainty. We develop a theoretical approach to extract the two noise components from experiments and show that negative feedback results in significant total noise reduction by reducing extrinsic noise while marginally increasing intrinsic noise. We compare the results to simple negative regulation, where a constitutively transcribed transcription factor represses a reporter protein. We observe that the control architecture also reduces the extrinsic noise but results in substantially higher intrinsic fluctuations. We conclude that negative feedback is the most efficient way to mitigate the effects of extrinsic fluctuations by a sole regulatory wiring.

Combined model of intrinsic and extrinsic variability for computational network design with application to synthetic biology

Biological systems are inherently variable, with their dynamics influenced by intrinsic and extrinsic sources. These systems are often only partially characterized, with large uncertainties about specific sources of extrinsic variability and biochemical properties. Moreover, it is not yet well understood how different sources of variability combine and affect biological systems in concert. To successfully design biomedical therapies or synthetic circuits with robust performance, it is crucial to account for uncertainty and effects of variability. Here we introduce an efficient modeling and simulation framework to study systems that are simultaneously subject to multiple sources of variability, and apply it to make design decisions on small genetic networks that play a role of basic design elements of synthetic circuits. Specifically, the framework was used to explore the effect of transcriptional and post-transcriptional autoregulation on fluctuations in protein expression in simple genetic networks. We found that autoregulation could either suppress or increase the output variability, depending on specific noise sources and network parameters. We showed that transcriptional autoregulation was more successful than post-transcriptional in suppressing variability across a wide range of intrinsic and extrinsic magnitudes and sources. We derived the following design principles to guide the design of circuits that best suppress variability: (i) high protein cooperativity and low miRNA cooperativity, (ii) imperfect complementarity between miRNA and mRNA was preferred to perfect complementarity, and (iii) correlated expression of mRNA and miRNA--for example, on the same transcript--was best for suppression of protein variability. Results further showed that correlations in kinetic parameters between cells affected the ability to suppress variability, and that variability in transient states did not necessarily follow the same principles as variability in the steady state. Our model and findings provide a general framework to guide design principles in synthetic biology.

The utility of paradoxical components in biological circuits

A recurring theme in biological circuits is the existence of components that are antagonistically bifunctional, in the sense that they simultaneously have two opposing effects on the same target or biological process. Examples include bifunctional enzymes that carry out two opposing reactions such as phosphorylating and dephosphorylating the same target, regulators that activate and also repress a gene in circuits called incoherent feedforward loops, and cytokines that signal immune cells to both proliferate and die. Such components are termed "paradoxical", and in this review we discuss how they can provide useful features to cell circuits that are otherwise difficult to achieve. In particular, we summarize how paradoxical components can provide robustness, generate temporal pulses, and provide fold-change detection, in which circuits respond to relative rather than absolute changes in signals.

Rate of environmental change determines stress response specificity

Cells use general stress response pathways to activate diverse target genes in response to a variety of stresses. However, general stress responses coexist with more specific pathways that are activated by individual stresses, provoking the fundamental question of whether and how cells control the generality or specificity of their response to a particular stress. Here we address this issue using quantitative time-lapse microscopy of the Bacillus subtilis environmental stress response, mediated by σ(B). We analyzed σ(B) activation in response to stresses such as salt and ethanol imposed at varying rates of increase. Dynamically, σ(B) responded to these stresses with a single adaptive activity pulse, whose amplitude depended on the rate at which the stress increased. This rate-responsive behavior can be understood from mathematical modeling of a key negative feedback loop in the underlying regulatory circuit. Using RNAseq we analyzed the effects of both rapid and gradual increases of ethanol and salt stress across the genome. Because of the rate responsiveness of σ(B) activation, salt and ethanol regulons overlap under rapid, but not gradual, increases in stress. Thus, the cell responds specifically to individual stresses that appear gradually, while using σ(B) to broaden the cellular response under more rapidly deteriorating conditions. Such dynamic control of specificity could be a critical function of other general stress response pathways.

Using topology to tame the complex biochemistry of genetic networks

Living cells are controlled by networks of interacting genes, proteins and biochemicals. Cells use the emergent collective dynamics of these networks to probe their surroundings, perform computations and generate appropriate responses. Here, we consider genetic networks, interacting sets of genes that regulate one another's expression. It is possible to infer the interaction topology of genetic networks from high-throughput experimental measurements. However, such experiments rarely provide information on the detailed nature of each interaction. We show that topological approaches provide powerful means of dealing with the missing biochemical data. We first discuss the biochemical basis of gene regulation, and describe how genes can be connected into networks. We then show that, given weak constraints on the underlying biochemistry, topology alone determines the emergent properties of certain simple networks. Finally, we apply these approaches to the realistic example of quorum-sensing networks: chemical communication systems that coordinate the responses of bacterial populations.

Consequences of mRNA transport on stochastic variability in protein levels

Homogeneous cell populations can exhibit considerable cell-to-cell variability in protein levels arising from the stochastic nature of the gene-expression process. In particular, transcriptional bursting of mRNAs from the promoter has been implicated as a major source of stochasticity in the expression of many genes. In eukaryotes, transcribed pre-mRNAs have to be exported outside the nucleus and in many cases, export rates can be slow and comparable to mRNA turnover rates. We investigate whether such export processes can be effective mechanisms in buffering protein levels from transcriptional bursting of pre-mRNAs in the nucleus. For a stochastic gene-expression model with both transcriptional bursting and export, we derive an exact solution of the steady-state probability-generating function for both the nuclear and the cytoplasmic mRNA levels. These formulas reveal that decreasing export rates can dramatically reduce variability in cytoplasmic mRNA levels. However, our results also show that decreasing export rates enhance mRNA autocorrelation times, which function to increase heterogeneity in protein levels. Our overall analysis concludes that under physiologically relevant parameter regimes, a pre-mRNA export step can decrease steady-state variability at the mRNA level but not at the protein level. Finally, we reinforce previous observations that saturation in the pre-mRNA transport machinery can be an important mechanism in suppressing protein variability from underlying transcriptional bursts.

Functional roles of slow enzyme conformational changes in network dynamics

Extensive studies from different fields reveal that many macromolecules, especially enzymes, show slow transitions among different conformations. This phenomenon is named such things as dynamic disorder, heterogeneity, hysteretic or mnemonic enzymes across these different fields, and has been directly demonstrated by single molecule enzymology and NMR studies recently. We analyzed enzyme slow conformational changes in the context of regulatory networks. A single enzymatic reaction with slow conformational changes can filter upstream network noises, and can either resonantly respond to the system stimulus at certain frequencies or respond adaptively for sustained input signals of the network fluctuations. It thus can serve as a basic functional motif with properties that are normally for larger intermolecular networks in the field of systems biology. We further analyzed examples including enzymes functioning against pH fluctuations, metabolic state change of Artemia embryos, and kinetic insulation of fluctuations in metabolic networks. The study also suggests that hysteretic enzymes may be building blocks of synthetic networks with various properties such as narrow-banded filtering. The work fills the missing gap between studies on enzyme biophysics and network level dynamics, and reveals that the coupling between the two is functionally important; it also suggests that the conformational dynamics of some enzymes may be evolutionally selected.

