Selection of a Minimal Suboptimal Set of EFMs for Dynamic Metabolic Modelling

Hybrid Dynamic Models of Bioprocesses Based on Elementary Flux Modes and Multilayer Perceptrons

“…The EFM reduction method has been originally developed in [24,42], and only a brief overview is provided in this section. The 4-step method, illustrated in Figure 3, is divided into (i) the initial generation of the modes, (ii) the biological interpretation of the reaction scheme, (iii) a preliminary reduction up to Ω modes and (iv) the selection of a minimal set of Λ EFMs.…”

“…In connection with this, Hebing et al [22] used an EFM reduction procedure based on a geometrical collinearity criterion. More recently, several procedures of EFM reduction have been developed by our research group, i.e., Abbate [23] selected the best EFM candidates based on the formulation of a linear optimization problem and Maton [24] developed a reduction methodology based on a combination of several criteria based on collinearity and a series of constrained least-square problems.…”

“…This latter situation corresponds to the starting point of this study. Indeed, the application of our EFM reduction algorithm [24,42] yields, on the one hand, a candidate stoichiometric matrix and, on the other hand, the time-evolution of the metabolic fluxes corresponding to the selected EFMs. These fluxes may have a complex time evolution resulting from the combination of several phenomena triggered by different culture species.…”

A systematic elementary flux mode selection procedure for deriving macroscopic bioreaction models from metabolic networks

“…Recently, [21,27] have applied column generation techniques to determine subsets of elementary flux modes in metabolic networks and [28] introduces the poly-pathway model approach to account for the metabolic behavior of multiple experimental conditions. Recently, our research group has developed two procedures, e.g., [29] picks the best EFMs candidates based on a linear optimization problem, and [30] uses a two-step reduction based on cosine-linearity and optimization, to identify and retain the most informative EFMs to develop macroscopic models.…”

“…This study extends this latter work by proposing several significant improvements to the original algorithm, which now proceeds in four steps, in order to tackle problems such as the enumeration of the initial set of elementary flux modes, the differentiate consideration of positivity constraints on the fluxes, and the prediction error of reduced macroscopic reaction sets (reduced below the number of measured components). The algorithm is also tested with data of batch cultures of CHO-320 cells, on the basis of a larger metabolic network than the one considered in [30]. Finally, a discussion about the construction of dynamic macroscopic models including the prediction of the biomass is included.…”