Thirteen years of building constraint-based in silico models of Escherichia coli

Putative regulatory sites unraveled by network-embedded thermodynamic analysis of metabolome data

As one of the most recent members of the omics family, large-scale quantitative metabolomics data are currently complementing our systems biology data pool and offer the chance to integrate the metabolite level into the functional analysis of cellular networks. Network-embedded thermodynamic analysis (NET analysis) is presented as a framework for mechanistic and model-based analysis of these data. By coupling the data to an operating metabolic network via the second law of thermodynamics and the metabolites' Gibbs energies of formation, NET analysis allows inferring functional principles from quantitative metabolite data; for example it identifies reactions that are subject to active allosteric or genetic regulation as exemplified with quantitative metabolite data from Escherichia coli and Saccharomyces cerevisiae. Moreover, the optimization framework of NET analysis was demonstrated to be a valuable tool to systematically investigate data sets for consistency, for the extension of sub-omic metabolome data sets and for resolving intracompartmental concentrations from cell-averaged metabolome data. Without requiring any kind of kinetic modeling, NET analysis represents a perfectly scalable and unbiased approach to uncover insights from quantitative metabolome data.

Towards multidimensional genome annotation

Our information about the gene content of organisms continues to grow as more genomes are sequenced and gene products are characterized. Sequence-based annotation efforts have led to a list of cellular components, which can be thought of as a one-dimensional annotation. With growing information about component interactions, facilitated by the advancement of various high-throughput technologies, systemic, or two-dimensional, annotations can be generated. Knowledge about the physical arrangement of chromosomes will lead to a three-dimensional spatial annotation of the genome and a fourth dimension of annotation will arise from the study of changes in genome sequences that occur during adaptive evolution. Here we discuss all four levels of genome annotation, with specific emphasis on two-dimensional annotation methods.

A kinetic model of oxygen regulation of cytochrome production in Escherichia coli

Recent experimental work has identified the principal components arrayed by Escherichia coli in its sensing of, and response to, varying levels of oxygen. This apparatus may be leveraged/modified by the metabolic engineer to identify nonuniform oxygen and glucose regimens that deliver better yields than their uniform counterparts. Toward this end we build and analyse a mathematical model that captures the role played by oxygen in the regulation of cytochrome production in E. coli.

Theodor Bücher Lecture. Metabolomics, modelling and machine learning in systems biology - towards an understanding of the languages of cells. Delivered on 3 July 2005 at the 30th FEBS Congress and the 9th IUBMB conference in Budapest

The newly emerging field of systems biology involves a judicious interplay between high-throughput 'wet' experimentation, computational modelling and technology development, coupled to the world of ideas and theory. This interplay involves iterative cycles, such that systems biology is not at all confined to hypothesis-dependent studies, with intelligent, principled, hypothesis-generating studies being of high importance and consequently very far from aimless fishing expeditions. I seek to illustrate each of these facets. Novel technology development in metabolomics can increase substantially the dynamic range and number of metabolites that one can detect, and these can be exploited as disease markers and in the consequent and principled generation of hypotheses that are consistent with the data and achieve this in a value-free manner. Much of classical biochemistry and signalling pathway analysis has concentrated on the analyses of changes in the concentrations of intermediates, with 'local' equations - such as that of Michaelis and Menten v=(Vmax x S)/(S+K m) - that describe individual steps being based solely on the instantaneous values of these concentrations. Recent work using single cells (that are not subject to the intellectually unsupportable averaging of the variable displayed by heterogeneous cells possessing nonlinear kinetics) has led to the recognition that some protein signalling pathways may encode their signals not (just) as concentrations (AM or amplitude-modulated in a radio analogy) but via changes in the dynamics of those concentrations (the signals are FM or frequency-modulated). This contributes in principle to a straightforward solution of the crosstalk problem, leads to a profound reassessment of how to understand the downstream effects of dynamic changes in the concentrations of elements in these pathways, and stresses the role of signal processing (and not merely the intermediates) in biological signalling. It is this signal processing that lies at the heart of understanding the languages of cells. The resolution of many of the modern and postgenomic problems of biochemistry requires the development of a myriad of new technologies (and maybe a new culture), and thus regular input from the physical sciences, engineering, mathematics and computer science. One solution, that we are adopting in the Manchester Interdisciplinary Biocentre (http://www.mib.ac.uk/) and the Manchester Centre for Integrative Systems Biology (http://www.mcisb.org/), is thus to colocate individuals with the necessary combinations of skills. Novel disciplines that require such an integrative approach continue to emerge. These include fields such as chemical genomics, synthetic biology, distributed computational environments for biological data and modelling, single cell diagnostics/bionanotechnology, and computational linguistics/text mining.

Metabolic engineering in the -omics era: elucidating and modulating regulatory networks

The importance of regulatory control in metabolic processes is widely acknowledged, and several enquiries (both local and global) are being made in understanding regulation at various levels of the metabolic hierarchy. The wealth of biological information has enabled identifying the individual components (genes, proteins, and metabolites) of a biological system, and we are now in a position to understand the interactions between these components. Since phenotype is the net result of these interactions, it is immensely important to elucidate them not only for an integrated understanding of physiology, but also for practical applications of using biological systems as cell factories. We present some of the recent "-omics" approaches that have expanded our understanding of regulation at the gene, protein, and metabolite level, followed by analysis of the impact of this progress on the advancement of metabolic engineering. Although this review is by no means exhaustive, we attempt to convey our ideology that combining global information from various levels of metabolic hierarchy is absolutely essential in understanding and subsequently predicting the relationship between changes in gene expression and the resulting phenotype. The ultimate aim of this review is to provide metabolic engineers with an overview of recent advances in complementary aspects of regulation at the gene, protein, and metabolite level and those involved in fundamental research with potential hurdles in the path to implementing their discoveries in practical applications.