Quantitative, non-disruptive monitoring of transcription in single cells with a broad-host range GFP-luxCDABE dual reporter system

A dual promoter probe system based on a tandem bi-cistronic GFP-luxCDABE reporter cassette is described and implemented. This system is assembled in two synthetic, modular, broad-host range plasmids based on pBBR1 and RK2 origins of replication, allowing its utilization in an extensive number of gram-negative bacteria. We analyze the performance of this dual cassette in two hosts, Escherichia coli and Pseudomonas putida, by examining the induction properties of the lacI(q)-Ptrc expression system in the first host and the Pb promoter of the benzoate degradation pathway in the second host. By quantifying the bioluminescence signal produced through the expression of the lux genes, we explore the dynamic range of induction for the two systems (Ptrc-based and Pb-based) in response to the two inducers. In addition, by quantifying the fluorescence signals produced by GFP expression, we were able to monitor the single-cell expression profile and to explore stochasticity of the same two promoters by flow cytometry. The results provided here demonstrate the power of the dual GFP-luxCDABE cassette as a new, single-step tool to assess promoter properties at both the population and single-cell levels in gram-negative bacteria.

Noise propagation in gene regulation networks involving interlinked positive and negative feedback loops

It is well known that noise is inevitable in gene regulatory networks due to the low-copy numbers of molecules and local environmental fluctuations. The prediction of noise effects is a key issue in ensuring reliable transmission of information. Interlinked positive and negative feedback loops are essential signal transduction motifs in biological networks. Positive feedback loops are generally believed to induce a switch-like behavior, whereas negative feedback loops are thought to suppress noise effects. Here, by using the signal sensitivity (susceptibility) and noise amplification to quantify noise propagation, we analyze an abstract model of the Myc/E2F/MiR-17-92 network that is composed of a coupling between the E2F/Myc positive feedback loop and the E2F/Myc/miR-17-92 negative feedback loop. The role of the feedback loop on noise effects is found to depend on the dynamic properties of the system. When the system is in monostability or bistability with high protein concentrations, noise is consistently suppressed. However, the negative feedback loop reduces this suppression ability (or improves the noise propagation) and enhances signal sensitivity. In the case of excitability, bistability, or monostability, noise is enhanced at low protein concentrations. The negative feedback loop reduces this noise enhancement as well as the signal sensitivity. In all cases, the positive feedback loop acts contrary to the negative feedback loop. We also found that increasing the time scale of the protein module or decreasing the noise autocorrelation time can enhance noise suppression; however, the systems sensitivity remains unchanged. Taken together, our results suggest that the negative/positive feedback mechanisms in coupled feedback loop dynamically buffer noise effects rather than only suppressing or amplifying the noise.

miR-451 regulates dendritic cell cytokine responses to influenza infection

MicroRNAs (miRNAs) are important posttranscriptional regulators in immune cells, but how viral infection regulates miRNA expression to shape dendritic cell (DC) responses has not been well characterized. We identified 20 miRNAs that were differentially expressed in primary murine DCs in response to the dsRNA agonist polyinosinic-polycytidylic acid, a subset of which were modestly regulated by influenza infection. miR-451 was unique because it was induced more strongly in primary splenic and lung DCs by live viral infection than by purified agonists of pattern recognition receptors. We determined that miR-451 regulates a subset of proinflammatory cytokine responses. Three types of primary DCs treated with antisense RNA antagomirs directed against miR-451 secreted elevated levels of IL-6, TNF, CCL5/RANTES, and CCL3/MIP1α, and these results were confirmed using miR-451(null) cells. miR-451 negatively regulates YWHAZ/14-3-3ζ protein levels in various cell types, and we measured a similar inhibition of YWHAZ levels in DCs. It is known that YWHAZ can control the activity of two negative regulators of cytokine production: FOXO3, which is an inhibitory transcription factor, and ZFP36/Tristetraprolin, which binds to AU-rich elements within 3'-untranslated regions to destabilize cytokine mRNAs. Inhibition of miR-451 expression correlated with increased YWHAZ protein expression and decreased ZFP36 expression, providing a possible mechanism for the elevated secretion of IL-6, TNF, CCL5/RANTES, and CCL3/MIP1α. miR-451 levels are themselves increased by IL-6 and type I IFN, potentially forming a regulatory loop. These data suggest that viral infection specifically induces a miRNA that directs a negative regulatory cascade to tune DC cytokine production.

Gene autoregulation via intronic microRNAs and its functions

Background

MicroRNAs, post-transcriptional repressors of gene expression, play a pivotal role in gene regulatory networks. They are involved in core cellular processes and their dysregulation is associated to a broad range of human diseases. This paper focus on a minimal microRNA-mediated regulatory circuit, in which a protein-coding gene (host gene) is targeted by a microRNA located inside one of its introns.

Results

Autoregulation via intronic microRNAs is widespread in the human regulatory network, as confirmed by our bioinformatic analysis, and can perform several regulatory tasks despite its simple topology. Our analysis, based on analytical calculations and simulations, indicates that this circuitry alters the dynamics of the host gene expression, can induce complex responses implementing adaptation and Weber’s law, and efficiently filters fluctuations propagating from the upstream network to the host gene. A fine-tuning of the circuit parameters can optimize each of these functions. Interestingly, they are all related to gene expression homeostasis, in agreement with the increasing evidence suggesting a role of microRNA regulation in conferring robustness to biological processes. In addition to model analysis, we present a list of bioinformatically predicted candidate circuits in human for future experimental tests.

Conclusions

The results presented here suggest a potentially relevant functional role for negative self-regulation via intronic microRNAs, in particular as a homeostatic control mechanism of gene expression. Moreover, the map of circuit functions in terms of experimentally measurable parameters, resulting from our analysis, can be a useful guideline for possible applications in synthetic biology.

A synthetic biology approach to understanding cellular information processing

The survival of cells and organisms requires proper responses to environmental signals. These responses are governed by cellular networks, which serve to process diverse environmental cues. Biological networks often contain recurring network topologies called "motifs". It has been recognized that the study of such motifs allows one to predict the response of a biological network and thus cellular behavior. However, studying a single motif in complete isolation of all other network motifs in a natural setting is difficult. Synthetic biology has emerged as a powerful approach to understanding the dynamic properties of network motifs. In addition to testing existing theoretical predictions, construction and analysis of synthetic gene circuits has led to the discovery of novel motif dynamics, such as how the combination of simple motifs can lead to autonomous dynamics or how noise in transcription and translation can affect the dynamics of a motif. Here, we review developments in synthetic biology as they pertain to increasing our understanding of cellular information processing. We highlight several types of dynamic behaviors that diverse motifs can generate, including the control of input/output responses, the generation of autonomous spatial and temporal dynamics, as well as the influence of noise in motif dynamics and cellular behavior.

