Dynamic analysis of optimality in myocardial energy metabolism under normal and ischemic conditions

Metabolic Modelling as a Framework for Metabolomics Data Integration and Analysis

Metabolic networks are regulated to ensure the dynamic adaptation of biochemical reaction fluxes to maintain cell homeostasis and optimal metabolic fitness in response to endogenous and exogenous perturbations. To this end, metabolism is tightly controlled by dynamic and intricate regulatory mechanisms involving allostery, enzyme abundance and post-translational modifications. The study of the molecular entities involved in these complex mechanisms has been boosted by the advent of high-throughput technologies. The so-called omics enable the quantification of the different molecular entities at different system layers, connecting the genotype with the phenotype. Therefore, the study of the overall behavior of a metabolic network and the omics data integration and analysis must be approached from a holistic perspective. Due to the close relationship between metabolism and cellular phenotype, metabolic modelling has emerged as a valuable tool to decipher the underlying mechanisms governing cell phenotype. Constraint-based modelling and kinetic modelling are among the most widely used methods to study cell metabolism at different scales, ranging from cells to tissues and organisms. These approaches enable integrating metabolomic data, among others, to enhance model predictive capabilities. In this review, we describe the current state of the art in metabolic modelling and discuss future perspectives and current challenges in the field.

Introducing an Optimization- and explicit Runge-Kutta- based Approach to Perform Dynamic Flux Balance Analysis

In this work we introduce the generalized Optimization- and explicit Runge-Kutta-based Approach (ORKA) to perform dynamic Flux Balance Analysis (dFBA), which is numerically more accurate and computationally tractable than existing approaches. ORKA is applied to a four-tissue (leaf, root, seed, and stem) model of Arabidopsis thaliana, p-ath773, uniquely capturing the core-metabolism of several stages of growth from seedling to senescence at hourly intervals. Model p-ath773 has been designed to show broad agreement with published plant-scale properties such as mass, maintenance, and senescence, yet leaving reaction-level behavior unconstrainted. Hence, it serves as a framework to study the reaction-level behavior necessary for observed plant-scale behavior. Two such case studies of reaction-level behavior include the lifecycle progression of sulfur metabolism and the diurnal flow of water throughout the plant. Specifically, p-ath773 shows how transpiration drives water flow through the plant and how water produced by leaf tissue metabolism may contribute significantly to transpired water. Investigation of sulfur metabolism elucidates frequent cross-compartment exchange of a standing pool of amino acids which is used to regulate the proton flow. Overall, p-ath773 and ORKA serve as scaffolds for dFBA-based lifecycle modeling of plants and other systems to further broaden the scope of in silico metabolic investigation.

Metabolic acclimation-a key to enhancing photosynthesis in changing environments?

Plants adjust their photosynthetic capacity in response to their environment in a way that optimizes their yield and fitness. There is growing evidence that this acclimation is a response to changes in the leaf metabolome, but the extent to which these are linked and how this is optimized remain poorly understood. Using as an example the metabolic perturbations occurring in response to cold, we define the different stages required for acclimation, discuss the evidence for a metabolic temperature sensor, and suggest further work towards designing climate-smart crops. In particular, we discuss how constraint-based and kinetic metabolic modelling approaches can be used to generate targeted hypotheses about relevant pathways, and argue that a stronger integration of experimental and in silico studies will help us to understand the tightly regulated interplay of carbon partitioning and resource allocation required for photosynthetic acclimation to different environmental conditions.

Clostridium butyricum population balance model: Predicting dynamic metabolic flux distributions using an objective function related to extracellular glycerol content

BACKGROUND

Extensive experimentation has been conducted to increment 1,3-propanediol (PDO) production using Clostridium butyricum cultures in glycerol, but computational predictions are limited. Previously, we reconstructed the genome-scale metabolic (GSM) model iCbu641, the first such model of a PDO-producing Clostridium strain, which was validated at steady state using flux balance analysis (FBA). However, the prediction ability of FBA is limited for batch and fed-batch cultures, which are the most often employed industrial processes.

