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At least 19 recordsLinked to original sources
PubMedDate not supplied

Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems.

The elucidation of organism-scale metabolic networks necessitates the development of integrative methods to analyze and interpret the systemic properties of cellular metabolism. A shift in emphasis from single metabolic reactions to systemically defined pathways is one consequence of such an integrative analysis of metabolic systems. The constraints of systemic stoichiometry, and limited thermodynamics have led to the definition of the flux space within the context of convex analysis. The flux space of the metabolic system, containing all allowable flux distributions, is constrained to a convex polyhedral cone in a high-dimensional space. From metabolic pathway analysis, the edges of the high-dimensional flux cone are vectors that correspond to systemically defined "extreme pathways" spanning the capabilities of the system. The addition of maximum flux capacities of individual metabolic reactions serves to further constrain the flux space and has led to the development of flux balance analysis using linear optimization to calculate optimal flux distributions. Here we provide the precise theoretical connections between pathway analysis and flux balance analysis allowing for their combined application to study integrated metabolic function. Shifts in metabolic behavior are calculated using linear optimization and are then interpreted using the extreme pathways to demonstrate the concept of pathway utilization. Changes to the reaction network, such as the removal of a reaction, can lead to the generation of suboptimal phenotypes that can be directly attributed to the loss of pathway function and capabilities. Optimal growth phenotypes are calculated as a function of environmental variables, such as the availability of substrate and oxygen, leading to the definition of phenotypic phase planes. It is illustrated how optimality properties of the computed flux distributions can be interpreted in terms of the extreme pathways. Together these developments are applied to an example network and to core metabolism of Escherichia coli demonstrating the connections between the extreme pathways, optimal flux distributions, and phenotypic phase planes. The consequences of changing environmental and internal conditions of the network are examined for growth on glucose and succinate in the face of a variety of gene deletions. The convergence of the calculation of optimal phenotypes through linear programming and the definition of extreme pathways establishes a different perspective for the understanding of how a defined metabolic network is best used under different environmental and internal conditions or, in other words, a pathway basis for the interpretation of the metabolic reaction norm.

Glucose↗
PubMed2003

Data reconciliation and parameter estimation in flux-balance analysis.

Flux blance analysis (FBA) has been shown to be a very effective tool to interpret and predict the metabolism of various microorganisms when the set of available measurements is not sufficient to determine the fluxes within the cell. In this methodology, an underdetermined stoichiometric model is solved using a linear programming (LP) approach. The predictions of FBA models can be improved if noisy measurements are checked for consistency, and these in turn are used to estimate model parameters. In this work, a formal methodology for data reconciliation and parameter estimation with underdetermined stoichiometric models is developed and assessed. The procedure is formulated as a nonlinear optimization problem, where the LP is transformed into a set of nonlinear constraints. However, some of these constraints violate standard regularity conditions, making the direct numerical solution very difficult. Hence, a barrier formulation is used to represent these constraints, and an iterative procedure is defined that allows solving the problem to the desired degree of convergence. This methodology is assessed using a stoichiometric yeast model. The procedure is used for data reconciliation where more reliable estimations of noisy measurements are computed. On the other hand, assuming unknown biomass composition, the procedure is applied for simultaneous data reconciliation and biomass composition estimation. In both cases it is verified that the f measurements required to get unbiased and reliable estimations is reduced if the LP approach is included as additional constraints in the optimization.

Acetates↗
PubMed2006

Flux balance analysis in the era of metabolomics.

Flux balance analysis (FBA) has emerged as an effective means to analyse biological networks in a quantitative manner. Much progress has been made on the extension of FBA to incorporate a priori biological knowledge, provide more practical descriptions of observed cell behaviours, and predict the outcome of network perturbations. Metabolomics is independently advancing as a set of high-throughput data acquisition tools providing dynamic profiles of metabolites in an unbiased manner. These data sets are neither yet sufficiently comprehensive nor accurate enough for generating large-scale kinetic models. Thus, there is a pressing need to develop quantitative techniques that can make use of the emerging data and embrace the associated uncertainties. This article reviews recent advances in FBA to meet this need and discusses the utility of FBA as a complement to metabolomics and the expected synergy as a result of combining these two techniques.

Animals↗
PubMed2002

Dynamic flux balance analysis of diauxic growth in Escherichia coli.