A reconfigurable NAND/NOR genetic logic gate

BACKGROUND

Engineering genetic Boolean logic circuits is a major research theme of synthetic biology. By altering or introducing connections between genetic components, novel regulatory networks are built in order to mimic the behaviour of electronic devices such as logic gates. While electronics is a highly standardized science, genetic logic is still in its infancy, with few agreed standards. In this paper we focus on the interpretation of logical values in terms of molecular concentrations.

RESULTS

We describe the results of computational investigations of a novel circuit that is able to trigger specific differential responses depending on the input standard used. The circuit can therefore be dynamically reconfigured (without modification) to serve as both a NAND/NOR logic gate. This multi-functional behaviour is achieved by a) varying the meanings of inputs, and b) using branch predictions (as in computer science) to display a constrained output. A thorough computational study is performed, which provides valuable insights for the future laboratory validation. The simulations focus on both single-cell and population behaviours. The latter give particular insights into the spatial behaviour of our engineered cells on a surface with a non-homogeneous distribution of inputs.

CONCLUSIONS

We present a dynamically-reconfigurable NAND/NOR genetic logic circuit that can be switched between modes of operation via a simple shift in input signal concentration. The circuit addresses important issues in genetic logic that will have significance for more complex synthetic biology applications.

A reconfigurable NAND/NOR genetic logic gate

BACKGROUND

Engineering genetic Boolean logic circuits is a major research theme of synthetic biology. By altering or introducing connections between genetic components, novel regulatory networks are built in order to mimic the behaviour of electronic devices such as logic gates. While electronics is a highly standardized science, genetic logic is still in its infancy, with few agreed standards. In this paper we focus on the interpretation of logical values in terms of molecular concentrations.

RESULTS

We describe the results of computational investigations of a novel circuit that is able to trigger specific differential responses depending on the input standard used. The circuit can therefore be dynamically reconfigured (without modification) to serve as both a NAND/NOR logic gate. This multi-functional behaviour is achieved by a) varying the meanings of inputs, and b) using branch predictions (as in computer science) to display a constrained output. A thorough computational study is performed, which provides valuable insights for the future laboratory validation. The simulations focus on both single-cell and population behaviours. The latter give particular insights into the spatial behaviour of our engineered cells on a surface with a non-homogeneous distribution of inputs.

CONCLUSIONS

We present a dynamically-reconfigurable NAND/NOR genetic logic circuit that can be switched between modes of operation via a simple shift in input signal concentration. The circuit addresses important issues in genetic logic that will have significance for more complex synthetic biology applications.

Culture history and population heterogeneity as determinants of bacterial adaptation: the adaptomics of a single environmental transition

Diversity in adaptive responses is common within species and populations, especially when the heterogeneity of the frequently large populations found in environments is considered. By focusing on events in a single clonal population undergoing a single transition, we discuss how environmental cues and changes in growth rate initiate a multiplicity of adaptive pathways. Adaptation is a comprehensive process, and stochastic, regulatory, epigenetic, and mutational changes can contribute to fitness and overlap in timing and frequency. We identify culture history as a major determinant of both regulatory adaptations and microevolutionary change. Population history before a transition determines heterogeneities due to errors in translation, stochastic differences in regulation, the presence of aged, damaged, cheating, or dormant cells, and variations in intracellular metabolite or regulator concentrations. It matters whether bacteria come from dense, slow-growing, stressed, or structured states. Genotypic adaptations are history dependent due to variations in mutation supply, contingency gene changes, phase variation, lateral gene transfer, and genome amplifications. Phenotypic adaptations underpin genotypic changes in situations such as stress-induced mutagenesis or prophage induction or in biofilms to give a continuum of adaptive possibilities. Evolutionary selection additionally provides diverse adaptive outcomes in a single transition and generally does not result in single fitter types. The totality of heterogeneities in an adapting population increases the chance that at least some individuals meet immediate or future challenges. However, heterogeneity complicates the adaptomics of single transitions, and we propose that subpopulations will need to be integrated into future population biology and systems biology predictions of bacterial behavior.

The negative feedback-loop between the oncomir Mir-24-1 and menin modulates the Men1 tumorigenesis by mimicking the "Knudson's second hit"

Multiple endocrine neoplasia type 1 (MEN1) syndrome is a rare hereditary cancer disorder characterized by tumors of the parathyroids, of the neuroendocrine cells, of the gastro-entero-pancreatic tract, of the anterior pituitary, and by non-endocrine neoplasms and lesions. MEN1 gene, a tumor suppressor gene, encodes menin protein. Loss of heterozygosity at 11q13 is typical of MEN1 tumors, in agreement with the Knudson’s two-hit hypothesis. In silico analysis with Target Scan, Miranda and Pictar-Vert softwares for the prediction of miRNA targets indicated miR-24-1 as capable to bind to the 3′UTR of MEN1 mRNA. We investigated this possibility by analysis of miR-24-1 expression profiles in parathyroid adenomatous tissues from MEN1 gene mutation carriers, in their sporadic non-MEN1 counterparts, and in normal parathyroid tissue. Interestingly, the MEN1 tumorigenesis seems to be under the control of a “negative feedback loop” between miR-24-1 and menin protein, that mimics the second hit of Knudson’s hypothesis and that could buffer the effect of the stochastic factors that contribute to the onset and progression of this disease. Our data show an alternative way to MEN1 tumorigenesis and, probably, to the “two-hit dogma”. The functional significance of this regulatory mechanism in MEN1 tumorigenesis is also the basis for opening future developments of RNA antagomir(s)-based strategies in the in vivo control of tumorigenesis in MEN1 carriers.

Influence of the feedback loops in the trp operon of B. subtilis on the system dynamic response and noise amplitude

In this paper we introduce a mathematical model for the tryptophan operon regulatory pathway in Bacillus subtilis. This model considers the transcription-attenuation, and the enzyme-inhibition regulatory mechanisms. Special attention is paid to the estimation of all the model parameters from reported experimental data. With the aid of this model we investigate, from a mathematical-modeling point of view, whether the existing multiplicity of regulatory feedback loops is advantageous in some sense, regarding the dynamic response and the biochemical noise in the system. The tryptophan operon dynamic behavior is studied by means of deterministic numeric simulations, while the biochemical noise is analyzed with the aid of stochastic simulations. The model feasibility is tested comparing its stochastic and deterministic results with experimental reports. Our results for the wildtype and for a couple of mutant bacterial strains suggest that the enzyme-inhibition feedback loop, dynamically accelerates the operon response, and plays a major role in the reduction of biochemical noise. Also, the transcription-attenuation feedback loop makes the trp operon sensitive to changes in the endogenous tryptophan level, and increases the amplitude of the biochemical noise.

