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For any one genotype, we use flux balance analysis (FBA) [ 17- 19] to determine the maximum biomass flux obtainable for this genotype in a given chemical environment.
Specifically, we consider a genotype to be "viable" in a given chemical environment if and only if its maximum biomass flux is nonzero.
(Note that the addition of such reactions in and by itself cannot cause loss of viability in our framework: if a genotype produces a maximum biomass flux F under FBA, then including extra reactions cannot decrease F).
Note that if a genotype produces a maximum biomass flux F under FBA, then adding further reactions can only increase F; as a consequence, in our framework, many properties will be monotonic in the number of reactions n.
To this end, we first determined those reactions in the E. coli metabolic network that have nonzero flux in an optimal flux distribution with maximum biomass flux for each of the 89 minimal environments considered here.
We consider a genotype to be viable in a given environment if and only if the maximum biomass flux predicted by FBA for the genotype is nonzero; otherwise we consider the genotype to be non-viable (see Additional File 1 Figure S1b).
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In general, in silico metabolic studies take a metabolic network's fitness to be proportional to the maximum biomass growth flux the network can attain in a given environment.
In general, in silico metabolic studies take a metabolic network's "fitness" in a given chemical environment to be proportional to the maximum biomass growth flux the network can attain.
Reduced cost analysis indicated that if any of the other reactions were forced to carry a flux, the maximum biomass produced would decrease (Table 4).
In contrast, FBA predicted no transhydrogenase activity for the model, and FVA confirmed that under the constraint of maximum biomass production, no significant transhydrogenase flux is possible.
Rather, a vector-valued objective function or multiple objective functions must be considered, resulting in the Pareto optimal set to represent the metabolic fluxes [27], where the influential objective function may be the maximum ATP yield, maximum biomass yield, and minimum sum of absolute fluxes (which corresponds to minimum enzyme investment).
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maximum possibility flux
maximum output flux
maximum biomass accumulation
maximum biomass productivity
maximum biomass use
maximum fluorescence flux
maximum permeate flux
maximum photon flux
maximum biomass concentration
maximum mass flux
maximum biomass weight
maximum biomass production
maximum acid flux
maximum biomass load
maximum biomass yield
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