Combinatorial gene regulation using auto-regulation

Holimap: an accurate and efficient method for solving stochastic gene network dynamics

Gene-gene interactions are crucial to the control of sub-cellular processes but our understanding of their stochastic dynamics is hindered by the lack of simulation methods that can accurately and efficiently predict how the distributions of gene product numbers vary across parameter space. To overcome these difficulties, here we present Holimap (high-order linear-mapping approximation), an approach that approximates the protein or mRNA number distributions of a complex gene regulatory network by the distributions of a much simpler reaction system. We demonstrate Holimap's computational advantages over conventional methods by applying it to predict the stochastic time-dependent dynamics of various gene networks, including transcriptional networks ranging from simple autoregulatory loops to complex randomly connected networks, post-transcriptional networks, and post-translational networks. Holimap is ideally suited to study how the intricate network of gene-gene interactions results in precise coordination and control of gene expression.

The Arabidopsis HDZIP class II transcription factor ABA INSENSITIVE TO GROWTH 1 functions in leaf development

Leaf laminar growth and adaxial-abaxial boundary formation are fundamental outcomes of plant development. Boundary and laminar growth coordinate the further patterning and growth of the leaf, directing the differentiation of cell types within the top and bottom domains and promoting initiation of lateral organs along their adaxial or abaxial axis. Leaf adaxial-abaxial polarity specification and laminar outgrowth are regulated by two transcription factors, REVOLUTA (REV) and KANADI (KAN). ABA INSENSITIVE TO GROWTH 1 (ABIG1) encodes a HOMEODOMAIN-LEUCINE ZIPPER (HD-ZIP) class II transcription factor and is a direct target of the adaxial-abaxial regulators REV and KAN. To investigate the role of ABIG1 in leaf development and in the establishment of polarity, we examined the phenotypes of both gain-of-function and loss-of-function mutants. Through genetic interaction analysis with REV and KAN mutants, we determined that ABIG1 plays a role in leaf laminar growth as well as in adaxial-abaxial polarity establishment. Genetic and physical interaction assays showed that ABIG1 interacts with the transcriptional TOPLESS corepressor. This study provides new evidence that ABIG1, another HD-ZIP II, facilitates growth through the corepressor TOPLESS.

Bistability in cell signalling and its significance in identifying potential drug targets

MOTIVATION

Bistability is one of the salient dynamical features in various all-or-none kinds of decision-making processes. The presence of bistability in a cell signalling network plays a key role in input-output (I/O) relation. Our study is aiming to capture and emphasise the role of motif structure influencing the I/O relation between two nodes in the context of bistability. Here, a model-based analysis is made to investigate the critical conditions responsible for the emergence of different bistable protein-protein interaction (PPI) motifs and their possible applications to find the potential drug targets.

RESULTS

The global sensitivity analysis is used to identify sensitive parameters and their role in maintaining the bistability. Additionally, the bistable switching through hysteresis is explored to develop an understanding of the underlying mechanisms involved in the cell signalling processes, when significant motifs exhibiting bistability have emerged. Further, we elaborate the application of the results by the implication of the emerged PPI motifs to identify potential drug-targets in three cancer networks, which is validated with existing databases. The influence of stochastic perturbations that could hinder desired functionality of any signalling networks is also described here.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Epistatic Effect of Regulators to the Adaptive Growth of Escherichia coli

Bacteria survive in the environment with three steps: a sensing environmental conditions, a responding to sensed signals, and an adaptation for proper survival in the environment. An adapting bacterial cell occurs cell division to increase the number of sister cells, termed adaptive growth. Two-component systems (TCSs), representing the main bacterial signal transduction systems, consist of a pair of one sensor kinase (SK) and one response regulator (RR), and RR genes are abundant in most bacterial genomes as part of the core genome. The OmpR gene family, a group of RR genes, is conserved in 95% of known bacterial genomes. The Escherichia coli genome has an estimated 34 RR genes in total, including 14 genes of OmpR family genes. To reveal the contribution of TCSs for fast growth as an adaptive growth strategy of E. coli, we isolated a set of gene knockout strains by using newly developed genome editing technology, the HoSeI (Homologous Sequence Integration) method, based on CRISPR-Cas9. The statistics of single cell observation show a knockout of an arbitrary pair of phoP, phoB, and ompR genes, stably expressed by positive feedback regulation, dramatically inhibit the optimum adaptive growth of E. coli. These insights suggest that the adaptive growth of bacteria is fulfilled by the optimum high intracellular level of regulators acquired during growth under environmental conditions.

