The carbon assimilation network in Escherichia coli is densely connected and largely sign-determined by directions of metabolic fluxes

An ensemble of mathematical models showing diauxic growth behaviour

Background

Carbon catabolite repression (CCR) controls the order in which different carbon sources are metabolised. Although this system is one of the paradigms of regulation in bacteria, the underlying mechanisms remain controversial. CCR involves the coordination of different subsystems of the cell - responsible for the uptake of carbon sources, their breakdown for the production of energy and precursors, and the conversion of the latter to biomass. The complexity of this integrated system, with regulatory mechanisms cutting across metabolism, gene expression, and signalling, has motivated important modelling efforts over the past four decades, especially in the enterobacterium Escherichia coli.

Results

Starting from a simple core model with only four intracellular metabolites, we develop an ensemble of model variants, all showing diauxic growth behaviour during a batch process. The model variants fall into one of the four categories: flux balance models, kinetic models with growth dilution, kinetic models with regulation, and resource allocation models. The model variants differ from one another in only a single aspect, each breaking the symmetry between the two substrate assimilation pathways in a different manner, and can be quantitatively compared using a so-called diauxic growth index. For each of the model variants, we predict the behaviour in two new experimental conditions, namely a glucose pulse for a culture growing in minimal medium with lactose and a batch culture with different initial concentrations of the components of the transport systems. When qualitatively comparing these predictions with experimental data for these two conditions, a number of models can be excluded while other model variants are still not discriminable. The best-performing model variants are based on inducer inclusion and activation of enzymatic genes by a global transcription factor, but the other proposed factors may complement these well-known regulatory mechanisms.

Conclusions

The model ensemble presented here offers a better understanding of the variety of mechanisms that have been proposed to play a role in CCR. In addition, it provides an educational resource for systems biology, as it gives an introduction to a broad range of modeling approaches in the context of a simple but biologically relevant example.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0604-8) contains supplementary material, which is available to authorized users.

Principal process analysis of biological models

BACKGROUND

Understanding the dynamical behaviour of biological systems is challenged by their large number of components and interactions. While efforts have been made in this direction to reduce model complexity, they often prove insufficient to grasp which and when model processes play a crucial role. Answering these questions is fundamental to unravel the functioning of living organisms.

RESULTS

We design a method for dealing with model complexity, based on the analysis of dynamical models by means of Principal Process Analysis. We apply the method to a well-known model of circadian rhythms in mammals. The knowledge of the system trajectories allows us to decompose the system dynamics into processes that are active or inactive with respect to a certain threshold value. Process activities are graphically represented by Boolean and Dynamical Process Maps. We detect model processes that are always inactive, or inactive on some time interval. Eliminating these processes reduces the complex dynamics of the original model to the much simpler dynamics of the core processes, in a succession of sub-models that are easier to analyse. We quantify by means of global relative errors the extent to which the simplified models reproduce the main features of the original system dynamics and apply global sensitivity analysis to test the influence of model parameters on the errors.

CONCLUSION

The results obtained prove the robustness of the method. The analysis of the sub-model dynamics allows us to identify the source of circadian oscillations. We find that the negative feedback loop involving proteins PER, CRY, CLOCK-BMAL1 is the main oscillator, in agreement with previous modelling and experimental studies. In conclusion, Principal Process Analysis is a simple-to-use method, which constitutes an additional and useful tool for analysing the complex dynamical behaviour of biological systems.

Analysis Tools for Interconnected Boolean Networks With Biological Applications

Boolean networks with asynchronous updates are a class of logical models particularly well adapted to describe the dynamics of biological networks with uncertain measures. The state space of these models can be described by an asynchronous state transition graph, which represents all the possible exits from every single state, and gives a global image of all the possible trajectories of the system. In addition, the asynchronous state transition graph can be associated with an absorbing Markov chain, further providing a semi-quantitative framework where it becomes possible to compute probabilities for the different trajectories. For large networks, however, such direct analyses become computationally untractable, given the exponential dimension of the graph. Exploiting the general modularity of biological systems, we have introduced the novel concept of asymptotic graph, computed as an interconnection of several asynchronous transition graphs and recovering all asymptotic behaviors of a large interconnected system from the behavior of its smaller modules. From a modeling point of view, the interconnection of networks is very useful to address for instance the interplay between known biological modules and to test different hypotheses on the nature of their mutual regulatory links. This paper develops two new features of this general methodology: a quantitative dimension is added to the asymptotic graph, through the computation of relative probabilities for each final attractor and a companion cross-graph is introduced to complement the method on a theoretical point of view.

