## 3 Results
### Conversion of the Flux Variables to a Classification Model Based on QPAML  
From the behavior of the ten fluxes per reaction obtained after each perturbation regarding the tryptophan or biomass production, the QPA led us to select six qualitative variables (pFBA optima, any flux, biomass-correlated, metabolite-correlated, flux variation, and essential) for the QPAML construction. These qualitative variables were fed to GBDT to identify if they adequately represent the relationship between reactions and tryptophan production, comparing predictions with experimental evidence. The qualitative variable hierarchy for the trained model was elucidated as delineated in Figure 4. The qualitative variables assess (1) whether reactions are part of the 76 pFBA optima reactions to tryptophan production; (2) if reactions contribute to biomass but not to metabolite production; (3) the presence of flux variation across the 76 simulations; (4) the contribution of flux to tryptophan production; (5) the essentiality of reactions for biomass production; and (6) the maintenance of flux in reactions across any simulation. This latter variable is intrinsically linked to flux variation. The model groups the reactions into five metabolic classes: low flux, biomass, overexpression, knockout (KO), and knockdown (KD). The last three classes are relevant for trying genetic modifications. The model uses the following criteria for classification (see Supplementary Figure S6):  
FSEOF designates reactions with no variation as unrelated to target metabolite production [30]. [PERSON] and colleagues [61] interrupted genes that utilize unavailable carbon sources in the media with no observed effect on growth or metabolite production. [PERSON] removed 332 superfluous genes from _Bacillus subtilis_ is without changes in the metabolic flux [96]. Using these analogies, reactions that cannot sustain any flux in simulations are categorized as reactions without effect. Extending the behavior of these reactions, those with no variation in flux or variations lacking a clear correlation with tryptophan production are classified as reactions with low flux or without effect. A pertinent example in this context is the _poxB_ gene, representing a secondary pathway of acetate production. This pathway is less active than the one governed by _pla-ackA_ genes and tends to be active only in the stationary phase [8]. Although we named this variable low flux, this class encompasses  
Figure 3: Comparison of QPAML and FSEOF performance in predicting 27 overexpressed reactions validated for tryptophan production. The bottom blue circle represents the 27 experimentally validated overexpressed reactions; the light salmon circle represents the FASEOF predictions; and the green circle represents the QPAML predictions. The number in the intersections represents the shared predictions concerning the experimentally validated reactions. several kinds of reactions: the reactions with zero flux because their substrates are not available; reactions with stoichiometric unfavourability represented in the model as zero flux, but they present fluxes in the cell due to biochemical noise and leaks of metabolism; and other reactions with an unclear relationship. Reactions with fluxes showing a consistent positive relationship with the metabolite production in most perturbations are selected for overexpression (see Supplementary Figure S5c), reflecting an approach similar to that employed by the FSEOF algorithm [30]. An illustrative example is the NAD(P) transhydrogenase (THD2 pp) encoded by the \(pntBA\) genes [9]. Additionally, the algorithm identifies pFBA optima reactions for overexpression, even when they do not exhibit a positive relationship with tryptophan production in most perturbations, complementing those already documented in the literature--for instance, the isocitrate dehydrogenase (NADP) reaction (ICDHyr) [9].