Translational control of gene expression via interacting feedback loops

Translation is a key step in the synthesis of proteins. Accordingly, cells have evolved an intricate array of control mechanisms to regulate this process. By constructing a multicomponent mathematical framework we uncover how translation may be controlled via interacting feedback loops. Our results reveal that this interplay gives rise to a remarkable range of protein synthesis dynamics, including oscillations, step change, and bistability. This suggests that cells may have recourse to a much richer set of control mechanisms than was previously understood.

Overcoming the Cost of Positive Autoregulation by Accelerating the Response with a Coupled Negative Feedback

A fundamental trade-off between rapid response and optimal expression of genes below cytotoxic levels exists for many signaling circuits, particularly for positively autoregulated systems with an inherent response delay. Here, we describe a regulatory scheme in the E. coli PhoB-PhoR two-component system, which overcomes the cost of positive feedback and achieves both fast and optimal steadystate response for maximal fitness across different environments. Quantitation of the cellular activities enables accurate modeling of the response dynamics to describe how requirements for optimal protein concentrations place limits on response speed. An observed fast response that exceeds the limit led to the prediction and discovery of a coupled negative autoregulation, which allows fast gene expression without increasing steady-state levels. We demonstrate the fitness advantages for the coupled feedbacks in both dynamic and stable environments. Such regulatory schemes offer great flexibility for accurate control of gene expression levels and dynamics upon environmental changes.

Positive autoregulation of transcription produces a delayed response. Gao and Stock describe the limit of response delay caused by requirements of optimal protein levels in the PhoBR twocomponent system. Coupled negative autoregulation is discovered to allow a strong promoter for fast response without incurring cost of increasing protein expression levels.

Integrative transcriptomic analysis suggests new autoregulatory splicing events coupled with nonsense-mediated mRNA decay

Nonsense-mediated decay (NMD) is a eukaryotic mRNA surveillance system that selectively degrades transcripts with premature termination codons (PTC). Many RNA-binding proteins (RBP) regulate their expression levels by a negative feedback loop, in which RBP binds its own pre-mRNA and causes alternative splicing to introduce a PTC. We present a bioinformatic analysis integrating three data sources, eCLIP assays for a large RBP panel, shRNA inactivation of NMD pathway, and shRNA-depletion of RBPs followed by RNA-seq, to identify novel such autoregulatory feedback loops. We show that RBPs frequently bind their own pre-mRNAs, their exons respond prominently to NMD pathway disruption, and that the responding exons are enriched with nearby eCLIP peaks. We confirm previously proposed models of autoregulation in SRSF7 and U2AF1 genes and present two novel models, in which (i) SFPQ binds its mRNA and promotes switching to an alternative distal 3'-UTR that is targeted by NMD, and (ii) RPS3 binding activates a poison 5'-splice site in its pre-mRNA that leads to a frame shift and degradation by NMD. We also suggest specific splicing events that could be implicated in autoregulatory feedback loops in RBM39, HNRNPM, and U2AF2 genes. The results are available through a UCSC Genome Browser track hub.

