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Due to the highly coupled regulation of flux and concentrations in metabolic networks [ 28], it is not surprising that the MINLP-based formulations, especially the flux based R-DFBA and R-DFBA CF, outperform the rest of the investigated approaches.
The norm range of the reaction groups identified by the proposed approach is [2 15] while that for the flux based approach is [2 21].
Nonetheless, the use of structure of metabolic network identified some dependent reaction groups that were not identified by the flux based approach due to the use of reaction directionality as described in Reaction dependency and grouping.
The lower range of the proposed approach could be due to the strict use of the structure of the metabolic network in contrast to the flux based approach which can place structurally unconnected reactions in a group.
While the proposed graph based approach found 114 reaction groups (containing 291 unique reactions) with norm more than 1 in the yeast model used in case study 2, the flux based approach identified 86 dependent reaction groups (with 277 unique reactions).
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Taking into account that the equations are scaled (as described in the Additional file 1), a recalculation of the fluxes, based on literature values for the intracellular components, leads to the flux distribution shown in Figure 10.
Regarding the influence of the filaments, we calculated temperature gradients across the substrate caused by the radiative heat and the gas flux, based on the assumption that the gas extends collision-free, from the filament grid.
This spatial discretization avoids the characteristic decomposition of the convective flux based on the approximate Riemann solvers and the operator splitting technique required by classical upwind schemes.
We consider how to capture the impacts of past flow patterns via the average discounted flow (ADF) which discounts the past flux based on the time lapsed – more recent fluxes are given more weight.
In our CFD calculations, this effect should be automatically taken care of because we determine the oxygen flux based on the local pressure not on the bulk or global partial pressures measure at the inlet of the fee side and outlet of the permeate side.
Additionally, a linear regression model and an Artificial Neural Network (ANN) model were developed to predict the filtrate flux based on the test variables.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com