Flux Balance Analysis (FBA) has been used in the past to analyze microbial metabolic networks. Typically, FBA is used to study the metabolic flux at a particular steady state of the system. However, there are many situations where the reprogramming of the metabolic network is important. Therefore, the dynamics of these metabolic networks have to be studied. In this paper, we have extended FBA to account for dynamics and present two different formulations for dynamic FBA. These two approaches were used in the analysis of diauxic growth in Escherichia coli. Dynamic FBA was used to simulate the batch growth of E. coli on glucose, and the predictions were found to qualitatively match experimental data. The dynamic FBA formalism was also used to study the sensitivity to the objective function. It was found that an instantaneous objective function resulted in better predictions than a terminal-type objective function. The constraints that govern the growth at different phases in the batch culture were also identified. Therefore, dynamic FBA provides a framework for analyzing the transience of metabolism due to metabolic reprogramming and for obtaining insights for the design of metabolic networks.

Cell Division↗
PubMed2001

Flux-balance analysis of mitochondrial energy metabolism: consequences of systemic stoichiometric constraints.

Mitochondrial metabolism is a critical component in the functioning and maintenance of cellular organs. The stoichiometry of biochemical reaction networks imposes constraints on mitochondrial function. A modeling framework, flux-balance analysis (FBA), was used to characterize the optimal flux distributions for maximal ATP production in the mitochondrion. The model predicted the expected ATP yields for glucose, lactate, and palmitate. Genetic defects that affect mitochondrial functions have been implicated in several human diseases. FBA can characterize the metabolic behavior due to genetic deletions at the metabolic level, and the effect of mutations in the tricarboxylic acid (TCA) cycle on mitochondrial ATP production was simulated. The mitochondrial ATP production is severely affected by TCA-cycle mutations. In addition, the model predicts the secretion of TCA-cycle intermediates, which is observed in clinical studies of mitochondriopathies such as those associated with fumarase deficiency. The model provides a systemic perspective to characterize the effect of stoichiometric constraints and specific metabolic fluxes on mitochondrial function.

Adenosine Triphosphate↗
PubMed2000

Metabolic flux balance analysis and the in silico analysis of Escherichia coli K-12 gene deletions.

BACKGROUND: Genome sequencing and bioinformatics are producing detailed lists of the molecular components contained in many prokaryotic organisms. From this 'parts catalogue' of a microbial cell, in silico representations of integrated metabolic functions can be constructed and analyzed using flux balance analysis (FBA). FBA is particularly well-suited to study metabolic networks based on genomic, biochemical, and strain specific information. RESULTS: Herein, we have utilized FBA to interpret and analyze the metabolic capabilities of Escherichia coli. We have computationally mapped the metabolic capabilities of E. coli using FBA and examined the optimal utilization of the E. coli metabolic pathways as a function of environmental variables. We have used an in silico analysis to identify seven gene products of central metabolism (glycolysis, pentose phosphate pathway, TCA cycle, electron transport system) essential for aerobic growth of E. coli on glucose minimal media, and 15 gene products essential for anaerobic growth on glucose minimal media. The in silico tpi-, zwf, and pta- mutant strains were examined in more detail by mapping the capabilities of these in silico isogenic strains. CONCLUSIONS: We found that computational models of E. coli metabolism based on physicochemical constraints can be used to interpret mutant behavior. These in silica results lead to a further understanding of the complex genotype-phenotype relation.

Computational Biology↗
PubMedDate not supplied

Flux balance analysis of photoautotrophic metabolism.

Photosynthesis is the principal process responsible for fixation of inorganic carbon dioxide into organic molecules with sunlight as the energy source. Potentially, many chemicals could be inexpensively produced by photosynthetic organisms. Mathematical modeling of photoautotrophic metabolism is therefore important to evaluate maximum theoretical product yields and to deeply understand the interactions between biochemical energy, carbon fixation, and assimilation pathways. Flux balance analysis based on linear programming is applied to photoautotrophic metabolism. The stoichiometric network of a model photosynthetic prokaryote, Synechocystis sp. PCC 6803, has been reconstructed from genomic data and biochemical literature and coupled with a model of the photophosphorylation processes. Flux map topologies for the hetero-, auto-, and mixotrophic modes of metabolism under conditions of optimal growth were determined and compared. The roles of important metabolic reactions such as the glyoxylate shunt and the transhydrogenase reaction were analyzed. We also theoretically evaluated the effect of gene deletions or additions on biomass yield and metabolic flux distributions.

Biomass↗
PubMed2003

Advances in flux balance analysis.

