###### Abstract
\"That is because they need previously prepared stocks of cell-cultures, and substrate(s), of different concentrations (a-priori in-silico determined), to be fed for every 'time-arc' of the batch (that is a batch-time division in which the feeding composition is constant; self-understood, the feeding of time-'arcs' usually differ between them). This is the price paid for achieving FBR best performances [5; 29; 32; 33]\". Other constructive solutions can be adopted [5; 34]. The current (default) approach to solve the model-based design, optimization and control problems of industrial biological reactors is the use of unstructured kinetic models of Monod type (for cell culture reactors) or of Michaelis-Menten type (if only enzymatic reactions are retained) that ignores detailed representations of cell processes. The applied engineering rules are similar to those used by the (bio)chemical engineering and inspired from the nonlinear system control theory [3; 15; 30; 35; 36; 37; 38; 39; 40]. However, by accounting for only key process variables (biomass, substrate and product concentrations), these global (apparent) models do not properly reflect the metabolic changes, being unsuitable to accurately predict the cell response to environmental perturbations by means of (self-) regulated cell metabolism (e.g., this paper, and Maria and Luta [41]). An alternative compromise is to use hybrid structured modular dynamic (kinetic) models (HSMDMs) [35] that combine unstructured with structured process characteristics to generate more precise predictions [35; 41; 42]. The purpose of kinetic HSMDMs is to interconnect process variables (individual or lumped) belonging to at least two hierarchical levels of model details. The resulting composite model is able to simulate the bioreactor dynamics simultaneously at various levels of interest. Thus, the dynamics of the bioreactor macroscopic state variables (i.e., species present in the liquid bulk) are simulated concomitantly with those of the nano-scale key variables, describing the cell metabolic processes of interest together with the core of the central carbon metabolism (CCM), because the macro-/nano-scale species are closely linked, as long as some cell metabolites are imported/excited from/in the bioreactor bulk. Even if such an extended kinetic model, including complex cell metabolic pathways, requires more experimental and computational efforts to be built-up and identified from structured kinetic data, the resulting hybrid (bi-level) dynamic model presents major and remarkable advantages, as pointed out by [PERSON] [35]:  
Figure 1: An oversimplified scheme of a BR or a FBR used to conduct biological processes. In the BR operating mode, the substrate(s), biocatalyst, and additives are only initially loaded in recommended amounts (concentrations). In the FBR operating mode, the substrate(s)/biocatalyst, and additives (nutrients, pH-control substances, etc.) are continuously fed, following a certain (optimal) strategy, to be determined [5]. The FBR presents a similar construction to a BR, and a similar modelling hypothesis. However, unlike BR, the reactants and/or biocatalyst are added during the batch, following a time-step-wise variable (optimal) policy, to be determined off-line [5], or on-line [18]. 1. This model allows for in silico engineering analyses ( bioreactor design, off-line optimization) of a higher accuracy, and of a higher degree of detail (the number of considered state variables) compared to the unstructured (empirical, global) models. For instance, this model could better predict the optimal time-step-wise variable feeding strategy of a FBR to maximize its productivity. This numerical analysis is carried out in this paper. 2. The extended hybrid HSMDM model can also be used for bioinformatics purposes, by evaluating the influence of the bioreactor operating conditions (control variables) on the dynamics of cell key-species and metabolic fluxes involved in the synthesis of target metabolites.