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\begin{document}

\title{On structural identifiability analysis of cascaded linear time varying
systems in dynamic isotope experiments}



\author[1]{Weilu Lin}%
\author[2]{Mingzhi Huang}%
\author[3]{Zejian Wang}%
\author[4]{Ju Chu}%
\author[3]{Yingping Zhuang}%
\author[3]{Siliang Zhang}%
\affil[1]{East China University of Technology}%
\affil[2]{Affiliation not available}%
\affil[3]{East China University of Science Technology}%
\affil[4]{East China University of Science \& Technology, Institute of Fine Chemicals, State Key Laboratory of Bioreactor Engineering}%


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  \date{May 18, 2024}


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\begin{abstract}
A well known \textbackslash{}emph\{in silico\} analysis in metabolic
flux analysis 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 \textbackslash{}emph\{et al.\}, Math Biosci. 2018;
300:122-12).%
\end{abstract}%



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