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Flux Balance Analysis (FBA) has been successfully applied to facilitate the understanding of cellular metabolism in model organisms. Standard formulations of FBA can be applied to large systems, but the accuracy of predictions may vary significantly depending on environmental conditions, genetic perturbations, or complex unknown regulatory constraints. Here we present an FBA-based approach to infer the biomass compositions that best describe multiple physiological states of a cell. Specifically, we seek to use experimental data (such as flux measurements, or mRNA expression levels) to infer best matching stoichiometrically balanced fluxes and metabolite sinks. Our algorithm is designed to provide predictions based on the comparative analysis of two metabolic states (e.g. wild-type and knockout, or two different time points), so as to be independent from possible arbitrary scaling factors. We test our algorithm using experimental data for metabolic fluxes in wild type and gene deletion strains of E. coli. In addition to demonstrating the capacity of our approach to correctly identify known exchange fluxes and biomass compositions, we analyze E. coli central carbon metabolism to show the changes of metabolic objectives and potential compensation for reducing power due to single enzyme gene deletion in pentose phosphate pathway.
PMCID: PMC3245841  PMID: 19425132
flux balance analysis; systems biology; data integration; metabolic objectives
2.  Development and experimental verification of a genome-scale metabolic model for Corynebacterium glutamicum 
In silico genome-scale metabolic models enable the analysis of the characteristics of metabolic systems of organisms. In this study, we reconstructed a genome-scale metabolic model of Corynebacterium glutamicum on the basis of genome sequence annotation and physiological data. The metabolic characteristics were analyzed using flux balance analysis (FBA), and the results of FBA were validated using data from culture experiments performed at different oxygen uptake rates.
The reconstructed genome-scale metabolic model of C. glutamicum contains 502 reactions and 423 metabolites. We collected the reactions and biomass components from the database and literatures, and made the model available for the flux balance analysis by filling gaps in the reaction networks and removing inadequate loop reactions. Using the framework of FBA and our genome-scale metabolic model, we first simulated the changes in the metabolic flux profiles that occur on changing the oxygen uptake rate. The predicted production yields of carbon dioxide and organic acids agreed well with the experimental data. The metabolic profiles of amino acid production phases were also investigated. A comprehensive gene deletion study was performed in which the effects of gene deletions on metabolic fluxes were simulated; this helped in the identification of several genes whose deletion resulted in an improvement in organic acid production.
The genome-scale metabolic model provides useful information for the evaluation of the metabolic capabilities and prediction of the metabolic characteristics of C. glutamicum. This can form a basis for the in silico design of C. glutamicum metabolic networks for improved bioproduction of desirable metabolites.
PMCID: PMC2728707  PMID: 19646286
3.  Including metabolite concentrations into flux balance analysis: thermodynamic realizability as a constraint on flux distributions in metabolic networks 
BMC Systems Biology  2007;1:23.
In recent years, constrained optimization – usually referred to as flux balance analysis (FBA) – has become a widely applied method for the computation of stationary fluxes in large-scale metabolic networks. The striking advantage of FBA as compared to kinetic modeling is that it basically requires only knowledge of the stoichiometry of the network. On the other hand, results of FBA are to a large degree hypothetical because the method relies on plausible but hardly provable optimality principles that are thought to govern metabolic flux distributions.
To augment the reliability of FBA-based flux calculations we propose an additional side constraint which assures thermodynamic realizability, i.e. that the flux directions are consistent with the corresponding changes of Gibb's free energies. The latter depend on metabolite levels for which plausible ranges can be inferred from experimental data. Computationally, our method results in the solution of a mixed integer linear optimization problem with quadratic scoring function. An optimal flux distribution together with a metabolite profile is determined which assures thermodynamic realizability with minimal deviations of metabolite levels from their expected values. We applied our novel approach to two exemplary metabolic networks of different complexity, the metabolic core network of erythrocytes (30 reactions) and the metabolic network iJR904 of Escherichia coli (931 reactions). Our calculations show that increasing network complexity entails increasing sensitivity of predicted flux distributions to variations of standard Gibb's free energy changes and metabolite concentration ranges. We demonstrate the usefulness of our method for assessing critical concentrations of external metabolites preventing attainment of a metabolic steady state.
Our method incorporates the thermodynamic link between flux directions and metabolite concentrations into a practical computational algorithm. The weakness of conventional FBA to rely on intuitive assumptions about the reversibility of biochemical reactions is overcome. This enables the computation of reliable flux distributions even under extreme conditions of the network (e.g. enzyme inhibition, depletion of substrates or accumulation of end products) where metabolite concentrations may be drastically altered.
PMCID: PMC1903363  PMID: 17543097
4.  Construction and completion of flux balance models from pathway databases 
Bioinformatics  2012;28(3):388-396.
