Analytical Reduction of Nonlinear Metabolic Networks Accounting for Dynamics in Enzymatic Reactions

International audienceMetabolic modeling has been particularly efficient to understand the conditions affecting the metabolism of an organism. But so far, metabolic models have mainly considered static situations, assuming balanced growth. Some organisms are always far from equilibrium and metabolic modeling must account for their dynamics. This leads to high dimensional models were metabolic fluxes are no more constant but vary depending on the intracellular concentrations. Such metabolic models must be reduced and simplified so that they can be calibrated and analyzed. Reducing these models of large dimension down to a model of smaller dimension is very challenging, specially, when dealing with non linear metabolic rates. Here, we propose a rigorous approach to reduce metabolic models using Quasi Steady State Reduction based on Tikhonov's Theorem, with characterized and bounded reduction error. We assume that the metabolic network can be represented with Michaelis-Menten enzymatic reactions, with two time scales in the reactions. In this simplest approach, some metabolites can accumulate. We consider the case with a continuous (slowly) varying input in the model, such as light for microalgae, so that the system is never at steady state. Furthermore, our analysis proves that the metabolites which can accumulate reach higher concentrations (by one order of magnitude) than the fast metabolites. A simple example illustrates our approach and the resulting accuracy of the reduction method