RESULTS

We used the iCbu641 GSM model to develop a dynamic flux balance analysis (DFBA) approach to predict the PDO production of the Colombian strain Clostridium sp IBUN 158B. First, we compared the predictions of the dynamic optimization approach (DOA), static optimization approach (SOA), and direct approach (DA). We found no differences between approaches, but the DOA simulation duration was nearly 5000 times that of the SOA and DA simulations. Experimental results at glycerol limitation and glycerol excess allowed for validating dynamic predictions of growth, glycerol consumption, and PDO formation. These results indicated a 4.4% error in PDO prediction and therefore validated the previously proposed objective functions. We performed two global sensitivity analyses, finding that the kinetic input parameters of glycerol uptake flux had the most significant effect on PDO predictions. The other input parameters evaluated during global sensitivity analysis were biomass composition (precursors and macromolecules), death constants, and the kinetic parameters of acetic acid secretion flux. These last input parameters, all obtained from other Clostridium butyricum cultures, were used to develop a population balance model (PBM). Finally, we simulated fed-batch cultures, predicting a final PDO production near to 66 g/L, almost three times the PDO predicted in the best batch culture.

CONCLUSIONS

We developed and validated a dynamic approach to predict PDO production using the iCbu641 GSM model and the previously proposed objective functions. This validated approach was used to propose a population model and then an increment in predictions of PDO production through fed-batch cultures. Therefore, this dynamic model could predict different scenarios, including its integration into downstream processes to predict technical-economic feasibilities and reducing the time and costs associated with experimentation.

Compound danshen dripping pills modulate the perturbed energy metabolism in a rat model of acute myocardial ischemia

The continuous administration of compound danshen dripping pills (CDDP) showed good efficacy in relieving myocardial ischemia clinically. To probe the underlying mechanism, metabolic features were evaluated in a rat model of acute myocardial ischemia induced by isoproterenol (ISO) and administrated with CDDP using a metabolomics platform. Our data revealed that the ISO-induced animal model showed obvious myocardial injury, decreased energy production, and a marked change in metabolomic patterns in plasma and heart tissue. CDDP pretreatment increased energy production, ameliorated biochemical indices, modulated the changes and metabolomic pattern induced by ISO, especially in heart tissue. For the first time, we found that ISO induced myocardial ischemia was accomplished with a reduced fatty acids metabolism and an elevated glycolysis for energy supply upon the ischemic stress; while CDDP pretreatment prevented the tendency induced by ISO and enhanced a metabolic shift towards fatty acids metabolism that conventionally dominates energy supply to cardiac muscle cells. These data suggested that the underlying mechanism of CDDP involved regulating the dominant energy production mode and enhancing a metabolic shift toward fatty acids metabolism in ischemic heart. It was further indicated that CDDP had the potential to prevent myocardial ischemia in clinic.

Integration of transcriptomics and metabolomics data specifies the metabolic response of Chlamydomonas to rapamycin treatment

Flux phenotypes predicted by constraint-based methods can be refined by the inclusion of heterogeneous data. While recent advances facilitate the integration of transcriptomics and proteomics data, purely stoichiometry-based approaches for the prediction of flux phenotypes by considering metabolomics data are lacking. Here we propose a constraint-based method, termed TREM-Flux, for integrating time-resolved metabolomics and transcriptomics data. We demonstrate the applicability of TREM-Flux in the dissection of the metabolic response of Chlamydomonas reinhardtii to rapamycin treatment by integrating the expression levels of 982 genes and the content of 45 metabolites obtained from two growth conditions. The findings pinpoint cysteine and methionine metabolism to be most affected by the rapamycin treatment. Our study shows that the integration of time-resolved unlabeled metabolomics data in addition to transcriptomics data can specify the metabolic pathways involved in the system's response to a studied treatment.