Identification of metabolic system parameters using global optimization methods

BACKGROUND

The problem of estimating the parameters of dynamic models of complex biological systems from time series data is becoming increasingly important.

METHODS AND RESULTS

Particular consideration is given to metabolic systems that are formulated as Generalized Mass Action (GMA) models. The estimation problem is posed as a global optimization task, for which novel techniques can be applied to determine the best set of parameter values given the measured responses of the biological system. The challenge is that this task is nonconvex. Nonetheless, deterministic optimization techniques can be used to find a global solution that best reconciles the model parameters and measurements. Specifically, the paper employs branch-and-bound principles to identify the best set of model parameters from observed time course data and illustrates this method with an existing model of the fermentation pathway in Saccharomyces cerevisiae. This is a relatively simple yet representative system with five dependent states and a total of 19 unknown parameters of which the values are to be determined.

CONCLUSION

The efficacy of the branch-and-reduce algorithm is illustrated by the S. cerevisiae example. The method described in this paper is likely to be widely applicable in the dynamic modeling of metabolic networks.

Characterizing phenotype with tracer based metabolomics

In the post-genomic era, a pressing challenge to biological scientists is to understand the organization of gene functions, the interaction between gene and nutrient environment, and the genesis of phenotypes. Metabolomics, the quantitation of low molecular weight compounds, has been used to provide a phenotypic description of a cell or tissue by a set of metabolites. Gene function is hypothesized from its correlation with the corresponding set of macromolecules by transcriptomics or proteomics. Another approach to genotype-phenotype correlation is by the reconstruction of genome-scale metabolic maps. The utilization of specific pathways as predicted by reaction network analysis provides the phenotypic characterization of a cell, which can be plotted on a phenotypic phase plane. Tracer based metabolomics is the experimental approach to reaction network analysis using stable isotope tracers. The redistribution of the isotope tracer among metabolic intermediates is used to identify a finite number of pathways, the utilization of which is characteristic of the phenotypic behavior of cells. In this paper, we review tracer based metabolomic methods for the construction of phenotypic phase plane plots, and discuss the functional implications of phenotypic phase plane analysis. Examples of phenotypic changes in response to differentiation, inhibition of signaling pathways and perturbation in nutrient environment are provided.

Use of constraint-based modeling for the prediction and validation of antimicrobial targets

The overall process of antimicrobial drug discovery and development seems simple, to cure infectious disease by identifying suitable antibiotic drugs. However, this goal has been difficult to fulfill in recent years. Despite the promise of the high-throughput innovations sparked by the genomics revolution, discovery, and development of new antibiotics has lagged in recent years exacerbating the already serious problem of evolution of antibiotic resistance. Therefore, both new antimicrobials are desperately needed as are improvements to speed up or improve nearly all steps in the process of discovering novel antibiotics and bringing these to clinical use. Another product of the genomic revolution is the modeling of metabolism using computational methodologies. Genomic-scale networks of metabolic reactions based on stoichiometry, thermodynamics and other physico-chemical constraints that emulate microbial metabolism have been developed into valuable research tools in metabolic engineering and other fields. This constraint-based modeling is predictive in identifying critical reactions, metabolites, and genes in metabolism. This is extremely useful in determining and rationalizing cellular metabolic requirements. In turn, these methods can be used to predict potential metabolic targets for antimicrobial research especially if used to increase the confidence in prioritization of metabolic targets. The many different capacities of constraint-based modeling also enable prediction of cellular response to specific inhibitors such as antibiotics and this may, ultimately find a role in drug discovery and development. Herein, we describe the principles of metabolic modeling and how they might initially be applied to antimicrobial research.

Generalized concept of minimal cut sets in biochemical networks

Recently, the concept of minimal cut sets has been introduced for studying structural fragility and identifying knock-out strategies in biochemical reaction networks. A minimal cut set (MCS) has been defined as a minimal set of reactions whose removal blocks the operation of a chosen objective reaction. In this report the theoretical framework of MCSs is refined and extended increasing the practical applicability significantly. An MCS is now defined as a minimal (irreducible) set of structural interventions (removal of network elements) repressing a certain functionality specified by a deletion task. A deletion task describes unambiguously the flux patterns (or the functionality) to be repressed. It is shown that the MCSs can be computed from the set of target modes, which comprises all elementary modes that exhibit the functionality to be attacked. Since a deletion task can be specified by several Boolean rules, MCSs can now be determined for a large variety of complex deletion problems and may be utilized for inhibiting very special flux patterns. It is additionally shown that the other way around is also possible: the elementary modes belonging to a certain functionality can be computed from the respective set of MCSs. Therefore, elementary modes and MCSs can be seen as dual representations of network functions and both can be converted into each other. Moreover, there exist a strong relationship to minimal hitting sets known from set theory: the MCSs are the minimal hitting sets of the collection of target modes and vice versa. Another generalization introduced herein is that MCSs need not to be restricted to the removal of reactions they may also contain network nodes. In the light of the extended framework of MCSs, applications for assessing, manipulating, and designing metabolic networks in silico are discussed.