Mathematical modelling of microbes: metabolism, gene expression and growth

The growth of microorganisms involves the conversion of nutrients in the environment into biomass, mostly proteins and other macromolecules. This conversion is accomplished by networks of biochemical reactions cutting across cellular functions, such as metabolism, gene expression, transport and signalling. Mathematical modelling is a powerful tool for gaining an understanding of the functioning of this large and complex system and the role played by individual constituents and mechanisms. This requires models of microbial growth that provide an integrated view of the reaction networks and bridge the scale from individual reactions to the growth of a population. In this review, we derive a general framework for the kinetic modelling of microbial growth from basic hypotheses about the underlying reaction systems. Moreover, we show that several families of approximate models presented in the literature, notably flux balance models and coarse-grained whole-cell models, can be derived with the help of additional simplifying hypotheses. This perspective clearly brings out how apparently quite different modelling approaches are related on a deeper level, and suggests directions for further research.

Metabolic regulation is sufficient for global and robust coordination of glucose uptake, catabolism, energy production and growth in Escherichia coli

The metabolism of microorganisms is regulated through two main mechanisms: changes of enzyme capacities as a consequence of gene expression modulation (“hierarchical control”) and changes of enzyme activities through metabolite-enzyme interactions. An increasing body of evidence indicates that hierarchical control is insufficient to explain metabolic behaviors, but the system-wide impact of metabolic regulation remains largely uncharacterized. To clarify its role, we developed and validated a detailed kinetic model of Escherichia coli central metabolism that links growth to environment. Metabolic control analyses confirm that the control is widely distributed across the network and highlight strong interconnections between all the pathways. Exploration of the model solution space reveals that several robust properties emerge from metabolic regulation, from the molecular level (e.g. homeostasis of total metabolite pool) to the overall cellular physiology (e.g. coordination of carbon uptake, catabolism, energy and redox production, and growth), while allowing a large degree of flexibility at most individual metabolic steps. These properties have important physiological implications for E. coli and significantly expand the self-regulating capacities of its metabolism.

Metabolism is a fundamental biochemical process that enables cells to operate and grow by converting nutrients into ‘building blocks’ and energy. Metabolism happens through the work of enzymes, which are encoded by genes. Thus, genes and their regulation are often thought of controlling metabolism, somewhat at the top of a hierarchical control system. However, an increasing body of evidence indicates that metabolism plays an active role in the control of its own operation via a dense network of metabolite-enzyme interactions. The system-wide role of metabolic regulation is hard to dissect and so far remains largely uncharacterized. To better understand its role, we constructed a detailed kinetic model of the carbon and energy metabolism of the bacterium Escherichia coli, a model organism in Systems and Synthetic biology. Model simulations indicate that kinetic considerations of metabolism alone can explain data from hundreds of experiments, without needing to invoke regulation of gene expression. In particular, metabolic regulation is sufficient to coordinate carbon utilization, redox and energy production, and growth, while maintaining local flexibility at individual metabolic steps. These findings indicate that the self-regulating capacities of E. coli metabolism are far more significant than previously expected, and improve our understanding on how cells work.

