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Mathematical framework of three constraint-based modeling (CBM) methods: flux balance analysis (FBA), flux variability analysis (FVA), and parsimonious FBA (pFBA). S = stoichiometric matrix, v = vector of reaction fluxes, b = vector of changes in metabolite concentration, Zobj = objective function, vbiomass = biomass reaction flux, lb = lower flux bounds, ub = upper flux bounds.
