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What is flux balance analysis?
Jeffrey D Orth, Ines Thiele & Bernhard Palsson
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.
2010 Nature America, Inc. All rights reserved.
Flux balance analysis (FBA) is a widely used approach for studying biochemi
cal networks, in particular the genome-scale metabolic network reconstructions that have been built in the past decade1-4. 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 bio-technologically important metabolite. With metabolic models for 35 organisms already available (http://systemsbiology.ucsd.edu/In_Silico_Organisms/Other_Organisms
Web End =http://systemsbiology.ucsd.edu/ http://systemsbiology.ucsd.edu/In_Silico_Organisms/Other_Organisms
Web End =In_Silico_Organisms/Other_Organisms ) and high-throughput technologies enabling the construction of many more each year5-7,
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 predict the maximum 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 ten 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 and Fig. 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. 2a,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 dependent on biophysical equations that require many difficult-to-measure kinetic parameters8,9.
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...