Abstract
Chemical organisation theory is a framework developed to simplify the analysis of long-term behaviour of chemical systems. An organisation is a set of objects which are closed and self-maintaining. In this paper, 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, to study quantitative properties regarding movement between these organisations and to construct an organisation-based coarse graining of the model that can be used to approximate and predict the behaviour of the original reaction network.
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Acknowledgements
The authors acknowledge support from the European Union through funding under FP7–ICT–2011–8 project HIERATIC (316705). We also thank the anonymous reviewers for their helpful and detailed comments.
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APPENDIX: Supplementary Details for Examples 5 and 6
APPENDIX: Supplementary Details for Examples 5 and 6
Example 5 in the PRISM modelling language
Example 5: CTMC model with 4 SCCs and 1 BSCC
CTMC for the reaction network from Example 6, with 28 SCCs and 6 BSCCs.
Transition probabilities (bounds/averages) between all SCCs of the CTMC for Example 6 and expected leaving times.
Transition probabilities (bounds and average) between good SCCs for Example 6 and the expected time to leave them.
Example 6: transition probabilities in bounds among the lattice of molecules
Organisation dynamics predication via master equation simulation over the average coarse-grained model(left) and the original model(right) of Example 6, for \(N_{\max }=10\) with rates: \(\sharp a * \sharp b\), \(\sharp b * \sharp c\), \(\sharp c \), \(\sharp b * \sharp d\), \(\sharp b * \sharp b\), \(\sharp c \), \(\sharp d \) for each reaction rule respectively. (Color figure online)
Organisation dynamics predication via master equation simulation over the average coarse-grained model(left) and the original model(right) of Example 6, for \(N_{\max }=10\) with rates: \(\sharp a * \sharp b\), \(\sharp b * \sharp c\), \(\sharp c * \sharp c\), \(\sharp b * \sharp d\), \(\sharp b * \sharp b\), \(\sharp c * \sharp c\), \(\sharp d * \sharp d\) for each reaction rule respectively. (Color figure online)
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Mu, C., Dittrich, P., Parker, D., Rowe, J.E. (2016). Formal Quantitative Analysis of Reaction Networks Using Chemical Organisation Theory. In: Bartocci, E., Lio, P., Paoletti, N. (eds) Computational Methods in Systems Biology. CMSB 2016. Lecture Notes in Computer Science(), vol 9859. Springer, Cham. https://doi.org/10.1007/978-3-319-45177-0_15
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