Editing Metabolic engineering (section)

===Analyzing a metabolic pathway===
The completed metabolic pathway is modeled mathematically to find the theoretical yield of the product or the reaction fluxes in the cell.  A flux is the rate at which a given reaction in the network occurs.  Simple metabolic pathway analysis can be done by hand, but most require the use of software to perform the computations.<ref>Schellenberger, J., Que, R., Fleming, R., et al. (2011). "Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0". ''Nature Protocols.'' 6(9):1290-1307</ref>  These programs use complex linear algebra algorithms to solve these models. To solve a network using the equation for determined systems shown below, one must input the necessary information about the relevant reactions and their fluxes. Information about the reaction (such as the reactants and stoichiometry) are contained in the matrices G<sub>x</sub> and G<sub>m</sub>. Matrices V<sub>m</sub> and V<sub>x</sub> contain the fluxes of the relevant reactions.  When solved, the equation yields the values of all the unknown fluxes (contained in V<sub>x</sub>).

:<math>V_x=-(G_x)^{-1}*(G_m * V_m)</math>