Hierarchy and feedback in the evolution of the Escherichia coli transcription network

Competition and evolutionary selection among core regulatory motifs in gene expression control

Gene products that are beneficial in one environment may become burdensome in another, prompting the emergence of diverse regulatory schemes that carry their own bioenergetic cost. By ensuring that regulators are only expressed when needed, we demonstrate that autoregulation generally offers an advantage in an environment combining mutation and time-varying selection. Whether positive or negative feedback emerges as dominant depends primarily on the demand for the target gene product, typically to ensure that the detrimental impact of inevitable mutations is minimized. While self-repression of the regulator curbs the spread of these loss-of-function mutations, self-activation instead facilitates their propagation. By analyzing the transcription network of multiple model organisms, we reveal that reduced bioenergetic cost may contribute to the preferential selection of autoregulation among transcription factors. Our results not only uncover how seemingly equivalent regulatory motifs have fundamentally different impact on population structure, growth dynamics, and evolutionary outcomes, but they can also be leveraged to promote the design of evolutionarily robust synthetic gene circuits.

Feedbacks from the metabolic network to the genetic network reveal regulatory modules in E. coli and B. subtilis

The genetic regulatory network (GRN) plays a key role in controlling the response of the cell to changes in the environment. Although the structure of GRNs has been the subject of many studies, their large scale structure in the light of feedbacks from the metabolic network (MN) has received relatively little attention. Here we study the causal structure of the GRNs, namely the chain of influence of one component on the other, taking into account feedback from the MN. First we consider the GRNs of E. coli and B. subtilis without feedback from MN and illustrate their causal structure. Next we augment the GRNs with feedback from their respective MNs by including (a) links from genes coding for enzymes to metabolites produced or consumed in reactions catalyzed by those enzymes and (b) links from metabolites to genes coding for transcription factors whose transcriptional activity the metabolites alter by binding to them. We find that the inclusion of feedback from MN into GRN significantly affects its causal structure, in particular the number of levels and relative positions of nodes in the hierarchy, and the number and size of the strongly connected components (SCCs). We then study the functional significance of the SCCs. For this we identify condition specific feedbacks from the MN into the GRN by retaining only those enzymes that are essential for growth in specific environmental conditions simulated via the technique of flux balance analysis (FBA). We find that the SCCs of the GRN augmented by these feedbacks can be ascribed specific functional roles in the organism. Our algorithmic approach thus reveals relatively autonomous subsystems with specific functionality, or regulatory modules in the organism. This automated approach could be useful in identifying biologically relevant modules in other organisms for which network data is available, but whose biology is less well studied.

Stochastic timing in gene expression for simple regulatory strategies

Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to reach in a precise time a threshold level of expression that triggers a specific downstream process. However, gene expression is subject to stochastic fluctuations, naturally inducing an uncertainty in this threshold-crossing time with potential consequences on biological functions and phenotypes. Here, we consider such ‘timing fluctuations’ and we ask how they can be controlled. Our analytical estimates and simulations show that, for an induced gene, timing variability is minimal if the threshold level of expression is approximately half of the steady-state level. Timing fluctuations can be reduced by increasing the transcription rate, while they are insensitive to the translation rate. In presence of self-regulatory strategies, we show that self-repression reduces timing noise for threshold levels that have to be reached quickly, while self-activation is optimal at long times. These results lay a framework for understanding stochasticity of endogenous systems such as the cell cycle, as well as for the design of synthetic trigger circuits.

Control of MarRAB Operon in Escherichia coli via Autoactivation and Autorepression

Choice of network topology for gene regulation has been a question of interest for a long time. How do simple and more complex topologies arise? In this work, we analyze the topology of the marRAB operon in Escherichia coli, which is associated with control of expression of genes associated with conferring resistance to low-level antibiotics to the bacterium. Among the 2102 promoters in E. coli, the marRAB promoter is the only one that encodes for an autoactivator and an autorepressor. What advantages does this topology confer to the bacterium? In this work, we demonstrate that, compared to control by a single regulator, the marRAB regulatory arrangement has the least control cost associated with modulating gene expression in response to environmental stimuli. In addition, the presence of dual regulators allows the regulon to exhibit a diverse range of dynamics, a feature that is not observed in genes controlled by a single regulator.

Cross-Disciplinary Network Comparison: Matchmaking Between Hairballs

Biological systems are complex. In particular, the interactions between molecular components often form dense networks that, more often than not, are criticized for being inscrutable 'hairballs'. We argue that one way of untangling these hairballs is through cross-disciplinary network comparison-leveraging advances in other disciplines to obtain new biological insights. In some cases, such comparisons enable the direct transfer of mathematical formalism between disciplines, precisely describing the abstract associations between entities and allowing us to apply a variety of sophisticated formalisms to biology. In cases where the detailed structure of the network does not permit the transfer of complete formalisms between disciplines, comparison of mechanistic interactions in systems for which we have significant day-to-day experience can provide analogies for interpreting relatively more abstruse biological networks. Here, we illustrate how these comparisons benefit the field with a few specific examples related to network growth, organizational hierarchies, and the evolution of adaptive systems.

Transcription Factors Exhibit Differential Conservation in Bacteria with Reduced Genomes

The description of transcriptional regulatory networks has been pivotal in the understanding of operating principles under which organisms respond and adapt to varying conditions. While the study of the topology and dynamics of these networks has been the subject of considerable work, the investigation of the evolution of their topology, as a result of the adaptation of organisms to different environmental conditions, has received little attention. In this work, we study the evolution of transcriptional regulatory networks in bacteria from a genome reduction perspective, which manifests itself as the loss of genes at different degrees. We used the transcriptional regulatory network of Escherichia coli as a reference to compare 113 smaller, phylogenetically-related γ-proteobacteria, including 19 genomes of symbionts. We found that the type of regulatory action exerted by transcription factors, as genomes get progressively smaller, correlates well with their degree of conservation, with dual regulators being more conserved than repressors and activators in conditions of extreme reduction. In addition, we found that the preponderant conservation of dual regulators might be due to their role as both global regulators and nucleoid-associated proteins. We summarize our results in a conceptual model of how each TF type is gradually lost as genomes become smaller and give a rationale for the order in which this phenomenon occurs.