Low-rank network decomposition reveals structural characteristics of small-world networks

Small-world networks occur naturally throughout biological, technological, and social systems. With their prevalence, it is particularly important to prudently identify small-world networks and further characterize their unique connection structure with respect to network function. In this work we develop a formalism for classifying networks and identifying small-world structure using a decomposition of network connectivity matrices into low-rank and sparse components, corresponding to connections within clusters of highly connected nodes and sparse interconnections between clusters, respectively. We show that the network decomposition is independent of node indexing and define associated bounded measures of connectivity structure, which provide insight into the clustering and regularity of network connections. While many existing network characterizations rely on constructing benchmark networks for comparison or fail to describe the structural properties of relatively densely connected networks, our classification relies only on the intrinsic network structure and is quite robust with respect to changes in connection density, producing stable results across network realizations. Using this framework, we analyze several real-world networks and reveal new structural properties, which are often indiscernible by previously established characterizations of network connectivity.

Modeling the Interplay of EIIANtr with the Potassium Transporter KdpFABC

The nitrogen phosphotransferase system (PTS^Ntr) of <i>Pseudomonas putida</i> is a key regulatory device that participates in controlling many physiological processes in a posttranscriptional fashion. One of the target functions of the PTS^Ntr is the regulation of potassium transport. This is mediated by the direct interaction of one of its components with the sensor kinase KdpD of the two-component system controlling transcription of the <i>kdpFABC</i> genes. From a detailed experimental analysis of the activity of the <i>kdpF</i> promoter in <i>P. putida</i> wild-type and <i>pts</i> mutant strains with varying potassium concentrations, we had highly time-resolved data at hand, describing the influence of the PTS^Ntr on the transcription of the KdpFABC potassium transporter. Here, this data was used to construct a mathematical model based on a black box approach. The model was able to describe the data quantitatively with convincing accuracy. The qualitative interpretation of the model allowed the prediction of two general points describing the interplay between the PTS^Ntr and the KdpFABC potassium transporter: (1) the influence of cell number on the performance of the <i>kdpF</i> promoter is mainly by dilution by growth and (2) potassium uptake is regulated not only by the activity of the KdpD/KdpE two-component system (in turn influenced by PtsN). An additional controller with integrative behavior is predicted by the model structure. This suggests the presence of a novel physiological mechanism during regulation of potassium uptake with the KdpFABC transporter and may serve as a starting point for further investigations.

A novel characterization of amalgamated networks in natural systems

Densely-connected networks are prominent among natural systems, exhibiting structural characteristics often optimized for biological function. To reveal such features in highly-connected networks, we introduce a new network characterization determined by a decomposition of network-connectivity into low-rank and sparse components. Based on these components, we discover a new class of networks we define as amalgamated networks, which exhibit large functional groups and dense connectivity. Analyzing recent experimental findings on cerebral cortex, food-web, and gene regulatory networks, we establish the unique importance of amalgamated networks in fostering biologically advantageous properties, including rapid communication among nodes, structural stability under attacks, and separation of network activity into distinct functional modules. We further observe that our network characterization is scalable with network size and connectivity, thereby identifying robust features significant to diverse physical systems, which are typically undetectable by conventional characterizations of connectivity. We expect that studying the amalgamation properties of biological networks may offer new insights into understanding their structure-function relationships.

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).

Understanding carbon catabolite repression in Escherichia coli using quantitative models

Carbon catabolite repression (CCR) controls the order in which different carbon sources are metabolized. Although this system is one of the paradigms of the regulation of gene expression in bacteria, the underlying mechanisms remain controversial. CCR involves the coordination of different subsystems of the cell that are responsible for the uptake of carbon sources, their breakdown for the production of energy and precursors, and the conversion of the latter to biomass. The complexity of this integrated system, with regulatory mechanisms cutting across metabolism, gene expression, and signaling, and that are subject to global physical and physiological constraints, has motivated important modeling efforts over the past four decades, especially in the enterobacterium Escherichia coli. Different hypotheses concerning the dynamic functioning of the system have been explored by a variety of modeling approaches. We review these studies and summarize their contributions to the quantitative understanding of CCR, focusing on diauxic growth in E. coli. Moreover, we propose a highly simplified representation of diauxic growth that makes it possible to bring out the salient features of the models proposed in the literature and confront and compare the explanations they provide.

