In recent years, dynamic metabolic flux analysis (DMFA) has been developed in order to evaluate the dynamic evolution of the metabolic fluxes. Most of the proposed approaches are dedicated to exactly determined or overdetermined systems. When an underdetermined system is considered, the literature suggests the use of dynamic flux balance analysis (DFBA). However the main challenge of this approach is to determine an appropriate objective function, which remains valid over the whole culture. In this work, we propose an alternative dynamic metabolic flux analysis based on convex analysis, DMFCA, which allows the determination of bounded intervals for the fluxes using the available knowledge of the metabolic network and information provided by the time evolution of extracellular component concentrations. Smoothing splines and mass balance differential equations are used to estimate the time evolution of the uptake and excretion rates from this experimental data. The main advantage of the proposed procedure is that it does not require additional constraints or objective functions, and provides relatively narrow intervals for the intracellular metabolic fluxes. DMFCA is applied to experimental data from hybridoma HB58 cell perfusion cultures, in order to investigate the influence of the operating mode (batch and perfusion) on the metabolic flux distribution.

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