Multi-hierarchical profiling: an emerging and quantitative approach to characterizing diverse biological networks

Multi-hierarchical profiling may offer valuable insights into the structural stability and functional direction of biological networks in cellular development, pathological process and disease variation. Owing to the emergence of several new techniques, such as bioinformatics for omics data, structural biology and structural bioinformatics, the pace of network hierarchical research has accelerated a lot in recent years. Here, we discuss and compare the techniques available for quantifying multilevel hierarchies, with a focus on their features, capabilities and drawbacks when used for different applications. Then, we classify these methods into three types: topological spatial-scales, multilevel hierarchical control and feature ordering. We observe that challenges and limitations do exist in functional hierarchical identification. And, we also provide useful suggestions on how to analyze the dynamic data of complex network studies.

Hierarchical decomposition of dynamically evolving regulatory networks

Background

Gene regulatory networks describe the interplay between genes and their products. These networks control almost every biological activity in the cell through interactions. The hierarchy of genes in these networks as defined by their interactions gives important insights into how these functions are governed. Accurately determining the hierarchy of genes is however a computationally difficult problem. This problem is further complicated by the fact that an intrinsic characteristic of regulatory networks is that the wiring of interactions can change over time. Determining how the hierarchy in the gene regulatory networks changes with dynamically evolving network topology remains to be an unsolved challenge.

Results

In this study, we develop a new method, named D-HIDEN (Dynamic-HIerarchical DEcomposition of Networks) to find the hierarchy of the genes in dynamically evolving gene regulatory network topologies. Unlike earlier methods, which recompute the hierarchy from scratch when the network topology changes, our method adapts the hierarchy based on the wiring of the interactions only for the nodes which have the potential to move in the hierarchy.

Conclusions

We compare D-HIDEN to five currently available hierarchical decomposition methods on synthetic and real gene regulatory networks. Our experiments demonstrate that D-HIDEN significantly outperforms existing methods in running time, accuracy, or both. Furthermore, our method is robust against dynamic changes in hierarchy. Our experiments on human gene regulatory networks suggest that our method may be used to reconstruct hierarchy in gene regulatory networks.

ncRDeathDB: A comprehensive bioinformatics resource for deciphering network organization of the ncRNA-mediated cell death system

Programmed cell death (PCD) is a critical biological process involved in many important processes, and defects in PCD have been linked with numerous human diseases. In recent years, the protein architecture in different PCD subroutines has been explored, but our understanding of the global network organization of the noncoding RNA (ncRNA)-mediated cell death system is limited and ambiguous. Hence, we developed the comprehensive bioinformatics resource (ncRDeathDB, www.rna-society.org/ncrdeathdb ) to archive ncRNA-associated cell death interactions. The current version of ncRDeathDB documents a total of more than 4600 ncRNA-mediated PCD entries in 12 species. ncRDeathDB provides a user-friendly interface to query, browse and manipulate these ncRNA-associated cell death interactions. Furthermore, this resource will help to visualize and navigate current knowledge of the noncoding RNA component of cell death and autophagy, to uncover the generic organizing principles of ncRNA-associated cell death systems, and to generate valuable biological hypotheses.

Analysis of the hierarchical structure of the B. subtilis transcriptional regulatory network

Hierarchical decomposition of transcriptional regulators into Top, Middle and Bottom levels in theB. subtilistranscriptional regulatory network.

Inherent directionality explains the lack of feedback loops in empirical networks

We explore the hypothesis that the relative abundance of feedback loops in many empirical complex networks is severely reduced owing to the presence of an inherent global directionality. Aimed at quantifying this idea, we propose a simple probabilistic model in which a free parameter γ controls the degree of inherent directionality. Upon strengthening such directionality, the model predicts a drastic reduction in the fraction of loops which are also feedback loops. To test this prediction, we extensively enumerated loops and feedback loops in many empirical biological, ecological and socio-technological directed networks. We show that, in almost all cases, empirical networks have a much smaller fraction of feedback loops than network randomizations. Quite remarkably, this empirical finding is quantitatively reproduced, for all loop lengths, by our model by fitting its only parameter γ. Moreover, the fitted value of γ correlates quite well with another direct measurement of network directionality, performed by means of a novel algorithm. We conclude that the existence of an inherent network directionality provides a parsimonious quantitative explanation for the observed lack of feedback loops in empirical networks.

Cross-species gene-family fluctuations reveal the dynamics of horizontal transfers

Prokaryotes vary their protein repertoire mainly through horizontal transfer and gene loss. To elucidate the links between these processes and the cross-species gene-family statistics, we perform a large-scale data analysis of the cross-species variability of gene-family abundance (the number of members of the family found on a given genome). We find that abundance fluctuations are related to the rate of horizontal transfers. This is rationalized by a minimal theoretical model, which predicts this link. The families that are not captured by the model show abundance profiles that are markedly peaked around a mean value, possibly because of specific abundance selection. Based on these results, we define an abundance variability index that captures a family's evolutionary behavior (and thus some of its relevant functional properties) purely based on its cross-species abundance fluctuations. Analysis and model, combined, show a quantitative link between cross-species family abundance statistics and horizontal transfer dynamics, which can be used to analyze genome ‘flux’. Groups of families with different values of the abundance variability index correspond to genome sub-parts having different plasticity in terms of the level of horizontal exchange allowed by natural selection.