Emergent Properties in Complex Synthetic Bacterial Promoters

Regulation of gene expression in bacteria results from the interplay between hundreds of transcriptional factors (TFs) at target promoters. However, how the arrangement of binding sites for TFs generates the regulatory logic of promoters is not well-known. Here, we generated and fully characterized a library of synthetic complex promoters for the global regulators, CRP and IHF, in Escherichia coli, which are formed by a weak -35/-10 consensus sequence preceded by four combinatorial binding sites for these two TFs. Using this approach, we found that while cis-elements for CRP preferentially activate promoters when located immediately upstream of the promoter consensus, binding sites for IHF mainly function as "UP" elements and stimulate transcription in several different architectures in the absence of this protein. However, the combination of CRP- and IHF-binding sites resulted in emergent properties in these complex promoters, where the activity of combinatorial promoters cannot be predicted from the individual behavior of its components. Taken together, the results presented here add to the information on architecture-logic of complex promoters in bacteria.

Deconstructing a multiple antibiotic resistance regulation through the quantification of its input function

Many essential bacterial responses present complex transcriptional regulation of gene expression. To what extent can the study of these responses substantiate the logic of their regulation? Here, we show how the input function of the genes constituting the response, i.e., the information of how their transcription rates change as function of the signals acting on the regulators, can serve as a quantitative tool to deconstruct the corresponding regulatory logic. To demonstrate this approach, we consider the multiple antibiotic resistance (mar) response in Escherichia coli. By characterizing the input function of its representative genes in wild-type and mutant bacteria, we recognize a dual autoregulation motif as main determinant of the response, which is further adjusted by the interplay with other regulators. We show that basic attributes, like its reaction to a wide range of stress or its moderate expression change, are associated with a strong negative autoregulation, while others, like the buffering of metabolic signals or the lack of memory to previous stress, are related to a weak positive autoregulation. With a mathematical model of the input functions, we identify some constraints fixing the molecular attributes of the regulators, and also notice the relevance of the bicystronic architecture harboring the dual autoregulation that is unique in E. coli. The input function emerges then as a tool to disentangle the rationale behind most of the attributes defining the mar phenotype. Overall, the present study supports the value of characterizing input functions to deconstruct the complexity of regulatory architectures in prokaryotic and eukaryotic systems.

Many cellular responses result from the integration of numerous regulatory signals. To deconstruct the regulation of one of these responses, which enables resistance to multiple antibiotics in Escherichia coli, a team led by Juan F. Poyatos at the National Center for Biotechnology in Madrid studied the response input function by combining theoretical models and experiments. This function quantifies the rate of transcription of the genes constituting the response with respect to the signals acting on its cognate regulators. By examining how the shape of the function changes in different situations, e.g., when a given regulator is mutated, the team identified the implications for the specificity and dynamics of the response of a dual autoregulation at the core of the control architecture. The use of input functions as quantitative tools allows us to reverse engineer the complex regulations that dictate essential physiological functions in both prokaryotic and eukaryotic cells.

Heterodimer Autorepression Loop: A Robust and Flexible Pulse-Generating Genetic Module

We investigate the dynamics of the heterodimer autorepression loop (HAL), a small genetic module in which a protein A acts as an autorepressor and binds to a second protein B to form an AB dimer. For suitable values of the rate constants, the HAL produces pulses of A alternating with pulses of B. By means of analytical and numerical calculations, we show that the duration of A pulses is extremely robust against variation of the rate constants while the duration of the B pulses can be flexibly adjusted. The HAL is thus a minimal genetic module generating robust pulses with a tunable duration, an interesting property for cellular signaling.

Engineering Synthetic cis-Regulatory Elements for Simultaneous Recognition of Three Transcriptional Factors in Bacteria

Recognition of cis-regulatory elements by transcription factors (TF) at target promoters is crucial to gene regulation in bacteria. In this process, binding of TFs to their cognate sequences depends on a set of physical interactions between these proteins and specific nucleotides in the operator region. Previously, we showed that in silico optimization algorithms are able to generate short sequences that are recognized by two different TFs of Escherichia coli, namely, CRP and IHF, thus generating an AND logic gate. Here, we expanded this approach in order to engineer DNA sequences that can be simultaneously recognized by three unrelated TFs (CRP, IHF, and Fis). Using in silico optimization and experimental validation strategies, we were able to obtain a candidate promoter (Plac-CFI1) regulated by only two TFs with an AND logic, thus demonstrating a limitation in the design. Subsequently, we modified the algorithm to allow the optimization of extended sequences, and were able to design two synthetic promoters (PCFI20-1 and PCFI22-5) that were functional in vivo. Expression assays in E. coli mutant strains for each TF revealed that while CRP positively regulates the promoter activities, IHF and Fis are strong repressors of both the promoter variants. Taken together, our results demonstrate the potential of in silico strategies in bacterial synthetic promoter engineering. Furthermore, the study also shows how small modifications in cis-regulatory elements can drastically affect the final logic of the resulting promoter.