Development of a software tool for in silico simulation of Escherichia coli using a visual programming environment

This study describes the development of a software tool, EcoSim, to assist users in implementing quantitative in silico simulation easily. It consists of four parts: extracellular environment and constraints setting mode, table for optimal metabolic flux distribution and chart for changes of substrate concentration, dynamic flux distribution viewer and dynamic hierarchical regulatory network viewer. Representation of a hierarchical regulatory network was constructed with defined modeling symbols and weight in the central Escherichia coli metabolism. All programming procedures for EcoSim were accomplished in a visual programming environment (LabVIEW). To illustrate quantitative in silico simulation with EcoSim, this program was performed on E. coli using glucose and acetate as carbon sources. The simulation results were in agreement with the experimental data obtained from the literature. EcoSim can be used to assist biologists and engineers in predicting and interpreting dynamic behaviors of E. coli under a variety of environmental conditions.

From genomes to in silico cells via metabolic networks

Genome-scale metabolic models are the focal point of systems biology as they allow the collection of various data types in a form suitable for mathematical analysis. High-quality metabolic networks and metabolic networks with incorporated regulation have been successfully used for the analysis of phenotypes from phenotypic arrays and in gene-deletion studies. They have also been used for gene expression analysis guided by metabolic network structure, leading to the identification of commonly regulated genes. Thus, genome-scale metabolic modeling currently stands out as one of the most promising approaches to obtain an in silico prediction of cellular function based on the interaction of all of the cellular components.

Metabolic footprinting and systems biology: the medium is the message

One element of classical systems analysis treats a system as a black or grey box, the inner structure and behaviour of which can be analysed and modelled by varying an internal or external condition, probing it from outside and studying the effect of the variation on the external observables. The result is an understanding of the inner make-up and workings of the system. The equivalent of this in biology is to observe what a cell or system excretes under controlled conditions - the 'metabolic footprint' or exometabolome - as this is readily and accurately measurable. Here, we review the principles, experimental approaches and scientific outcomes that have been obtained with this useful and convenient strategy.

Regulatory on/off minimization of metabolic flux changes after genetic perturbations

Predicting the metabolic state of an organism after a gene knockout is a challenging task, because the regulatory system governs a series of transient metabolic changes that converge to a steady-state condition. Regulatory on/off minimization (ROOM) is a constraint-based algorithm for predicting the metabolic steady state after gene knockouts. It aims to minimize the number of significant flux changes (hence on/off) with respect to the wild type. ROOM is shown to accurately predict steady-state metabolic fluxes that maintain flux linearity, in agreement with experimental flux measurements, and to correctly identify short alternative pathways used for rerouting metabolic flux in response to gene knockouts. ROOM's growth rate and flux predictions are compared with previously suggested algorithms, minimization of metabolic adjustment, and flux balance analysis (FBA). We find that minimization of metabolic adjustment provides accurate predictions for the initial transient growth rates observed during the early postperturbation state, whereas ROOM and FBA more successfully predict final higher steady-state growth rates. Although FBA explicitly maximizes the growth rate, ROOM does not, and only implicitly favors flux distributions having high growth rates. This indicates that, even though the cell has not evolved to cope with specific mutations, regulatory mechanisms aiming to minimize flux changes after genetic perturbations may indeed work to this effect. Further work is needed to identify metrics that characterize the complete trajectory from the initial to the final metabolic steady states after genetic perturbations.

Large-scale 13C-flux analysis reveals mechanistic principles of metabolic network robustness to null mutations in yeast

Genome-scale 13^C-flux analysis in Saccharomyces cerevisiae revealed that the apparent dispensability of knockout mutants with metabolic function can be explained by gene inactivity under a particular condition, by network redundancy through duplicated genes or by alternative pathways.

Background

Quantification of intracellular metabolite fluxes by ¹³C-tracer experiments is maturing into a routine higher-throughput analysis. The question now arises as to which mutants should be analyzed. Here we identify key experiments in a systems biology approach with a genome-scale model of Saccharomyces cerevisiae metabolism, thereby reducing the workload for experimental network analyses and functional genomics.

Results

Genome-scale ¹³C flux analysis revealed that about half of the 745 biochemical reactions were active during growth on glucose, but that alternative pathways exist for only 51 gene-encoded reactions with significant flux. These flexible reactions identified in silico are key targets for experimental flux analysis, and we present the first large-scale metabolic flux data for yeast, covering half of these mutants during growth on glucose. The metabolic lesions were often counteracted by flux rerouting, but knockout of cofactor-dependent reactions, as in the adh1, ald6, cox5A, fum1, mdh1, pda1, and zwf1 mutations, caused flux responses in more distant parts of the network. By integrating computational analyses, flux data, and physiological phenotypes of all mutants in active reactions, we quantified the relative importance of 'genetic buffering' through alternative pathways and network redundancy through duplicate genes for genetic robustness of the network.

Conclusions

The apparent dispensability of knockout mutants with metabolic function is explained by gene inactivity under a particular condition in about half of the cases. For the remaining 207 viable mutants of active reactions, network redundancy through duplicate genes was the major (75%) and alternative pathways the minor (25%) molecular mechanism of genetic network robustness in S. cerevisiae.