Dependency of cellular decision making in physiology and influence of preceding growth conditions

Events from the past growth conditions influence the course of physiology, and it gets reflected in the present cell behaviour. During this process, cells acquire a metabolic option which carries signature of the past, and it dictates the performance in the present situation. Study uses Escherichia coli as a sample organism wherein three scenarios of preceding growth conditions were created with varying nutritional status and pre-treatment strategies. This exercise leads to different seed cultures, which were subjected to growth using the four different substrates. The different seed culture behaviours were analysed by observing the respirometric rate of the seed culture and were followed by growth dynamics with different substrates. These two data sets were independently analysed by three-way ANOVA to arrive at strategic coupling of programming conditions to relate the available (respirometric rates) and executable physiology (growth kinetics).

Coordination of microbial metabolism

Beyond fuelling cellular activities with building blocks and energy, metabolism also integrates environmental conditions into intracellular signals. The underlying regulatory network is complex and multifaceted: it ranges from slow interactions, such as changing gene expression, to rapid ones, such as the modulation of protein activity via post-translational modification or the allosteric binding of small molecules. In this Review, we outline the coordination of common metabolic tasks, including nutrient uptake, central metabolism, the generation of energy, the supply of amino acids and protein synthesis. Increasingly, a set of key metabolites is recognized to control individual regulatory circuits, which carry out specific functions of information input and regulatory output. Such a modular view of microbial metabolism facilitates an intuitive understanding of the molecular mechanisms that underlie cellular decision making.

QSSPN: dynamic simulation of molecular interaction networks describing gene regulation, signalling and whole-cell metabolism in human cells

MOTIVATION

Dynamic simulation of genome-scale molecular interaction networks will enable the mechanistic prediction of genotype-phenotype relationships. Despite advances in quantitative biology, full parameterization of whole-cell models is not yet possible. Simulation methods capable of using available qualitative data are required to develop dynamic whole-cell models through an iterative process of modelling and experimental validation.

RESULTS

We formulate quasi-steady state Petri nets (QSSPN), a novel method integrating Petri nets and constraint-based analysis to predict the feasibility of qualitative dynamic behaviours in qualitative models of gene regulation, signalling and whole-cell metabolism. We present the first dynamic simulations including regulatory mechanisms and a genome-scale metabolic network in human cell, using bile acid homeostasis in human hepatocytes as a case study. QSSPN simulations reproduce experimentally determined qualitative dynamic behaviours and permit mechanistic analysis of genotype-phenotype relationships.

AVAILABILITY AND IMPLEMENTATION

The model and simulation software implemented in C++ are available in supplementary material and at http://sysbio3.fhms.surrey.ac.uk/qsspn/.

Identification of key regulators in glycogen utilization in E. coli based on the simulations from a hybrid functional Petri net model

BACKGROUND

Glycogen and glucose are two sugar sources available during the lag phase of E. coli, but the mechanism that regulates their utilization is still unclear.

METHODS

Attempting to unveil the relationship between glucose and glycogen, we propose an integrated hybrid functional Petri net (HFPN) model including glycolysis, PTS, glycogen metabolic pathway, and their internal regulatory systems.

RESULTS AND CONCLUSIONS

By comparing known biological results to this model, basic necessary regulatory mechanism for utilizing glucose and glycogen were identified as a feedback circuit in which HPr and EIIAGlc play key roles. Based on this regulatory HFPN model, we discuss the process of glycogen utilization in E. coli in the context of a systematic understanding of carbohydrate metabolism.

Shared control of gene expression in bacteria by transcription factors and global physiology of the cell

A simple, parameterless mathematical model, in combination with real-time monitoring of promoter activities, shows how control of gene expression in bacteria is shared between transcription factors and global physiological effects.

We present an approach based on a simple, paramaterless mathematical model to analyze the control of gene expression by transcription factors and the global physiological state of the cell.

We illustrate the strength of this approach by means of time-resolved measurements of the transcriptional activities of genes in a central regulatory circuit in Escherichia coli.