Motivation: Flux balance analysis (FBA) is a well-known technique for genome-scale modeling of metabolic flux. Typically, an FBA formulation requires the accurate specification of four sets: biochemical reactions, biomass metabolites, nutrients and secreted metabolites. The development of FBA models can be time consuming and tedious because of the difficulty in assembling completely accurate descriptions of these sets, and in identifying errors in the composition of these sets. For example, the presence of a single non-producible metabolite in the biomass will make the entire model infeasible. Other difficulties in FBA modeling are that model distributions, and predicted fluxes, can be cryptic and difficult to understand.
Results: We present a multiple gap-filling method to accelerate the development of FBA models using a new tool, called MetaFlux, based on mixed integer linear programming (MILP). The method suggests corrections to the sets of reactions, biomass metabolites, nutrients and secretions. The method generates FBA models directly from Pathway/Genome Databases. Thus, FBA models developed in this framework are easily queried and visualized using the Pathway Tools software. Predicted fluxes are more easily comprehended by visualizing them on diagrams of individual metabolic pathways or of metabolic maps. MetaFlux can also remove redundant high-flux loops, solve FBA models once they are generated and model the effects of gene knockouts. MetaFlux has been validated through construction of FBA models for Escherichia coli and Homo sapiens.
Availability: Pathway Tools with MetaFlux is freely available to academic users, and for a fee to commercial users. Download from:
Supplementary information: Supplementary data are available at Bioinformatics online.
PMCID: PMC3268246  PMID: 22262672
5.  Conservation of high-flux backbone in alternate optimal and near-optimal flux distributions of metabolic networks 
Systems and Synthetic Biology  2009;2(3-4):83-93.
Constraint-based flux balance analysis (FBA) has proven successful in predicting the flux distribution of metabolic networks in diverse environmental conditions. FBA finds one of the alternate optimal solutions that maximizes the biomass production rate. Almaas et al. have shown that the flux distribution follows a power law, and it is possible to associate with most metabolites two reactions which maximally produce and consume a given metabolite, respectively. This observation led to the concept of high-flux backbone (HFB) in metabolic networks. In previous work, the HFB has been computed using a particular optima obtained using FBA. In this paper, we investigate the conservation of HFB of a particular solution for a given medium across different alternate optima and near-optima in metabolic networks of E. coli and S. cerevisiae. Using flux variability analysis (FVA), we propose a method to determine reactions that are guaranteed to be in HFB regardless of alternate solutions. We find that the HFB of a particular optima is largely conserved across alternate optima in E. coli, while it is only moderately conserved in S. cerevisiae. However, the HFB of a particular near-optima shows a large variation across alternate near-optima in both organisms. We show that the conserved set of reactions in HFB across alternate near-optima has a large overlap with essential reactions and reactions which are both uniquely consuming (UC) and uniquely producing (UP). Our findings suggest that the structure of the metabolic network admits a high degree of redundancy and plasticity in near-optimal flow patterns enhancing system robustness for a given environmental condition.
PMCID: PMC2735644  PMID: 19484377
Complex network; Flux balance analysis (FBA); Alternate optima and near-optima; Flux variability analysis (FVA); Flux plasticity
6.  Conservation of high-flux backbone in alternate optimal and near-optimal flux distributions of metabolic networks 
Systems and Synthetic Biology  2009;2(3-4):83-93.
Constraint-based flux balance analysis (FBA) has proven successful in predicting the flux distribution of metabolic networks in diverse environmental conditions. FBA finds one of the alternate optimal solutions that maximizes the biomass production rate. Almaas et al. have shown that the flux distribution follows a power law, and it is possible to associate with most metabolites two reactions which maximally produce and consume a given metabolite, respectively. This observation led to the concept of high-flux backbone (HFB) in metabolic networks. In previous work, the HFB has been computed using a particular optima obtained using FBA. In this paper, we investigate the conservation of HFB of a particular solution for a given medium across different alternate optima and near-optima in metabolic networks of E. coli and S. cerevisiae. Using flux variability analysis (FVA), we propose a method to determine reactions that are guaranteed to be in HFB regardless of alternate solutions. We find that the HFB of a particular optima is largely conserved across alternate optima in E. coli, while it is only moderately conserved in S. cerevisiae. However, the HFB of a particular near-optima shows a large variation across alternate near-optima in both organisms. We show that the conserved set of reactions in HFB across alternate near-optima has a large overlap with essential reactions and reactions which are both uniquely consuming (UC) and uniquely producing (UP). Our findings suggest that the structure of the metabolic network admits a high degree of redundancy and plasticity in near-optimal flow patterns enhancing system robustness for a given environmental condition.
PMCID: PMC2735644  PMID: 19484377
Complex network; Flux balance analysis (FBA); Alternate optima and near-optima; Flux variability analysis (FVA); Flux plasticity
7.  Genome-level transcription data of Yersinia pestis analyzed with a New metabolic constraint-based approach 
BMC Systems Biology  2012;6:150.