Biology is going through a paradigm shift from reductionist to holistic, systems-based approaches. The complete genome sequence for a number of organisms is available and the analysis of genome sequence data is proving very useful. Thus, genome sequencing projects and bioinformatic analyses are leading to a complete 'parts catalog' of the molecular components in many organisms. The next challenge will be to reconstruct and simulate overall cellular functions based on the extensive reductionist information. Recent advances have been made in the area of flux balance analysis, a mathematical modeling approach often utilized by metabolic engineers to quantitatively simulate microbial metabolism.

Computational Biology↗
PubMed2005

Flux balance analysis of mycolic acid pathway: targets for anti-tubercular drugs.

Mycobacterium tuberculosis is the focus of several investigations for design of newer drugs, as tuberculosis remains a major epidemic despite the availability of several drugs and a vaccine. Mycobacteria owe many of their unique qualities to mycolic acids, which are known to be important for their growth, survival, and pathogenicity. Mycolic acid biosynthesis has therefore been the focus of a number of biochemical and genetic studies. It also turns out to be the pathway inhibited by front-line anti-tubercular drugs such as isoniazid and ethionamide. Recent years have seen the emergence of systems-based methodologies that can be used to study microbial metabolism. Here, we seek to apply insights from flux balance analyses of the mycolic acid pathway (MAP) for the identification of anti-tubercular drug targets. We present a comprehensive model of mycolic acid synthesis in the pathogen M. tuberculosis involving 197 metabolites participating in 219 reactions catalysed by 28 proteins. Flux balance analysis (FBA) has been performed on the MAP model, which has provided insights into the metabolic capabilities of the pathway. In silico systematic gene deletions and inhibition of InhA by isoniazid, studied here, provide clues about proteins essential for the pathway and hence lead to a rational identification of possible drug targets. Feasibility studies using sequence analysis of the M. tuberculosis H37Rv and human proteomes indicate that, apart from the known InhA, potential targets for anti-tubercular drug design are AccD3, Fas, FabH, Pks13, DesA1/2, and DesA3. Proteins identified as essential by FBA correlate well with those previously identified experimentally through transposon site hybridisation mutagenesis. This study demonstrates the application of FBA for rational identification of potential anti-tubercular drug targets, which can indeed be a general strategy in drug design. The targets, chosen based on the critical points in the pathway, form a ready shortlist for experimental testing.

Algorithms↗
PubMedDate not supplied

Toward metabolic phenomics: analysis of genomic data using flux balances.

Small genome sequencing and annotations are leading to the definition of metabolic genotypes in an increasing number of organisms. Proteomics is beginning to give insights into the use of the metabolic genotype under given growth conditions. These data sets give the basis for systemically studying the genotype-phenotype relationship. Methods of systems science need to be employed to analyze, interpret, and predict this complex relationship. These endeavors will lead to the development of a new field, tentatively named phenomics. This article illustrates how the metabolic characteristics of annotated small genomes can be analyzed using flux balance analysis (FBA). A general algorithm for the formulation of in silico metabolic genotypes is described. Illustrative analyses of the in silico Escherichia coli K-12 metabolic genotypes are used to show how FBA can be used to study the capabilities of this strain.

Biotechnology↗
PubMed2002

Genome-scale metabolic model of Helicobacter pylori 26695.

A genome-scale metabolic model of Helicobacter pylori 26695 was constructed from genome sequence annotation, biochemical, and physiological data. This represents an in silico model largely derived from genomic information for an organism for which there is substantially less biochemical information available relative to previously modeled organisms such as Escherichia coli. The reconstructed metabolic network contains 388 enzymatic and transport reactions and accounts for 291 open reading frames. Within the paradigm of constraint-based modeling, extreme-pathway analysis and flux balance analysis were used to explore the metabolic capabilities of the in silico model. General network properties were analyzed and compared to similar results previously generated for Haemophilus influenzae. A minimal medium required by the model to generate required biomass constituents was calculated, indicating the requirement of eight amino acids, six of which correspond to essential human amino acids. In addition a list of potential substrates capable of fulfilling the bulk carbon requirements of H. pylori were identified. A deletion study was performed wherein reactions and associated genes in central metabolism were deleted and their effects were simulated under a variety of substrate availability conditions, yielding a number of reactions that are deemed essential. Deletion results were compared to recently published in vitro essentiality determinations for 17 genes. The in silico model accurately predicted 10 of 17 deletion cases, with partial support for additional cases. Collectively, the results presented herein suggest an effective strategy of combining in silico modeling with experimental technologies to enhance biological discovery for less characterized organisms and their genomes.

Amino Acids↗
PubMed2005

Identification of distributed metabolic objectives in the hypermetabolic liver by flux and energy balance analysis.