Determining the control circuitry of redox metabolism at the genome-scale

Determining how facultative anaerobic organisms sense and direct cellular responses to electron acceptor availability has been a subject of intense study. However, even in the model organism Escherichia coli, established mechanisms only explain a small fraction of the hundreds of genes that are regulated during electron acceptor shifts. Here we propose a qualitative model that accounts for the full breadth of regulated genes by detailing how two global transcription factors (TFs), ArcA and Fnr of E. coli, sense key metabolic redox ratios and act on a genome-wide basis to regulate anabolic, catabolic, and energy generation pathways. We first fill gaps in our knowledge of this transcriptional regulatory network by carrying out ChIP-chip and gene expression experiments to identify 463 regulatory events. We then interfaced this reconstructed regulatory network with a highly curated genome-scale metabolic model to show that ArcA and Fnr regulate >80% of total metabolic flux and 96% of differential gene expression across fermentative and nitrate respiratory conditions. Based on the data, we propose a feedforward with feedback trim regulatory scheme, given the extensive repression of catabolic genes by ArcA and extensive activation of chemiosmotic genes by Fnr. We further corroborated this regulatory scheme by showing a 0.71 r(2) (p<1e-6) correlation between changes in metabolic flux and changes in regulatory activity across fermentative and nitrate respiratory conditions. Finally, we are able to relate the proposed model to a wealth of previously generated data by contextualizing the existing transcriptional regulatory network.

Emotion: The Self-regulatory Sense

While emotion is a central component of human health and well-being, traditional approaches to understanding its biological function have been wanting. A dynamic systems model, however, broadly redefines and recasts emotion as a primary sensory system-perhaps the first sensory system to have emerged, serving the ancient autopoietic function of "self-regulation." Drawing upon molecular biology and revelations from the field of epigenetics, the model suggests that human emotional perceptions provide an ongoing stream of "self-relevant" sensory information concerning optimally adaptive states between the organism and its immediate environment, along with coupled behavioral corrections that honor a universal self-regulatory logic, one still encoded within cellular signaling and immune functions. Exemplified by the fundamental molecular circuitry of sensorimotor control in the E coli bacterium, the model suggests that the hedonic (affective) categories emerge directly from positive and negative feedback processes, their good/bad binary appraisals relating to dual self-regulatory behavioral regimes-evolutionary purposes, through which organisms actively participate in natural selection, and through which humans can interpret optimal or deficit states of balanced being and becoming. The self-regulatory sensory paradigm transcends anthropomorphism, unites divergent theoretical perspectives and isolated bodies of literature, while challenging time-honored assumptions. While suppressive regulatory strategies abound, it suggests that emotions are better understood as regulating us, providing a service crucial to all semantic language, learning systems, evaluative decision-making, and fundamental to optimal physical, mental, and social health.

On the origins of hierarchy in complex networks

Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting from the convergence of theoretical morphology and network theory that allows constructing a 3D morphospace of hierarchies and hence comparing the hierarchical organization of ecological, cellular, technological, and social networks. Embedded within large voids in the morphospace of all possible hierarchies, four major groups are identified. Two of them match the expected from random networks with similar connectivity, thus suggesting that nonadaptive factors are at work. Ecological and gene networks define the other two, indicating that their topological order is the result of functional constraints. These results are consistent with an exploration of the morphospace, using in silico evolved networks.

The architecture of the gene regulatory networks of different tissues

Summary: The great variety of human cell types in morphology and function is due to the diverse gene expression profiles that are governed by the distinctive regulatory networks in different cell types. It is still a challenging task to explain how the regulatory networks achieve the diversity of different cell types. Here, we report on our studies of the design principles of the tissue regulatory system by constructing the regulatory networks of eight human tissues, which subsume the regulatory interactions between transcription factors (TFs), microRNAs (miRNAs) and non-TF target genes. The results show that there are in-/out-hubs of high in-/out-degrees in tissue networks. Some hubs (strong hubs) maintain the hub status in all the tissues where they are expressed, whereas others (weak hubs), in spite of their ubiquitous expression, are hubs only in some tissues. The network motifs are mostly feed-forward loops. Some of them having no miRNAs are the common motifs shared by all tissues, whereas the others containing miRNAs are the tissue-specific ones owned by one or several tissues, indicating that the transcriptional regulation is more conserved across tissues than the post-transcriptional regulation. In particular, a common bow-tie framework was found that underlies the motif instances and shows diverse patterns in different tissues. Such bow-tie framework reflects the utilization efficiency of the regulatory system as well as its high variability in different tissues, and could serve as the model to further understand the structural adaptation of the regulatory system to the specific requirements of different cell functions.

Contact:edgar.wingender@bioinf.med.uni-goettingen.de; jwang@nju.edu.cn

Supplementary information:Supplementary data are available at Bioinformatics online.

Genomic analysis reveals epistatic silencing of "expensive" genes in Escherichia coli K-12

A barrier for horizontal gene transfer is high gene expression, which is metabolically expensive. Silencing of horizontally-acquired genes in the bacterium Escherichia coli is caused by the global transcriptional repressor H-NS. The activity of H-NS is enhanced or diminished by other proteins including its homologue StpA, and Hha and YdgT. The interconnections of H-NS with these regulators and their role in silencing gene expression in E. coli are not well understood on a genomic scale. In this study, we use transcriptome sequencing to show that there is a bi-layered gene silencing system - involving the homologous H-NS and StpA - operating on horizontally-acquired genes among others. We show that H-NS-repressed genes belong to two types, termed "epistatic" and "unilateral". In the absence of H-NS, the expression of "epistatically controlled genes" is repressed by StpA, whereas that of "unilaterally controlled genes" is not. Epistatic genes show a higher tendency to be non-essential and recently acquired, when compared to unilateral genes. Epistatic genes reach much higher expression levels than unilateral genes in the absence of the silencing system. Finally, epistatic genes contain more high affinity H-NS binding motifs than unilateral genes. Therefore, both the DNA binding sites of H-NS as well as the function of StpA as a backup system might be selected for silencing highly transcribable genes.

