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The solution to this optimization problem is a set of interventions and a corresponding optimal flux value for the target reaction.
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The 13C-FLUX software was used for estimation of optimal flux values and 90% confidence intervals of flux values were calculated by Monte Carlo sampling method [ 22].
Similar to MCOpt, MCEval repeatedly solves a series of optimization problems to generate a distribution of optimal target flux values.
In Figure 3, the intervention sets (U for the up-regulation set) identified by each optimization method are shown above their corresponding optimal target flux values.
Repeating the process (sampling and optimization) many times, we obtain a distribution of optimal target flux values.
Optimal relative flux values for each carbon source are indicated with dashed lines.
The solution to this problem is an optimal flux distribution, v, a vector that contains flux values for each reaction in the network.
While the optimal value z in (4) is always unique, infinite optimal flux vectors r achieving the maximal z may exist (especially in genome-scale networks).
The output of FBA is an optimal flux distribution for each reaction in the model and a maximum value for the objective function.
The optimization was started 10000 times from random initial values to evaluate the uniqueness of the optimal flux distribution.
A flux value of 81.68 mmol/gDW/h for the reduced cytochrome c production was necessary for the optimal growth rate of 0.2864 h-1, and a metabolic perturbation of a drain flux of cytochrome c entailed a compromise on the growth rate.
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