Mathematical Methods to Analysis of Topology, Functional Variability and Evolution of Metabolic Systems Based on Different Decomposition Concepts

Complexity of metabolic systems can be undertaken at different scales (metabolites, metabolic pathways, metabolic network map, biological population) and under different aspects (structural, functional, evolutive). To analyse such a complexity, metabolic systems need to be decomposed into different components according to different concepts. Four concepts are presented here consisting in considering metabolic systems as sets of metabolites, chemical reactions, metabolic pathways or successive processes. From a metabolomic dataset, such decompositions are performed using different mathematical methods including correlation, stoichiometric, ordination, classification, combinatorial and kinetic analyses. Correlation analysis detects and quantifies affinities/oppositions between metabolites. Stoichiometric analysis aims to identify the organisation of a metabolic network into different metabolic pathways on the hand, and to quantify/optimize metabolic flux distributions through the different chemical reactions of the system. Ordination and classification analyses help to identify different metabolic trends and their associated metabolites leading to highlight chemical polymorphism representing different variability poles of the metabolic system. Then, metabolic processes/correlations responsible for such a polymorphism can be extracted in silico by combining metabolic profiles representative of different metabolic trends according to a weighting bootstrap approach. Finally, evolution of metabolic processes in time can be analysed by different kinetic/dynamic modelling approaches.