Three-state network design for robust loop-searching systems

Self-recovery of function is one of the remarkable properties of biological systems, and its implementation in autonomous distributed systems is highly desirable. In this study, we propose an autonomous distributed system which is capable of searching for closed loops in a network in which nodes are connected by unidirectional paths. A closed loop is defined as a phase synchronization of a group of oscillators belonging to the corresponding nodes. In addition, to develop a system capable of self-recovery (the ability to find a loop when one of the connections in the existing loop is suddenly removed), we have developed regulatory rules for the interaction between nodes. These rules are used to construct a regulation network in which the stability of nodes and that of loops are mutually sustained, allowing the system to function as a loop-searching system with self-recovery properties.

A formalized design process for bacterial consortia that perform logic computing

The concept of microbial consortia is of great attractiveness in synthetic biology. Despite of all its benefits, however, there are still problems remaining for large-scaled multicellular gene circuits, for example, how to reliably design and distribute the circuits in microbial consortia with limited number of well-behaved genetic modules and wiring quorum-sensing molecules. To manage such problem, here we propose a formalized design process: (i) determine the basic logic units (AND, OR and NOT gates) based on mathematical and biological considerations; (ii) establish rules to search and distribute simplest logic design; (iii) assemble assigned basic logic units in each logic operating cell; and (iv) fine-tune the circuiting interface between logic operators. We in silico analyzed gene circuits with inputs ranging from two to four, comparing our method with the pre-existing ones. Results showed that this formalized design process is more feasible concerning numbers of cells required. Furthermore, as a proof of principle, an Escherichia coli consortium that performs XOR function, a typical complex computing operation, was designed. The construction and characterization of logic operators is independent of “wiring” and provides predictive information for fine-tuning. This formalized design process provides guidance for the design of microbial consortia that perform distributed biological computation.

Hierarchical dynamics of a transcription factors network in E. coli

In the present work we study the transcription-factor regulatory network that controls the synthesis of flagella in E. coli. Our objective is to address how the transcription-factor dynamics (in terms of their promoter activities and associated rates) correlate with their positions in the hierarchical organization of this regulatory network. Our results suggest that global-regulator promoters express at higher rates than those of local regulators, particularly when the bacterial populations are actively growing. Furthermore, promoter activity decreases together with the rate of cellular division. And finally, local-regulator promoters reach their maximal activity later than global-regulator promoters do. In summary, our results suggest a strong correlation between promoter activities and their hierarchical organization in this particular regulatory network.

Monochromaticity in neutral evolutionary network models

Recent studies on epistatic networks of model organisms have unveiled a certain type of modular property called monochromaticity in which the networks are clustered into functional modules that interact with each other through the same type of epistasis. Here, we propose and study three epistatic network models that are inspired by the duplication-divergence mechanism to gain insight into the evolutionary basis of monochromaticity and to test if it can be explained as the outcome of a neutral evolutionary hypothesis. We show that the epistatic networks formed by these stochastic evolutionary models have monochromaticity conflict distributions that are centered close to zero and are statistically significantly different from their randomized counterparts. In particular, the last model we propose yields a strictly monochromatic solution. Our results agree with the monochromaticity findings in real organisms and point toward the possible role of a neutral mechanism in the evolution of this phenomenon.

Architecture of the human regulatory network derived from ENCODE data

Transcription factors bind in a combinatorial fashion to specify the on-and-off states of genes; the ensemble of these binding events forms a regulatory network, constituting the wiring diagram for a cell. To examine the principles of the human transcriptional regulatory network, we determined the genomic binding information of 119 transcription-related factors in over 450 distinct experiments. We found the combinatorial, co-association of transcription factors to be highly context specific: distinct combinations of factors bind at specific genomic locations. In particular, there are significant differences in the binding proximal and distal to genes. We organized all the transcription factor binding into a hierarchy and integrated it with other genomic information (for example, microRNA regulation), forming a dense meta-network. Factors at different levels have different properties; for instance, top-level transcription factors more strongly influence expression and middle-level ones co-regulate targets to mitigate information-flow bottlenecks. Moreover, these co-regulations give rise to many enriched network motifs (for example, noise-buffering feed-forward loops). Finally, more connected network components are under stronger selection and exhibit a greater degree of allele-specific activity (that is, differential binding to the two parental alleles). The regulatory information obtained in this study will be crucial for interpreting personal genome sequences and understanding basic principles of human biology and disease.

Motif Participation by Genes in E. coli Transcriptional Networks

Motifs are patterns of recurring connections among the genes of genetic networks that occur more frequently than would be expected from randomized networks with the same degree sequence. Although the abundance of certain three-node motifs, such as the feed-forward loop, is positively correlated with a networks’ ability to tolerate moderate disruptions to gene expression, little is known regarding the connectivity of individual genes participating in multiple motifs. Using the transcriptional network of the bacterium Escherichia coli, we investigate this feature by reconstructing the distribution of genes participating in feed-forward loop motifs from its largest connected network component. We contrast these motif participation distributions with those obtained from model networks built using the preferential attachment mechanism employed by many biological and man-made networks. We report that, although some of these model networks support a motif participation distribution that appears qualitatively similar to that obtained from the bacterium E. coli, the probability for a node to support a feed-forward loop motif may instead be strongly influenced by only a few master transcriptional regulators within the network. From these analyses we conclude that such master regulators may be a crucial ingredient to describe coupling among feed-forward loop motifs in transcriptional regulatory networks.

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.

The co-regulation mechanism of transcription factors in the human gene regulatory network

The co-regulation of transcription factors (TFs) has been widely observed in various species. Why is such a co-regulation mechanism needed for transcriptional regulation? To answer this question, the following experiments and analyses were performed. First, examination of the human gene regulatory network (GRN) indicated that co-regulation was significantly enriched in the human GRN. Second, mathematical simulation of an artificial regulatory network showed that the co-regulation mechanism was related to the biphasic dose-response patterns of TFs. Third, the relationship between the co-regulation mechanism and the biphasic dose-response pattern was confirmed using microarray experiments examining different time points and different doses of the toxicant tetrachlorodibenzodioxin. Finally, two mathematical models were constructed to mimic highly co-regulated networks (HCNs) and little co-regulated networks (LCNs), and we found that HCNs were more robust to parameter perturbation than LCNs, whereas LCNs were faster in adaptation to environmental changes than HCNs.