Constraint-based computational approaches, such as flux balance analysis (FBA), have proven successful in modeling genome-level metabolic behavior for conditions where a set of simple cellular objectives can be clearly articulated. Recently, the necessity to expand the current range of constraint-based methods to incorporate high-throughput experimental data has been acknowledged by the proposal of several methods. However, these methods have rarely been used to address cellular metabolic responses to some relevant perturbations such as antimicrobial or temperature-induced stress. Here, we present a new method for combining gene-expression data with FBA (GX-FBA) that allows modeling of genome-level metabolic response to a broad range of environmental perturbations within a constraint-based framework. The method uses mRNA expression data to guide hierarchical regulation of cellular metabolism subject to the interconnectivity of the metabolic network.
We applied GX-FBA to a genome-scale model of metabolism in the gram negative bacterium Yersinia pestis and analyzed its metabolic response to (i) variations in temperature known to induce virulence, and (ii) antibiotic stress. Without imposition of any a priori behavioral constraints, our results show strong agreement with reported phenotypes. Our analyses also lead to novel insights into how Y. pestis uses metabolic adjustments to counter different forms of stress.
Comparisons of GX-FBA predicted metabolic states with fluxomic measurements and different reported post-stress phenotypes suggest that mass conservation constraints and network connectivity can be an effective representative of metabolic flux regulation in constraint-based models. We believe that our approach will be of aid in the in silico evaluation of cellular goals under different conditions and can be used for a variety of analyses such as identification of potential drug targets and their action.
PMCID: PMC3572438  PMID: 23216785
Flux balance analysis; Gene-expression; Yersinia pestis; Stress response; Metabolism
8.  Genome-Scale Reconstruction and Analysis of the Pseudomonas putida KT2440 Metabolic Network Facilitates Applications in Biotechnology 
PLoS Computational Biology  2008;4(10):e1000210.
A cornerstone of biotechnology is the use of microorganisms for the efficient production of chemicals and the elimination of harmful waste. Pseudomonas putida is an archetype of such microbes due to its metabolic versatility, stress resistance, amenability to genetic modifications, and vast potential for environmental and industrial applications. To address both the elucidation of the metabolic wiring in P. putida and its uses in biocatalysis, in particular for the production of non-growth-related biochemicals, we developed and present here a genome-scale constraint-based model of the metabolism of P. putida KT2440. Network reconstruction and flux balance analysis (FBA) enabled definition of the structure of the metabolic network, identification of knowledge gaps, and pin-pointing of essential metabolic functions, facilitating thereby the refinement of gene annotations. FBA and flux variability analysis were used to analyze the properties, potential, and limits of the model. These analyses allowed identification, under various conditions, of key features of metabolism such as growth yield, resource distribution, network robustness, and gene essentiality. The model was validated with data from continuous cell cultures, high-throughput phenotyping data, 13C-measurement of internal flux distributions, and specifically generated knock-out mutants. Auxotrophy was correctly predicted in 75% of the cases. These systematic analyses revealed that the metabolic network structure is the main factor determining the accuracy of predictions, whereas biomass composition has negligible influence. Finally, we drew on the model to devise metabolic engineering strategies to improve production of polyhydroxyalkanoates, a class of biotechnologically useful compounds whose synthesis is not coupled to cell survival. The solidly validated model yields valuable insights into genotype–phenotype relationships and provides a sound framework to explore this versatile bacterium and to capitalize on its vast biotechnological potential.
Author Summary
The pseudomonads include a diverse set of bacteria whose metabolic versatility and genetic plasticity have enabled their survival in a broad range of environments. Many members of this family are able to either degrade toxic compounds or to efficiently produce high value compounds and are therefore of interest for both bioremediation and bulk chemical production. To better understand the growth and metabolism of these bacteria, we developed a large-scale mathematical model of the metabolism of Pseudomonas putida, a representative of the industrially relevant pseudomonads. The model was initially expanded and validated with substrate utilization data and carbon-tracking data. Next, the model was used to identify key features of metabolism such as growth yield, internal distribution of resources, and network robustness. We then used the model to predict novel strategies for the production of precursors for bioplastics of medical and industrial relevance. Such an integrated computational and experimental approach can be used to study its metabolism and to explore the potential of other industrially and environmentally important microorganisms.
PMCID: PMC2563689  PMID: 18974823
9.  Dynamic strain scanning optimization: an efficient strain design strategy for balanced yield, titer, and productivity. DySScO strategy for strain design 
BMC Biotechnology  2013;13:8.
In recent years, constraint-based metabolic models have emerged as an important tool for metabolic engineering; a number of computational algorithms have been developed for identifying metabolic engineering strategies where the production of the desired chemical is coupled with the growth of the organism. A caveat of the existing algorithms is that they do not take the bioprocess into consideration; as a result, while the product yield can be optimized using these algorithms, the product titer and productivity cannot be optimized. In order to address this issue, we developed the Dynamic Strain Scanning Optimization (DySScO) strategy, which integrates the Dynamic Flux Balance Analysis (dFBA) method with existing strain algorithms.