Molecular-Level Tuning of Cellular Autonomy Controls the Collective Behaviors of Cell Populations

A rigorous understanding of how multicellular behaviors arise from the actions of single cells requires quantitative frameworks that bridge the gap between genetic circuits, the arrangement of cells in space, and population-level behaviors. Here, we provide such a framework for a ubiquitous class of multicellular systems-namely, "secrete-and-sense cells" that communicate by secreting and sensing a signaling molecule. By using formal, mathematical arguments and introducing the concept of a phenotype diagram, we show how these cells tune their degrees of autonomous and collective behavior to realize distinct single-cell and population-level phenotypes; these phenomena have biological analogs, such as quorum sensing or paracrine signaling. We also define the "entropy of population," a measurement of the number of arrangements that a population of cells can assume, and demonstrate how a decrease in the entropy of population accompanies the formation of ordered spatial patterns. Our conceptual framework ties together diverse systems, including tissues and microbes, with common principles.

Dynamics of Transcription Factor Binding Site Evolution

Evolution of gene regulation is crucial for our understanding of the phenotypic differences between species, populations and individuals. Sequence-specific binding of transcription factors to the regulatory regions on the DNA is a key regulatory mechanism that determines gene expression and hence heritable phenotypic variation. We use a biophysical model for directional selection on gene expression to estimate the rates of gain and loss of transcription factor binding sites (TFBS) in finite populations under both point and insertion/deletion mutations. Our results show that these rates are typically slow for a single TFBS in an isolated DNA region, unless the selection is extremely strong. These rates decrease drastically with increasing TFBS length or increasingly specific protein-DNA interactions, making the evolution of sites longer than ∼ 10 bp unlikely on typical eukaryotic speciation timescales. Similarly, evolution converges to the stationary distribution of binding sequences very slowly, making the equilibrium assumption questionable. The availability of longer regulatory sequences in which multiple binding sites can evolve simultaneously, the presence of “pre-sites” or partially decayed old sites in the initial sequence, and biophysical cooperativity between transcription factors, can all facilitate gain of TFBS and reconcile theoretical calculations with timescales inferred from comparative genomics.

Evolution has produced a remarkable diversity of living forms that manifests in qualitative differences as well as quantitative traits. An essential factor that underlies this variability is transcription factor binding sites, short pieces of DNA that control gene expression levels. Nevertheless, we lack a thorough theoretical understanding of the evolutionary times required for the appearance and disappearance of these sites. By combining a biophysically realistic model for how cells read out information in transcription factor binding sites with model for DNA sequence evolution, we explore these timescales and ask what factors crucially affect them. We find that the emergence of binding sites from a random sequence is generically slow under point and insertion/deletion mutational mechanisms. Strong selection, sufficient genomic sequence in which the sites can evolve, the existence of partially decayed old binding sites in the sequence, as well as certain biophysical mechanisms such as cooperativity, can accelerate the binding site gain times and make them consistent with the timescales suggested by comparative analyses of genomic data.

