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The maximal flux values, calculated using sample points from the distributions of enzyme level modifications (N u and N d, form a capacity distribution.
FVA uses linear programming methods to find the minimal and maximal flux values that can be achieved by each reaction while contributing to maximal production of the objective reaction.
This method was conducted through the analysis of trends in reaction flux variability in response to varying the flux of target chemical production from initial to maximal flux values under GR constraints.
In FVA, the minimum and maximal flux values are computed for each reaction in the model, by choosing each reaction individually as objective function and performing FBA for that reaction (31, 69).
First, the theoretical minimal and maximal flux values for the target product formation were calculated using constraints-based flux analysis by minimizing and maximizing the target product formation rate with GR constraints.
The metabolic flux distribution and the changes of metabolic fluxes under several perturbed conditions were examined by flux variability analysis (FVA) [ 26, 27] that calculates minimal and maximal flux values of each reaction for an objective function of maximum cell growth rate.
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We use the maximal flux value as the corresponding reaction flux capacity.
For each reaction in the network, the reaction flux capacity is the set to the maximal flux value of the reaction from the flux distributions.
When performing Flux Variability Analysis [ 17, 50], we selected reactions that could increase or decrease by 25% of their maximal flux value for further analysis.
The ratio of flux span (FSr) was calculated, using the following formula FSr = abs (FVAmaxi,Healthy-FVAmini,Healthy)/abs(FVAmaxi,IEM-FVAmini,IEM), where FVAmax is the maximal flux value and FVAmin is the minimal flux value under healthy and IEM conditions.
In rFBA, regulatory rules can constrain a reaction only by setting its flux value to 0. PROM [ 24] is based on regulatory network reconstruction through inference from microarray data and is able to constrain a reaction to a certain percentage of its maximal flux value.
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