Modeling suggests that gene circuit architecture controls phenotypic variability in a bacterial persistence network

BACKGROUND

Bacterial persistence is a non-inherited bet-hedging mechanism where a subpopulation of cells enters a dormant state, allowing those cells to survive environmental stress such as treatment with antibiotics. Persister cells are not mutants; they are formed by natural stochastic variation in gene expression. Understanding how regulatory architecture influences the level of phenotypic variability can help us explain how the frequency of persistence events can be tuned.

RESULTS

We present a model of the regulatory network controlling the HipBA toxin-antitoxin system from Escherichia coli. Using a biologically realistic model we first determine that the persistence phenotype is not the result of bistability within the network. Next, we develop a stochastic model and show that cells can enter persistence due to random fluctuations in transcription, translation, degradation, and complex formation. We then examine alternative gene circuit architectures for controlling hipBA expression and show that networks with more noise (more persisters) and less noise (fewer persisters) are straightforward to achieve. Thus, we propose that the gene circuit architecture can be used to tune the frequency of persistence, a trait that can be selected for by evolution.

CONCLUSIONS

We develop deterministic and stochastic models describing how the regulation of toxin and antitoxin expression influences phenotypic variation within a population. Persistence events are the result of stochastic fluctuations in toxin levels that cross a threshold, and their frequency is controlled by the regulatory topology governing gene expression.

The magnitude and colour of noise in genetic negative feedback systems

The comparative ability of transcriptional and small RNA-mediated negative feedback to control fluctuations or ‘noise’ in gene expression remains unexplored. Both autoregulatory mechanisms usually suppress the average (mean) of the protein level and its variability across cells. The variance of the number of proteins per molecule of mean expression is also typically reduced compared with the unregulated system, but is almost never below the value of one. This relative variance often substantially exceeds a recently obtained, theoretical lower limit for biochemical feedback systems. Adding the transcriptional or small RNA-mediated control has different effects. Transcriptional autorepression robustly reduces both the relative variance and persistence (lifetime) of fluctuations. Both benefits combine to reduce noise in downstream gene expression. Autorepression via small RNA can achieve more extreme noise reduction and typically has less effect on the mean expression level. However, it is often more costly to implement and is more sensitive to rate parameters. Theoretical lower limits on the relative variance are known to decrease slowly as a measure of the cost per molecule of mean expression increases. However, the proportional increase in cost to achieve substantial noise suppression can be different away from the optimal frontier—for transcriptional autorepression, it is frequently negligible.

A GFP-lacZ bicistronic reporter system for promoter analysis in environmental gram-negative bacteria

Here, we describe a bicistronic reporter system for the analysis of promoter activity in a variety of Gram-negative bacteria at both the population and single-cell levels. This synthetic genetic tool utilizes an artificial operon comprising the gfp and lacZ genes that are assembled in a suicide vector, which is integrated at specific sites within the chromosome of the target bacterium, thereby creating a monocopy reporter system. This tool was instrumental for the complete in vivo characterization of two promoters, Pb and Pc, that drive the expression of the benzoate and catechol degradation pathways, respectively, of the soil bacterium Pseudomonas putida KT2440. The parameterization of these promoters in a population (using β-galactosidase assays) and in single cells (using flow cytometry) was necessary to examine the basic numerical features of these systems, such as the basal and maximal levels and the induction kinetics in response to an inducer (benzoate). Remarkably, GFP afforded a view of the process at a much higher resolution compared with standard lacZ tests; changes in fluorescence faithfully reflected variations in the transcriptional regimes of individual bacteria. The broad host range of the vector/reporter platform is an asset for the characterization of promoters in different bacteria, thereby expanding the diversity of genomic chasses amenable to Synthetic Biology methods.

Relating network rigidity, time scale hierarchies, and expression noise in gene networks

Fluctuation-dissipation theorems can be used to predict characteristics of noise from characteristics of the macroscopic response of a system. In the case of gene networks, feedback control determines the "network rigidity," defined as resistance to slow external changes. We propose an effective Fokker-Planck equation that relates gene expression noise to topology and to time scales of the gene network. We distinguish between two situations referred to as normal and inverted time hierarchies. The noise can be buffered by network feedback in the first situation, whereas it can be topology independent in the latter.

Negative feedback through mRNA provides the best control of gene-expression noise

Genetically identical cell populations exposed to the same environment can exhibit considerable cell-to-cell variation in the levels of specific proteins. This variation or expression noise arises from the inherent stochastic nature of biochemical reactions that constitute gene expression. Negative feedback loops are common motifs in gene networks that reduce expression noise and intercellular variability in protein levels. Using stochastic models of gene expression we here compare different feedback architectures in their ability to reduce stochasticity in protein levels. A mathematically controlled comparison shows that in physiologically relevant parameter regimes, feedback regulation through the mRNA provides the best suppression of expression noise. Consistent with our theoretical results we find negative feedback loops though the mRNA in essential eukaryotic genes, where feedback is mediated via intron-derived microRNAs. Finally, we find that contrary to previous results, protein-mediated translational regulation may not always provide significantly better noise suppression than protein-mediated transcriptional regulation.

Kinetics in signal transduction pathways involving promiscuous oligomerizing receptors can be determined by receptor specificity: apoptosis induction by TRAIL

Here we show by computer modeling that kinetics and outcome of signal transduction in case of hetero-oligomerizing receptors of a promiscuous ligand largely depend on the relative amounts of its receptors. Promiscuous ligands can trigger the formation of nonproductive receptor complexes, which slows down the formation of active receptor complexes and thus can block signal transduction. Our model predicts that increasing the receptor specificity of the ligand without changing its binding parameters should result in faster receptor activation and enhanced signaling. We experimentally validated this hypothesis using the cytokine tumor necrosis factor-related apoptosis-inducing ligand (TRAIL) and its four membrane-bound receptors as an example. Bypassing ligand-induced receptor hetero-oligomerization by receptor-selective TRAIL variants enhanced the kinetics of receptor activation and augmented apoptosis. Our results suggest that control of signaling pathways by promiscuous ligands could result in apparent slow biological kinetics and blocking signal transmission. By modulating the relative amount of the different receptors for the ligand, signaling processes like apoptosis can be accelerated or decelerated and even inhibited. It also implies that more effective treatments using protein therapeutics could be achieved simply by altering specificity.

ON EXPLORING EFFECTS OF MOLECULAR NOISE IN A SIMPLE VIRAL INFECTION MODEL

Intrinsic and extrinsic noises are all believed to be important in the development and function of many living organisms. In this study, we investigate the sources of the intrinsic noise and the influence of the extrinsic noise on an intracellular viral infection system. The contribution of the intrinsic noise from each reaction is measured by means of a special form of stochastic differential equations (SDEs), chemical Langevin equation. The intrinsic noise of the system is a linear sum of the noise in each of the reactions. The intrinsic noise mainly arises from the degradation of mRNA and the transcription processes. We then study the effects of extrinsic noise by the means of a general form of SDE. It is found that the noise of the viral components grows logarithmically with the increasing noise intensities. The system is most susceptible to the noise in the virus assembly process. A high level of noise in this process can even inhibit the growth of the viruses. This study also demonstrates the utility of SDEs in analyzing genetic regulatory networks perturbed by either inherent or parametric stochasticity.

