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Figure 1 | BMC Systems Biology

Figure 1

From: An objective function exploiting suboptimal solutions in metabolic networks

Figure 1

FBA, MOMA and PSEUDO approaches to predicting metabolic fluxes. (A) In FBA wild-type flux space is constrained to a polytope defined by thermodynamic and conservation-of-mass requirements. A linear objective describing cell growth, the green arrow, is maximized within this region. If the growth vector is perpendicular to a facet of the constrained polytope then a range of fluxes allow equally optimum growth, indicated by the heavy green edge. However, a linear programming solver can return only a single optimal point, the green target. (B) Mutations are represented as additional linear constraints that reduce the size of the allowed flux polytope. The yellow region represents the subset of wild-type fluxes allowed under a mutation. FBA finds a new optimum within this space as for the wild type. The green face represents a range of equally optimal mutant solutions. The blue target is a single point that a solver might return. (C) MOMA is an alternative approach for predicting mutant fluxes. The point in the mutant region, blue target, is found that minimizes the distance to a wild-type solution, green target. If FBA was used to generate the wild-type solution, then alternative optima may exist along the heavy green edge. (D) The PSEUDO strategy does not use FBA to select a wild-type flux vector. Instead we define a degenerate optimal region that contains all flux distributions capable of supporting near-maximal growth. A solution within the mutant region is found with minimum distance to this degenerate optimal region. Note that PSEUDO may select a point in mutant flux space different from the MOMA solution and closer to the growth-optimal region.

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