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Optimization-based framework with flux balance analysis (FBA) and metabolic pathway analysis (MPA) for identifying metabolic objective functions
Fig 8
The optimization-based framework of TIObjFind.
(A) Step 1 reformulates the optimization problem as a single-level problem using the duality theorem of linear programming, subject to thermodynamic, mass balance, and uptake constraints. These dual variables, ui and g, reflect the sensitivity of the optimal objective value Zp to changes in their associated constraints. The reaction fluxes 
are the dual variables for the dual constraints, and 
denotes weights for any potential cellular objective (e.g., biomass formation or energy production). The computed fluxes 
are then mapped in the dual network. (B) Step 2 maps the FBA solutions, 
, onto the Mass Flow Graph. In the dual formulation, primal reactions become metabolites in the dual network, while primal metabolites serve as constraints in the dual. Self-loops represent autocatalytic reactions, where products also act as reactants, capturing internal metabolic fluxes. (C) Step 3 shows the normalization of the pathway importance (represented as edge weights, w, in the Mass Flow Graph), leading to a new objective reaction flux distribution.
doi: https://doi.org/10.1371/journal.pcbi.1013635.g008