Stoichiometric Network Analysis as tool for stability analysis of the models of complex reaction systems

2019. 05. 02. 12:00
Stevan Maćešić

Oscillating chemical reactions are complex nonlinear reaction systems capable to display complex behavior under different experimental conditions. Main characteristic of these systems is their ability to exhibit diverse dynamics such as: simple oscillations, mixed-mode oscillations, intermittent oscillations and chaos. Modeling of the oscillating chemical reactions is very complicated task which consist from several steps. Stability analysis and bifurcation analysis are most important steps in the modeling process since they allow efficient model optimization. Detection of the reactions and intermediate species responsible for existence of the certain types of dynamics is crucial for model optimization. But, in the case of the complex models this can be very difficult task.

Stoichiometric network analysis (SNA) is powerful method which allows efficient and systematic analysis of such complex models. This method is based on determining possible reaction routes which can occur in steady-state and finding those which can produce instabilities. In this way, stability of the steady-states and detection of the bifurcations such as Andronov-Hopf and saddle-node can be achieved solely based on the analysis of the structure of the proposed chemical network. This method allows efficient detection of the chemical species and reactions essential for existence of oscillatory dynamics and bistability in the analyzed model and derivation of the analytical expressions which describe conditions for their emergence. Therefore, in this paper application of the SNA will be explained.