Impact of the cell division cycle on gene circuits

In growing cells, protein synthesis and cell growth are typically not synchronous, and, thus, protein concentrations vary over the cell division cycle. We have developed a theoretical description of genetic regulatory systems in bacteria that explicitly considers the cell division cycle to investigate its impact on gene expression. We calculate the cell-to-cell variations arising from cells being at different stages in the division cycle for unregulated genes and for basic regulatory mechanisms. These variations contribute to the extrinsic noise observed in single-cell experiments, and are most significant for proteins with short lifetimes. Negative autoregulation buffers against variation of protein concentration over the division cycle, but the effect is found to be relatively weak. Stronger buffering is achieved by an increased protein lifetime. Positive autoregulation can strongly amplify such variation if the parameters are set to values that lead to resonance-like behaviour. For cooperative positive autoregulation, the concentration variation over the division cycle diminishes the parameter region of bistability and modulates the switching times between the two stable states. The same effects are seen for a two-gene mutual-repression toggle switch. By contrast, an oscillatory circuit, the repressilator, is only weakly affected by the division cycle.

Signal integration by the CYP1A1 promoter--a quantitative study

Genes involved in detoxification of foreign compounds exhibit complex spatiotemporal expression patterns in liver. Cytochrome P450 1A1 (CYP1A1), for example, is restricted to the pericentral region of liver lobules in response to the interplay between aryl hydrocarbon receptor (AhR) and Wnt/β-catenin signaling pathways. However, the mechanisms by which the two pathways orchestrate gene expression are still poorly understood. With the help of 29 mutant constructs of the human CYP1A1 promoter and a mathematical model that combines Wnt/β-catenin and AhR signaling with the statistical mechanics of the promoter, we systematically quantified the regulatory influence of different transcription factor binding sites on gene induction within the promoter. The model unveils how different binding sites cooperate and how they establish the promoter logic; it quantitatively predicts two-dimensional stimulus-response curves. Furthermore, it shows that crosstalk between Wnt/β-catenin and AhR signaling is crucial to understand the complex zonated expression patterns found in liver lobules. This study exemplifies how statistical mechanical modeling together with combinatorial reporter assays has the capacity to disentangle the promoter logic that establishes physiological gene expression patterns.

Mathematical modeling of the apo and holo transcriptional regulation in Escherichia coli

Transcription factors can bind to DNA either with their effector bound (holo conformation), or as free proteins (apo conformation).

Stochastic oscillations induced by intrinsic fluctuations in a self-repressing gene

Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Thus, it is important to understand how regularity can emerge from noise. Here, we study the stochastic dynamics of a self-repressing gene with arbitrarily long or short response time. We find that when the mRNA and protein half-lives are approximately equal to the gene response time, fluctuations can induce relatively regular oscillations in the protein concentration. To gain insight into this phenomenon at the crossroads of determinism and stochasticity, we use an intermediate theoretical approach, based on a moment-closure approximation of the master equation, which allows us to take into account the binary character of gene activity. We thereby obtain differential equations that describe how nonlinearity can feed-back fluctuations into the mean-field equations to trigger oscillations. Finally, our results suggest that the self-repressing Hes1 gene circuit exploits this phenomenon to generate robust oscillations, inasmuch as its time constants satisfy precisely the conditions we have identified.

Expanding the logic of bacterial promoters using engineered overlapping operators for global regulators

The understanding of how the architecture of cis-regulatory elements at bacterial promoters determines their final output is of central interest in modern biology. In this work, we attempt to gain insight into this process by analyzing complex promoter architectures in the model organism Escherichia coli. By focusing on the relationship between different TFs at the genomic scale in terms of their binding site arrangement and their effect on the target promoters, we found no strong constraint limiting the combinatorial assembly of TF pairs in E. coli. More strikingly, overlapping binding sites were found equally associated with both equivalent (both TFs have the same effect on the promoter) and opposite (one TF activates while the other repress the promoter) effects on gene expression. With this information on hand, we set an in silico approach to design overlapping sites for three global regulators (GRs) of E. coli, specifically CRP, Fis, and IHF. Using random sequence assembly and an evolutionary algorithm, we were able to identify potential overlapping operators for all TF pairs. In order to validate our prediction, we constructed two lac promoter variants containing overlapping sites for CRP and IHF designed in silico. By assaying the synthetic promoters using a GFP reporter system, we demonstrated that these variants were functional and activated by CRP and IHF in vivo. Taken together, presented results add new information on the mechanisms of signal integration in bacterial promoters and provide new strategies for the engineering of synthetic regulatory circuits in bacteria.