Integration of metabolomics data into metabolic networks

Metabolite levels together with their corresponding metabolic fluxes are integrative outcomes of biochemical transformations and regulatory processes and they can be used to characterize the response of biological systems to genetic and/or environmental changes. However, while changes in transcript or to some extent protein levels can usually be traced back to one or several responsible genes, changes in fluxes and particularly changes in metabolite levels do not follow such rationale and are often the outcome of complex interactions of several components. The increasing quality and coverage of metabolomics technologies have fostered the development of computational approaches for integrating metabolic read-outs with large-scale models to predict the physiological state of a system. Constraint-based approaches, relying on the stoichiometry of the considered reactions, provide a modeling framework amenable to analyses of large-scale systems and to the integration of high-throughput data. Here we review the existing approaches that integrate metabolomics data in variants of constrained-based approaches to refine model reconstructions, to constrain flux predictions in metabolic models, and to relate network structural properties to metabolite levels. Finally, we discuss the challenges and perspectives in the developments of constraint-based modeling approaches driven by metabolomics data.

MetDFBA: incorporating time-resolved metabolomics measurements into dynamic flux balance analysis

This paper presents MetDFBA, a new approach incorporating experimental metabolomics time-series into constraint-based modeling. The method can be used for hypothesis testing and predicting dynamic flux profiles.

Metabonomic analysis of Allium macrostemon Bunge as a treatment for acute myocardial ischemia in rats

Myocardial ischemia (MI) refers to a pathological state of the heart caused by reduced cardiac blood perfusion, which leads to a decreased oxygen supply in the heart and an abnormal myocardial energy metabolism. Acute myocardial ischemia (AMI) has posed a significant health risk for humans. Allium macrostemon Bunge (AMB), a popular traditional Chinese medicine, is used for MI treatment. The therapeutic effects of AMB were assessed and the detailed mechanisms of AMB for AMI treatment were investigated. We characterized the metabonomic variations in rats from the sham surgery, AMI, and AMB-pretreated AMI groups through a combination of nuclear magnetic resonance (NMR) spectroscopy and multivariate statistical analysis. Thirty-five metabolites including carbohydrates, a range of amino acids, and organic acids were detected. The (1)H NMR spectra of the rat serum were analyzed using the principal component analysis (PCA) and orthogonal projection to latent structures discriminate analysis (OPLS-DA). Results showed that AMI induced some physiological changes in rats and also led to metabolic disorders related to glycolysis promotion, amino acid metabolism disruption, and other metabolite metabolism perturbation. AMB pretreatment reduced the AMI injury and maintained metabolic balance, possibly by limiting the change in energy metabolism and regulating amino acid metabolism. These findings provide a comprehensive insight on the metabolic response of AMI rats to AMB pretreatment and are important for the use of AMB for AMI therapy.

Dynamic regulatory on/off minimization for biological systems under internal temporal perturbations

Background

Flux balance analysis (FBA) together with its extension, dynamic FBA, have proven instrumental for analyzing the robustness and dynamics of metabolic networks by employing only the stoichiometry of the included reactions coupled with adequately chosen objective function. In addition, under the assumption of minimization of metabolic adjustment, dynamic FBA has recently been employed to analyze the transition between metabolic states.

Results

Here, we propose a suite of novel methods for analyzing the dynamics of (internally perturbed) metabolic networks and for quantifying their robustness with limited knowledge of kinetic parameters. Following the biochemically meaningful premise that metabolite concentrations exhibit smooth temporal changes, the proposed methods rely on minimizing the significant fluctuations of metabolic profiles to predict the time-resolved metabolic state, characterized by both fluxes and concentrations. By conducting a comparative analysis with a kinetic model of the Calvin-Benson cycle and a model of plant carbohydrate metabolism, we demonstrate that the principle of regulatory on/off minimization coupled with dynamic FBA can accurately predict the changes in metabolic states.

Conclusions

Our methods outperform the existing dynamic FBA-based modeling alternatives, and could help in revealing the mechanisms for maintaining robustness of dynamic processes in metabolic networks over time.

