Flux Balance Constraint (analysis)

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Analysis title
Differential-algebraic-equations-Flux-Balance-Constraint-icon.png Flux Balance Constraint
Institute of Systems Biology
biouml.plugins.fbc (Flux Balance)

Flux Balance Analysis

Flux balance analysis is a mathematical approach for analyzing the flow of metabolites through a metabolic network.

Metabolic reactions are represented as a stoichiometric matrix S. The flux through all of the reactions in a network is represented by the vector v. Flux Balance Analysis seeks to maximize or minimize an objective function Z = cTv, which can be any linear combination of fluxes, where c is a vector of weights, indicating how much each reaction contributes to the objective function. FBA can thus be defined as the use of linear programming to solve the equation Sv = 0 given a set of upper and lower bounds on v and a linear combination of fluxes as an objective function.


  • Diagram – Path to input diagram
  • Data table – Path to the table with initial FBC data (bounds, objective function coefficients)
  • Output path – Path to table with fluxes values
  • Optimization type (expert) – Type of objective function optimization which will be used (maximize or minimize)
  • Solver type (expert) – Type of the solver which will be used to find fluxes
  • Max iter (expert) – Maximal iteration number

One should use Building Flux Balance DataTable or Score based FBC table builder analyses to generate FBC data table.


FBC syntax example: a simple four reaction pathway. The reactions are R1, R2, X1, X2 with fixed species IN, OUT, ATP, NADH and variable species A, B.

Differential-algebraic-equations-Flux-Balance-Constraint-fbc 1.png

Using the reagent identity and stoichiometry it is possible to compactly describe this network in terms of its reaction stoichiometry:

Differential-algebraic-equations-Flux-Balance-Constraint-fbc 2.png
Differential-algebraic-equations-Flux-Balance-Constraint-fbc 3.png

There are capacity constraints in this example:

Differential-algebraic-equations-Flux-Balance-Constraint-fbc 4.png

In this example the flux through reaction R2 will be maximized. Solving this we find that maximization of flux through R2 gives an optimal solution R2 = 1 with one possible solution for v.

Differential-algebraic-equations-Flux-Balance-Constraint-fbc 5.png
  1. Jeffrey D. Orth, Ines Thiele and Bernhard O. Palsson, "What is flux balance analysis?". Nature Biotechnology 28, 245-248 2010.
  2. SBML Level 3 Package Specification
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