Mathematical Description
Mathematically, a flux balance analysis is characterized at the intersection of two fields, graph theory and mathematical optimization. The first step in the analysis is creating the appropriate metabolic network. This network is a graph composed of chemical compounds (nodes) connected by chemical reactions (edges). The key point is that the edges do not need to contain any rate related information, since that is what the model solves for. It simply needs to encode the appropriate stoichiometric coefficients. The properties of such a network are well studied in mathematics, and many conclusions can be drawn directly from it. However, the flux balance analysis involves applying linear optimization directly to the network by representing it as a matrix. The properties of this matrix are well known and thus a biological problem becomes amenable to computational analysis. A real biological system is extremely complex which in turn leads to problems measuring enough parameters to define the system and in some cases requiring a huge amount of computing time to perform simulations. Flux-balance analysis simplifies the representation of the biological system, requiring fewer parameters (such as enzyme kinetic rates, compound concentrations and diffusion constants) and greatly reduces the computer time required for simulations.
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