## 4 Discussion
### Prioritization in Inactivating Reactions and Objective Function  
The QPAML classified specific reactions, supported by experimental evidence of being inactivated, as either low flux or biomass-related. For example, prephenate dehydrogenase (PPND), encoded by the _tyrA_ gene, competes for prephenate with prephenate dehydratase (PPNDH), encoded by the _pheA_ gene. Both genes have been inactivated to enhance tryptophan production, but not in the same genetic background [7]. In our tested mutants, _pheA_ produces IAA that increases by 132.81%. In contrast, the _tyrA_ mutant does not significantly increase, aligning with model predictions. The preference for a pathway could be explained  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reaction** & **Enzyme** & **L-Tryptophan Precursor** & **Reference** \\ \hline GHMT2r & Glycine hydroxymethyltransferase & L-serine & [78; 79; 80] \\ \hline SERD\_L & L-serine deaminase & L-serine & [5; 78; 80; 81] \\ \hline HPYRP & 3-phosphohydroxypruvate phosphatase & L-serine & [102] \\ \hline GLUN & Glutaminase & L-glutamine & [103] \\ \hline ICL & Isocitrate lyase & L-glutamate (L-proline) & [45] \\ \hline FRD2 & Fumarate reductase & L-glutamate (L-alanine) & [66] \\ \hline FRD3 & Fumarate reductase & L-glutamate (L-alanine) & [66] \\ \hline MGSA & Methylglyoxal synthase & L-glutamate (L-alanine) & [66] \\ \hline ACALD & Acetaldehyde dehydrogenase & L-glutamate (L-alanine) & [66] \\ \hline LDH\_D & D-lactate dehydrogenase & L-glutamate (L-alanine) & [66] \\ \hline PFL & Pyruvate formate lyase & Pyruvate & [104] \\ \hline EDD & 6-phosphoglucate dehydratase & Phosphoenolpyruvate & [105] \\ \hline F6 PA & Fructose 6-phosphate aldolase & Phosphoenolpyruvate & [105] \\ \hline TALA & Transaldolase & D-erythrose-4-phosphate & [106] \\ \hline \hline \end{tabular}
\end{table}
Table 3: Reactions classified for disruption related to tryptophan precursors.  
using NAD as a cofactor by PPND; this observation can be rationalized because surplus fluxes of perturbations are redirected to biomass production to maximize the objective function, as documented by [PERSON] et al. [29].  
Acetate secretion represents a carbon waste in _E. coli_; two pathways produce it. The primary pathway involves the conversion of acetyl-CoA to acetyl-phosphate via phosphotransacetylase (\(pta/eutD\)), followed by acetate and ATP formation through acetate kinase (\(ackA/tdcD/purT\)). In the secondary pathway, pyruvate oxidase B (POX) converts pyruvate to acetate. Deletion of \(poxB\) amplifies pyruvate accumulation [87], but its effect on tryptophan production is paradoxical, potentially diminishing its production [11]. The POX reaction is classified as low flux by QPAML, contrasting with the primary pathway reactions (PTAr and ACKr) designated for the knockout.  
In the \(poxB\) mutant, no statistically significant enhancement in IAA production is observed. ACKr knockdown, via \(ackA\) or \(tdcD\) deletions, improves IAA production by 79.03% and 176.15%, respectively. Analogously to the \(pheA\) and \(tyrA\) genes, \(poxB\) appears less proficient in biomass synthesis, given that the primary pathway yields one ATP molecule per acetate molecule produced.  
The \(mtr\) mutant showed the most significant enhancement, with a 193.3% increase in IAA production. The increase in IAA production in the \(mtr\) and \(tnaB\) mutant aligns with the significant role of tryptophan transport, as explained in the molecular dynamic model created by [PERSON] et al. [4]. It is important to note that the purpose of testing individual mutations on specific genes of the Keio collection was to assess the contribution of each mutant and validate the model to some extent. However, this does not represent a comprehensive model validation, nor is it the intention to optimize tryptophan or IAA production.