Model-based confirmation of alternative substrates of mitochondrial electron transport chain

Discrimination of metabolic models based on high throughput metabolomics data, reflecting various internal and external perturbations, is essential for identifying the components that contribute to the emerging behavior of metabolic processes. Here, we investigate 12 different models of the mitochondrial electron transport chain (ETC) in Arabidopsis thaliana during dark-induced senescence in order to elucidate the alternative substrates to this metabolic pathway. Our findings demonstrate that the coupling of the proposed computational approach, based on dynamic flux balance analysis, with time-resolved metabolomics data results in model-based confirmations of the hypotheses that, during dark-induced senescence in Arabidopsis, (i) under conditions where the main substrate for the ETC are not fully available, isovaleryl-CoA dehydrogenase and 2-hydroxyglutarate dehydrogenase are able to donate electrons to the ETC, (ii) phytanoyl-CoA does not act even as an indirect substrate of the electron transfer flavoprotein/electron-transfer flavoprotein:ubiquinone oxidoreductase complex, and (iii) the mitochondrial γ-aminobutyric acid transporter has functional significance in maintaining mitochondrial metabolism. Our study provides a basic framework for future in silico studies of alternative pathways in mitochondrial metabolism under extended darkness whereby the role of its components can be computationally discriminated based on available molecular profile data.

Astrocyte-neuron lactate shuttle may boost more ATP supply to the neuron under hypoxic conditions--in silico study supported by in vitro expression data

Background

Neuro-glial interactions are important for normal functioning of the brain as well as brain energy metabolism. There are two major working models - in the classical view, both neurons and astrocytes can utilize glucose as the energy source through oxidative metabolism, whereas in the astrocyte-neuron lactate shuttle hypothesis (ANLSH) it is the astrocyte which can consume glucose through anaerobic glycolysis to pyruvate and then to lactate, and this lactate is secreted to the extracellular space to be taken up by the neuron for further oxidative degradation.

Results

In this computational study, we have included hypoxia-induced genetic regulation of these enzymes and transporters, and analyzed whether the ANLSH model can provide an advantage to either cell type in terms of supplying the energy demand. We have based this module on our own experimental analysis of hypoxia-dependent regulation of transcription of key metabolic enzymes. Using this experimentation-supported in silico modeling, we show that under both normoxic and hypoxic conditions in a given time period ANLSH model does indeed provide the neuron with more ATP than in the classical view.

Conclusions

Although the ANLSH is energetically more favorable for the neuron, it is not the case for the astrocyte in the long term. Considering the fact that astrocytes are more resilient to hypoxia, we would propose that there is likely a switch between the two models, based on the energy demand of the neuron, so as to maintain the survival of the neuron under hypoxic or glucose-and-oxygen-deprived conditions.

Myocardial contractile and metabolic properties of familial hypertrophic cardiomyopathy caused by cardiac troponin I gene mutations: a simulation study

Familial hypertrophic cardiomyopathy (FHC) is an inherited disease that is caused by sarcomeric protein gene mutations. The mechanism by which these mutant proteins cause disease is uncertain. Experimentally, cardiac troponin I (CTnI) gene mutations mainly alter myocardial performance via increases in the Ca(2+) sensitivity of cardiac contractility. In this study, we used an integrated simulation that links electrophysiology, contractile activity and energy metabolism of the myocardium to investigate alterations in myocardial contractile function and energy metabolism regulation as a result of increased Ca(2+) sensitivity in CTnI mutations. Simulation results reproduced the following typical features of FHC: (1) slower relaxation (diastolic dysfunction) caused by prolonged [Ca(2+)](i) and force transients; (2) higher energy consumption with the increase in Ca(2+) sensitivity; and (3) reduced fatty acid oxidation and enhanced glucose utilization in hypertrophied heart metabolism. Furthermore, the simulation indicated that in conditions of high energy consumption (that is, more than an 18.3% increase in total energy consumption), the myocardial energetic metabolic network switched from a net consumer to a net producer of lactate, resulting in a low coupling of glucose oxidation to glycolysis, which is a common feature of hypertrophied hearts. This study provides a novel systematic myocardial contractile and metabolic analysis to help elucidate the pathogenesis of FHC and suggests that the alterations in resting heart energy supply and demand could contribute to disease progression.