In order to demonstrate the effective of the DySScO strategy, we applied this strategy to the design of Escherichia coli strains targeted for succinate and 1,4-butanediol production respectively. We evaluated consequences of the tradeoff between growth yield and product yield with respect to titer and productivity, and showed that the DySScO strategy is capable of producing strains that balance the product yield, titer, and productivity. In addition, we evaluated the economic viability of the designed strain, and showed that the economic performance of a strain can be strongly affected by the price difference between the product and the feedstock.
Our study demonstrated that the DySScO strategy is a useful computational tool for designing microbial strains with balanced yield, titer, and productivity, and has potential applications in evaluating the economic performance of the design strains.
PMCID: PMC3574860  PMID: 23388063
Metabolic modeling; Process modeling; Strain design; Dynamic strain design
10.  Metabolic flux balance analysis and the in silico analysis of Escherichia coli K-12 gene deletions 
BMC Bioinformatics  2000;1:1.
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.
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.
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.
Supplementary information:
PMCID: PMC29061  PMID: 11001586
11.  Bayesian flux balance analysis applied to a skeletal muscle metabolic model 
Journal of theoretical biology  2007;248(1):91-110.
In this article, the steady state condition for the multi-compartment models for cellular metabolism is considered. The problem is to estimate the reaction and transport fluxes, as well as the concentrations in venous blood when the stoichiometry and bound constraints for the fluxes and the concentrations are given. The problem has been addressed previously by a number of authors, and optimization based approaches as well as extreme pathway analysis have been proposed. These approaches are briefly discussed here. The main emphasis of this work is a Bayesian statistical approach to the flux balance analysis (FBA). We show how the bound constraints and optimality conditions such as maximizing the oxidative phosphorylation flux can be incorporated into the model in the Bayesian framework by proper construction of the prior densities. We propose an effective Markov Chain Monte Carlo (MCMC) scheme to explore the posterior densities, and compare the results with those obtained via the previously studied Linear Programming (LP) approach. The proposed methodology, which is applied here to a two-compartment model for skeletal muscle metabolism, can be extended to more complex models.
PMCID: PMC2065751  PMID: 17568615
Flux balance analysis; steady state; skeletal muscle metabolism; linear programming; Bayesian statistics; Markov Chain Monte Carlo; Gibbs sampler
12.  Dynamic Analysis of Integrated Signaling, Metabolic, and Regulatory Networks 
PLoS Computational Biology  2008;4(5):e1000086.
Extracellular cues affect signaling, metabolic, and regulatory processes to elicit cellular responses. Although intracellular signaling, metabolic, and regulatory networks are highly integrated, previous analyses have largely focused on independent processes (e.g., metabolism) without considering the interplay that exists among them. However, there is evidence that many diseases arise from multifunctional components with roles throughout signaling, metabolic, and regulatory networks. Therefore, in this study, we propose a flux balance analysis (FBA)–based strategy, referred to as integrated dynamic FBA (idFBA), that dynamically simulates cellular phenotypes arising from integrated networks. The idFBA framework requires an integrated stoichiometric reconstruction of signaling, metabolic, and regulatory processes. It assumes quasi-steady-state conditions for “fast” reactions and incorporates “slow” reactions into the stoichiometric formalism in a time-delayed manner. To assess the efficacy of idFBA, we developed a prototypic integrated system comprising signaling, metabolic, and regulatory processes with network features characteristic of actual systems and incorporating kinetic parameters based on typical time scales observed in literature. idFBA was applied to the prototypic system, which was evaluated for different environments and gene regulatory rules. In addition, we applied the idFBA framework in a similar manner to a representative module of the single-cell eukaryotic organism Saccharomyces cerevisiae. Ultimately, idFBA facilitated quantitative, dynamic analysis of systemic effects of extracellular cues on cellular phenotypes and generated comparable time-course predictions when contrasted with an equivalent kinetic model. Since idFBA solves a linear programming problem and does not require an exhaustive list of detailed kinetic parameters, it may be efficiently scaled to integrated intracellular systems that incorporate signaling, metabolic, and regulatory processes at the genome scale, such as the S. cerevisiae system presented here.
Author Summary
Cellular systems comprise many diverse components and component interactions spanning signal transduction, transcriptional regulation, and metabolism. Although signaling, metabolic, and regulatory activities are often investigated independently of one another, there is growing evidence that considerable interplay occurs among them, and that the malfunctioning of this interplay is associated with disease. The computational analysis of integrated networks has been challenging because of the varying time scales involved as well as the sheer magnitude of such systems (e.g., the numbers of rate constants involved). To this end, we developed a novel computational framework called integrated dynamic flux balance analysis (idFBA) that generates quantitative, dynamic predictions of species concentrations spanning signaling, regulatory, and metabolic processes. idFBA extends an existing approach called flux balance analysis (FBA) in that it couples “fast” and “slow” reactions, thereby facilitating the study of whole-cell phenotypes and not just sub-cellular network properties. We applied this framework to a prototypic integrated system derived from literature as well as a representative integrated yeast module (the high-osmolarity glycerol [HOG] pathway) and generated time-course predictions that matched with available experimental data. By extending this framework to larger-scale systems, phenotypic profiles of whole-cell systems could be attained expeditiously.
