Network transformation-based analysis of biochemical systems

TL;DR

This paper develops methods for transforming biochemical reaction networks to facilitate analysis, preserving key dynamical properties while enabling the study of complex systems through network modifications.

Contribution

It introduces network transformations that preserve dynamics, improves existing theories, and provides algorithms for converting systems into more analyzable forms.

Findings

Positive dependent networks can be translated to weakly reversible networks.

Transformed systems with positive deficiency aid biochemical analysis.

Algorithm for transforming NFK systems to CFK systems enhances existing theorems.

Abstract

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 \textit{Populus 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.