Emergence of robustness against noise: A structural phase transition in evolved models of gene regulatory networks

We investigate the evolution of Boolean networks subject to a selective pressure which favors robustness against noise, as a model of evolved genetic regulatory systems. By mapping the evolutionary process into a statistical ensemble and minimizing its associated free energy, we find the structural properties which emerge as the selective pressure is increased and identify a phase transition from a random topology to a "segregated-core" structure, where a smaller and more densely connected subset of the nodes is responsible for most of the regulation in the network. This segregated structure is very similar qualitatively to what is found in gene regulatory networks, where only a much smaller subset of genes--those responsible for transcription factors-is responsible for global regulation. We obtain the full phase diagram of the evolutionary process as a function of selective pressure and the average number of inputs per node. We compare the theoretical predictions with Monte Carlo simulations of evolved networks and with empirical data for Saccharomyces cerevisiae and Escherichia coli.

Stochastic signalling rewires the interaction map of a multiple feedback network during yeast evolution

During evolution, genetic networks are rewired through strengthening or weakening their interactions to develop new regulatory schemes. In the galactose network, the GAL1/GAL3 paralogues and the GAL2 gene enhance their own expression mediated by the Gal4p transcriptional activator. The wiring strength in these feedback loops is set by the number of Gal4p binding sites. Here we show using synthetic circuits that multiplying the binding sites increases the expression of a gene under the direct control of an activator, but this enhancement is not fed back in the circuit. The feedback loops are rather activated by genes that have frequent stochastic bursts and fast RNA decay rates. In this way, rapid adaptation to galactose can be triggered even by weakly expressed genes. Our results indicate that nonlinear stochastic transcriptional responses enable feedback loops to function autonomously, or contrary to what is dictated by the strength of interactions enclosing the circuit.

Non-transcriptional regulatory processes shape transcriptional network dynamics

Information about the extra- or intracellular environment is often captured as biochemical signals that propagate through regulatory networks. These signals eventually drive phenotypic changes, typically by altering gene expression programmes in the cell. Reconstruction of transcriptional regulatory networks has given a compelling picture of bacterial physiology, but transcriptional network maps alone often fail to describe phenotypes. Cellular response dynamics are ultimately determined by interactions between transcriptional and non-transcriptional networks, with dramatic implications for physiology and evolution. Here, we provide an overview of non-transcriptional interactions that can affect the performance of natural and synthetic bacterial regulatory networks.

Analytically solvable processes on networks

We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process, the two most basic processes on networks. Our class differs from previous models of interactions (such as the stochastic Ising model, cellular automata, infinite particle systems, and the voter model) in several ways, the two most important being (i) the model is analytically solvable even when the dynamical equation for each node may be different and the network may have an arbitrary finite graph and influence structure and (ii) when local dynamics is described by the same evolution equation, the model is decomposable, with the equilibrium behavior of the system expressed as an explicit function of network topology and node dynamics.

Networks for systems biology: conceptual connection of data and function

The purpose of this study is to survey the use of networks and network-based methods in systems biology. This study starts with an introduction to graph theory and basic measures allowing to quantify structural properties of networks. Then, the authors present important network classes and gene networks as well as methods for their analysis. In the last part of this study, the authors review approaches that aim at analysing the functional organisation of gene networks and the use of networks in medicine. In addition to this, the authors advocate networks as a systematic approach to general problems in systems biology, because networks are capable of assuming multiple roles that are very beneficial connecting experimental data with a functional interpretation in biological terms.

The Regulatory Network of Pseudomonas aeruginosa

Background

Pseudomonas aeruginosa is an important bacterial model due to its metabolic and pathogenic abilities, which allow it to interact and colonize a wide range of hosts, including plants and animals. In this work we compile and analyze the structure and organization of an experimentally supported regulatory network in this bacterium.

Results

The regulatory network consists of 690 genes and 1020 regulatory interactions between their products (12% of total genes: 54% sigma and 16% of transcription factors). This complex interplay makes the third largest regulatory network of those reported in bacteria. The entire network is enriched for activating interactions and, peculiarly, self-activation seems to occur more prominent for transcription factors (TFs), which contrasts with other biological networks where self-repression is dominant. The network contains a giant component of 650 genes organized into 11 hierarchies, encompassing important biological processes, such as, biofilms formation, production of exopolysaccharide alginate and several virulence factors, and of the so-called quorum sensing regulons.

Conclusions

The study of gene regulation in P. aeruginosa is biased towards pathogenesis and virulence processes, all of which are interconnected. The network shows power-law distribution -input degree -, and we identified the top ten global regulators, six two-element cycles, the longest paths have ten steps, six biological modules and the main motifs containing three and four elements. We think this work can provide insights for the design of further studies to cover the many gaps in knowledge of this important bacterial model, and for the design of systems strategies to combat this bacterium.

Measuring the hierarchy of feedforward networks

In this paper we explore the concept of hierarchy as a quantifiable descriptor of ordered structures, departing from the definition of three conditions to be satisfied for a hierarchical structure: order, predictability, and pyramidal structure. According to these principles, we define a hierarchical index taking concepts from graph and information theory. This estimator allows to quantify the hierarchical character of any system susceptible to be abstracted in a feedforward causal graph, i.e., a directed acyclic graph defined in a single connected structure. Our hierarchical index is a balance between this predictability and pyramidal condition by the definition of two entropies: one attending the onward flow and the other for the backward reversion. We show how this index allows to identify hierarchical, antihierarchical, and nonhierarchical structures. Our formalism reveals that departing from the defined conditions for a hierarchical structure, feedforward trees and the inverted tree graphs emerge as the only causal structures of maximal hierarchical and antihierarchical systems respectively. Conversely, null values of the hierarchical index are attributed to a number of different configuration networks; from linear chains, due to their lack of pyramid structure, to full-connected feedforward graphs where the diversity of onward pathways is canceled by the uncertainty (lack of predictability) when going backward. Some illustrative examples are provided for the distinction among these three types of hierarchical causal graphs.