We conclude that global physiological effects rather than transcription factors dominate the control of gene expression during a growth transition.

Our results call for a reappraisal of the role of transcription factors, which may be most appropriately viewed as complementing and finetuning global control exerted by the physiological state of the cell.

Gene expression is controlled by the joint effect of (i) the global physiological state of the cell, in particular the activity of the gene expression machinery, and (ii) DNA-binding transcription factors and other specific regulators. We present a model-based approach to distinguish between these two effects using time-resolved measurements of promoter activities. We demonstrate the strength of the approach by analyzing a circuit involved in the regulation of carbon metabolism in E. coli. Our results show that the transcriptional response of the network is controlled by the physiological state of the cell and the signaling metabolite cyclic AMP (cAMP). The absence of a strong regulatory effect of transcription factors suggests that they are not the main coordinators of gene expression changes during growth transitions, but rather that they complement the effect of global physiological control mechanisms. This change of perspective has important consequences for the interpretation of transcriptome data and the design of biological networks in biotechnology and synthetic biology.

A genome-wide screen for identifying all regulators of a target gene

We have developed a new screening methodology for identifying all genes that control the expression of a target gene through genetic or metabolic interactions. The screen combines mutant libraries with luciferase reporter constructs, whose expression can be monitored in vivo and over time in different environmental conditions. We apply the method to identify the genes that control the expression of the gene acs, encoding the acetyl coenzyme A synthetase, in Escherichia coli. We confirm most of the known genetic regulators, including CRP-cAMP, IHF and components of the phosphotransferase system. In addition, we identify new regulatory interactions, many of which involve metabolic intermediates or metabolic sensing, such as the genes pgi, pfkA, sucB and lpdA, encoding enzymes in glycolysis and the TCA cycle. Some of these novel interactions were validated by quantitative reverse transcriptase-polymerase chain reaction. More generally, we observe that a large number of mutants directly or indirectly influence acs expression, an effect confirmed for a second promoter, sdhC. The method is applicable to any promoter fused to a luminescent reporter gene in combination with a deletion mutant library.

Information theoretical methods for complex network structure reconstruction

Purpose

Complex networks seem to be ubiquitous objects in contemporary research, both in the natural and social sciences. An important area of research regarding the applicability and modeling of graph- theoretical-oriented approaches to complex systems, is the probabilistic inference of such networks. There exist different methods and algorithms designed for this purpose, most of them are inspired in statistical mechanics and rely on information theoretical grounds. An important shortcoming for most of these methods, when it comes to disentangle the actual structure of complex networks, is that they fail to distinguish between direct and indirect interactions. Here, we suggest a method to discover and assess for such indirect interactions within the framework of information theory.

Methods

Information-theoretical measures (in particular, Mutual Information) are applied for the probabilistic inference of complex networks. Data Processing Inequality is used to find and assess for direct and indirect interactions impact in complex networks.

Results

We outline the mathematical basis of information-theoretical assessment of complex network structure and discuss some examples of application in the fields of biological systems and social networks.

Conclusions

Information theory provides to the field of complex networks analysis with effective means for structural assessment with a computational burden low enough to be useful in both, Biological and Social network analysis.

Global stability of reversible enzymatic metabolic chains

We consider metabolic networks with reversible enzymatic reactions. The model is written as a system of ordinary differential equations, possibly with inputs and outputs. We prove the global stability of the equilibrium (if it exists), using techniques of monotone systems and compartmental matrices. We show that the equilibrium does not always exist. Finally, we consider a metabolic system coupled with a genetic network, and we study the dependence of the metabolic equilibrium (if it exists) with respect to concentrations of enzymes. We give some conclusions concerning the dynamical behavior of coupled genetic/metabolic systems.

Towards multiscale plant models: integrating cellular networks

One of the ambitions of 'crop systems biology' is to combine information from molecular biology with a broader view of plant development and growth. In the context of modeling, this calls for a multiscale perspective that focuses on the interplay between cellular and macroscopic studies. With this in mind, in this review we aim to draw attention to a panel of approaches that were developed in the context of systems biology and are used for analyzing and describing the behavior of cellular networks. Ultimately, insights obtained from these methods can be exploited to refine the description of plant processes, leading to integrated plant-cellular models.

