Metabolic Flux Analysis : an Approach for Solving Non-stationary Underdetermined Systems

The aim of this paper is to present an approach to analyse time-varying metabolic fluxes. The traditional tool to perform such analysis is called Metabolic Flux Analysis (MFA) and provides a flux distribution which is a constant vector, solution of a linear system constructed from the stoichiometric matrix. A basic limitation is that MFA is usually stated for a given and fixed configuration of the metabolic network that does not account for the cell adaptation to its environment and particularly to the substrate availability. Our concern in this paper is to consider the situation where the cells adapt their metabolism in such a manner that the metabolic network structure is changing during the cell life. This is achieved by decomposing the cell life in a succession of phases during each of which the metabolism is described by a metabolic network. Then for each phase, the flux distribution is described as a combination of Elementary Flux Modes. Finally, the complete flux distribution is obtained by smoothly switching from phase to phase. The approach is illustrated with batch cultures of Chinese Hamster Ovary (CHO) cells.