Functional ingredient production: application of global metabolic models

The biotechnology industry continuously explores new ways to improve the performance of microbial strains in fermentation processes. Recent focus has been on new genome-wide modelling approaches in functional genomics, which aim to take full advantage of genome sequence data, transcription profiling, proteomics and metabolite profiling for strain improvement. The integration of global metabolic models with genetic and regulatory models will be essential for the practice of metabolic engineering for strain improvement to move forward, simply because we cannot rely on our intuition to grasp the complexity of the biological systems involved.

Uniform sampling of steady-state flux spaces: means to design experiments and to interpret enzymopathies

Reconstruction of genome-scale metabolic networks is now possible using multiple different data types. Constraint-based modeling is an approach to interrogate capabilities of reconstructed networks by constraining possible cellular behavior through the imposition of physicochemical laws. As a result, a steady-state flux space is defined that contains all possible functional states of the network. Uniform random sampling of the steady-state flux space allows for the unbiased appraisal of its contents. Monte Carlo sampling of the steady-state flux space of the reconstructed human red blood cell metabolic network under simulated physiologic conditions yielded the following key results: 1), probability distributions for the values of individual metabolic fluxes showed a wide variety of shapes that could not have been inferred without computation; 2), pairwise correlation coefficients were calculated between all fluxes, determining the level of independence between the measurement of any two fluxes, and identifying highly correlated reaction sets; and 3), the network-wide effects of the change in one (or a few) variables (i.e., a simulated enzymopathy or fixing a flux range based on measurements) were computed. Mathematical models provide the most compact and informative representation of a hypothesis of how a cell works. Thus, understanding model predictions clearly is vital to driving forward the iterative model-building procedure that is at the heart of systems biology. Taken together, the Monte Carlo sampling procedure provides a broadening of the constraint-based approach by allowing for the unbiased and detailed assessment of the impact of the applied physicochemical constraints on a reconstructed network.

Genome-scale reconstruction of the metabolic network in Staphylococcus aureus N315: an initial draft to the two-dimensional annotation

Background

Several strains of bacteria have sequenced and annotated genomes, which have been used in conjunction with biochemical and physiological data to reconstruct genome-scale metabolic networks. Such reconstruction amounts to a two-dimensional annotation of the genome. These networks have been analyzed with a constraint-based formalism and a variety of biologically meaningful results have emerged. Staphylococcus aureus is a pathogenic bacterium that has evolved resistance to many antibiotics, representing a significant health care concern. We present the first manually curated elementally and charge balanced genome-scale reconstruction and model of S. aureus' metabolic networks and compute some of its properties.

Results

We reconstructed a genome-scale metabolic network of S. aureus strain N315. This reconstruction, termed iSB619, consists of 619 genes that catalyze 640 metabolic reactions. For 91% of the reactions, open reading frames are explicitly linked to proteins and to the reaction. All but three of the metabolic reactions are both charge and elementally balanced. The reaction list is the most complete to date for this pathogen. When the capabilities of the reconstructed network were analyzed in the context of maximal growth, we formed hypotheses regarding growth requirements, the efficiency of growth on different carbon sources, and potential drug targets. These hypotheses can be tested experimentally and the data gathered can be used to improve subsequent versions of the reconstruction.

Conclusion

iSB619 represents comprehensive biochemically and genetically structured information about the metabolism of S. aureus to date. The reconstructed metabolic network can be used to predict cellular phenotypes and thus advance our understanding of a troublesome pathogen.

Revealing metabolic phenotypes in plants: inputs from NMR analysis

Assessing the performance of the plant metabolic network, with its varied biosynthetic capacity and its characteristic subcellular compartmentation, remains a considerable challenge. The complexity of the network is such that it is not yet possible to build large-scale predictive models of the fluxes it supports, whether on the basis of genomic and gene expression analysis or on the basis of more traditional measurements of metabolites and their interconversions. This limits the agronomic and biotechnological exploitation of plant metabolism, and it undermines the important objective of establishing a rational metabolic engineering strategy. Metabolic analysis is central to removing this obstacle and currently there is particular interest in harnessing high-throughput and/or large-scale analyses to the task of defining metabolic phenotypes. Nuclear magnetic resonance (NMR) spectroscopy contributes to this objective by providing a versatile suite of analytical techniques for the detection of metabolites and the fluxes between them. The principles that underpin the analysis of plant metabolism by NMR are described, including a discussion of the measurement options for the detection of metabolites in vivo and in vitro, and a description of the stable isotope labelling experiments that provide the basis for metabolic flux analysis. Despite a relatively low sensitivity, NMR is suitable for high-throughput system-wide analyses of the metabolome, providing methods for both metabolite fingerprinting and metabolite profiling, and in these areas NMR can contribute to the definition of plant metabolic phenotypes that are based on metabolic composition. NMR can also be used to investigate the operation of plant metabolic networks. Labelling experiments provide information on the operation of specific pathways within the network, and the quantitative analysis of steady-state labelling experiments leads to the definition of large-scale flux maps for heterotrophic carbon metabolism. These maps define multiple unidirectional fluxes between branch-points in the metabolic network, highlighting the existence of substrate cycles and discriminating in favourable cases between fluxes in the cytosol and plastid. Flux maps can be used to define a functionally relevant metabolic phenotype and the extensive application of such maps in microbial systems suggests that they could have important applications in characterising the genotypes produced by plant genetic engineering.