A simple negative interaction in the positive transcriptional feedback of a single gene is sufficient to produce reliable oscillations

Negative and positive transcriptional feedback loops are present in natural and synthetic genetic oscillators. A single gene with negative transcriptional feedback needs a time delay and sufficiently strong nonlinearity in the transmission of the feedback signal in order to produce biochemical rhythms. A single gene with only positive transcriptional feedback does not produce oscillations. Here, we demonstrate that this single-gene network in conjunction with a simple negative interaction can also easily produce rhythms. We examine a model comprised of two well-differentiated parts. The first is a positive feedback created by a protein that binds to the promoter of its own gene and activates the transcription. The second is a negative interaction in which a repressor molecule prevents this protein from binding to its promoter. A stochastic study shows that the system is robust to noise. A deterministic study identifies that the dynamics of the oscillator are mainly driven by two types of biomolecules: the protein, and the complex formed by the repressor and this protein. The main conclusion of this paper is that a simple and usual negative interaction, such as degradation, sequestration or inhibition, acting on the positive transcriptional feedback of a single gene is a sufficient condition to produce reliable oscillations. One gene is enough and the positive transcriptional feedback signal does not need to activate a second repressor gene. This means that at the genetic level an explicit negative feedback loop is not necessary. The model needs neither cooperative binding reactions nor the formation of protein multimers. Therefore, our findings could help to clarify the design principles of cellular clocks and constitute a new efficient tool for engineering synthetic genetic oscillators.

Quantifying negative feedback regulation by micro-RNAs

Micro-RNAs (miRNAs) play a crucial role in post-transcriptional gene regulation by pairing with target mRNAs to repress protein production. It has been shown that over one-third of human genes are targeted by miRNA. Although hundreds of miRNAs have been identified in mammalian genomes, the function of miRNA-based repression in the context of gene regulation networks still remains unclear. In this study, we explore the functional roles of feedback regulation by miRNAs. In a model where repression of translation occurs by sequestration of mRNA by miRNA, we find that miRNA and mRNA levels are anti-correlated, resulting in larger fluctuation in protein levels than theoretically expected assuming no correlation between miRNA and mRNA levels. If miRNA repression is due to a catalytic suppression of translation rates, we analytically show that the protein fluctuations can be strongly repressed with miRNA regulation. We also discuss how either of these modes may be relevant for cell function.

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.

Quantification of mRNA and protein and integration with protein turnover in a bacterium

Determination of the average cellular copy number of 400 proteins under different growth conditions and integration with protein turnover and absolute mRNA levels reveals the dynamics of protein expression in the genome-reduced bacterium Mycoplasma pneumoniae.

Our study provides a fine-grained, quantitative picture to unprecedented detail in an established model organism for systems-wide studies.

Our integrative approach reveals a novel, dynamic view on the processes, interactions and regulations underlying the central dogma pathway and the composition of protein complexes.

Simulations using our quantitative data on mRNA, protein and turnover show how an organism copes with stochastic noise in gene expression in vivo.

Our data serve as an important resource for colleagues both within our field of research and in related disciplines.

A hallmark of Systems Biology is the integration of diverse, large quantitative data sets with the aim to gain novel insights into how biological processes work. We measured individual mRNA and protein abundances as well as protein turnover in the bacterium Mycoplasma pneumoniae. This human pathogen is an ideal model organism for organism-wide studies. It can be readily cultured under laboratory conditions and it has a very small genome with only 690 protein-coding genes. This comparably low complexity allows for the exhaustive analysis of major cellular biomolecules avoiding constrains introduced by limitations of available analysis techniques.

Using a recently developed mass spectrometry-based approach, we determined the average cellular copy number for over 400 individual proteins under different growth and stress conditions. The 20 most abundant proteins, including Elongation factor Tu, cellular chaperones, and proteins involved in metabolizing glucose, the major energy source of M. pneumoniae account for nearly 44% of the total cellular protein mass. We observed abundance changes of many expected and several unexpected proteins in response to cellular stress, such as heat shock, DNA damage and osmotic stress, as well as along batch culture growth over 4 days.

Integration of the protein abundance data with quantitative mRNA measurements revealed a modest correlation between these two classes of biomolecules. However, for several classical stress-induced proteins, we observed a correlated induction of mRNA and protein in response to heat shock. A focused analysis of mRNA–protein abundance dynamics during batch culture growth suggested that the regulation of gene expression is largely decoupled from protein dynamics in M. pneumoniae, indicating extensive post-transcriptional and post-translational regulation influencing the cellular mRNA–protein ratios.

To investigate the factors influencing the cellular protein abundance, we measured individual protein turnover rates by mass spectrometry using a label-chase approach involving stable isotope-labelled amino acids. The average half-life of a protein in M. pneumoniae is 23 h. Based on the measured quantitative mRNA data, the protein abundances and their half-lives, we established an ordinary differential equations model for the estimation of individual in vivo protein degradation and translation efficiency rates. We found out that translation efficiency rather than protein turnover is the dominating factor influencing protein abundance. Using our abundance and turnover data, we additionally performed stochastic simulations of gene expression. We observed that long protein half-life and low translational efficiency buffers gene expression noise propagating from low cellular mRNA levels in vivo.

We compared the abundance ratios of proteins associating into complexes in vivo with their expected functional stoichiometries. We observed that for stable protein complexes, such as the GroEL/ES chaperonin or DNA gyrase, our measured abundance ratios reflected the expected subunit stoichiometries. More dynamic protein complexes, such as the DnaK/J/GrpE chaperone system or RNA polymerase, showed several unusual subunit ratios, pointing towards transient interaction of sub-stoichiometric subunits for function. A detailed, quantitative analysis of the ribosome, the largest cellular protein complex, revealed large abundance differences of the 51 subunits. This observation indicates a multi-functionality for several, abundant ribosomal proteins.

Finally, a comparison of the determined average cellular protein abundances with a different pathogenic bacterium, Leptospira interrogans, revealed that cellular protein abundances closely reflect their respective lifestyles.

Our study represents an organism-wide, quantitative analysis of cellular protein abundances. Integrating our proteomics data with determined mRNA levels and protein turnover rates reveals insights into the dynamic interplay and regulation of mRNA and proteins, the central biomolecules of a cell.

Biological function and cellular responses to environmental perturbations are regulated by a complex interplay of DNA, RNA, proteins and metabolites inside cells. To understand these central processes in living systems at the molecular level, we integrated experimentally determined abundance data for mRNA, proteins, as well as individual protein half-lives from the genome-reduced bacterium Mycoplasma pneumoniae. We provide a fine-grained, quantitative analysis of basic intracellular processes under various external conditions. Proteome composition changes in response to cellular perturbations reveal specific stress response strategies. The regulation of gene expression is largely decoupled from protein dynamics and translation efficiency has a higher regulatory impact on protein abundance than protein turnover. Stochastic simulations using in vivo data show how low translation efficiency and long protein half-lives effectively reduce biological noise in gene expression. Protein abundances are regulated in functional units, such as complexes or pathways, and reflect cellular lifestyles. Our study provides a detailed integrative analysis of average cellular protein abundances and the dynamic interplay of mRNA and proteins, the central biomolecules of a cell.

