Organisation-Oriented Coarse Graining and Refinement of Stochastic Reaction Networks

Abstract

Chemical organisation theory is a framework developed to simplify the analysis of long-term behaviour of chemical systems. In this work, we build on these ideas to develop novel techniques for formal quantitative analysis of chemical reaction networks, using discrete stochastic models represented as continuous-time Markov chains. We propose methods to identify organisations, and to study quantitative properties regarding movements between these organisations. We then construct and formalise a coarse-grained Markov chain model of hierarchic organisations for a given reaction network, which can be used to approximate the behaviour of the original reaction network. As an application of the coarse-grained model, we predict the behaviour of the reaction network systems over time via the master equation. Experiments show that our predictions can mimic the main pattern of the concrete behaviour in the long run, but the precision varies for different models and reaction rule rates. Finally, we propose an algorithm to selectively refine the coarse-grained models and show experiments demonstrating that the precision of the prediction has been improved.

Structure and Hierarchy of Influenza Virus Models Revealed by Reaction Network Analysis

“…Furthermore, our approach is open to include other dynamically relevant components like treatment and vaccination strategies. Another task for future work would be to study the transient virus immune system in more detail, for example, by mapping the basin of attraction of each organization or by systematically analyzing the transition dynamics in-between organizations [33,34].…”