PMCID: PMC2377155  PMID: 18483615
Analytical chemistry  2010;82(23):9812-9817.
Metabolic flux, the flow of metabolites through networks of enzymes, represents the dynamic productive output of cells. Improved understanding of intracellular metabolic fluxes will enable targeted manipulation of metabolic pathways of medical and industrial importance to a greater degree than is currently possible. Flux balance analysis (FBA) is a constraint-based approach to modeling metabolic fluxes, but its utility is limited by a lack of experimental measurements. Incorporation of experimentally measured fluxes as system constraints will significantly improve the overall accuracy of FBA. We applied a novel, two-tiered approach in the yeast Saccharomyces cerevisiae to measure nutrient consumption rates (extracellular fluxes) and a targeted intracellular flux using a 14C-labeled precursor with HPLC separation and flux quantitation by accelerator mass spectrometry (AMS). The use of AMS to trace the intracellular fate of 14C-glutamine allowed the calculation of intracellular metabolic flux through this pathway, with glutathione as the metabolic endpoint. Measured flux values provided global constraints for the yeast FBA model which reduced model uncertainty by more than 20%, proving the importance of additional constraints in improving the accuracy of model predictions and demonstrating the use of AMS to measure intracellular metabolic fluxes. Our results highlight the need to use intracellular fluxes to constrain the models. We show that inclusion of just one such measurement alone can reduce the average variability of model predicted fluxes by 10%.
PMCID: PMC2995814  PMID: 21062031
Metabolic flux analysis; Flux balance analysis; Accelerator mass spectrometry; glutathione; glutamate; glutamine; yeast
14.  Linking genome-scale metabolic modeling and genome annotation 
Genome-scale metabolic network reconstructions, assembled from annotated genomes, serve as a platform for integrating data from heterogeneous sources and generating hypotheses for further experimental validation. Implementing constraint-based modeling techniques such as Flux Balance Analysis (FBA) on network reconstructions allow for interrogating metabolism at a systems-level, which aids in identifying and rectifying gaps in knowledge. With genome sequences for various organisms from prokaryotes to eukaryotes becoming increasingly available, a significant bottleneck lies in the structural and functional annotation of these sequences. Using topologically-based and biologically-inspired metabolic network refinement, we can better characterize enzymatic functions present in an organism and link annotation of these functions to candidate transcripts, both steps that can be experimentally validated.
PMCID: PMC4079539  PMID: 23417799
metabolic network; gap filling; orphan reactions; flux balance analysis
15.  Fumaric Acid Production in Saccharomyces cerevisiae by In Silico Aided Metabolic Engineering 
PLoS ONE  2012;7(12):e52086.
Fumaric acid (FA) is a promising biomass-derived building-block chemical. Bio-based FA production from renewable feedstock is a promising and sustainable alternative to petroleum-based chemical synthesis. Here we report on FA production by direct fermentation using metabolically engineered Saccharomyces cerevisiae with the aid of in silico analysis of a genome-scale metabolic model. First, FUM1 was selected as the target gene on the basis of extensive literature mining. Flux balance analysis (FBA) revealed that FUM1 deletion can lead to FA production and slightly lower growth of S. cerevisiae. The engineered S. cerevisiae strain obtained by deleting FUM1 can produce FA up to a concentration of 610±31 mg L–1 without any apparent change in growth in fed-batch culture. FT-IR and 1H and 13C NMR spectra confirmed that FA was synthesized by the engineered S. cerevisiae strain. FBA identified pyruvate carboxylase as one of the factors limiting higher FA production. When the RoPYC gene was introduced, S. cerevisiae produced 1134±48 mg L–1 FA. Furthermore, the final engineered S. cerevisiae strain was able to produce 1675±52 mg L–1 FA in batch culture when the SFC1 gene encoding a succinate–fumarate transporter was introduced. These results demonstrate that the model shows great predictive capability for metabolic engineering. Moreover, FA production in S. cerevisiae can be efficiently developed with the aid of in silico metabolic engineering.
PMCID: PMC3530589  PMID: 23300594
16.  Modeling Lactococcus lactis using a genome-scale flux model 
BMC Microbiology  2005;5:39.
Genome-scale flux models are useful tools to represent and analyze microbial metabolism. In this work we reconstructed the metabolic network of the lactic acid bacteria Lactococcus lactis and developed a genome-scale flux model able to simulate and analyze network capabilities and whole-cell function under aerobic and anaerobic continuous cultures. Flux balance analysis (FBA) and minimization of metabolic adjustment (MOMA) were used as modeling frameworks.