Negative auto-regulation increases the input dynamic-range of the arabinose system of Escherichia coli

Background

Gene regulation networks are made of recurring regulatory patterns, called network motifs. One of the most common network motifs is negative auto-regulation, in which a transcription factor represses its own production. Negative auto-regulation has several potential functions: it can shorten the response time (time to reach halfway to steady-state), stabilize expression against noise, and linearize the gene's input-output response curve. This latter function of negative auto-regulation, which increases the range of input signals over which downstream genes respond, has been studied by theory and synthetic gene circuits. Here we ask whether negative auto-regulation preserves this function also in the context of a natural system, where it is embedded within many additional interactions. To address this, we studied the negative auto-regulation motif in the arabinose utilization system of Escherichia coli, in which negative auto-regulation is part of a complex regulatory network.

Results

We find that when negative auto-regulation is disrupted by placing the regulator araC under constitutive expression, the input dynamic range of the arabinose system is reduced by 10-fold. The apparent Hill coefficient of the induction curve changes from about n = 1 with negative auto-regulation, to about n = 2 when it is disrupted. We present a mathematical model that describes how negative auto-regulation can increase input dynamic-range, by coupling the transcription factor protein level to the input signal.

Conclusions

Here we demonstrate that the negative auto-regulation motif in the native arabinose system of Escherichia coli increases the range of arabinose signals over which the system can respond. In this way, negative auto-regulation may help to increase the input dynamic-range while maintaining the specificity of cooperative regulatory systems. This function may contribute to explaining the common occurrence of negative auto-regulation in biological systems.

Impact of gene expression noise on organismal fitness and the efficacy of natural selection

Gene expression noise is a universal phenomenon across all life forms. Although beneficial under certain circumstances, expression noise is generally thought to be deleterious. However, neither the magnitude of the deleterious effect nor the primary mechanism of this effect is known. Here, we model the impact of expression noise on the fitness of unicellular organisms by considering the influence of suboptimal expressions of enzymes on the rate of biomass production and the energetic cost associated with imprecise amounts of protein synthesis. Our theoretical modeling and empirical analysis of yeast data show four findings. (i) Expression noise reduces the mean fitness of a cell by at least 25%, and this reduction cannot be substantially alleviated by gene overexpression. (ii) Higher sensitivity of fitness to the expression fluctuations of essential genes than nonessential genes creates stronger selection against noise in essential genes, resulting in a decrease in their noise. (iii) Reduction of expression noise by genome doubling offers a substantial fitness advantage to diploids over haploids, even in the absence of sex. (iv) Expression noise generates fitness variation among isogenic cells, which lowers the efficacy of natural selection similar to the effect of population shrinkage. Thus, expression noise renders organisms both less adapted and less adaptable. Because expression noise is only one of many manifestations of the stochasticity in cellular molecular processes, our results suggest a much more fundamental role of molecular stochasticity in evolution than is currently appreciated.

The role of incoherent microRNA-mediated feedforward loops in noise buffering

MicroRNAs are endogenous non-coding RNAs which negatively regulate the expression of protein-coding genes in plants and animals. They are known to play an important role in several biological processes and, together with transcription factors, form a complex and highly interconnected regulatory network. Looking at the structure of this network, it is possible to recognize a few overrepresented motifs which are expected to perform important elementary regulatory functions. Among them, a special role is played by the microRNA-mediated feedforward loop in which a master transcription factor regulates a microRNA and, together with it, a set of target genes. In this paper we show analytically and through simulations that the incoherent version of this motif can couple the fine-tuning of a target protein level with an efficient noise control, thus conferring precision and stability to the overall gene expression program, especially in the presence of fluctuations in upstream regulators. Among the other results, a nontrivial prediction of our model is that the optimal attenuation of fluctuations coincides with a modest repression of the target expression. This feature is coherent with the expected fine-tuning function and in agreement with experimental observations of the actual impact of a wide class of microRNAs on the protein output of their targets. Finally, we describe the impact on noise-buffering efficiency of the cross-talk between microRNA targets that can naturally arise if the microRNA-mediated circuit is not considered as isolated, but embedded in a larger network of regulations.

Gene regulatory networks and the role of robustness and stochasticity in the control of gene expression

In any given cell, thousands of genes are expressed and work in concert to ensure the cell's function, fitness, and survival. Each gene, in turn, must be expressed at the proper time and in the proper amounts to ensure the appropriate functional outcome. The regulation and expression of some genes are highly robust; their expression is controlled by invariable expression programs. For instance, developmental gene expression is extremely similar in a given cell type from one individual to another. The expression of other genes is more variable: Their levels are noisy and are different from cell to cell and from individual to individual. This can be highly beneficial in physiological responses to outside cues and stresses. Recent advances have enabled the analysis of differential gene expression at a systems level. Gene regulatory networks (GRNs) involving interactions between large numbers of genes and their regulators have been mapped onto graphic diagrams that are used to visualize the regulatory relationships. The further characterization of GRNs has already uncovered global principles of gene regulation. Together with synthetic network biology, such studies are starting to provide insights into the transcriptional mechanisms that cause robust versus stochastic gene expression and their relationships to phenotypic robustness and variability. Here, we discuss GRNs and their topological properties in relation to transcriptional and phenotypic outputs in development and organismal physiology.

Stochastic simulations of the tetracycline operon

Background

The tetracycline operon is a self-regulated system. It is found naturally in bacteria where it confers resistance to antibiotic tetracycline. Because of the performance of the molecular elements of the tetracycline operon, these elements are widely used as parts of synthetic gene networks where the protein production can be efficiently turned on and off in response to the presence or the absence of tetracycline. In this paper, we investigate the dynamics of the tetracycline operon. To this end, we develop a mathematical model guided by experimental findings. Our model consists of biochemical reactions that capture the biomolecular interactions of this intriguing system. Having in mind that small biological systems are subjects to stochasticity, we use a stochastic algorithm to simulate the tetracycline operon behavior. A sensitivity analysis of two critical parameters embodied this system is also performed providing a useful understanding of the function of this system.

Results

Simulations generate a timeline of biomolecular events that confer resistance to bacteria against tetracycline. We monitor the amounts of intracellular TetR2 and TetA proteins, the two important regulatory and resistance molecules, as a function of intrecellular tetracycline. We find that lack of one of the promoters of the tetracycline operon has no influence on the total behavior of this system inferring that this promoter is not essential for Escherichia coli. Sensitivity analysis with respect to the binding strength of tetracycline to repressor and of repressor to operators suggests that these two parameters play a predominant role in the behavior of the system. The results of the simulations agree well with experimental observations such as tight repression, fast gene expression, induction with tetracycline, and small intracellular TetR2 amounts.

