Graph-based, Dynamics-Preserving Reduction of Chemical Systems using Thomas-Style Qualitative Stability Analysis

BentaraDe Silva

University of Lethbridge

"Graph-based, Dynamics-Preserving Reduction of Chemical Systems using Thomas-Style Qualitative Stability Analysis"

Abstract A biochemical system includes a network of chemical reactions often exhibiting complex behaviors such as oscillations, spatial patterns, and multistability. The parameter values of these models are often unknown or difficult to measure, and even some details of the reaction networks may be uncertain. Since these models tend to be large and complex, it is useful to create a simplified version of these models. However, traditional model-reduction methods depend on knowledge of parameter values which make them difficult to apply. Qualitative stability analysis methods provide an alternative approach without necessarily requiring parameter values. When reducing models with non-trivial dynamics arising from an instability, one must ensure that the conditions for instability are preserved, which depend mainly on the presence of circuits, and their signs. Roussel and Soares presented dynamics-preserving reductions based on Ivanova's qualitative conditions for instabilities (J. Math. Biol. 89, 42). The main objective of this research is to implement a similar framework based on the concepts outlined in that paper. However, instead of using Ivanova's conditions for instability, we will apply the Thomas qualitative stability analysis method to preserve the structures in the interaction graph that generate instability. An Oregonator-class model for oscillations in the photosensitive Belousov-Zhabotinsky (BZ) reaction due to Amemiya and coworkers is used in an initial exploration of possible reduction rules in interaction graphs. Given that the interaction graph discards information about the kinetics of a reaction, some attention will have to be given to the potential loss of important nonlinear terms while implementing the new method.
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