Secreting and sensing the same molecule allows cells to achieve versatile social behaviors

Cells that secrete and sense the same signaling molecule are ubiquitous. To uncover the functional capabilities of the core "secrete-and-sense" circuit motif shared by these cells, we engineered yeast to secrete and sense the mating pheromone. Perturbing each circuit element revealed parameters that control the degree to which the cell communicated with itself versus with its neighbors. This tunable interplay of self-communication and neighbor communication enables cells to span a diverse repertoire of cellular behaviors. These include a cell being asocial by responding only to itself and social through quorum sensing, and an isogenic population of cells splitting into social and asocial subpopulations. A mathematical model explained these behaviors. The versatility of the secrete-and-sense circuit motif may explain its recurrence across species.

FOXM1 and its oncogenic signaling in pancreatic cancer pathogenesis

Pancreatic cancer is a devastating disease with an overall 5-year survival rate less than 5%. Multiple signaling pathways are implicated in the pathogenesis of pancreatic cancer, such as Wnt/β-catenin, Notch, Hedgehog, hypoxia-inducible factor, signal transducer and activator of transcription, specificity proteins/Krüppel-like factors, and Forkhead box (FOX). Recently, increasing evidence has demonstrated that the transcription factor FOXM1 plays important roles in the initiation, progression, and metastasis of a variety of human tumors, including pancreatic cancer. In this review, we focus on the current understanding of the molecular pathogenesis of pancreatic cancer with a special focus on the function and regulation of FOXM1 and rationale for FOXM1 as a novel molecular target for pancreatic cancer prevention and treatment.

Taking into account nucleosomes for predicting gene expression

The eukaryotic genome is organized in a chain of nucleosomes that consist of 145-147 bp of DNA wrapped around a histone octamer protein core. Binding of transcription factors (TF) to nucleosomal DNA is frequently impeded, which makes it a challenging task to calculate TF occupancy at a given regulatory genomic site for predicting gene expression. Here, we review methods to calculate TF binding to DNA in the presence of nucleosomes. The main theoretical problems are (i) the computation speed that is becoming a bottleneck when partial unwrapping of DNA from the nucleosome is considered, (ii) the perturbation of the binding equilibrium by the activity of ATP-dependent chromatin remodelers, which translocate nucleosomes along the DNA, and (iii) the model parameterization from high-throughput sequencing data and fluorescence microscopy experiments in living cells. We discuss strategies that address these issues to efficiently compute transcription factor binding in chromatin.

Neurogenin3 cooperates with Foxa2 to autoactivate its own expression

The transcription factor Neurogenin3 functions as a master regulator of endocrine pancreas formation, and its deficiency leads to the development of diabetes in humans and mice. In the embryonic pancreas, Neurogenin3 is transiently expressed at high levels for a narrow time window to initiate endocrine differentiation in scattered progenitor cells. The mechanisms controlling these rapid and robust changes in Neurogenin3 expression are poorly understood. In this study, we characterize a Neurogenin3 positive autoregulatory loop whereby this factor may rapidly induce its own levels. We show that Neurogenin3 binds to a conserved upstream fragment of its own gene, inducing deposition of active chromatin marks and the activation of Neurog3 transcription. Additionally, we show that the broadly expressed endodermal forkhead factors Foxa1 and Foxa2 can cooperate synergistically to amplify Neurogenin3 autoregulation in vitro. However, only Foxa2 colocalizes with Neurogenin3 in pancreatic progenitors, thus indicating a primary role for this factor in regulating Neurogenin3 expression in vivo. Furthermore, in addition to decreasing Neurog3 autoregulation, inhibition of Foxa2 by RNA interference attenuates Neurogenin3-dependent activation of the endocrine developmental program in cultured duct mPAC cells. Hence, these data uncover the potential functional cooperation between the endocrine lineage-determining factor Neurogenin3 and the widespread endoderm progenitor factor Foxa2 in the implementation of the endocrine developmental program in the pancreas.