Early Career Research Award Lecture. Structure, evolution and dynamics of transcriptional regulatory networks

The availability of entire genome sequences and the wealth of literature on gene regulation have enabled researchers to model an organism's transcriptional regulation system in the form of a network. In such a network, TFs (transcription factors) and TGs (target genes) are represented as nodes and regulatory interactions between TFs and TGs are represented as directed links. In the present review, I address the following topics pertaining to transcriptional regulatory networks. (i) Structure and organization: first, I introduce the concept of networks and discuss our understanding of the structure and organization of transcriptional networks. (ii) Evolution: I then describe the different mechanisms and forces that influence network evolution and shape network structure. (iii) Dynamics: I discuss studies that have integrated information on dynamics such as mRNA abundance or half-life, with data on transcriptional network in order to elucidate general principles of regulatory network dynamics. In particular, I discuss how cell-to-cell variability in the expression level of TFs could permit differential utilization of the same underlying network by distinct members of a genetically identical cell population. Finally, I conclude by discussing open questions for future research and highlighting the implications for evolution, development, disease and applications such as genetic engineering.

Identity and divergence of protein domain architectures after the yeast whole-genome duplication event

Gene duplication is a key mechanism in evolution for generating new functionality, and it is known to have produced a large proportion of genes. Duplication mechanisms include small-scale, or "local", events such as unequal crossing over and retroposition, together with global events, such as chromosomal or whole genome duplication (WGD). In particular, different studies confirmed that the yeast S. cerevisiae arose from a 100-150 million-year old whole-genome duplication. Detection and study of duplications are usually based on sequence alignment, synteny and phylogenetic techniques, but protein domains are also useful in assessing protein homology. We develop a simple and computationally efficient protein domain architecture comparison method based on the domain assignments available from public databases. We test the accuracy and the reliability of this method in detecting instances of gene duplication in the yeast S. cerevisiae. In particular, we analyze the evolution of WGD and non-WGD paralogs from the domain viewpoint, in comparison with a more standard functional analysis of the genes. A large number of domains is shared by genes that underwent local and global duplications, indicating the existence of a common set of "duplicable" domains. On the other hand, WGD and non-WGD paralogs tend to have different functions. We find evidence that this comes from functional migration within similar domain superfamilies, but also from the existence of small sets of WGD and non-WGD specific domain superfamilies with largely different functions. This observation gives a novel perspective on the finding that WGD paralogs tend to be functionally different from small-scale paralogs. WGD and non-WGD superfamilies carry distinct functions. Finally, the Gene Ontology similarity of paralogs tends to decrease with duplication age, while this tendency is weaker or not observable by the comparison of the domain architectures of paralogs. This suggests that the set of domains composing a protein tends to be maintained, while its function, cellular process or localization diversifies. Overall, the gathered evidence gives a different viewpoint on the biological specificity of the WGD and at the same time points out the validity of domain architecture comparison as a tool for detecting homology.

Evolution of gene regulatory networks by fluctuating selection and intrinsic constraints

Various characteristics of complex gene regulatory networks (GRNs) have been discovered during the last decade, e.g., redundancy, exponential indegree distributions, scale-free outdegree distributions, mutational robustness, and evolvability. Although progress has been made in this field, it is not well understood whether these characteristics are the direct products of selection or those of other evolutionary forces such as mutational biases and biophysical constraints. To elucidate the causal factors that promoted the evolution of complex GRNs, we examined the effect of fluctuating environmental selection and some intrinsic constraining factors on GRN evolution by using an individual-based model. We found that the evolution of complex GRNs is remarkably promoted by fixation of beneficial gene duplications under unpredictably fluctuating environmental conditions and that some internal factors inherent in organisms, such as mutational bias, gene expression costs, and constraints on expression dynamics, are also important for the evolution of GRNs. The results indicate that various biological properties observed in GRNs could evolve as a result of not only adaptation to unpredictable environmental changes but also non-adaptive processes owing to the properties of the organisms themselves. Our study emphasizes that evolutionary models considering such intrinsic constraining factors should be used as null models to analyze the effect of selection on GRN evolution.

Various organismal traits, including the morphology of multicellular species and metabolism in unicellular species, are determined by the amount and combinations of proteins in the cell. The complex regulatory network plays an important role in controlling the protein profiles in a cell. Recent studies have revealed that gene regulatory networks have many interesting structural and mutational features such as their scale-free structure, mutational robustness, and evolvability. However, why and how these features have emerged from evolution is unknown. In this paper, we constructed an evolutionary model of gene regulatory networks and simulated its evolution under various environmental conditions. The results show that most features of known gene regulatory networks evolve as a result of adaptation to unpredictable environmental fluctuations. In addition, some internal organismal factors, such as mutational bias, gene expression costs, and constraints on expression dynamics, are also important for GRN evolution observed in real organisms. Thus, these GRN features appear to evolve as a result of not only adaptation to unpredictable environmental changes but also non-adaptive processes owing to the properties of the organisms themselves.

Ordered structure of the transcription network inherited from the yeast whole-genome duplication

Background

Gene duplication, a major evolutionary path to genomic innovation, can occur at the scale of an entire genome. One such "whole-genome duplication" (WGD) event among the Ascomycota fungi gave rise to genes with distinct biological properties compared to small-scale duplications.

Results

We studied the evolution of transcriptional interactions of whole-genome duplicates, to understand how they are wired into the yeast regulatory system. Our work combines network analysis and modeling of the large-scale structure of the interactions stemming from the WGD.

