Analysis of biochemical systems via reaction network operations

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 present eight reaction network operations that can modify a reaction network while preserving the dynamical system. In particular, we study the structural and kinetic properties of these transformed systems, such as stoichiometric alignment, concordance and existence of equilibria. To illustrate our approach, we use the kinetic realizations of the following biochemical systems: (1) calcium signaling in the olfactory system, (2) metabolic insulin signaling and (3) monolignol biosynthesis in \textit{Populus xylem}. Furthermore, we present a sufficient condition for the invariance of concordance under a network transformation and introduce an algorithm for a network transformation of a weakly reversible non-CFK system to a weakly reversible CFK system. We review the work of Hong et al. on network translation, discussing its relevance in this study. Finally, we end by highlighting some benefits of positive deficiency kinetic realizations for the analysis of biochemical systems.Comment: 40 pages. arXiv admin note: text overlap with arXiv:1109.2923 by other author