Table 1.

Optimization methods with additional constraints

Method	Enzymatic cost	Constraint
FBAwMC [44]	$\sum a_i{J}_i$	≤1
MOMENT [46]	$\sum g_i·{\mathit{\text{MW}}}_i$	≤C
Tepper et al. [47]	$\sum M_i+\delta ·\sum g_i$	minimize
Shlomi et al. [49]	$\sum \frac{{\mathit{\text{MW}}}_i{J}_i}{k_{{\mathit{\text{cat}}}_i}}$	≤C
Holzhütter [28]	$\sum \underset{i}{\overset{+}{J}}+k_{{\mathit{\text{eq}}}_i}·J_i^{-}$	minimize
corsoFBA	$\sum J_i·{\mathit{\text{MW}}}_i·\mathit{\text{exp}}\left(\frac{\alpha ·{\Delta }_r{G^{\prime }}_i^o}{R·T}\right)$	minimize
Variables
a - crowding coefficient
J - flux through the reaction
g - enzyme concentration
MW - molecular weight of associated enzyme
M - metabolite levels
δ - model parameter
k cat - turnover number
k eq - thermodynamic equilibrium constant
C - fraction of dry weight mass associated with proteins

These methods calculate an overall cost through the metabolism by summing individual costs associated with each reaction. While previous methods have been used to constrain the FBA solution, corsoFBA optimizes this cost for any given growth rate.