Towards multiscale plant models: integrating cellular networks

One of the ambitions of 'crop systems biology' is to combine information from molecular biology with a broader view of plant development and growth. In the context of modeling, this calls for a multiscale perspective that focuses on the interplay between cellular and macroscopic studies. With this in mind, in this review we aim to draw attention to a panel of approaches that were developed in the context of systems biology and are used for analyzing and describing the behavior of cellular networks. Ultimately, insights obtained from these methods can be exploited to refine the description of plant processes, leading to integrated plant-cellular models.

Analysis and Design of Stimulus Response Curves of E. coli

Metabolism and signalling are tightly coupled in bacteria. Combining several theoretical approaches, a core model is presented that describes transcriptional and allosteric control of glycolysis in Escherichia coli. Experimental data based on microarrays, signaling components and extracellular metabolites are used to estimate kinetic parameters. A newly designed strain was used that adjusts the incoming glucose flux into the system and allows a kinetic analysis. Based on the results, prediction for intracelluar metabolite concentrations over a broad range of the growth rate could be performed and compared with data from literature.

Structural and dynamical analysis of biological networks

Biological networks are currently being studied with approaches derived from the mathematical and physical sciences. Their structural analysis enables to highlight nodes with special properties that have sometimes been correlated with the biological importance of a gene or a protein. However, biological networks are dynamic both on the evolutionary time-scale, and on the much shorter time-scale of physiological processes. There is therefore no unique network for a given cellular process, but potentially many realizations, each with different properties as a consequence of regulatory mechanisms. Such realizations provide snapshots of a same network in different conditions, enabling the study of condition-dependent structural properties. True dynamical analysis can be obtained through detailed mathematical modeling techniques that are not easily scalable to full network models.

Recent advances in engineering the central carbon metabolism of industrially important bacteria

This paper gives an overview of the recent advances in engineering the central carbon metabolism of the industrially important bacteria Escherichia coli, Bacillus subtilis, Corynobacterium glutamicum, Streptomyces spp., Lactococcus lactis and other lactic acid bacteria. All of them are established producers of important classes of products, e.g. proteins, amino acids, organic acids, antibiotics, high-value metabolites for the food industry and also, promising producers of a large number of industrially or therapeutically important chemicals. Optimization of existing or introduction of new cellular processes in these microorganisms is often achieved through manipulation of targets that reside at major points of central metabolic pathways, such as glycolysis, gluconeogenesis, the pentose phosphate pathway and the tricarboxylic acid cycle with the glyoxylate shunt. Based on the huge progress made in recent years in biochemical, genetic and regulatory studies, new fascinating engineering approaches aim at ensuring an optimal carbon and energy flow within central metabolism in order to achieve optimized metabolite production.

Reusing and composing models of cell fate regulation of human bone precursor cells

In order to treat osteoporosis and other bone mass disorders it is necessary to understand the regulatory processes that control the cell fate decisions responsible for going from bone precursor cells to bone tissue. Many processes interact to regulate cell division, differentiation and apoptosis. There are models for these basic processes, but not for their interactions. In this work we use the theory of switched systems, reuse and composition of validated models to describe the cell fate decisions leading to bone and fat formation. We describe the differentiation of osteo-adipo progenitor cells by composing its model with differentiation stimuli. We use the activation of the Wnt pathway as stimulus to osteoblast lineage, including regulation of cell division and apoptosis. This model is our first step to simulate physiological responses in silico to treatments for bone mass disorders.

