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FBA uses the matrix of reactions in a genome scale model to find the optimal combination of reactions that consume available nutrients (e.g. glucose and ammonium) to produce the metabolites (e.g. sugars, fats, high energy molecules) required for new cellular growth (also described as biomass production).
We used the EC numbers and the updated KEGG reaction database [ 60] to build a bipartite metabolic network, which was constructed based on the connection matrix of reactions [ 61].
The connection matrix of reactions [ 34, 35] was substantially improved in this work by updating the enzyme reaction database to the newer version of KEGG Ligand (Status August 2009).
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S = [ s i, j] m× n and T = [ t j, i] n× m are the stoichiometric coefficient matrices of reactions.
N · v → = 0 a j ≤ v j ≤ b j where N is the stoichiometric matrix of all reactions and v is the flux vector representing the reaction fluxes.
These approaches are based on a stoichiometric matrix of chemical reactions and static analyses.
In order to avoid any confusion, we point out that a solution for Ax = 0 is considered a loop only if A is the stoichiometric matrix of internal reactions.
From the following Proposition, it follows that L ^ (x ) satisfies all the properties of a weighted Laplacian matrix of a reaction network corresponding to a complex graph with vertex set V - V o Consider a chemical reaction network with weighted Laplacian matrix L (x ) ∈ R c × c corresponding to the concentration vector x.
Exploring the properties of a balanced weighted Laplacian matrix of the reaction network and the Laplacian of the simplicial complex, we characterize the space of equilibrium points and provide a simple stability analysis on the state space modulo the space of equilibrium points.
It is noteworthy that unlike previous applications of this method (30, 31) samples were prepared under entirely aqueous conditions and without altering the biochemical matrix of the reaction.
These used the simpler thermodynamically dependent form when the stoichiometric matrix of the reaction system has full column rank, and the more complex thermodynamically independent form otherwise.
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