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

Network reconstructions are a common denominator in systems biology. Bottom-up metabolic network reconstructions have developed over the past 10 years. These reconstructions represent structured knowledge-bases that abstract pertinent information on the biochemical transformations taking place within specific target organisms. The conversion of a reconstruction into a mathematical format facilitates myriad computational biological studies including evaluation of network content, hypothesis testing and generation, analysis of phenotypic characteristics, and metabolic engineering. To date, genome-scale metabolic reconstructions for more than 30 organisms have been published and this number is expected to increase rapidly. However, these reconstructions differ in quality and coverage that may minimize their predictive potential and use as knowledge-bases. Here, we present a comprehensive protocol describing each step necessary to build a high-quality genome-scale metabolic reconstruction as well as common trials and tribulations. Therefore, this protocol provides a helpful manual for all stages of the reconstruction process.

An updated genome-scale reconstruction of the metabolic network in Escherichia coli K-12 MG1655 is presented. This updated metabolic reconstruction includes: (1) an alignment with the latest genome annotation and the metabolic content of EcoCyc leading to the inclusion of the activities of 1260 ORFs, (2) characterization and quantification of the biomass components and maintenance requirements associated with growth of E. coli and (3) thermodynamic information for the included chemical reactions. The conversion of this metabolic network reconstruction into an in silico model is detailed. A new step in the metabolic reconstruction process, termed thermodynamic consistency analysis, is introduced, in which reactions were checked for consistency with thermodynamic reversibility estimates. Applications demonstrating the capabilities of the genome-scale metabolic model to predict high-throughput experimental growth and gene deletion phenotypic screens are presented. The increased scope and computational capability using this new reconstruction is expected to broaden the spectrum of both basic biology and applied systems biology studies of E. coli metabolism.