The JAK-STAT signaling network in the human B-cell: an extreme signaling pathway analysis

Large-scale models of signaling networks are beginning to be reconstructed and corresponding analysis frameworks are being developed. Herein, a reconstruction of the JAK-STAT signaling system in the human B-cell is described and a scalable framework for its network analysis is presented. This approach is called extreme signaling pathway analysis and involves the description of network properties with systemically independent basis vectors called extreme pathways. From the extreme signaling pathways, emergent systems properties of the JAK-STAT signaling network have been characterized, including 1), a mathematical definition of network crosstalk; 2), an analysis of redundancy in signaling inputs and outputs; 3), a study of reaction participation in the network; and 4), a delineation of 85 correlated reaction sets, or systemic signaling modules. This study is the first such analysis of an actual biological signaling system. Extreme signaling pathway analysis is a topologically based approach and assumes a balanced use of the signaling network. As large-scale reconstructions of signaling networks emerge, such scalable analyses will lead to a description of the fundamental systems properties of signal transduction networks.

k-Cone analysis: determining all candidate values for kinetic parameters on a network scale

The absence of comprehensive measured kinetic values and the observed inconsistency in the available in vitro kinetic data has hindered the formulation of network-scale kinetic models of biochemical reaction networks. To meet this challenge we present an approach to construct a convex space, termed the k-cone, which contains all the allowable numerical values of the kinetic constants in large-scale biochemical networks. The definition of the k-cone relies on the incorporation of in vivo concentration data and a simplified approach to represent enzyme kinetics within an established constraint-based modeling approach. The k-cone approach was implemented to define the allowable combination of numerical values for a full kinetic model of human red blood cell metabolism and to study its correlated kinetic parameters. The k-cone approach can be used to determine consistency between in vitro measured kinetic values and in vivo concentration and flux measurements when used in a network-scale kinetic model. k-Cone analysis was successful in determining whether in vitro measured kinetic values used in the reconstruction of a kinetic-based model of Saccharomyces cerevisiae central metabolism could reproduce in vivo measurements. Further, the k-cone can be used to determine which numerical values of in vitro measured parameters are required to be changed in a kinetic model if in vivo measured values are not reproduced. k-Cone analysis could identify what minimum number of in vitro determined kinetic parameters needed to be adjusted in the S. cerevisiae model to be consistent with the in vivo data. Applying the k-cone analysis a priori to kinetic model development may reduce the time and effort involved in model building and parameter adjustment. With the recent developments in high-throughput profiling of metabolite concentrations at a whole-cell scale and advances in metabolomics technologies, the k-cone approach presented here may hold the promise for kinetic characterization of metabolic networks as well as other biological functions at a whole-cell level.

Using metabolic flux data to further constrain the metabolic solution space and predict internal flux patterns: the Escherichia coli spectrum

Constraint-based metabolic modeling has been used to capture the genome-scale, systems properties of an organism's metabolism. The first generation of these models has been built on annotated gene sequence. To further this field, we now need to develop methods to incorporate additional "omic" data types including transcriptomics, metabolomics, and fluxomics to further facilitate the construction, validation, and predictive capabilities of these models. The work herein combines metabolic flux data with an in silico model of central metabolism of Escherichia coli for model centric integration of the flux data. The extreme pathways for this network, which define the allowable solution space for all possible flux distributions, are analyzed using the alpha-spectrum. The alpha-spectrum determines which extreme pathways can and cannot contribute to the metabolic flux distribution for a given condition and gives the allowable range of weightings on each extreme pathway that can contribute. Since many extreme pathways cannot be used under certain conditions, the result is a "condition-specific" solution space that is a subset of the original solution space. The alpha-spectrum results are used to create a "condition-specific" extreme pathway matrix that can be analyzed using singular value decomposition (SVD). The first mode of the SVD analysis characterizes the solution space for a given condition. We show that SVD analysis of the alpha-spectrum extreme pathway matrix that incorporates measured uptake and byproduct secretion rates, can predict internal flux trends for different experimental conditions. These predicted internal flux trends are, in general, consistent with the flux trends measured using experimental metabolic flux analysis techniques.

Candidate metabolic network states in human mitochondria. Impact of diabetes, ischemia, and diet

The human mitochondrial metabolic network was recently reconstructed based on proteomic and biochemical data. Linear programming and uniform random sampling were applied herein to identify candidate steady states of the metabolic network that were consistent with the imposed physico-chemical constraints and available experimental data. The activity of the mitochondrion was studied under four metabolic conditions: normal physiologic, diabetic, ischemic, and dietetic. Pairwise correlations between steady-state reaction fluxes were calculated in each condition to evaluate the dependence among the reactions in the network. Applying constraints on exchange fluxes resulted in predictions for intracellular fluxes that agreed with experimental data. Analyses of the steady-state flux distributions showed that the experimentally observed reduced activity of pyruvate dehydrogenase in vivo could be a result of stoichiometric constraints and therefore would not necessarily require enzymatic inhibition. The observed changes in the energy metabolism of the mitochondrion under diabetic conditions were used to evaluate the impact of previously suggested treatments. The results showed that neither normalized glucose uptake nor decreased ketone body uptake have a positive effect on the mitochondrial energy metabolism or network flexibility. Taken together, this study showed that sampling of the steady-state flux space is a powerful method to investigate network properties under different conditions and provides a basis for in silico evaluations of effects of potential disease treatments.