A methodology for inferring distributed metabolic objectives from time series flux data is developed by combining metabolic flux analysis, pathway identification, free energy balances, and nested optimization. This methodology is used to investigate the metabolic response of the rat liver to burn injury-induced whole body inflammation. Gibbs free energy changes were computed for stoichiometrically balanced sequences of reactions, or pathways, rather than individual reactions, to account for energetic coupling between reactions. Systematic enumeration of pathways proceeded by elementary flux mode (EFM) analysis. Together with stoichiometric balances and external metabolite flux measurements, the DeltaG(PATH)(o) criterion provided sufficient constraints to solve a series of nested optimization problems on the metabolic goal functions and associated flux distributions of fasted livers during the first-week time course of burn injury. The optimization results suggest that there is a consistent metabolic goal function for the liver that is insensitive to the changing metabolic burdens experienced by the liver during the first-week time course. As defined by the goal function coefficients, the global metabolic objective was to distribute the metabolic resources between amino acid metabolism and ketone body synthesis. These findings point to a role for the time-invariant structure of the metabolic reaction network, expressed as stoichiometric and thermodynamic constraints, in shaping the cellular metabolic objective.

Animals↗
PubMed2006

Using the topology of metabolic networks to predict viability of mutant strains.

Understanding the relationships between the structure (topology) and function of biological networks is a central question of systems biology. The idea that topology is a major determinant of systems function has become an attractive and highly disputed hypothesis. Although structural analysis of interaction networks demonstrates a correlation between the topological properties of a node (protein, gene) in the network and its functional essentiality, the analysis of metabolic networks fails to find such correlations. In contrast, approaches utilizing both the topology and biochemical parameters of metabolic networks, e.g., flux balance analysis, are more successful in predicting phenotypes of knockout strains. We reconcile these seemingly conflicting results by showing that the topology of the metabolic networks of both Escherichia coli and Saccharomyces cerevisiae are, in fact, sufficient to predict the viability of knockout strains with accuracy comparable to flux balance analysis on large, unbiased mutant data sets. This surprising result is obtained by introducing a novel topology-based measure of network transport: synthetic accessibility. We also show that other popular topology-based characteristics such as node degree, graph diameter, and node usage (betweenness) fail to predict the viability of E. coli mutant strains. The success of synthetic accessibility demonstrates its ability to capture the essential properties of the metabolic network, such as the branching of chemical reactions and the directed transport of material from inputs to outputs. Our results strongly support a link between the topology and function of biological networks and, in agreement with recent genetic studies, emphasize the minimal role of flux rerouting in providing robustness of mutant strains.

Algorithms↗
PubMed2005

The activity reaction core and plasticity of metabolic networks.

Understanding the system-level adaptive changes taking place in an organism in response to variations in the environment is a key issue of contemporary biology. Current modeling approaches, such as constraint-based flux-balance analysis, have proved highly successful in analyzing the capabilities of cellular metabolism, including its capacity to predict deletion phenotypes, the ability to calculate the relative flux values of metabolic reactions, and the capability to identify properties of optimal growth states. Here, we use flux-balance analysis to thoroughly assess the activity of Escherichia coli, Helicobacter pylori, and Saccharomyces cerevisiae metabolism in 30,000 diverse simulated environments. We identify a set of metabolic reactions forming a connected metabolic core that carry non-zero fluxes under all growth conditions, and whose flux variations are highly correlated. Furthermore, we find that the enzymes catalyzing the core reactions display a considerably higher fraction of phenotypic essentiality and evolutionary conservation than those catalyzing noncore reactions. Cellular metabolism is characterized by a large number of species-specific conditionally active reactions organized around an evolutionary conserved, but always active, metabolic core. Finally, we find that most current antibiotics interfering with bacterial metabolism target the core enzymes, indicating that our findings may have important implications for antimicrobial drug-target discovery.

Escherichia coli↗
PubMed2004

High-throughput metabolic flux analysis based on gas chromatography-mass spectrometry derived 13C constraints.

13C-constrained flux balancing analysis based on gas chromatography-mass spectrometry data is presented here as a simple and robust method for the estimation of intracellular carbon fluxes. In this approach, the underdetermined system of metabolite balances deduced from stoichiometric relations and measured extracellular rates is complemented with 13C constraints from metabolic flux ratio analysis. Fluxes in central carbon metabolism of exponentially growing Escherichia coli were estimated by 13C-constrained flux balancing from three different 13C-labeled glucose experiments. The best resolution of the network was achieved using 13C constraints derived from [U-13C]glucose and [1-13C]glucose experiments. The corresponding flux estimate was in excellent agreement with a solution that was independently obtained with a comprehensive isotopomer model. This new methodology was also demonstrated to faithfully capture the intracellular flux distribution in E. coli shake flasks and 1-ml deep-well microtiter plates. Due to its simplicity, speed, and robustness, 13C-constrained metabolic flux balancing is promising for routine and high-throughput analysis on a miniaturized scale.