Conclusions

The results uncover the WGD as a major source for the evolution of a complex interconnected block of transcriptional pathways. The inheritance of interactions among WGD duplicates follows elementary "duplication subgraphs", relating ancestral interactions with newly formed ones. Duplication subgraphs are correlated with their neighbours and give rise to higher order circuits with two elementary properties: newly formed transcriptional pathways remain connected (paths are not broken), and are preferentially cross-connected with ancestral ones. The result is a coherent and connected "WGD-network", where duplication subgraphs are arranged in an astonishingly ordered configuration.

Performance of modularity maximization in practical contexts

Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its performance in such situations. First, we revisit and clarify the resolution limit phenomenon for modularity maximization. Second, we show that the modularity function Q exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum. Third, we derive the limiting behavior of the maximum modularity Qmax for one model of infinitely modular networks, showing that it depends strongly both on the size of the network and on the number of modules it contains. Finally, using three real-world metabolic networks as examples, we show that the degenerate solutions can fundamentally disagree on many, but not all, partition properties such as the composition of the largest modules and the distribution of module sizes. These results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts. They also explain why many heuristics are often successful at finding high-scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network. We conclude by discussing avenues for mitigating some of these behaviors, such as combining information from many degenerate solutions or using generative models.

Analysis of diverse regulatory networks in a hierarchical context shows consistent tendencies for collaboration in the middle levels

Gene regulatory networks have been shown to share some common aspects with commonplace social governance structures. Thus, we can get some intuition into their organization by arranging them into well-known hierarchical layouts. These hierarchies, in turn, can be placed between the extremes of autocracies, with well-defined levels and clear chains of command, and democracies, without such defined levels and with more co-regulatory partnerships between regulators. In general, the presence of partnerships decreases the variation in information flow amongst nodes within a level, more evenly distributing stress. Here we study various regulatory networks (transcriptional, modification, and phosphorylation) for five diverse species, Escherichia coli to human. We specify three levels of regulators--top, middle, and bottom--which collectively govern the non-regulator targets lying in the lowest fourth level. We define quantities for nodes, levels, and entire networks that measure their degree of collaboration and autocratic vs. democratic character. We show individual regulators have a range of partnership tendencies: Some regulate their targets in combination with other regulators in local instantiations of democratic structure, whereas others regulate mostly in isolation, in more autocratic fashion. Overall, we show that in all networks studied the middle level has the highest collaborative propensity and coregulatory partnerships occur most frequently amongst midlevel regulators, an observation that has parallels in corporate settings where middle managers must interact most to ensure organizational effectiveness. There is, however, one notable difference between networks in different species: The amount of collaborative regulation and democratic character increases markedly with overall genomic complexity.

DREAM3: network inference using dynamic context likelihood of relatedness and the inferelator

Background

Many current works aiming to learn regulatory networks from systems biology data must balance model complexity with respect to data availability and quality. Methods that learn regulatory associations based on unit-less metrics, such as Mutual Information, are attractive in that they scale well and reduce the number of free parameters (model complexity) per interaction to a minimum. In contrast, methods for learning regulatory networks based on explicit dynamical models are more complex and scale less gracefully, but are attractive as they may allow direct prediction of transcriptional dynamics and resolve the directionality of many regulatory interactions.

Methodology

We aim to investigate whether scalable information based methods (like the Context Likelihood of Relatedness method) and more explicit dynamical models (like Inferelator 1.0) prove synergistic when combined. We test a pipeline where a novel modification of the Context Likelihood of Relatedness (mixed-CLR, modified to use time series data) is first used to define likely regulatory interactions and then Inferelator 1.0 is used for final model selection and to build an explicit dynamical model.

Conclusions/Significance

Our method ranked 2nd out of 22 in the DREAM3 100-gene in silico networks challenge. Mixed-CLR and Inferelator 1.0 are complementary, demonstrating a large performance gain relative to any single tested method, with precision being especially high at low recall values. Partitioning the provided data set into four groups (knock-down, knock-out, time-series, and combined) revealed that using comprehensive knock-out data alone provides optimal performance. Inferelator 1.0 proved particularly powerful at resolving the directionality of regulatory interactions, i.e. “who regulates who” (approximately of identified true positives were correctly resolved). Performance drops for high in-degree genes, i.e. as the number of regulators per target gene increases, but not with out-degree, i.e. performance is not affected by the presence of regulatory hubs.

On the need for widespread horizontal gene transfers under genome size constraint

Background

While eukaryotes primarily evolve by duplication-divergence expansion (and reduction) of their own gene repertoire with only rare horizontal gene transfers, prokaryotes appear to evolve under both gene duplications and widespread horizontal gene transfers over long evolutionary time scales. But, the evolutionary origin of this striking difference in the importance of horizontal gene transfers remains by and large a mystery.

Hypothesis

We propose that the abundance of horizontal gene transfers in free-living prokaryotes is a simple but necessary consequence of two opposite effects: i) their apparent genome size constraint compared to typical eukaryote genomes and ii) their underlying genome expansion dynamics through gene duplication-divergence evolution, as demonstrated by the presence of many tandem and block repeated genes. In principle, this combination of genome size constraint and underlying duplication expansion should lead to a coalescent-like process with extensive turnover of functional genes. This would, however, imply the unlikely, systematic reinvention of functions from discarded genes within independent phylogenetic lineages. Instead, we propose that the long-term evolutionary adaptation of free-living prokaryotes must have resulted in the emergence of efficient non-phylogenetic pathways to circumvent gene loss.

Implications

This need for widespread horizontal gene transfers due to genome size constraint implies, in particular, that prokaryotes must remain under strong selection pressure in order to maintain the long-term evolutionary adaptation of their "mutualized" gene pool, beyond the inevitable turnover of individual prokaryote species. By contrast, the absence of genome size constraint for typical eukaryotes has presumably relaxed their need for widespread horizontal gene transfers and strong selection pressure. Yet, the resulting loss of genetic functions, due to weak selection pressure and inefficient gene recovery mechanisms, must have ultimately favored the emergence of more complex life styles and ecological integration of many eukaryotes.

