What is flux balance analysis?

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Nature Biotechnology
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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.

At a glance


  1. The conceptual basis of constraint-based modeling.
    Figure 1: The conceptual basis of constraint-based modeling.

    With no constraints, the flux distribution of a biological network may lie at any point in a solution space. When mass balance constraints imposed by the stoichiometric matrix S (labeled 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (labeled 2) are applied to a network, it defines an allowable solution space. The network may acquire any flux distribution within this space, but points outside this space are denied by the constraints. Through optimization of an objective function, FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space.

  2. Formulation of an FBA problem.
    Figure 2: Formulation of an FBA problem.

    (a) A metabolic network reconstruction consists of a list of stoichiometrically balanced biochemical reactions. (b) This reconstruction is converted into a mathematical model by forming a matrix (labeled S), in which each row represents a metabolite and each column represents a reaction. Growth is incorporated into the reconstruction with a biomass reaction (yellow column), which simulates metabolites consumed during biomass production. Exchange reactions (green columns) are used to represent the flow of metabolites, such as glucose and oxygen, in and out of the cell. (c) At steady state, the flux through each reaction is given by Sv = 0, which defines a system of linear equations. As large models contain more reactions than metabolites, there is more than one possible solution to these equations. (d) Solving the equations to predict the maximum growth rate requires defining an objective function Z = cTv (c is a vector of weights indicating how much each reaction (v) contributes to the objective). In practice, when only one reaction, such as biomass production, is desired for maximization or minimization, c is a vector of zeros with a value of 1 at the position of the reaction of interest. In the growth example, the objective function is Z = vbiomass (that is, c has a value of 1 at the position of the biomass reaction). (e) Linear programming is used to identify a flux distribution that maximizes or minimizes the objective function within the space of allowable fluxes (blue region) defined by the constraints imposed by the mass balance equations and reaction bounds. The thick red arrow indicates the direction of increasing Z. As the optimal solution point lies as far in this direction as possible, the thin red arrows depict the process of linear programming, which identifies an optimal point at an edge or corner of the solution space.


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  1. Jeffrey D. Orth and Bernhard Ø. Palsson are at the University of California San Diego, La Jolla, California, USA.

  2. Ines Thiele is at the University of Iceland, Reykjavik, Iceland.

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