Catching transcriptional regulation by thermostatistical modeling

Gene expression is frequently regulated by multiple transcription factors (TFs). Thermostatistical methods allow for a quantitative description of interactions between TFs, RNA polymerase and DNA, and their impact on the transcription rates. We illustrate three different scales of the thermostatistical approach: the microscale of TF molecules, the mesoscale of promoter energy levels and the macroscale of transcriptionally active and inactive cells in a cell population. We demonstrate versatility of combinatorial transcriptional activation by exemplifying logic functions, such as AND and OR gates. We discuss a metric for cell-to-cell transcriptional activation variability known as Fermi entropy. Suitability of thermostatistical modeling is illustrated by describing the experimental data on transcriptional induction of NFκB and the c-Fos protein.

VirB-mediated positive feedback control of the virulence gene regulatory cascade of Shigella flexneri

Shigella flexneri is a facultative intracellular pathogen that relies on a type III secretion system and its associated effector proteins to cause bacillary dysentery in humans. The genes that encode this virulence system are located on a 230-kbp plasmid and are transcribed in response to thermal, osmotic, and pH signals that are characteristic of the human lower gut. The virulence genes are organized within a regulatory cascade, and the nucleoid-associated protein H-NS represses each of the key promoters. Transcription derepression depends first on the VirF AraC-like transcription factor, a protein that antagonizes H-NS-mediated repression at the intermediate regulatory gene virB. The VirB protein in turn remodels the H-NS-DNA nucleoprotein complexes at the promoters of the genes encoding the type III secretion system and effector proteins, causing these genes to become derepressed. In this study, we show that the VirB protein also positively regulates the expression of its own gene (virB) via a cis-acting regulatory sequence. In addition, VirB positively regulates the gene coding for the VirF protein. This study reveals two hitherto uncharacterized feedback regulatory loops in the S. flexneri virulence cascade that provide a mechanism for the enhanced expression of the principal virulence regulatory genes.

Optimizing information flow in small genetic networks. III. A self-interacting gene

Living cells must control the reading out or "expression" of information encoded in their genomes, and this regulation often is mediated by transcription factors--proteins that bind to DNA and either enhance or repress the expression of nearby genes. But the expression of transcription factor proteins is itself regulated, and many transcription factors regulate their own expression in addition to responding to other input signals. Here we analyze the simplest of such self-regulatory circuits, asking how parameters can be chosen to optimize information transmission from inputs to outputs in the steady state. Some nonzero level of self-regulation is almost always optimal, with self-activation dominant when transcription factor concentrations are low and self-repression dominant when concentrations are high. In steady state the optimal self-activation is never strong enough to induce bistability, although there is a limit in which the optimal parameters are very close to the critical point.

Comparison and calibration of different reporters for quantitative analysis of gene expression

Absolute levels of gene expression in bacteria are observed to vary over as much as six orders of magnitude. Thermodynamic models have been proposed as a tool to describe the expression levels of a given transcriptional circuit. In this context, it is essential to understand both the limitations and linear range of the different methods for measuring gene expression and to determine to what extent measurements from different reporters can be directly compared with one aim being the stringent testing of theoretical descriptions of gene expression. In this article, we compare two protein reporters by measuring both the absolute level of expression and fold-change in expression using the fluorescent protein EYFP and the enzymatic reporter β-galactosidase. We determine their dynamic and linear range and show that they are interchangeable for measuring mean levels of expression over four orders of magnitude. By calibrating these reporters such that they can be interpreted in terms of absolute molecular counts, we establish limits for their applicability: autofluorescence on the lower end of expression for EYFP (at ∼10 molecules per cell) and interference with cellular growth on the high end for β-galactosidase (at ∼20,000 molecules per cell). These qualities make the reporters complementary and necessary when trying to experimentally verify the predictions from the theoretical models.