Importance of metabolic coupling for the dynamics of gene expression following a diauxic shift in Escherichia coli

Gene regulatory networks consist of direct interactions, but also include indirect interactions mediated by metabolism. We investigate to which extent these indirect interactions arising from metabolic coupling influence the dynamics of the system. To this end, we build a qualitative model of the gene regulatory network controlling carbon assimilation in Escherichia coli, and use this model to study the changes in gene expression following a diauxic shift from glucose to acetate. In particular, we compare the relative variation in the steady-state concentrations of enzymes and transcription regulators during growth on glucose and acetate, as well as the dynamic response of gene expression to the exhaustion of glucose and the subsequent assimilation of acetate. We find significant differences between the dynamics of the system in the absence and presence of metabolic coupling. This shows that interactions arising from metabolic coupling cannot be ignored when studying the dynamics of gene regulatory networks.

The logic layout of the TOL network of Pseudomonas putida pWW0 plasmid stems from a metabolic amplifier motif (MAM) that optimizes biodegradation of m-xylene

Background

The genetic network of the TOL plasmid pWW0 of the soil bacterium Pseudomonas putida mt-2 for catabolism of m-xylene is an archetypal model for environmental biodegradation of aromatic pollutants. Although nearly every metabolic and transcriptional component of this regulatory system is known to an extraordinary molecular detail, the complexity of its architecture is still perplexing. To gain an insight into the inner layout of this network a logic model of the TOL system was implemented, simulated and experimentally validated. This analysis made sense of the specific regulatory topology out on the basis of an unprecedented network motif around which the entire genetic circuit for m-xylene catabolism gravitates.

Results

The most salient feature of the whole TOL regulatory network is the control exerted by two distinct but still intertwined regulators (XylR and XylS) on expression of two separated catabolic operons (upper and lower) for catabolism of m-xylene. Following model reduction, a minimal modular circuit composed by five basic variables appeared to suffice for fully describing the operation of the entire system. In silico simulation of the effect of various perturbations were compared with experimental data in which specific portions of the network were activated with selected inducers: m-xylene, o-xylene, 3-methylbenzylalcohol and 3-methylbenzoate. The results accredited the ability of the model to faithfully describe network dynamics. This analysis revealed that the entire regulatory structure of the TOL system enables the action an unprecedented metabolic amplifier motif (MAM). This motif synchronizes expression of the upper and lower portions of a very long metabolic system when cells face the head pathway substrate, m-xylene.

Conclusion

Logic modeling of the TOL circuit accounted for the intricate regulatory topology of this otherwise simple metabolic device. The found MAM appears to ensure a simultaneous expression of the upper and lower segments of the m-xylene catabolic route that would be difficult to bring about with a standard substrate-responsive single promoter. Furthermore, it is plausible that the MAM helps to avoid biochemical conflicts between competing plasmid-encoded and chromosomally-encoded pathways in this bacterium.

Systems approaches to modelling pathways and networks

It has become commonly accepted that systems approaches to biology are of outstanding importance to gain understanding from the vast amount of data which is presently being generated by advancing high-throughput technologies. The diversity of methods to model pathways and networks has significantly expanded over the past two decades. Modern and traditional approaches are equally important and recent activities aim at integrating the advantages of both. While traditional methods, based on differential equations, are useful to study the dynamics of small systems, modern constraint-based models can be applied to genome-scale systems, but are not able to capture dynamic features. Integrating different approaches is important to develop consistent theoretical descriptions encompassing various scales of biological information. The rapid progress of the field of theoretical systems biology, however, demonstrates how our fundamental theoretical understanding of biology is gaining momentum. The scientific community has apparently accepted the challenge to truly understand the principles of life.

Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance

In quantitative genetics, the degree of resemblance between parents and offspring is described in terms of the additive variance (V(A)) relative to genetic (V(G)) and phenotypic (V(P)) variance. For populations with extreme allele frequencies, high V(A)/V(G) can be explained without considering properties of the genotype-phenotype (GP) map. We show that randomly generated GP maps in populations with intermediate allele frequencies generate far lower V(A)/V(G) values than empirically observed. The main reason is that order-breaking behaviour is ubiquitous in random GP maps. Rearrangement of genotypic values to introduce order-preservation for one or more loci causes a dramatic increase in V(A)/V(G). This suggests the existence of order-preserving design principles in the regulatory machinery underlying GP maps. We illustrate this feature by showing how the ubiquitously observed monotonicity of dose-response relationships gives much higher V(A)/V(G) values than a unimodal dose-response relationship in simple gene network models.

