Magombedze and Mulder (2013) studied the gene regulatory system of \textit{ Mycobacterium Tuberculosis} (\textit{ Mtb}) by partitioning this into three subsystems based on putative gene function and role in dormancy/latency development. Each subsystem, in the form of $S$-system, is represented by an embedded chemical reaction network (CRN), defined by a species subset and a reaction subset induced by the set of digraph vertices of the subsystem. Based on the network decomposition theory initiated by Feinberg in 1987, we have introduced the concept of incidence-independent and developed the theory of $\mathscr{ C}$- and $\mathscr{ C}^*$-decompositions including their structure theorems in terms of linkage classes. With the $S$-system CRN $\mathscr{ N}$ of Magombedze and Mulder's \textit{ Mtb} model, its reaction set partition induced decomposition of subnetworks that are not CRNs of $S$-system but constitute independent decomposition of $\mathscr{ N}$. We have also constructed a new $S$-system CRN $\mathscr{ N}^*$ for which the embedded networks are $\mathscr{ C}^*$-decomposition. We have shown that subnetworks of $\mathscr{ N}$ and the embedded networks (subnetworks of $\mathscr{ N}^*$) are digraph homomorphisms. Lastly, we attempted to explore modularity in the context of CRN.
Categories: q-bio.MN