. 2011 Sep 19;5:145. doi: 10.1186/1752-0509-5-145

Table 3.

The optimal solution for multi-synthesis maximization by E. coli

ε-value	$\frac{v_{P E P C}^{*}}{v_{P E P C}^{b a s a l}}$	$\frac{v_{S E R S}^{*}}{v_{S E R S}^{b a s a l}}$	$\frac{v_{D A H P S}^{*}}{v_{D A H P S}^{b a s a l}}$	Modulated enzymes	Optimal objective value $(η_{D}^{*})$
1	1.271	1.081	1.560	PK	0.970
	1.342	1.068	1.780	G6PDH	0.975

2	1.248	1.518	1.652	G6PDH, SERS	0.846
	1.211	1.409	1.456	PK, SERS	0.878^†
	1.778	1.106	2.185	PK, G6PDH	0.969

3	1.578	1.860	2.027	G6PDH, PK, SERS	0.782
	1.388	1.730	1.872	G6PDH, SERS, RPPK	0.814^†

4	1.801	1.973	2.225	G6PDH, PK, SERS, RPPK	0.778
	1.492	1.934	2.175	G6PDH, PK, SERS, DAHPS	0.787^†

5	1.597	2.258	2.467	G6PDH, PK, SERS, RPPK, DAHPS	0.763
	1.958	2.134	2.322	G6PDH, PK, SERS, RPPK, SYN1	0.786

The optimal enzymatic modulation to maximize aromatic amino acid, serine, and oxaloacetate synthesis rates simultaneously by E. coli without considering cell viability constraints. $γ_{x_{i}}^{L B}$ and $γ_{e_{i}}^{L B}$ are set to 0.2. $γ_{x_{i}}^{U B}$ and $γ_{e_{i}}^{U B}$ are set to 5.0. The superscript * means optimal solution, † denotes that the solution is not a Pareto solution, and ε is the number of allowed manipulated genes.