2.3 | Analysis of competing objectives
We constructed “phase diagrams” that depict tradeoffs between average
chain length and total production for each alcohol pathway by optimizing
enzyme concentrations to maximize or minimize average chain length at
different production levels. Briefly, to maximize average chain length,
we minimized Obj5, where Lnorm is the
normalized average chain length (i.e., average
Obj5 = (1-Lnorm)2 +
(Prodtarget- Prod)2 +
(Enztarget- Enz)4 (Eq. 5)
Obj6 = (4/18-Lnorm)2 +
(Prodtarget- Prod)2 +
(Enztarget- Enz)4 (Eq. 6)
chain length divided by 18, the maximum chain length),
Prodtarget is the desired alcohol concentration
(palmitic acid equivalents), Prod is the actual alcohol concentration,
Enztarget is the desired total enzyme concentration, and
Enz is the actual enzyme concentration. To minimize average chain
length, we minimized Obj6, where 4/18 is the minimum
achievable chain length. For all models, we constrained total enzyme
concentration (Enztarget) by supplementing the total
concentration in our base model with 10 μM of each pathway-specific
enzyme: 38 μM for a carboxylic acid reductase (CAR) model, 38 or 48 μM
for two acyl-CoA reductase (ACR2 and ACR1) models, and 18 or 108 μM for
an acyl-ACP reductase (ATR) model. During each optimization, the
concentrations of specific enzymes changed; we retained only results for
which differences in both (i) Prodtarget and Prod and
(ii) Enztarget and Enz differed by less than 5%.