Carbon Isotopes↗
PubMed2002

Analysis of optimality in natural and perturbed metabolic networks.

An important goal of whole-cell computational modeling is to integrate detailed biochemical information with biological intuition to produce testable predictions. Based on the premise that prokaryotes such as Escherichia coli have maximized their growth performance along evolution, flux balance analysis (FBA) predicts metabolic flux distributions at steady state by using linear programming. Corroborating earlier results, we show that recent intracellular flux data for wild-type E. coli JM101 display excellent agreement with FBA predictions. Although the assumption of optimality for a wild-type bacterium is justifiable, the same argument may not be valid for genetically engineered knockouts or other bacterial strains that were not exposed to long-term evolutionary pressure. We address this point by introducing the method of minimization of metabolic adjustment (MOMA), whereby we test the hypothesis that knockout metabolic fluxes undergo a minimal redistribution with respect to the flux configuration of the wild type. MOMA employs quadratic programming to identify a point in flux space, which is closest to the wild-type point, compatibly with the gene deletion constraint. Comparing MOMA and FBA predictions to experimental flux data for E. coli pyruvate kinase mutant PB25, we find that MOMA displays a significantly higher correlation than FBA. Our method is further supported by experimental data for E. coli knockout growth rates. It can therefore be used for predicting the behavior of perturbed metabolic networks, whose growth performance is in general suboptimal. MOMA and its possible future extensions may be useful in understanding the evolutionary optimization of metabolism.

Biomass↗
PubMed2005

Complementary identification of multiple flux distributions and multiple metabolic pathways.

Cell robustness and complexity have been recognized as unique features of biological systems. Such robustness and complexity of metabolic-reaction systems can be explored by discovering, or identifying, the multiple flux distributions (MFD) and redundant pathways that lead to a given external state; however, this is exceedingly cumbersome to accomplish. It is, therefore, highly desirable to establish an effective computational method for their identification, which, in turn, gives rise to a novel insight into the cellular function. An effective approach is proposed for complementarily identifying MFD in metabolic flux analysis and multiple metabolic pathways (MMP) in structural pathway analysis. This approach judiciously integrates flux balance analysis (FBA) based on linear programming and the graph-theoretic method for determining reaction pathways. A single metabolic pathway, with the concomitant flux distribution and the overall reaction manifesting itself as the desired phenotype under some environmental conditions, is determined by FBA from the initial candidate sequence of metabolic reactions. Subsequently, the graph-theoretic method recovers all feasible MMP and the corresponding MFD. The approach's efficacy is demonstrated by applying it to the in silico Escherichia coli model under various culture conditions. The resultant MMP and MFD attaining a unique external state reveal the surprising adaptability and robustness of the intricate cellular network as a key to cell survival against environmental or genetic changes. These results indicate that the proposed approach would be useful in facilitating drug discovery.

Algorithms↗
PubMed2006

Monte Carlo sampling and principal component analysis of flux distributions yield topological and modular information on metabolic networks.

The work presented here uses Monte Carlo random sampling combined with flux balance analysis and linear programming to analyse the steady-state flux distributions on the surface of the glucose-ammonia phenotypic phase plane of an Escherichia coli system grown on glucose-minimal medium. The distribution of allowable glucose and ammonia uptake rates showed a triangular shape, the apex corresponding to maximum growth rate. The exact shape, e.g. the diagonal boundary is determined by the relative amounts of nutrients required for growth. The logarithm of flux values has a normal distribution, e.g. there is a log normal distribution, and most of the reactions have an order of magnitude between 10(-1) and 1. The increase in the number of blocked reactions as growth switched from aerobic to micro-aerobic phase and the presence of alternate networks for a single optimal solution were both reflections of the variability of pathway utilization for survival and growth. Principal component analysis (PCA) provided us with significant clues on the correlations between individual reactions and correlations between sets of reactions. Furthermore, PCA identified the most influential reactions of the system. The PCA score plots clearly distinguish two different growth phases, micro-aerobic and aerobic. The loading plots for each growth phase showed both the impact of the reactions on the model and the clustering of reactions that are highly correlated. These results have proved that PCA is a promising way to analyse correlations in high-dimensional solution spaces and to detect modular patterns among reactions in a network.

Ammonia↗