Flux balance analysis is a mathematical approach for analyzing the flow of metabolites through a metabolic network. This primer covers the theoretical basis of the approach, several practical examples and a software toolbox for performing the calculations.Flux balance analysis (FBA) is a widely used approach for studying biochemical networks, in particular the genome-scale metabolic network reconstructions that have been built in the past decade [1][2][3][4][5] . These network reconstructions contain all of the known metabolic reactions in an organism and the genes that encode each enzyme. FBA calculates the flow of metabolites through this metabolic network, thereby making it possible to predict the growth rate of an organism or the rate of production of a biotechnologically important metabolite. With metabolic models for 35 organisms already available (http://systemsbiology.ucsd.edu/In_Silico_Organisms/Other_Organisms) and highthroughput technologies enabling the construction of many more each year 6, 7 , FBA is an important tool for harnessing the knowledge encoded in these models.In this primer, we illustrate the principles behind FBA by applying it to the prediction of the specific growth rate of Escherichia coli in the presence and absence of oxygen. The principles outlined can be applied in many other contexts to analyze the phenotypes and capabilities of organisms with different environmental and genetic perturbations (a supplementary tutorial provides six additional worked examples with figures and computer code). Flux balance analysis is based on constraintsThe first step in FBA is to mathematically represent metabolic reactions (Box 1). The core feature of this representation is a tabulation, in the form of a numerical matrix, of the stoichiometric coefficients of each reaction (Fig. 1a,b). These stoichiometries impose constraints on the flow of metabolites through the network. Constraints such as these lie at the heart of FBA, differentiating the approach from theory-based models based on biophysical equations that require many difficult-to-measure kinetic parameters 8,9 .Constraints are represented in two ways, as equations that balance reaction inputs and outputs and as inequalities that impose bounds on the system. The matrix of stoichiometries imposes flux (that is, mass) balance constraints on the system, ensuring that the total amount of any compound being produced must be equal to the total amount being consumed at steady state (Fig. 1c). Every reaction can also be given upper and lower bounds, which define the maximum and minimum allowable fluxes of the reactions. These balances and

The genome-scale metabolic network reconstruction of Escherichia coli, in use since 2000, is thoroughly updated based on the recent findings in the literature and new experiments. The improved reconstruction accounts for 1366 genes and can be used for constraint-based modeling of metabolic phenotypes.

Over the past decade, a growing community of researchers has emerged around the use of COnstraint-Based Reconstruction and Analysis (COBRA) methods to simulate, analyze and predict a variety of metabolic phenotypes using genome-scale models. The COBRA Toolbox, a MATLAB package for implementing COBRA methods, was presented earlier. Here we present a significant update of this in silico ToolBox. Version 2.0 of the COBRA Toolbox expands the scope of computations by including in silico analysis methods developed since its original release. New functions include: (1) network gap filling, (2) 13C analysis, (3) metabolic engineering, (4) omics-guided analysis, and (5) visualization. As with the first version, the COBRA Toolbox reads and writes Systems Biology Markup Language formatted models. In version 2.0, we improved performance, usability, and the level of documentation. A suite of test scripts can now be used to learn the core functionality of the Toolbox and validate results. This Toolbox lowers the barrier of entry to use powerful COBRA methods.

Genome-scale models (GEMs) of metabolism were constructed for 55 fully sequenced Escherichia coli and Shigella strains. The GEMs enable a systems approach to characterizing the pan and core metabolic capabilities of the E. coli species. The majority of pan metabolic content was found to consist of alternate catabolic pathways for unique nutrient sources. The GEMs were then used to systematically analyze growth capabilities in more than 650 different growth-supporting environments. The results show that unique strain-specific metabolic capabilities correspond to pathotypes and environmental niches. Twelve of the GEMs were used to predict growth on six differentiating nutrients, and the predictions were found to agree with 80% of experimental outcomes. Additionally, GEMs were used to predict strain-specific auxotrophies. Twelve of the strains modeled were predicted to be auxotrophic for vitamins niacin (vitamin B 3 ), thiamin (vitamin B 1 ), or folate (vitamin B 9 ). Six of the strains modeled have lost biosynthetic pathways for essential amino acids methionine, tryptophan, or leucine. Genome-scale analysis of multiple strains of a species can thus be used to define the metabolic essence of a microbial species and delineate growth differences that shed light on the adaptation process to a particular microenvironment.systems biology | mathematical modeling | core and pan genome

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Integrated approaches utilizing in silico analyses will be necessary to successfully advance the field of metabolic engineering. Here, we present an integrated approach through a systematic model-driven evaluation of the production potential for the bacterial production organism E. coli to produce multiple native products from different representative feedstocks through coupling metabolite production to growth rate. Designs were examined for eleven unique central metabolism and amino acid targets from three different substrates under aerobic and anaerobic conditions. Optimal strain designs were reported for designs which possess maximum yield, substrate-specific productivity, and strength of growth-coupling for up to ten reaction eliminations (knockouts). In total, growth-coupled designs could be identified for 36 out of the total 54 conditions tested, corresponding to eight out of the eleven targets. There were 17 different substrate/target pairs for which over 80% of the theoretical maximum potential could be achieved. The developed method introduces a new concept of objective function tilting for strain design. This study provides specific metabolic interventions (strain designs) for production strains that can be experimentally implemented, characterizes the potential for E. coli to produce native compounds, and outlines a strain design pipeline that can be utilized to design production strains for additional organisms.

Biochemical network reconstructions have become popular tools in systems biology. Metabolicnetwork reconstructions are biochemically, genetically, and genomically (BiGG) structured databases of biochemical reactions and metabolites. They contain information such as exact reaction stoichiometry, reaction reversibility, and the relationships between genes, proteins, and reactions. Network reconstructions have been used extensively to study the phenotypic behavior of wild-type and mutant stains under a variety of conditions, linking genotypes with phenotypes. Such phenotypic simulations have allowed for the prediction of growth after genetic manipulations, prediction of growth phenotypes after adaptive evolution, and prediction of essential genes. Additionally, because network reconstructions are organism specific, they can be used to understand differences between organisms of species in a functional context.There are different types of reconstructions representing various types of biological networks (metabolic, regulatory, transcription/translation). This chapter serves as an introduction to metabolic and regulatory network reconstructions and models and gives a complete description of the core Escherichia coli metabolic model. This model can be analyzed in any computational format (such as MATLAB or Mathematica) based on the information given in this chapter. The core E. coli model is a small-scale model that can be used for educational purposes. It is meant to be used by senior undergraduate and first-year graduate students learning about constraint-based modeling and systems biology. This model has enough reactions and pathways to enable interesting and insightful calculations, but it is also simple enough that the results of such calculations can be understoodeasily.

Genome-scale metabolic network reconstructions are built from all of the known metabolic reactions and genes in a target organism. However, since our knowledge of any organism is incomplete, these network reconstructions contain gaps. Reactions may be missing, resulting in dead-ends in pathways, while unknown gene products may catalyze known reactions. New computational methods that analyze data, such as growth phenotypes or gene essentiality, in the context of genome-scale metabolic networks, have been developed to predict these missing reactions or genes likely to fill these knowledge gaps. A growing number of experimental studies are appearing that address these computational predictions, leading to discovery of new metabolic capabilities in the target organism. Gap-filling methods can thus be used to improve metabolic network models while simultaneously leading to discovery of new metabolic gene functions.