On stability analysis of cascaded linear time varying systems in dynamic isotope experiments

Abstract

The dynamic 13C labeling experiment, as an emerging experimental technique, can be utilized to quantify intracellular fluxes of the cell culture under metabolic unsteady states conditions, for example, under fed batch mode. One main disadvantage of the current dynamic isotope experiment technique is that the intracellular metabolic pools have to be at pseudo‐steady state. Furthermore, to the best of our knowledge, the stability issue of dynamic isotope experiments is not addressed in the literature. In this work, if one assumes that concentrations of intracellular metabolites are nonsteady, it is shown that dynamic cumomer balance equations for any metabolic network are uniformly bounded‐input and bounded‐output stable regardless of the existence of traps. It is valid under very weak conditions. Specifically, it requires that the intracellular flux and the size of intracellular pool are finite and strictly greater than zero at any time. The new finding paves the way to utilize the dynamic isotope experiment to approximately quantify intracellular fluxes and sizes of intracellular pools under intracellular metabolic nonsteady state with piecewise affine fluxes.