Automated refinement and inference of analytical models for metabolic networks

The reverse engineering of metabolic networks from experimental data is traditionally a labor-intensive task requiring a priori systems knowledge. Using a proven model as a test system, we demonstrate an automated method to simplify this process by modifying an existing or related model--suggesting nonlinear terms and structural modifications--or even constructing a new model that agrees with the system's time series observations. In certain cases, this method can identify the full dynamical model from scratch without prior knowledge or structural assumptions. The algorithm selects between multiple candidate models by designing experiments to make their predictions disagree. We performed computational experiments to analyze a nonlinear seven-dimensional model of yeast glycolytic oscillations. This approach corrected mistakes reliably in both approximated and overspecified models. The method performed well to high levels of noise for most states, could identify the correct model de novo, and make better predictions than ordinary parametric regression and neural network models. We identified an invariant quantity in the model, which accurately derived kinetics and the numerical sensitivity coefficients of the system. Finally, we compared the system to dynamic flux estimation and discussed the scaling and application of this methodology to automated experiment design and control in biological systems in real time.

Expanding a dynamic flux balance model of yeast fermentation to genome-scale

Background

Yeast is considered to be a workhorse of the biotechnology industry for the production of many value-added chemicals, alcoholic beverages and biofuels. Optimization of the fermentation is a challenging task that greatly benefits from dynamic models able to accurately describe and predict the fermentation profile and resulting products under different genetic and environmental conditions. In this article, we developed and validated a genome-scale dynamic flux balance model, using experimentally determined kinetic constraints.

Results

Appropriate equations for maintenance, biomass composition, anaerobic metabolism and nutrient uptake are key to improve model performance, especially for predicting glycerol and ethanol synthesis. Prediction profiles of synthesis and consumption of the main metabolites involved in alcoholic fermentation closely agreed with experimental data obtained from numerous lab and industrial fermentations under different environmental conditions. Finally, fermentation simulations of genetically engineered yeasts closely reproduced previously reported experimental results regarding final concentrations of the main fermentation products such as ethanol and glycerol.

Conclusion

A useful tool to describe, understand and predict metabolite production in batch yeast cultures was developed. The resulting model, if used wisely, could help to search for new metabolic engineering strategies to manage ethanol content in batch fermentations.

Autophagy in heart disease: a strong hypothesis for an untouched metabolic reserve

Autophagy is a conserved catabolic process for long-lived proteins and organelles and is primarily responsible for nonspecific degradation of redundant or faulty cell components. Although autophagy has been described as the cell's major adaptive strategy in response to metabolic challenges, its influence on the cell's energy profile is poorly understood. In the myocardium, autophagy is active at basal levels and is crucial for maintaining its contractile function. Defects in the autophagic machinery cause cardiac dysfunction and heart failure. In this paper we propose that (1) autophagy contributes significantly to the metabolic balance sheet of the heart. (2) Increased autophagy contributes to an improved myocardial energy profile through changing the cardiac substrate preference. (3) Substrates generated through autophagy give rise to an alternative for ATP production with an oxygen-sparing effect. These elements identify autophagy in a new context of myocardial metabolic interregulation, which we discuss in the settings of myocardial infarction, heart failure and the diabetic heart. It is hoped that the hypothesis presented can lead to new insights aimed at exploiting autophagy to improve existing metabolic-based therapy in heart disease.

The application of flux balance analysis in systems biology

An increasing number of genome-scale reconstructions of intracellular biochemical networks are being generated. Coupled with these stoichiometric models, several systems-based approaches for probing these reconstructions in silico have been developed. One such approach, called flux balance analysis (FBA), has been effective at predicting systemic phenotypes in the form of fluxes through a reaction network. FBA employs a linear programming (LP) strategy to generate a flux distribution that is optimized toward a particular 'objective,' subject to a set of underlying physicochemical and thermodynamic constraints. Although classical FBA assumes steady-state conditions, several extensions have been proposed in recent years to constrain the allowable flux distributions and enable characterization of dynamic profiles even with minimal kinetic information. Furthermore, FBA coupled with techniques for measuring fluxes in vivo has facilitated integration of computational and experimental approaches, and is allowing pursuit of rational hypothesis-driven research. Ultimately, as we will describe in this review, studying intracellular reaction fluxes allows us to understand network structure and function and has broad applications ranging from metabolic engineering to drug discovery.