Genome-scale models of microbial cells: evaluating the consequences of constraints

Microbial cells operate under governing constraints that limit their range of possible functions. With the availability of annotated genome sequences, it has become possible to reconstruct genome-scale biochemical reaction networks for microorganisms. The imposition of governing constraints on a reconstructed biochemical network leads to the definition of achievable cellular functions. In recent years, a substantial and growing toolbox of computational analysis methods has been developed to study the characteristics and capabilities of microorganisms using a constraint-based reconstruction and analysis (COBRA) approach. This approach provides a biochemically and genetically consistent framework for the generation of hypotheses and the testing of functions of microbial cells.

Dynamic profiling of the glucose metabolic network in fasted rat hepatocytes using [1,2-13C2]glucose

Recent studies in metabolic profiling have underscored the importance of the concept of a metabolic network of pathways with special functional characteristics that differ from those of simple reaction sequences. The characterization of metabolic functions requires the simultaneous measurement of substrate fluxes of interconnecting pathways. Here we present a novel stable isotope method by which the forward and reverse fluxes of the futile cycles of the hepatic glucose metabolic network are simultaneously determined. Unlike previous radio-isotope methods, a single tracer [1,2-13C2]D-glucose and mass isotopomer analysis is used. Changes in fluxes of substrate cycles, in response to several gluconeogenic substrates, in isolated fasted hepatocytes from male Wistar rats were measured simultaneously. Incubation with these substrates resulted in a change in glucose-6-phosphatase/glucokinase and glycolytic/gluconeogenic flux ratios. Different net redistributions of intermediates in the glucose network were observed, resulting in distinct metabolic phenotypes of the fasted hepatocytes in response to each substrate condition. Our experimental observations show that the constraints of concentrations of shared intermediates, and enzyme kinetics of intersecting pathways of the metabolic network determine substrate redistribution throughout the network when it is perturbed. These results support the systems-biology notion that network analysis provides an integrated view of the physiological state. Interaction between metabolic intermediates and glycolytic/gluconeogenic pathways is a basic element of cross-talk in hepatocytes, and may explain some of the difficulties in genotype and phenotype correlation.

Genome-scale in silico models of E. coli have multiple equivalent phenotypic states: assessment of correlated reaction subsets that comprise network states

The constraint-based analysis of genome-scale metabolic and regulatory networks has been successful in predicting phenotypes and useful for analyzing high-throughput data sets. Within this modeling framework, linear optimization has been used to study genome-scale metabolic models, resulting in the enumeration of single optimal solutions describing the best use of the network to support growth. Here mixed-integer linear programming was used to calculate and study a subset of the alternate optimal solutions for a genome-scale metabolic model of Escherichia coli (iJR904) under a wide variety of environmental conditions. Analysis of the calculated sets of optimal solutions found that: (1) only a small subset of reactions in the network have variable fluxes across optima; (2) sets of reactions that are always used together in optimal solutions, correlated reaction sets, showed moderate agreement with the currently known transcriptional regulatory structure in E. coli and available expression data, and (3) reactions that are used under certain environmental conditions can provide clues about network regulatory needs. In addition, calculation of suboptimal flux distributions, using flux variability analysis, identified reactions which are used under significantly more environmental conditions suboptimally than optimally. Together these results demonstrate the utilization of reactions in genome-scale models under a variety of different growth conditions.

Integrated analysis of metabolic phenotypes in Saccharomyces cerevisiae

Background

The yeast Saccharomyces cerevisiae is an important microorganism for both industrial processes and scientific research. Consequently, there have been extensive efforts to characterize its cellular processes. In order to fully understand the relationship between yeast's genome and its physiology, the stockpiles of diverse biological data sets that describe its cellular components and phenotypic behavior must be integrated at the genome-scale. Genome-scale metabolic networks have been reconstructed for several microorganisms, including S. cerevisiae, and the properties of these networks have been successfully analyzed using a variety of constraint-based methods. Phenotypic phase plane analysis is a constraint-based method which provides a global view of how optimal growth rates are affected by changes in two environmental variables such as a carbon and an oxygen uptake rate. Some applications of phenotypic phase plane analysis include the study of optimal growth rates and of network capacity and function.

Results

In this study, the Saccharomyces cerevisiae genome-scale metabolic network was used to formulate a phenotypic phase plane that displays the maximum allowable growth rate and distinct patterns of metabolic pathway utilization for all combinations of glucose and oxygen uptake rates. In silico predictions of growth rate and secretion rates and in vivo data for three separate growth conditions (aerobic glucose-limited, oxidative-fermentative, and microaerobic) were concordant.

Conclusions

Taken together, this study examines the function and capacity of yeast's metabolic machinery and shows that the phenotypic phase plane can be used to accurately predict metabolic phenotypes and to interpret experimental data in the context of a genome-scale model.