Conclusions

Computer simulations of the tetracycline operon afford augmented insight into the interplay between its molecular components. They provide useful explanations of how the components and their interactions have evolved to best serve bacteria carrying this operon. Therefore, simulations may assist in designing novel gene network architectures consisting of tetracycline operon components.

Linearizer gene circuits with negative feedback regulation

Gene functional studies consist of phenotyping cells with altered gene expression. Improving the precision of current gene expression control techniques would enable more detailed studies of gene function. Here, we provide protocols for building synthetic gene constructs for tuning the expression of a gene in all the cells of a population precisely and uniformly, achieving expression levels proportional to the extracellular inducer concentration.

Stochastic approaches in systems biology

The discrete and random occurrence of chemical reactions far from thermodynamic equilibrium, and low copy numbers of chemical species, in systems biology necessitate stochastic approaches. This review is an effort to give the reader a flavor of the most important stochastic approaches relevant to systems biology. Notions of biochemical reaction systems and the relevant concepts of probability theory are introduced side by side. This leads to an intuitive and easy-to-follow presentation of a stochastic framework for modeling subcellular biochemical systems. In particular, we make an effort to show how the notion of propensity, the chemical master equation (CME), and the stochastic simulation algorithm arise as consequences of the Markov property. Most stochastic modeling reviews focus on stochastic simulation approaches--the exact stochastic simulation algorithm and its various improvements and approximations. We complement this with an outline of an analytical approximation. The most common formulation of stochastic models for biochemical networks is the CME. Although stochastic simulations are a practical way to realize the CME, analytical approximations offer more insight into the influence of randomness on system's behavior. Toward that end, we cover the chemical Langevin equation and the related Fokker-Planck equation and the two-moment approximation (2MA). Throughout the text, two pedagogical examples are used to key illustrate ideas. With extensive references to the literature, our goal is to clarify key concepts and thereby prepare the reader for more advanced texts.

Bimodal gene expression in noncooperative regulatory systems

Bimodality of gene expression, as a mechanism contributing to phenotypic diversity, enhances the survival of cells in a fluctuating environment. To date, the bimodal response of a gene regulatory system has been attributed to the cooperativity of transcription factor binding or to feedback loops. It has remained unclear whether noncooperative binding of transcription factors can give rise to bimodality in an open-loop system. We study a theoretical model of gene expression in a two-step cascade (a deterministically monostable system) in which the regulatory gene produces transcription factors that have a nonlinear effect on the activity of the target gene. We show that a unimodal distribution of transcription factors over the cell population can generate a bimodal steady-state output without cooperative transcription factor binding. We introduce a simple method of geometric construction that allows one to predict the onset of bimodality. The construction only involves the parameters of bursting of the regulatory gene and the dose-response curve of the target gene. Using this method, we show that the gene expression may switch between unimodal and bimodal as the concentration of inducers or corepressors is varied. These findings may explain the experimentally observed bimodal response of cascades consisting of a fluorescent protein reporter controlled by the tetracycline repressor. The geometric construction provides a useful tool for designing experiments and for interpretation of their results. Our findings may have important implications for understanding the strategies adopted by cell populations to survive in changing environments.

Design of regulation and dynamics in simple biochemical pathways

Complex regulation of biochemical pathways in a cell is brought about by the interaction of simpler regulatory structures. Among the basic regulatory designs, feedback inhibition of gene expression is the most common motif in gene regulation and a ubiquitous control structure found in nature. In this work, we have studied a common structural feature (delayed feedback) in gene organisation and shown, both theoretically and experimentally, its subtle but important functional role in gene expression kinetics in a negatively auto-regulated system. Using simple deterministic and stochastic models with varying levels of realism, we present detailed theoretical representations of negatively auto-regulated transcriptional circuits with increasing delays in the establishment of feedback of repression. The models of the circuits with and without delay are studied analytically as well as numerically for variation of parameters and delay lengths. The positive invariance, boundedness of the solutions, local and global asymptotic stability of both the systems around the unique positive steady state are studied analytically. Existence of transient temporal dynamics is shown mathematically. Comparison of the two types of model circuits shows that even though the long-term dynamics is stable and not affected by delays in repression, there is interesting variation in the transient dynamical features with increasing delays. Theoretical predictions are validated through experimentally constructed gene circuits of similar designs. This combined theoretical and experimental study helps delineate the opposing effects of delay-induced instability, and the stability-enhancing property of negative feedback in the pathway behaviour, and gives rationale for the abundance of similar designs in real biochemical pathways.

Fundamental limits on the suppression of molecular fluctuations

Negative feedback is common in biological processes and can increase a system’s stability to internal and external perturbations. But at the molecular level, control loops always involve signaling steps with finite rates for random births and deaths of individual molecules. By developing mathematical tools that merge control and information theory with physical chemistry we show that seemingly mild constraints on these rates place severe limits on the ability to suppress molecular fluctuations. Specifically, the minimum standard deviation in abundances decreases with the quartic root of the number of signaling events, making it extraordinarily expensive to increase accuracy. Our results are formulated in terms of experimental observables, and existing data show that cells use brute force when noise suppression is essential, e.g. transcribing regulatory genes 10,000s of times per cell cycle. The theory challenges conventional beliefs about biochemical accuracy and presents an approach to rigorously analyze poorly characterized biological systems.

Quantitative analysis of cellular metabolic dissipative, self-organized structures

One of the most important goals of the postgenomic era is understanding the metabolic dynamic processes and the functional structures generated by them. Extensive studies during the last three decades have shown that the dissipative self-organization of the functional enzymatic associations, the catalytic reactions produced during the metabolite channeling, the microcompartmentalization of these metabolic processes and the emergence of dissipative networks are the fundamental elements of the dynamical organization of cell metabolism. Here we present an overview of how mathematical models can be used to address the properties of dissipative metabolic structures at different organizational levels, both for individual enzymatic associations and for enzymatic networks. Recent analyses performed with dissipative metabolic networks have shown that unicellular organisms display a singular global enzymatic structure common to all living cellular organisms, which seems to be an intrinsic property of the functional metabolism as a whole. Mathematical models firmly based on experiments and their corresponding computational approaches are needed to fully grasp the molecular mechanisms of metabolic dynamical processes. They are necessary to enable the quantitative and qualitative analysis of the cellular catalytic reactions and also to help comprehend the conditions under which the structural dynamical phenomena and biological rhythms arise. Understanding the molecular mechanisms responsible for the metabolic dissipative structures is crucial for unraveling the dynamics of cellular life.