Dynamic metabolic flux analysis demonstrated on cultures where the limiting substrate is changed from carbon to nitrogen and vice versa

The main requirement for metabolic flux analysis (MFA) is that the cells are in a pseudo-steady state, that there is no accumulation or depletion of intracellular metabolites. In the past, the applications of MFA were limited to the analysis of continuous cultures. This contribution introduces the concept of dynamic MFA and extends MFA so that it is applicable to transient cultures. Time series of concentration measurements are transformed into flux values. This transformation involves differentiation, which typically increases the noisiness of the data. Therefore, a noise-reducing step is needed. In this work, polynomial smoothing was used. As a test case, dynamic MFA is applied on Escherichia coli cultivations shifting from carbon limitation to nitrogen limitation and vice versa. After switching the limiting substrate from N to C, a lag phase was observed accompanied with an increase in maintenance energy requirement. This lag phase did not occur in the C- to N-limitation case.

Computational biology approaches to plant metabolism and photosynthesis: applications for corals in times of climate change and environmental stress

Knowledge of factors that are important in reef resilience helps us to understand how reef ecosystems react following major anthropogenic and environmental disturbances. The symbiotic relationship between the photosynthetic zooxanthellae algal cells and corals is that the zooxanthellae provide the coral with carbon, while the coral provides protection and access to enough light for the zooxanthellae to photosynthesise. This article reviews some recent advances in computational biology relevant to photosynthetic organisms, including Beyesian approaches to kinetics, computational methods for flux balances in metabolic processes, and determination of clades of zooxanthallae. Application of these systems will be important in the conservation of coral reefs in times of climate change and environmental stress.

Transient metabolic modeling of Escherichia coli MG1655 and MG1655 DeltaackA-pta, DeltapoxB Deltapppc ppc-p37 for recombinant beta-galactosidase production

Escherichia coli is one of the most widely used hosts for the production of recombinant proteins, among other reasons because its genetics are far better characterized than those of any other microorganism. To improve the understanding of recombinant protein synthesis in E. coli, the production of a model recombinant protein, beta-galactosidase, was studied in response to the constitutive overexpression of the anaplerotic reaction afforded by PEP carboxylase. To this end, an IPTG wash-in experiment was performed starting from a well-defined steady-state condition for both the wild-type E. coli and a mutant with a defective acetate pathway and a constitutively overexpressed ppc. In order to compare the dynamics of the fluxes over time during the wash-in experiment, a method referred to as transient metabolic flux analysis, which is based on steady-state metabolic flux analysis, was used. This allowed us to track the intracellular changes/fluxes in both strains. It was observed that the flux towards fermentation products was 3.6 times lower in the ppc overexpression mutant compared to the wild-type E. coli. In the former on the other hand, the PPC flux is in general higher. In addition, the flux towards beta-galactosidase was higher (12.4 times), resulting in five times more protein activity. These results indicate that by constitutively overexpressing the anaplerotic ppc gene in E. coli, the TCA cycle intermediates are increasingly replenished. The additional supply of these protein precursors has a positive result on recombinant protein production.

Systems biology in heart diseases

Systems biology based on integrative computational analysis and high technology is in a position to construct networks, to study the interactions between molecular components and to develop models of cardiac function and anatomy. Clinical cardiology gets an integrated picture of parameters that are addressed to ventricular and vessel mechanics, cardiac metabolism and electrical activation. The achievement of clinical objectives is based on the interaction between modern technology and clinical phenotype. In this review the need for more sophisticated realization of the structure and function of the cardiovascular system is emphasized while the incorporation of the systems biology concept in predicting clinical phenotypes is a promising strategy that optimize diagnosis and treatment in cardiovascular disease.