The metabolic network was reconstructed using the annotated genome sequence from L. lactis ssp. lactis IL1403 together with physiological and biochemical information. The established network comprised a total of 621 reactions and 509 metabolites, representing the overall metabolism of L. lactis. Experimental data reported in the literature was used to fit the model to phenotypic observations. Regulatory constraints had to be included to simulate certain metabolic features, such as the shift from homo to heterolactic fermentation. A minimal medium for in silico growth was identified, indicating the requirement of four amino acids in addition to a sugar. Remarkably, de novo biosynthesis of four other amino acids was observed even when all amino acids were supplied, which is in good agreement with experimental observations. Additionally, enhanced metabolic engineering strategies for improved diacetyl producing strains were designed.
The L. lactis metabolic network can now be used for a better understanding of lactococcal metabolic capabilities and potential, for the design of enhanced metabolic engineering strategies and for integration with other types of 'omic' data, to assist in finding new information on cellular organization and function.
PMCID: PMC1185544  PMID: 15982422
17.  Predictive Potential of Flux Balance Analysis of Saccharomyces cerevisiae Using as Optimization Function Combinations of Cell Compartmental Objectives 
PLoS ONE  2012;7(8):e43006.
The main objective of flux balance analysis (FBA) is to obtain quantitative predictions of metabolic fluxes of an organism, and it is necessary to use an appropriate objective function to guarantee a good estimation of those fluxes.
In this study, the predictive performance of FBA was evaluated, using objective functions arising from the linear combination of different cellular objectives. This approach is most suitable for eukaryotic cells, owing to their multiplicity of cellular compartments. For this reason, Saccharomyces cerevisiae was used as model organism, and its metabolic network was represented using the genome-scale metabolic model iMM904. As the objective was to evaluate the predictive performance from the FBA using the kind of objective function previously described, substrate uptake and oxygen consumption were the only input data used for the FBA. Experimental information about microbial growth and exchange of metabolites with the environment was used to assess the quality of the predictions.
The quality of the predictions obtained with the FBA depends greatly on the knowledge of the oxygen uptake rate. For the most of studied classifications, the best predictions were obtained with “maximization of growth”, and with some combinations that include this objective. However, in the case of exponential growth with unknown oxygen exchange flux, the objective function “maximization of growth, plus minimization of NADH production in cytosol, plus minimization of NAD(P)H consumption in mitochondrion” gave much more accurate estimations of fluxes than the obtained with any other objective function explored in this study.
PMCID: PMC3415429  PMID: 22912775
18.  Natural computation meta-heuristics for the in silico optimization of microbial strains 
BMC Bioinformatics  2008;9:499.
One of the greatest challenges in Metabolic Engineering is to develop quantitative models and algorithms to identify a set of genetic manipulations that will result in a microbial strain with a desirable metabolic phenotype which typically means having a high yield/productivity. This challenge is not only due to the inherent complexity of the metabolic and regulatory networks, but also to the lack of appropriate modelling and optimization tools. To this end, Evolutionary Algorithms (EAs) have been proposed for in silico metabolic engineering, for example, to identify sets of gene deletions towards maximization of a desired physiological objective function. In this approach, each mutant strain is evaluated by resorting to the simulation of its phenotype using the Flux-Balance Analysis (FBA) approach, together with the premise that microorganisms have maximized their growth along natural evolution.
This work reports on improved EAs, as well as novel Simulated Annealing (SA) algorithms to address the task of in silico metabolic engineering. Both approaches use a variable size set-based representation, thereby allowing the automatic finding of the best number of gene deletions necessary for achieving a given productivity goal. The work presents extensive computational experiments, involving four case studies that consider the production of succinic and lactic acid as the targets, by using S. cerevisiae and E. coli as model organisms. The proposed algorithms are able to reach optimal/near-optimal solutions regarding the production of the desired compounds and presenting low variability among the several runs.
The results show that the proposed SA and EA both perform well in the optimization task. A comparison between them is favourable to the SA in terms of consistency in obtaining optimal solutions and faster convergence. In both cases, the use of variable size representations allows the automatic discovery of the approximate number of gene deletions, without compromising the optimality of the solutions.
PMCID: PMC2612012  PMID: 19038030
19.  Integration of expression data in genome-scale metabolic network reconstructions 
With the advent of high-throughput technologies, the field of systems biology has amassed an abundance of “omics” data, quantifying thousands of cellular components across a variety of scales, ranging from mRNA transcript levels to metabolite quantities. Methods are needed to not only integrate this omics data but to also use this data to heighten the predictive capabilities of computational models. Several recent studies have successfully demonstrated how flux balance analysis (FBA), a constraint-based modeling approach, can be used to integrate transcriptomic data into genome-scale metabolic network reconstructions to generate predictive computational models. In this review, we summarize such FBA-based methods for integrating expression data into genome-scale metabolic network reconstructions, highlighting their advantages as well as their limitations.
