Structural Properties of an S-system Model of Mycobacterium Tuberculosis Gene Regulation

Magombedze and Mulder in 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 digraph.Comment: arXiv admin note: substantial text overlap with arXiv:1909.0294

Chemical reaction network properties of S-systems and decompositions of reaction networks

This thesis examined two models of the gene regulatory system of Mycobacterium Tuberculosis (Mtb) presented as S-system by Magombedze and Mulder (2013). The models are partitioned into three subsystems based on putative gene function and role in dormancy/latency development. This study investigated the chemical reaction network (CRN) representation of the Mtb models and each subsystem to obtain new mathematical results in Chemical Reaction Network Theory. The subsystems are represented as embedded networks (an arc connecting two vertices that represent genes from different subsystems is retained). For the embedded networks of S_system CRNs (with at least two species) are discordant. Analyzing the subsystems as subnetworks, we formed a digraph homomorphism from the corresponding subnetworks to the embedded networks and explored the modularity concepts of digraph. Further analysis of the Mtb S-systems led us to develop different classes of decomposition of reaction networks based on the approach of Feinberg (1987) in decomposing a CRN and were used to correct a deficiency formula of Arceo et al. (2015)