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On structural identifiability analysis of cascaded linear time varying systems in dynamic isotope experiments
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  • Weilu Lin,
  • Mingzhi Huang,
  • Zejian Wang,
  • Ju Chu,
  • Yingping Zhuang,
  • Siliang Zhang
Weilu Lin
East China University of Technology
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Mingzhi Huang
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Zejian Wang
East China University of Science Technology
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Ju Chu
East China University of Science & Technology, Institute of Fine Chemicals, State Key Laboratory of Bioreactor Engineering
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Yingping Zhuang
East China University of Science Technology
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Siliang Zhang
East China University of Science Technology
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Abstract

A well known issue in metabolic flux analysis with labelling experiments is the structural identifiability analysis. It comes from the fact that some enrichment measurement sets cannot uniquely elucidate all intracellular fluxes. To the best of our knowledge, the structural identifiability analysis of dynamic isotope experiments is not available in the literature. In this work, it is shown that if one measurement plan makes the dynamic isotopic fractions balance equations structurally identifiable then for any arbitrary small time interval the plan also makes the equations structurally identifiable. Based on the fact, in order to resolve the local structural identifiablity problem of the dynamic isotopic fractions balance equations approximated with piecewise affine intracellular fluxes, one should check the local structural identifiablity for the corresponding cascaded linear time invariant system at each sampling point with the approach proposed in our earlier work (Lin \emph{et al.}, Math Biosci. 2018; 300:122-129).