PMCID: PMC3429070  PMID: 22934050
flux balance analysis; data integration; transcriptomics; expression data; metabolic networks
20.  Integrating Flux Balance Analysis into Kinetic Models to Decipher the Dynamic Metabolism of Shewanella oneidensis MR-1 
PLoS Computational Biology  2012;8(2):e1002376.
Shewanella oneidensis MR-1 sequentially utilizes lactate and its waste products (pyruvate and acetate) during batch culture. To decipher MR-1 metabolism, we integrated genome-scale flux balance analysis (FBA) into a multiple-substrate Monod model to perform the dynamic flux balance analysis (dFBA). The dFBA employed a static optimization approach (SOA) by dividing the batch time into small intervals (i.e., ∼400 mini-FBAs), then the Monod model provided time-dependent inflow/outflow fluxes to constrain the mini-FBAs to profile the pseudo-steady-state fluxes in each time interval. The mini-FBAs used a dual-objective function (a weighted combination of “maximizing growth rate” and “minimizing overall flux”) to capture trade-offs between optimal growth and minimal enzyme usage. By fitting the experimental data, a bi-level optimization of dFBA revealed that the optimal weight in the dual-objective function was time-dependent: the objective function was constant in the early growth stage, while the functional weight of minimal enzyme usage increased significantly when lactate became scarce. The dFBA profiled biologically meaningful dynamic MR-1 metabolisms: 1. the oxidative TCA cycle fluxes increased initially and then decreased in the late growth stage; 2. fluxes in the pentose phosphate pathway and gluconeogenesis were stable in the exponential growth period; and 3. the glyoxylate shunt was up-regulated when acetate became the main carbon source for MR-1 growth.
Author Summary
This study integrates two modeling approaches, a Monod kinetic model and genome-scale flux balance analysis, to analyze the dynamic metabolism of an environmentally important bacterium (S. oneidensis MR-1). The modeling results reveal that MR-1 metabolism is suboptimal for biomass growth, while MR-1 continuously reprograms the intracellular flux distributions in adaption to nutrient conditions. This innovative dFBA framework can be widely used to investigate transient cell metabolisms in response to environmental variations. Furthermore, the dFBA is able to simulate metabolite-labeling dynamics in 13C-tracer experiments, and thus can serve as a springboard to advanced 13C-assisted dynamic metabolic flux analysis by using labeled proteinogenic amino acids to improve flux results.
PMCID: PMC3271021  PMID: 22319437
21.  FASIMU: flexible software for flux-balance computation series in large metabolic networks 
BMC Bioinformatics  2011;12:28.
Flux-balance analysis based on linear optimization is widely used to compute metabolic fluxes in large metabolic networks and gains increasingly importance in network curation and structural analysis. Thus, a computational tool flexible enough to realize a wide variety of FBA algorithms and able to handle batch series of flux-balance optimizations is of great benefit.
We present FASIMU, a command line oriented software for the computation of flux distributions using a variety of the most common FBA algorithms, including the first available implementation of (i) weighted flux minimization, (ii) fitness maximization for partially inhibited enzymes, and (iii) of the concentration-based thermodynamic feasibility constraint. It allows batch computation with varying objectives and constraints suited for network pruning, leak analysis, flux-variability analysis, and systematic probing of metabolic objectives for network curation. Input and output supports SBML. FASIMU can work with free (lp_solve and GLPK) or commercial solvers (CPLEX, LINDO). A new plugin (faBiNA) for BiNA allows to conveniently visualize calculated flux distributions. The platform-independent program is an open-source project, freely available under GNU public license at including manual, tutorial, and plugins.
We present a flux-balance optimization program whose main merits are the implementation of thermodynamics as a constraint, batch series of computations, free availability of sources, choice on various external solvers, and the flexibility on metabolic objectives and constraints.
PMCID: PMC3038154  PMID: 21255455
22.  FBA-SimVis: interactive visualization of constraint-based metabolic models 
Bioinformatics  2009;25(20):2755-2757.
Summary: FBA-SimVis is a VANTED plug-in for the constraint-based analysis of metabolic models with special focus on the visual exploration of metabolic flux data resulting from model analysis. The program provides a user-friendly environment for model reconstruction, constraint-based model analysis, and interactive visualization of the simulation results. With the ability to quantitatively analyse metabolic fluxes in an interactive and visual manner, FBA-SimVis supports a comprehensive understanding of constraint-based metabolic flux models in both overview and detail.
Availability: Software with manual and tutorials are freely available at
Supplementary information: Examples and supplementary data are available at
PMCID: PMC2759546  PMID: 19578041
23.  sybil – Efficient constraint-based modelling in R 
BMC Systems Biology  2013;7:125.
Constraint-based analyses of metabolic networks are widely used to simulate the properties of genome-scale metabolic networks. Publicly available implementations tend to be slow, impeding large scale analyses such as the genome-wide computation of pairwise gene knock-outs, or the automated search for model improvements. Furthermore, available implementations cannot easily be extended or adapted by users.