Computational approaches to metabolomics

This chapter is intended to familiarize readers with the field of metabolomics and some of the algorithms, data analysis strategies, and computer programs used to analyze or interpret metabolomic data. Specifically, this chapter provides a brief overview of the experimental approaches and applications of metabolomics followed by a description of the spectral and statistical analysis tools for metabolomics. The chapter concludes with a discussion of the resources that can be used to interpret and analyze metabolomic data at a biological or clinical level. Emerging needs, challenges, and recent progress being made in these areas are also discussed.

Photosynthetic metabolism of C3 plants shows highly cooperative regulation under changing environments: a systems biological analysis

We studied the robustness of photosynthetic metabolism in the chloroplasts of C(3) plants under drought stress and at high CO(2) concentration conditions by using a method called Minimization of Metabolic Adjustment Dynamic Flux Balance Analysis (M_DFBA). Photosynthetic metabolism in the chloroplasts of C(3) plants applies highly cooperative regulation to minimize the fluctuation of metabolite concentration profiles in the face of transient perturbations. Our work suggests that highly cooperative regulation assures the robustness of the biological system and that there is closer cooperation under perturbation conditions than under normal conditions. This results in minimizing fluctuations in the profiles of metabolite concentrations, which is the key to maintaining a system's function. Our methods help in understanding such phenomena and the mechanisms of robustness for complex metabolic networks in dynamic processes.

Integrating metabolic, transcriptional regulatory and signal transduction models in Escherichia coli

MOTIVATION

The effort to build a whole-cell model requires the development of new modeling approaches, and in particular, the integration of models for different types of processes, each of which may be best described using different representation. Flux-balance analysis (FBA) has been useful for large-scale analysis of metabolic networks, and methods have been developed to incorporate transcriptional regulation (regulatory FBA, or rFBA). Of current interest is the integration of these approaches with detailed models based on ordinary differential equations (ODEs).

RESULTS

We developed an approach to modeling the dynamic behavior of metabolic, regulatory and signaling networks by combining FBA with regulatory Boolean logic, and ordinary differential equations. We use this approach (called integrated FBA, or iFBA) to create an integrated model of Escherichia coli which combines a flux-balance-based, central carbon metabolic and transcriptional regulatory model with an ODE-based, detailed model of carbohydrate uptake control. We compare the predicted Escherichia coli wild-type and single gene perturbation phenotypes for diauxic growth on glucose/lactose and glucose/glucose-6-phosphate with that of the individual models. We find that iFBA encapsulates the dynamics of three internal metabolites and three transporters inadequately predicted by rFBA. Furthermore, we find that iFBA predicts different and more accurate phenotypes than the ODE model for 85 of 334 single gene perturbation simulations, as well for the wild-type simulations. We conclude that iFBA is a significant improvement over the individual rFBA and ODE modeling paradigms.

AVAILABILITY

All MATLAB files used in this study are available at http://www.simtk.org/home/ifba/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

The regulatory network of E. coli metabolism as a Boolean dynamical system exhibits both homeostasis and flexibility of response

Background

Elucidating the architecture and dynamics of large scale genetic regulatory networks of cells is an important goal in systems biology. We study the system level dynamical properties of the genetic network of Escherichia coli that regulates its metabolism, and show how its design leads to biologically useful cellular properties. Our study uses the database (Covert et al., Nature 2004) containing 583 genes and 96 external metabolites which describes not only the network connections but also the Boolean rule at each gene node that controls the switching on or off of the gene as a function of its inputs.

Results

We have studied how the attractors of the Boolean dynamical system constructed from this database depend on the initial condition of the genes and on various environmental conditions corresponding to buffered minimal media. We find that the system exhibits homeostasis in that its attractors, that turn out to be fixed points or low period cycles, are highly insensitive to initial conditions or perturbations of gene configurations for any given fixed environment. At the same time the attractors show a wide variation when external media are varied implying that the system mounts a highly flexible response to changed environmental conditions. The regulatory dynamics acts to enhance the cellular growth rate under changed media.