Speed, sensitivity, and bistability in auto-activating signaling circuits

Cells employ a myriad of signaling circuits to detect environmental signals and drive specific gene expression responses. A common motif in these circuits is inducible auto-activation: a transcription factor that activates its own transcription upon activation by a ligand or by post-transcriptional modification. Examples range from the two-component signaling systems in bacteria and plants to the genetic circuits of animal viruses such as HIV. We here present a theoretical study of such circuits, based on analytical calculations, numerical computations, and simulation. Our results reveal several surprising characteristics. They show that auto-activation can drastically enhance the sensitivity of the circuit's response to input signals: even without molecular cooperativity, an ultra-sensitive threshold response can be obtained. However, the increased sensitivity comes at a cost: auto-activation tends to severely slow down the speed of induction, a stochastic effect that was strongly underestimated by earlier deterministic models. This slow-induction effect again requires no molecular cooperativity and is intimately related to the bimodality recently observed in non-cooperative auto-activation circuits. These phenomena pose strong constraints on the use of auto-activation in signaling networks. To achieve both a high sensitivity and a rapid induction, an inducible auto-activation circuit is predicted to acquire low cooperativity and low fold-induction. Examples from Escherichia coli's two-component signaling systems support these predictions.

Different times call for different measures. Therefore, cells adjust their protein levels depending on their environment. Upon the detection of certain environmental signals, transcription factors are activated, which activate or inhibit the production of specific sets of proteins. As it turns out, these transcription factors often also stimulate their own production. Indeed, such self-regulation is a common motif in signal–response systems of many organisms, including bacteria, animals, plants and viruses–but its function is not well understood. We have used mathematical models to study its benefits and drawbacks. On the one hand, calculations show that self-regulation can be a very useful tool if the cell needs to respond in a sensitive way to changes in its environment, or if it is supposed to respond only if the signal exceeds a threshold level. On the other hand, these benefits come at a cost: self-regulation severely slows down the cell's response to changes in the environment. We have analyzed how the cell can benefit from the advantages of self-regulation, while mitigating the drawbacks. This leads to strict design constraints that examples from the bacterium E. coli indeed seem to obey.

Calculating transcription factor binding maps for chromatin

Current high-throughput experiments already generate enough data for retrieving the DNA sequence-dependent binding affinities of transcription factors (TF) and other chromosomal proteins throughout the complete genome. However, the reverse task of calculating binding maps in a chromatin context for a given set of concentrations and TF affinities appears to be even more challenging and computationally demanding. The problem can be addressed by considering the DNA sequence as a one-dimensional lattice with units of one or more base pairs. To calculate protein occupancies in chromatin, one needs to consider the competition of TF and histone octamers for binding sites as well as the partial unwrapping of nucleosomal DNA. Here, we consider five different classes of algorithms to compute binding maps that include the binary variable, combinatorial, sequence generating function, transfer matrix and dynamic programming approaches. The calculation time of the binary variable algorithm scales exponentially with DNA length, which limits its use to the analysis of very small genomic regions. For regulatory regions with many overlapping binding sites, potentially applicable algorithms reduce either to the transfer matrix or dynamic programming approach. In addition to the recently proposed transfer matrix formalism for TF access to the nucleosomal organized DNA, we develop here a dynamic programming algorithm that accounts for this feature. In the absence of nucleosomes, dynamic programming outperforms the transfer matrix approach, but the latter is faster when nucleosome unwrapping has to be considered. Strategies are discussed that could further facilitate calculations to allow computing genome-wide TF binding maps.

Statistical method for revealing form-function relations in biological networks

Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions--lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to experiment), revealing the relationship between the topology of small subgraphs and their biological function has been a central goal. We here seek to pose this revelation as a statistical task, illustrated using a particular setup which has been constructed experimentally and for which parameterized models of transcriptional regulation have been studied extensively. The question "how does function follow form" is here mathematized by identifying which topological attributes correlate with the diverse possible information-processing tasks which a transcriptional regulatory network can realize. The resulting method reveals one form-function relationship which had earlier been predicted based on analytic results, and reveals a second for which we can provide an analytic interpretation. Resulting source code is distributed via http://formfunction.sourceforge.net.