By applying these criteria systematically as shown in the previous equation to each gene involved in a reaction flux, we obtained the overall effect of the gene regulation [[delta].sub.ijk] on that reaction under the given chemical perturbation [s.sub.i].
For that purpose, we used a sensitivity analysis method known as flux variability analysis (FVA), which provides an estimate of the upper and lower bounds of each steady-state reaction flux vi in the cell (Orth et al., 2010).
Once the optimal biomass [b.sub.0] has been calculated, in order to determine allowed upper and lower bounds for each flux, [v.sup.lb.sub.i], [v.sup.ub.sub.i], respectively for each reaction flux [v.sub.i], an optimization to maximize/minimize the flux is calculated under the additional constraint of setting the biomass to its optimal [b.sub.0]:
We simulated the experiment in silico and performed FBA to see the biomass reaction flux and compare it to wet-lab results.
For this purpose, we set the exchange reaction flux of glucose and ammonia to zero and instead we set the uptake rate of histidine to 10 mmol x g[DW.sup.-1] x [hr.sup.-1].
Armature reaction flux phasor ([[psi].sub.a]) is defined below:
Sum of armature reaction flux [[psi].sub.a] and magnet flux [[psi].sub.m] gives stator flux [[psi].sub.s] which has [delta] angle with [d.sup.e] axis.
where the [H.sub.ij] (i, j = A, B, C) terms are the reaction flux elasticities [25, 26]:
Now that we have introduced the reaction flux elasticity, H, the criteria for stability of the three-node network can be given by 
During model construction, most internal reaction fluxes
will likely be unbounded, due to the relatively limited biochemical and proteomics data available for most reactions and organisms; it is the exchange reaction fluxes
that must be constrained to reflect the nutrient availability of the organism's environment.
Anyone who has made these measurements is aware of the pitfalls, especially in systems in which small reaction fluxes
are superimposed upon large physical transport fluxes.
Therefore, for a certain distribution of reaction fluxes
, say v, the metabolic concentrations do not change during time.