Here, we present sybil, an open source software library for constraint-based analyses in R; R is a free, platform-independent environment for statistical computing and graphics that is widely used in bioinformatics. Among other functions, sybil currently provides efficient methods for flux-balance analysis (FBA), MOMA, and ROOM that are about ten times faster than previous implementations when calculating the effect of whole-genome single gene deletions in silico on a complete E. coli metabolic model.
Due to the object-oriented architecture of sybil, users can easily build analysis pipelines in R or even implement their own constraint-based algorithms. Based on its highly efficient communication with different mathematical optimisation programs, sybil facilitates the exploration of high-dimensional optimisation problems on small time scales. Sybil and all its dependencies are open source. Sybil and its documentation are available for download from the comprehensive R archive network (CRAN).
PMCID: PMC3843580  PMID: 24224957
Constraint-based modelling; Flux-balance analysis; FBA; MOMA; ROOM; GNU R
24.  A genome-scale computational study of the interplay between transcriptional regulation and metabolism 
This paper presents a new method, steady-state regulatory flux balance analysis (SR-FBA), for predicting gene expression and metabolic fluxes in a large-scale integrated metabolic–regulatory model. Using SR-FBA to study the metabolism of Escherichia coli, we quantify the extent to which the different levels of metabolic and transcriptional regulatory constraints determine metabolic behavior: metabolic constraints determine the flux activity state of 45–51% of metabolic genes, depending on the growth media, whereas transcription regulation determines the flux activity state of 13–20% of the genes. A considerable number of 36 genes are redundantly expressed, that is, they are expressed even though the fluxes of their associated reactions are zero, indicating that they are not optimally tuned for cellular flux demands. The undetermined state of the remaining ∼30% of the genes suggests that they may represent metabolic variability within a given growth medium. Overall, SR-FBA enables one to address a host of new questions concerning the interplay between regulation and metabolism.
PMCID: PMC1865583  PMID: 17437026
FBA; metabolism; MILP; regulation; SR-FBA
25.  Reconstruction and Validation of a Genome-Scale Metabolic Model for the Filamentous Fungus Neurospora crassa Using FARM 
PLoS Computational Biology  2013;9(7):e1003126.
The filamentous fungus Neurospora crassa played a central role in the development of twentieth-century genetics, biochemistry and molecular biology, and continues to serve as a model organism for eukaryotic biology. Here, we have reconstructed a genome-scale model of its metabolism. This model consists of 836 metabolic genes, 257 pathways, 6 cellular compartments, and is supported by extensive manual curation of 491 literature citations. To aid our reconstruction, we developed three optimization-based algorithms, which together comprise Fast Automated Reconstruction of Metabolism (FARM). These algorithms are: LInear MEtabolite Dilution Flux Balance Analysis (limed-FBA), which predicts flux while linearly accounting for metabolite dilution; One-step functional Pruning (OnePrune), which removes blocked reactions with a single compact linear program; and Consistent Reproduction Of growth/no-growth Phenotype (CROP), which reconciles differences between in silico and experimental gene essentiality faster than previous approaches. Against an independent test set of more than 300 essential/non-essential genes that were not used to train the model, the model displays 93% sensitivity and specificity. We also used the model to simulate the biochemical genetics experiments originally performed on Neurospora by comprehensively predicting nutrient rescue of essential genes and synthetic lethal interactions, and we provide detailed pathway-based mechanistic explanations of our predictions. Our model provides a reliable computational framework for the integration and interpretation of ongoing experimental efforts in Neurospora, and we anticipate that our methods will substantially reduce the manual effort required to develop high-quality genome-scale metabolic models for other organisms.
Author Summary
Few organisms have been as foundational to the development of modern genetics and cellular metabolism as Neurospora crassa. Given the wealth of knowledge available for this filamentous fungus, the effort required to manually curate a high-quality genome-scale metabolic reconstruction would be daunting. To aid the reconstruction process, we developed three optimization-based algorithms. The first algorithm predicts flux while linearly accounting for metabolite dilution; the second algorithm removes blocked reactions with one compact linear program; and the third algorithm reconciles differences between in silico predictions and experimental observations of mutant viability. We have used these algorithms to develop the first genome-scale metabolic model for Neurospora. We have validated the accuracy of our model against an independent test set of more than 300 growth/no-growth phenotypes, and our model displays 93% sensitivity and specificity. Simulating the biochemical genetics experiments originally performed on Neurospora, we comprehensively predicted essential genes, nutrient rescues of auxotroph mutants and synthetic lethal interactions. With these predictions, we provide potential mechanistic insight into known mutant phenotypes, and testable hypotheses for novel mutant phenotypes. The model, the algorithms and the testable hypotheses provide a computational foundation for the study of Neurospora crassa metabolism.
PMCID: PMC3730674  PMID: 23935467

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