Toward large-scale modeling of the microbial cell for computer simulation

In the post-genomic era, the large-scale, systematic, and functional analysis of all cellular components using transcriptomics, proteomics, and metabolomics, together with bioinformatics for the analysis of the massive amount of data generated by these "omics" methods are the focus of intensive research activities. As a consequence of these developments, systems biology, whose goal is to comprehend the organism as a complex system arising from interactions between its multiple elements, becomes a more tangible objective. Mathematical modeling of microorganisms and subsequent computer simulations are effective tools for systems biology, which will lead to a better understanding of the microbial cell and will have immense ramifications for biological, medical, environmental sciences, and the pharmaceutical industry. In this review, we describe various types of mathematical models (structured, unstructured, static, dynamic, etc.), of microorganisms that have been in use for a while, and others that are emerging. Several biochemical/cellular simulation platforms to manipulate such models are summarized and the E-Cell system developed in our laboratory is introduced. Finally, our strategy for building a "whole cell metabolism model", including the experimental approach, is presented.

Identifying constraints that govern cell behavior: a key to converting conceptual to computational models in biology?

Cells must abide by a number of constraints. The environmental constrains of cellular behavior and physicochemical limitations affect cellular processes. To regulate and adapt their functions, cells impose constraints on themselves. Enumerating, understanding, and applying these constraints leads to a constraints-based modeling formalism that has been helpful in converting conceptual models to computational models in biology. The continued success of the constraints-based approach depends upon identification and incorporation of new constraints to more accurately define cellular capabilities. This review considers constraints in terms of environmental, physicochemical, and self-imposed regulatory and evolutionary constraints with the purpose of refining current constraints-based models of cell phenotype.

Current status and challenges in connecting models of erythrocyte metabolism to experimental reality

Detailed kinetic models of human erythrocyte metabolism have served to summarize the vast literature and to predict outcomes from laboratory and "Nature's" experiments on this simple cell. Mathematical methods for handling the large array of nonlinear ordinary differential equations that describe the time dependence of this system are well developed, but experimental methods that can guide the evolution of the models are in short supply. NMR spectroscopy is one method that is non-selective with respect to analyte detection but is highly specific with respect to their identification and quantification. Thus time courses of metabolism are readily recorded for easily changed experimental conditions. While the data can be simulated, the systems of equations are too complex to allow solutions of the inverse problem, namely parameter-value estimation for the large number of enzyme and membrane-transport reactions operating in situ as opposed to in vitro. Other complications with the modelling include the dependence of cell volume on time, and the rates of membrane transport processes are often dependent on the membrane potential. These matters are discussed in the light of new modelling strategies.

From the sequence to cell modeling: comprehensive functional genomics in Escherichia coli

As a result of the enormous amount of information that has been collected with E. coli over the past half century (e.g. genome sequence, mutant phenotypes, metabolic and regulatory networks, etc.), we now have detailed knowledge about gene regulation, protein activity, several hundred enzyme reactions, metabolic pathways, macromolecular machines, and regulatory interactions for this model organism. However, understanding how all these processes interact to form a living cell will require further characterization, quantification, data integration, and mathematical modeling, systems biology. No organism can rival E. coli with respect to the amount of available basic information and experimental tractability for the technologies needed for this undertaking. A focused, systematic effort to understand the E. coli cell will accelerate the development of new post-genomic technologies, including both experimental and computational tools. It will also lead to new technologies that will be applicable to other organisms, from microbes to plants, animals, and humans. E. coli is not only the best studied free-living model organism, but is also an extensively used microbe for industrial applications, especially for the production of small molecules of interest. It is an excellent representative of Gram-negative commensal bacteria. E. coli may represent a perfect model organism for systems biology that is aimed at elucidating both its free-living and commensal life-styles, which should open the door to whole-cell modeling and simulation.

Integrating high-throughput and computational data elucidates bacterial networks

The flood of high-throughput biological data has led to the expectation that computational (or in silico) models can be used to direct biological discovery, enabling biologists to reconcile heterogeneous data types, find inconsistencies and systematically generate hypotheses. Such a process is fundamentally iterative, where each iteration involves making model predictions, obtaining experimental data, reconciling the predicted outcomes with experimental ones, and using discrepancies to update the in silico model. Here we have reconstructed, on the basis of information derived from literature and databases, the first integrated genome-scale computational model of a transcriptional regulatory and metabolic network. The model accounts for 1,010 genes in Escherichia coli, including 104 regulatory genes whose products together with other stimuli regulate the expression of 479 of the 906 genes in the reconstructed metabolic network. This model is able not only to predict the outcomes of high-throughput growth phenotyping and gene expression experiments, but also to indicate knowledge gaps and identify previously unknown components and interactions in the regulatory and metabolic networks. We find that a systems biology approach that combines genome-scale experimentation and computation can systematically generate hypotheses on the basis of disparate data sources.

Flux coupling analysis of genome-scale metabolic network reconstructions

In this paper, we introduce the Flux Coupling Finder (FCF) framework for elucidating the topological and flux connectivity features of genome-scale metabolic networks. The framework is demonstrated on genome-scale metabolic reconstructions of Helicobacter pylori, Escherichia coli, and Saccharomyces cerevisiae. The analysis allows one to determine whether any two metabolic fluxes, v(1) and v(2), are (1) directionally coupled, if a non-zero flux for v(1) implies a non-zero flux for v(2) but not necessarily the reverse; (2) partially coupled, if a non-zero flux for v(1) implies a non-zero, though variable, flux for v(2) and vice versa; or (3) fully coupled, if a non-zero flux for v(1) implies not only a non-zero but also a fixed flux for v(2) and vice versa. Flux coupling analysis also enables the global identification of blocked reactions, which are all reactions incapable of carrying flux under a certain condition; equivalent knockouts, defined as the set of all possible reactions whose deletion forces the flux through a particular reaction to zero; and sets of affected reactions denoting all reactions whose fluxes are forced to zero if a particular reaction is deleted. The FCF approach thus provides a novel and versatile tool for aiding metabolic reconstructions and guiding genetic manipulations.

