**Structural Properties of an S-system Model of Mycobacterium tuberculosis Gene Regulation**

Honeylou F. Farinas^{1,2}, Eduardo R. Mendoza^{2,3,4,5}, and Angelyn R. Lao^{2}*

^{1}Department of Mathematics, Mariano Marcos State University

Ilocos Norte 2906 Philippines^{2}Mathematics and Statistics Department, De La Salle University

Metro Manila 1004 Philippines^{3}Institute of Mathematical Sciences and Physics, University of the Philippines

Los Banos, Laguna 4031 Philippines^{4}Max Planck Institute of Biochemistry

Martinsried near Munich, Germany^{5}Faculty of Physics, Ludwig Maximilian University

Munich 80539 Germany

*Corresponding Author: This email address is being protected from spambots. You need JavaScript enabled to view it.

ABSTRACT

Magombedze and Mulder (2013) studied the gene regulatory system of *Mycobacterium tuberculosis* (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. For the embedded networks of S-system, we showed interesting structural properties and proved that all S-system CRNs (with at least two species) are discordant. Analyzing the subsystems as subnetworks, where arcs between vertices belonging to different subsystems are retained, we formed a digraph homomorphism from the corresponding subnetworks to the embedded networks. Lastly, we explored the modularity concept of CRN in the context of the digraph.

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