Interplay between intrinsic noise and the stochasticity of the cell cycle in bacterial colonies

Herein we report on the effects that different stochastic contributions induce in bacterial colonies in terms of protein concentration and production. In particular, we consider for what we believe to be the first time cell-to-cell diversity due to the unavoidable randomness of the cell-cycle duration and its interplay with other noise sources. To that end, we model a recent experimental setup that implements a protein dilution protocol by means of division events to characterize the gene regulatory function at the single cell level. This approach allows us to investigate the effect of different stochastic terms upon the total randomness experimentally reported for the gene regulatory function. In addition, we show that the interplay between intrinsic fluctuations and the stochasticity of the cell-cycle duration leads to different constructive roles. On the one hand, we show that there is an optimal value of protein concentration (alternatively an optimal value of the cell cycle phase) such that the noise in protein concentration attains a minimum. On the other hand, we reveal that there is an optimal value of the stochasticity of the cell cycle duration such that the coherence of the protein production with respect to the colony average production is maximized. The latter can be considered as a novel example of the recently reported phenomenon of diversity induced resonance.

Counter-intuitive stochastic behavior of simple gene circuits with negative feedback

It has often been taken for granted that negative feedback loops in gene regulation work as homeostatic control mechanisms. If one increases the regulation strength a less noisy signal is to be expected. However, recent theoretical studies have reported the exact contrary, counter-intuitive observation, which has left a question mark over the relationship between negative feedback loops and noise. We explore and systematically analyze several minimal models of gene regulation, where a transcriptional repressor negatively regulates its own expression. For models including a quasi-steady-state assumption, we identify processes that buffer noise change (RNA polymerase binding) or accentuate it (repressor dimerization) alongside increasing feedback strength. Moreover, we show that lumping together transcription and translation in simplified models clearly underestimates the impact of negative feedback strength on the system's noise. In contrast, in systems without a quasi-steady-state assumption, noise always increases with negative feedback strength. Hence, subtle mathematical properties and model assumptions yield different types of noise profiles and, by consequence, previous studies have simultaneously reported decrease, increase or persistence of noise levels with increasing feedback. We discuss our findings in terms of separation of timescales and time correlations between molecular species distributions, extending current theoretical findings on the topic and allowing us to propose what we believe new ways to better characterize noise.

Transcriptional feedbacks in mammalian signal transduction pathways facilitate rapid and reliable protein induction

Signal transduction pathways translate the cellular context into context-dependent expression of genes. In response to extracellular stimuli, proteins have to be up-regulated quickly and reliably. However, rapid and reliable control of target genes by a signalling pathway faces two major challenges. Firstly, swift changes in protein levels require short-lived proteins, which is not resource-optimal. Secondly, gene expression is an intrinsically noisy process, and fluctuations in the protein numbers are likely to reduce the functionality of the proteins. Mammalian signalling pathways frequently induce the transcription of their own inhibitors, resulting in negative feedback regulation. However, the functional role of these transcriptional feedbacks in mammalian signal transduction is unclear. Here, we analyse a mathematical model of a prototypical signalling pathway, the MAPK cascade, in order to investigate how transcriptional negative feedbacks may help to overcome the challenge of fast and reliable gene induction. It is shown that a transcriptional negative feedback helps to decouple protein stability and response times, thus allowing for swift up-regulation even of long-lived proteins. Furthermore, transcriptional negative feedbacks filter out the extrinsic component of gene expression noise, which dominates the uncertainty in gene expression in mammalian cells, thus making gene expression more reliable. Model analysis predicts that both goals can be achieved if (i) proteins and mRNAs of the feedback regulators and (ii) mRNAs of all targets are short-lived. These predictions are confirmed by large-scale measurements of mRNA and protein half-lives. Therefore, the design of the mammalian signal transduction network with its rapid feedback inhibition allows for swift and reliable target gene expression.

Phenotypic impact of regulatory noise in cellular stress-response pathways

Recent studies indicate that intrinsic promoter-mediated gene expression noise can confer a selective advantage under acute environmental stress by providing beneficial phenotypic diversity within cell populations. To investigate how extrinsic gene expression noise impacts the fitness of cell populations under stress, we engineered two nearly isogenic budding yeast strains; one carrying a two-step regulatory cascade that allows for precise control of the noise transmitted from a transcriptional regulator to a downstream stress-inducing gene, and one carrying a network with low constant upstream noise. The fitness and gene expression of these strains were compared under acute and prolonged stress exposure. Using a phenomenological modeling approach, we predicted that increased noise should confer a fitness advantage under high stress conditions, but reciprocally reduce the resistance of the population to low stress. The model also predicted that extrinsic noise might serve as a basis for phenotypic plasticity whereby gene expression distributions are modulated in response to prolonged stress. Experimentally, we confirmed the predicted differential fitness advantage of extrinsic noise under acute stress, as well as the predicted modulation of gene expression under prolonged stress. However, contrary to model predictions, strains with low and high extrinsic noise showed very similar adaptive responses to prolonged stress. This suggests that while phenotypic heterogeneity generated by noise in regulatory signals can confer increased robustness to acute stress, it is not a requirement for the observed long-term phenotypic plasticity.

Tuning and controlling gene expression noise in synthetic gene networks

Synthetic gene networks can be used to control gene expression and cellular phenotypes in a variety of applications. In many instances, however, such networks can behave unreliably due to gene expression noise. Accordingly, there is a need to develop systematic means to tune gene expression noise, so that it can be suppressed in some cases and harnessed in others, e.g. in cellular differentiation to create population-wide heterogeneity. Here, we present a method for controlling noise in synthetic eukaryotic gene expression systems, utilizing reduction of noise levels by TATA box mutations and noise propagation in transcriptional cascades. Specifically, we introduce TATA box mutations into promoters driving TetR expression and show that these mutations can be used to effectively tune the noise of a target gene while decoupling it from the mean, with negligible effects on the dynamic range and basal expression. We apply mathematical and computational modeling to explain the experimentally observed effects of TATA box mutations. This work, which highlights some important aspects of noise propagation in gene regulatory cascades, has practical implications for implementing gene expression control in synthetic gene networks.

Antiviral response dictated by choreographed cascade of transcription factors

The dendritic cell (DC) is a master regulator of immune responses. Pathogenic viruses subvert normal immune function in DCs through the expression of immune antagonists. Understanding how these antagonists interact with the host immune system requires knowledge of the underlying genetic regulatory network that operates during an uninhibited antiviral response. To isolate and identify this network, we studied DCs infected with Newcastle disease virus, which is able to stimulate innate immunity and DC maturation through activation of RIG-I signaling, but lacks the ability to evade the human IFN response. To analyze this experimental model, we developed a new approach integrating genome-wide expression kinetics and time-dependent promoter analysis. We found that the genetic program underlying the antiviral cell-state transition during the first 18 h postinfection could be explained by a single convergent regulatory network. Gene expression changes were driven by a stepwise multifactor cascading control mechanism, where the specific transcription factors controlling expression changed over time. Within this network, most individual genes were regulated by multiple factors, indicating robustness against virus-encoded immune evasion genes. In addition to effectively recapitulating current biological knowledge, we predicted, and validated experimentally, antiviral roles for several novel transcription factors. More generally, our results show how a genetic program can be temporally controlled through a single regulatory network to achieve the large-scale genetic reprogramming characteristic of cell-state transitions.