## 2 Materials and Methods
### Final Qualitative Variables  
The final qualitative variables were calculated from metabolic fluxes as described below. FVA [29] was performed to identify reactions in the GEM that cannot sustain flux because substrates are not available [61] or constraints are infeasible [94]; these reactions are referred to as blocked elsewhere. Essential reactions for biomass production were identified using the single-reaction-deletion method of COBRApy. Suppose a reaction whose slope does not overlap in any perturbation with those for tryptophan production. In that case, the reaction is tagged as having an unclear relationship or no flux variation. When all the reaction fluxes in the perturbations fit Equation (4), the reaction is tagged as biomass-correlated (See Supplementary Figure S5a). Reactions with most of the perturbations that have a positive relationship with tryptophan secretion are tagged as correlated to tryptophan (see Supplementary Figure S5c). The scripts and simulations are available at [[https://gitlab.com/amalib/qpaml](https://gitlab.com/amalib/qpaml)]([https://gitlab.com/amalib/qpaml](https://gitlab.com/amalib/qpaml)) (accessed on 31 January 2024).  
\[v_{i}=m\cdot v_{biomass}+b \tag{4}\]  
where  
\(v_{i}\): Flux of reaction.  
\(m\): Slope of line, most be greater than 0.  
\(b\): Intersection at origin, must be 0.  
\(v_{biomass}\): Flux of biomass.  
The interpretation of the QPAML model indicates that the resulting optimal pFBA reactions are candidates to be activated, although these could be reactions that have few fluxes in the metabolic network. Likewise, reactions whose fluxes behave similarly to the target reaction (See Supplementary Figure S5c) are candidates to be activated. Reactions that do not present variations in their fluxes are not good candidates to be modified. Some reactions are correlated to biomass production but not to tryptophan; these reactions could affect biomass production if they are mutated. Finally, the rest of the reactions are classified as candidates to be silenced if they are not essential for biomass production and candidates to be attenuated if essential (See Supplementary Figure S6).  
Distance Measurement of Relevant Reactions Respect the 76 pFBA Optima Reactions for Tyyptophan Production  
We were interested in observing the distribution of relevant predicted and experimentally validated reactions in the metabolic network for tryptophan production to identify some correlation of genetic modification concerning the metabolic network structure.  
After categorizing reactions for tryptophan production, we used pFBA optima, silence, and attenuation target reactions to construct a directed graph in NetworkX. The graph included the participating metabolites and the directionality of their reactions. We selected the 76 pFBA optima reactions in the graph and performed a search for the neighbors or outgoing nodes, avoiding highly connected metabolites. These first neighbor nodes were then chosen to repeat the search until no additional nodes could be added. The shortest distances from the central pathway were measured regarding reactions rather than nodes. This search methodology represents an adaptation of the Breadth-First Search algorithm [95].