The logicome of environmental bacteria: merging catabolic and regulatory events with Boolean formalisms

The regulatory and metabolic networks that rule biodegradation of pollutants by environmental bacteria are wired to the rest of the cellular physiology through both transcriptional factors and intermediary signal molecules. In this review, we examine some formalisms for describing catalytic/regulatory circuits of this sort and advocate the adoption of Boolean logic for combining transcriptional and enzymatic occurrences in the same biological system. As an example, we show how known regulatory and metabolic actions that bring about biodegradation of m-xylene by Pseudomonas putida mt-2 can be represented as clusters of binary operations and then reconstructed as a digital network. Despite the many simplifications, Boolean tools still capture the gross behaviour of the system even in the absence of kinetic constants determined experimentally. On this basis, we argue that still with a limited volume of data binary formalisms allow us to penetrate the raison d'être of extant regulatory and metabolic architectures.

Carbon metabolism and the sign of control coefficients in metabolic adaptations underlying K-ras transformation

Metabolic adaptations are associated with changes in enzyme activities. These adaptations are characterized by patterns of positive and negative changes in metabolic fluxes and concentrations of intermediate metabolites. Knowledge of the mechanism and parameters governing enzyme kinetics is rarely available. However, the signs-increases or decreases-of many of these changes can be predicted using the signs of metabolic control coefficients. These signs require the only knowledge of the structure of the metabolic network and a limited qualitative knowledge of the regulatory dependences, which is widely available for carbon metabolism. Here, as a case study, we identified control coefficients with fixed signs in order to predict the pattern of changes in key enzyme activities which can explain the observed changes in fluxes and concentrations underlying the metabolic adaptations in oncogenic K-ras transformation in NIH-3T3 cells. The fixed signs of control coefficients indicate that metabolic changes following the oncogenic transformation-increased glycolysis and oxidative branch of the pentose-phosphate pathway, and decreased concentration in sugar-phosphates-could be associated with increases in activity for glucose-6-phosphate dehydrogenase, pyruvate kinase and lactate dehydrogenase, and decrease for transketolase. These predictions were validated experimentally by measuring specific activities. We conclude that predictions based on fixed signs of control coefficients are a very robust tool for the identification of changes in enzyme activities that can explain observed metabolic adaptations in carbon metabolism.

Toward a quantitative modeling of the synthesis of the pectate lyases, essential virulence factors in Dickeya dadantii

A dynamic mathematical model has been developed and validated to describe the synthesis of pectate lyases (Pels), the major virulence factors in Dickeya dadantii. This work focuses on the simultaneous modeling of the metabolic degradation of pectin by Pel enzymes and the genetic regulation of pel genes by 2-keto-3-deoxygluconate (KDG), a catabolite product of pectin that inactivates KdgR, one of the main repressors of pel genes. This modeling scheme takes into account the fact that the system is composed of two time-varying compartments: the extracellular medium, where Pel enzymes cleave pectin into oligomers, and the bacterial cytoplasm where, after internalization, oligomers are converted to KDG. Using the quasi-stationary state approximations, the model consists of some nonlinear differential equations for which most of the parameters could be estimated from the literature or from independent experiments. The few remaining unknown parameters were obtained by fitting the model equations against a set of Pel activity data. Model predictions were verified by measuring the time courses of bacterial growth, Pel production, pel mRNA accumulation, and pectin consumption under various growth conditions. This work reveals that pectin is almost totally consumed before the burst of Pel production. This paradoxical behavior can be interpreted as an evolutionary strategy to control the diffusion process so that as soon as a small amount of pectin is detected by the bacteria in its surroundings, it anticipates more pectin to come. The model also predicts the possibility of bistable steady states in the presence of constant pectin compounds.