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

Table 1.

The optimal solution for maximizing ethanol productivity by S. cerevisiae

ε-value	$v_{P Y K}^{*} ∕ v_{P Y K}^{b a s a l}$	Modulated enzymes
1	2.092	HXT

2	2.452	HXT, PFK
	2.434 (SBB)^†	HXT, ATPase

3	3.152	HXT, PFK, PYK

4	3.592	HXT, PFK, PYK, TDH
	3.326 (LINDOGlobal, BARON)^†	HXT, PFK, PYK, ATPase

5	4.428	HXT, PFK, PYK, TDH, GLK

6	5.191	HXT, PFK, PYK, TDH, GLK, ATPase
	4.458 (DICOPT)^†	HXT, PFK, PYK, TDH, GLK, GOL

7	5.231	HXT, PFK, PYK, TDH, GLK, ATPase, GOL
	3.651 (DICOPT)^†	HXT, PFK, PYK, TDH, ATPase, GOL, TPS

8	5.231	HXT, PFK, PYK, TDH, GLK, ATPase, GOL, TPS

The optimal enzymatic modulations for maximizing ethanol productivity by S. cerevisiae obtained by solving the primal multi-objective optimization problem using various GAMS solvers (AlphaECP, BARON, BONMIN, COUENNE, DICOPT, LINDOGlobal, and SBB). $γ_{x_{i}}^{L B}$ 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 a premature result, and ε is the number of allowed manipulated genes.