Reviewers

This article was reviewed by Pierre Pontarotti, Eugene V Koonin and Sergei Maslov.

Genomic analysis reveals a tight link between transcription factor dynamics and regulatory network architecture

Although several studies have provided important insights into the general principles of biological networks, the link between network organization and the genome-scale dynamics of the underlying entities (genes, mRNAs, and proteins) and its role in systems behavior remain unclear. Here we show that transcription factor (TF) dynamics and regulatory network organization are tightly linked. By classifying TFs in the yeast regulatory network into three hierarchical layers (top, core, and bottom) and integrating diverse genome-scale datasets, we find that the TFs have static and dynamic properties that are similar within a layer and different across layers. At the protein level, the top-layer TFs are relatively abundant, long-lived, and noisy compared with the core- and bottom-layer TFs. Although variability in expression of top-layer TFs might confer a selective advantage, as this permits at least some members in a clonal cell population to initiate a response to changing conditions, tight regulation of the core- and bottom-layer TFs may minimize noise propagation and ensure fidelity in regulation. We propose that the interplay between network organization and TF dynamics could permit differential utilization of the same underlying network by distinct members of a clonal cell population.

On the basic computational structure of gene regulatory networks

Gene regulatory networks constitute the first layer of the cellular computation for cell adaptation and surveillance. In these webs, a set of causal relations is built up from thousands of interactions between transcription factors and their target genes. The large size of these webs and their entangled nature make it difficult to achieve a global view of their internal organisation. Here, this problem has been addressed through a comparative study of Escherichia coli, Bacillus subtilis and Saccharomyces cerevisiae gene regulatory networks. We extract the minimal core of causal relations, uncovering the hierarchical and modular organisation from a novel dynamical/causal perspective. Our results reveal a marked top-down hierarchy containing several small dynamical modules for E. coli and B. subtilis. Conversely, the yeast network displays a single but large dynamical module in the middle of a bow-tie structure. We found that these dynamical modules capture the relevant wiring among both common and organism-specific biological functions such as transcription initiation, metabolic control, signal transduction, response to stress, sporulation and cell cycle. Functional and topological results suggest that two fundamentally different forms of logic organisation may have evolved in bacteria and yeast.

Toolbox model of evolution of prokaryotic metabolic networks and their regulation

It has been reported that the number of transcription factors encoded in prokaryotic genomes scales approximately quadratically with their total number of genes. We propose a conceptual explanation of this finding and illustrate it using a simple model in which metabolic and regulatory networks of prokaryotes are shaped by horizontal gene transfer of coregulated metabolic pathways. Adapting to a new environmental condition monitored by a new transcription factor (e.g., learning to use another nutrient) involves both acquiring new enzymes and reusing some of the enzymes already encoded in the genome. As the repertoire of enzymes of an organism (its toolbox) grows larger, it can reuse its enzyme tools more often and thus needs to get fewer new ones to master each new task. From this observation, it logically follows that the number of functional tasks and their regulators increases faster than linearly with the total number of genes encoding enzymes. Genomes can also shrink, e.g., because of a loss of a nutrient from the environment, followed by deletion of its regulator and all enzymes that become redundant. We propose several simple models of network evolution elaborating on this toolbox argument and reproducing the empirically observed quadratic scaling. The distribution of lengths of pathway branches in our model agrees with that of the real-life metabolic network of Escherichia coli. Thus, our model provides a qualitative explanation for broad distributions of regulon sizes in prokaryotes.

Transcriptional regulation shapes the organization of genes on bacterial chromosomes

Transcription factors (TFs) are the key elements responsible for controlling the expression of genes in bacterial genomes and when visualized on a genomic scale form a dense network of transcriptional interactions among themselves and with other protein coding genes. Although the structure of transcriptional regulatory networks (TRNs) is well understood, it is not clear what constrains govern them. Here, we explore this question using the TRNs of model prokaryotes and provide a link between the transcriptional hierarchy of regulons and their genome organization. We show that, to drive the kinetics and concentration gradients, TFs belonging to big and small regulons, depending on the number of genes they regulate, organize themselves differently on the genome with respect to their targets. We then propose a conceptual model that can explain how the hierarchical structure of TRNs might be ultimately governed by the dynamic biophysical requirements for targeting DNA-binding sites by TFs. Our results suggest that the main parameters defining the position of a TF in the network hierarchy are the number and chromosomal distances of the genes they regulate and their protein concentration gradients. These observations give insights into how the hierarchical structure of transcriptional networks can be encoded on the chromosome to drive the kinetics and concentration gradients of TFs depending on the number of genes they regulate and could be a common theme valid for other prokaryotes, proposing the role of transcriptional regulation in shaping the organization of genes on a chromosome.

Regulation by transcription factors in bacteria: beyond description

Transcription is an essential step in gene expression and its understanding has been one of the major interests in molecular and cellular biology. By precisely tuning gene expression, transcriptional regulation determines the molecular machinery for developmental plasticity, homeostasis and adaptation. In this review, we transmit the main ideas or concepts behind regulation by transcription factors and give just enough examples to sustain these main ideas, thus avoiding a classical ennumeration of facts. We review recent concepts and developments: cis elements and trans regulatory factors, chromosome organization and structure, transcriptional regulatory networks (TRNs) and transcriptomics. We also summarize new important discoveries that will probably affect the direction of research in gene regulation: epigenetics and stochasticity in transcriptional regulation, synthetic circuits and plasticity and evolution of TRNs. Many of the new discoveries in gene regulation are not extensively tested with wetlab approaches. Consequently, we review this broad area in Inference of TRNs and Dynamical Models of TRNs. Finally, we have stepped backwards to trace the origins of these modern concepts, synthesizing their history in a timeline schema.