Network transformation-based analysis of biochemical systems

A dynamical system obtains a wide variety of kinetic realizations, which is advantageous for the analysis of biochemical systems. A reaction network, derived from a dynamical system, may or may not possess some properties needed for a thorough analysis. We improve and extend the work of M. Johnston \cite{JOHN2014} and Hong et al. \cite{HONG2023} on network translations to network transformations, where the network is modified while preserving the dynamical system. These transformations can shrink, extend, or retain the stoichiometric subspace. Here, we show that positive dependent network can be translated to a weakly reversible network. Using the kinetic realizations of (1) calcium signaling in the olfactory system and (2) metabolic insulin signaling, we demonstrate the benefits of transformed systems with positive deficiency for analyzing biochemical systems. Furthermore, we present an algorithm for a network transformation of a weakly reversible non-complex factorizable kinetic (NFK) system to a weakly reversible complex factorizable kinetic (CFK) system, thereby enhancing the Subspace Coincidence Theorem for NFK systems of Nazareno et al. \cite{NAZA2019}. Finally, using the transformed kinetic realization of monolignol biosynthesis in $\mathit{\text{Populus}}\mathit{\text{xylem}}$, we study the structural and kinetic properties of transformed systems,including the invariance of concordance and variation of injectivity and mono-/multi-stationarity under network transformation.