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Title:
Absolutely Complex Balanced Mass Action Kinetic Systems via Zero Deficiency Decomposition
Authors:
Jaysie Mher G. Tiongson ORCID iD 0009-0007-5269-3071
Dylan Antonio S.J Talabis ORCID iD 0000-0002-4468-688X
Lauro L. Fontanil
Volume
97
Issue
1
Year
2027
Pages
79-103
Abstract

The purpose of this study is to characterize absolutely complex balanced (ACB) systems with mass action kinetics (MAK) using zero deficiency decomposition (ZDD). To do this, we first introduce the mass action, \( \hat{T}- \)independent kinetic (MA-TIK) and mass action, non-\( \hat{T}- \)independent kinetic (MA-NTIK) systems, that is, MAK systems that are also PL-TIK and non-PL-TIK systems, respectively. Then, we develop an algorithm that can generate the ZDD of both MA-TIK and MA-NTIK systems. We show that for both MA-TIK and MA-NTIK systems, ZDD implies a PL-TIK decomposition, wherein each subnetwork is a PL-TIK system. We show the existence of ACB systems for non-zero deficiency MA-NTIK systems via their weakly reversible, zero deficiency, \( \mathcal{C}- \)decomposition. On the other hand, we also show the non-existence of ACB systems for non-zero deficiency MA-TIK systems. Lastly, we apply the results to the mathematical model of a mechanism for human dihydrofolate reductase (DHFR) catalysis.