Conclusion

Our study shows that the reconstructed genetic network regulating metabolism in E. coli is hierarchical, modular, and largely acyclic, with environmental variables controlling the root of the hierarchy. This architecture makes the cell highly robust to perturbations of gene configurations as well as highly responsive to environmental changes. The twin properties of homeostasis and response flexibility are achieved by this dynamical system even though it is not close to the edge of chaos.

An overview of cardiac systems biology

The cardiac system has been a major target for intensive studies in the multi-scale modeling field for many years. Reproduction of the action potential and the ionic currents of single cardiomyocytes, as well as the construction of a whole organ model is well established. Still, there are major hurdles to overcome in creating a realistic and predictive functional cardiac model due to the lack of a profound understanding of the complex molecular interactions and their outcomes controlling both normal and pathological cardiophysiology. The recent advent of systems biology offers the conceptual and practical frameworks to tackle such biological complexities. This review provides an overview of major themes in the developing field of cardiac systems biology, summarizing some of the high-throughput experiments and strategies used to integrate the datasets, and various types of computational approaches used for developing useful quantitative models capable of predicting complex biological behavior.

Metabolic flux analysis in plants: from intelligent design to rational engineering

Metabolic flux analysis (MFA) is a rapidly developing field concerned with the quantification and understanding of metabolism at the systems level. The application of MFA has produced detailed maps of flow through metabolic networks of a range of plant systems. These maps represent detailed metabolic phenotypes, contribute significantly to our understanding of metabolism in plants, and have led to the discovery of new metabolic routes. The presentation of thorough statistical evaluation with current flux maps has set a new standard for the quality of quantitative flux studies. In microbial systems, powerful methods have been developed for the reconstruction of metabolic networks from genomic and transcriptomic data, pathway analysis, and predictive modeling. This review brings together the recent developments in quantitative MFA and predictive modeling. The application of predictive tools to high quality flux maps in particular promises to be important in the rational metabolic engineering of plants.

Metabolic networks in motion: 13C-based flux analysis

Many properties of complex networks cannot be understood from monitoring the components—not even when comprehensively monitoring all protein or metabolite concentrations—unless such information is connected and integrated through mathematical models. The reason is that static component concentrations, albeit extremely informative, do not contain functional information per se. The functional behavior of a network emerges only through the nonlinear gene, protein, and metabolite interactions across multiple metabolic and regulatory layers. I argue here that intracellular reaction rates are the functional end points of these interactions in metabolic networks, hence are highly relevant for systems biology. Methods for experimental determination of metabolic fluxes differ fundamentally from component concentration measurements; that is, intracellular reaction rates cannot be detected directly, but must be estimated through computer model-based interpretation of stable isotope patterns in products of metabolism.

Thematic review series: Systems Biology Approaches to Metabolic and Cardiovascular Disorders. Network perspectives of cardiovascular metabolism

In this review, we examine cardiovascular metabolism from three different, but highly complementary, perspectives. First, from the abstract perspective of a metabolite network, composed of nodes and links. We present fundamental concepts in network theory, including emergence, to illustrate how nature has designed metabolism with a hierarchal modular scale-free topology to provide a robust system of energy delivery. Second, from the physical perspective of a modular spatially compartmentalized network. We review evidence that cardiovascular metabolism is functionally compartmentalized, such that oxidative phosphorylation, glycolysis, and glycogenolysis preferentially channel ATP to ATPases in different cellular compartments, using creatine kinase and adenylate kinase to maximize efficient energy delivery. Third, from the dynamics perspective, as a network of dynamically interactive metabolic modules capable of self-oscillation. Whereas normally, cardiac metabolism exists in a regime in which excitation-metabolism coupling closely matches energy supply and demand, we describe how under stressful conditions, the network can be pushed into a qualitatively new dynamic regime, manifested as cell-wide oscillations in ATP levels, in which the coordination between energy supply and demand is lost. We speculate how this state of "metabolic fibrillation" leads to cell death if not corrected and discuss the implications for cardioprotection.