Genome-scale analysis of the uses of the Escherichia coli genome: model-driven analysis of heterogeneous data sets

The recent availability of heterogeneous high-throughput data types has increased the need for scalable in silico methods with which to integrate data related to the processes of regulation, protein synthesis, and metabolism. A sequence-based framework for modeling transcription and translation in prokaryotes has been established and has been extended to study the expression state of the entire Escherichia coli genome. The resulting in silico analysis of the expression state highlighted three facets of gene expression in E. coli: (i) the metabolic resources required for genome expression and protein synthesis were found to be relatively invariant under the conditions tested; (ii) effective promoter strengths were estimated at the genome scale by using global mRNA abundance and half-life data, revealing genes subject to regulation under the experimental conditions tested; and (iii) large-scale genome location-dependent expression patterns with approximately 600-kb periodicity were detected in the E. coli genome based on the 49 expression data sets analyzed. These results support the notion that a structured model-driven analysis of expression data yields additional information that can be subjected to commonly used statistical analyses. The integration of heterogeneous genome-scale data (i.e., sequence, expression data, and mRNA half-life data) is readily achieved in the context of an in silico model.

Extending knowledge of Escherichia coli metabolism by modeling and experiment

Two recent studies integrate data from many different sources for Escherichia coli, using mathematical modeling and a combination of gene expression and protein levels to predict new gene functions and metabolic behaviors.

One of the challenges for 'post-genomic' biology is the integration of data from many different sources. Two recent studies independently take steps towards this goal for Escherichia coli, using mathematical modeling and a combination of gene expression and protein levels to predict new gene functions and metabolic behaviors.

Saccharomyces cerevisiae phenotypes can be predicted by using constraint-based analysis of a genome-scale reconstructed metabolic network

Full genome sequences of prokaryotic organisms have led to reconstruction of genome-scale metabolic networks and in silico computation of their integrated functions. The first genome-scale metabolic reconstruction for a eukaryotic cell, Saccharomyces cerevisiae, consisting of 1,175 metabolic reactions and 733 metabolites, has appeared. A constraint-based in silico analysis procedure was used to compute properties of the S. cerevisiae metabolic network. The computed number of ATP molecules produced per pair of electrons donated to the electron transport system (ETS) and energy-maintenance requirements were quantitatively in agreement with experimental results. Computed whole-cell functions of growth and metabolic by-product secretion in aerobic and anaerobic culture were consistent with experimental data, and thus mRNA expression profiles during metabolic shifts were computed. The computed consequences of gene knockouts on growth phenotypes were consistent with experimental observations. Thus, constraint-based analysis of a genome-scale metabolic network for the eukaryotic S. cerevisiae allows for computation of its integrated functions, producing in silico results that were consistent with observed phenotypic functions for approximately 70-80% of the conditions considered.

Identifying global regulators in transcriptional regulatory networks in bacteria

The machinery for cells to take decisions, when environmental conditions change, includes protein-DNA interactions defined by transcriptional factors and their targets around promoters. Properties of global regulators are revised attempting to reach diagnostic explicit criteria for their definition and eventual future computational identification. These include among others, the number of regulated genes, the number and type of co-regulators, the different sigma-classes of promoters and the number of transcriptional factors they regulate, the size of the evolutionary family they belong to, and the variety of conditions where they exert their control. As a consequence, global versus local regulation can be identified, as shown for Escherichia coli and eventually in other genomes.

An expanded genome-scale model of Escherichia coli K-12 (iJR904 GSM/GPR)

BACKGROUND

Diverse datasets, including genomic, transcriptomic, proteomic and metabolomic data, are becoming readily available for specific organisms. There is currently a need to integrate these datasets within an in silico modeling framework. Constraint-based models of Escherichia coli K-12 MG1655 have been developed and used to study the bacterium's metabolism and phenotypic behavior. The most comprehensive E. coli model to date (E. coli iJE660a GSM) accounts for 660 genes and includes 627 unique biochemical reactions.

RESULTS

An expanded genome-scale metabolic model of E. coli (iJR904 GSM/GPR) has been reconstructed which includes 904 genes and 931 unique biochemical reactions. The reactions in the expanded model are both elementally and charge balanced. Network gap analysis led to putative assignments for 55 open reading frames (ORFs). Gene to protein to reaction associations (GPR) are now directly included in the model. Comparisons between predictions made by iJR904 and iJE660a models show that they are generally similar but differ under certain circumstances. Analysis of genome-scale proton balancing shows how the flux of protons into and out of the medium is important for maximizing cellular growth.

CONCLUSIONS

E. coli iJR904 has improved capabilities over iJE660a. iJR904 is a more complete and chemically accurate description of E. coli metabolism than iJE660a. Perhaps most importantly, iJR904 can be used for analyzing and integrating the diverse datasets. iJR904 will help to outline the genotype-phenotype relationship for E. coli K-12, as it can account for genomic, transcriptomic, proteomic and fluxomic data simultaneously.