Abstract
It is well known that closure is a necessary topological property for a reaction network to be dynamically stable. In this work we combine notions of chemical organization theory with structural properties of reaction networks to distill a minimal set of closed reaction networks that encodes the non-trivial stable dynamical regimes of the network. In particular, these non-trivial closed sets are synergetic, in the sense that their dynamics cannot always be computed from the dynamics of its closed constituents. We introduce a notion of separability for reaction networks and prove that it is strictly related to the notion of synergy. In particular, we provide a characterization of the non-trivial closed reaction networks by means of their degree of internal synergy. The less trivial the dynamics of the reaction network, the less can be separated into constituents, and equivalently the more synergies the reaction network has. We also discuss the computational and analytical benefits of this new representation of the dynamical structure of a reaction network.
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Notes
- 1.
Those in \({\mathcal {R}}_{X\cup \text {prod}({\mathcal {R}}_X)}\).
- 2.
The algorithm presented in [18] is employed to build a restricted form of closed sets, called organizations, for specific class of reaction networks, known as flow systems, in which organizations have a lattice structure.
- 3.
In the sense that none of the reactions in the network is assigned with a zero value in the process.
References
Centler, F., di Fenizio, P.S., Matsumaru, N., Dittrich, P.: Chemical organizations in the central sugar metabolism of Escherichia Coli. In: Deutsch, A., Brusch, L., Byrne, H., Vries, G., Herzel, H. (eds.) Mathematical Modeling of Biological Systems, Volume I. MSSET, pp. 105–119. Birkhäuser, Boston (2007). https://doi.org/10.1007/978-0-8176-4558-8_10
Centler, F., Kaleta, C., di Fenizio, P.S., Dittrich, P.: Computing chemical organizations in biological networks. Bioinformatics 24(14), 1611–1618 (2008)
Centler, F., Kaleta, C., Speroni di Fenizio, P., Dittrich, P.: A parallel algorithm to compute chemical organizations in biological networks. Bioinformatics 26(14), 1788–1789 (2010)
Dittrich, P., Winter, L.: Chemical organizations in a toy model of the political system. Adv. Complex Syst. 11(04), 609–627 (2008)
Dittrich, P., Di Fenizio, P.S.: Chemical organisation theory. Bull. Math. Biol. 69(4), 1199–1231 (2007)
Garg, V.K.: Introduction to Lattice Theory with Computer Science Applications. Wiley, Hoboken (2015)
Horn, F., Jackson, R.: General mass action kinetics. Arch. Ration. Mech. Anal. 47(2), 81–116 (1972)
Kreyssig, P., Escuela, G., Reynaert, B., Veloz, T., Ibrahim, B., Dittrich, P.: Cycles and the qualitative evolution of chemical systems. PLoS ONE 7(10), e45772 (2012)
Kreyssig, P., Wozar, C., Peter, S., Veloz, T., Ibrahim, B., Dittrich, P.: Effects of small particle numbers on long-term behaviour in discrete biochemical systems. Bioinformatics 30(17), i475–i481 (2014)
Matsumaru, N., Centler, F., di Fenizio, P.S., Dittrich, P.: Chemical organization theory applied to virus dynamics (Theorie chemischer organisationen angewendet auf infektionsmodelle). Inf. Technol. 48(3), 154–160 (2006)
Matsumaru, N., Centler, F., di Fenizio, P.S., Dittrich, P.: Chemical organization theory as a theoretical base for chemical computing. In: Proceedings of the 2005 Workshop on Unconventional Computing: From Cellular Automata to Wetware, pp. 75–88. Luniver Press (2005)
Matsumaru, N., Lenser, T., Hinze, T., Dittrich, P.: Toward organization-oriented chemical programming: a case study with the maximal independent set problem. In: Dressler, F., Carreras, I. (eds.) Advances in Biologically Inspired Information Systems. SCI, vol. 69, pp. 147–163. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72693-7_8
Peter, S., Veloz, T., Dittrich, P.: Feasibility of organizations – a refinement of chemical organization theory with application to P systems. In: Gheorghe, M., Hinze, T., Păun, G., Rozenberg, G., Salomaa, A. (eds.) CMC 2010. LNCS, vol. 6501, pp. 325–337. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-18123-8_25
Peter, S., Dittrich, P.: On the relation between organizations and limit sets in chemical reaction systems. Adv. Complex Syst. 14(01), 77–96 (2011)
Reddy, V.N., Mavrovouniotis, M.L., Liebman, M.N.: Petri net representations in metabolic pathways. In: ISMB, vol. 93, pp. 328–336, July 1993
Schuster, S., Hilgetag, C.: On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Syst. 2(02), 165–182 (1994)
Schilling, C.H., Schuster, S., Palsson, B.O., Heinrich, R.: Metabolic pathway analysis: basic concepts and scientific applications in the postgenomic era. Biotechnol. Prog. 15(3), 296–303 (1999)
Speroni di Fenizio, P.: The lattice of chemical organisations. In: Artificial Life Conference Proceedings 13, pp. 242–248. MIT Press, Cambridge, July 2015
Strogatz, S.H.: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press, Boca Raton (2018)
Veloz, T.: A computational study of Algebraic Chemistry (Master’s thesis) (2010)
Veloz, T., Razeto-Barry, P., Dittrich, P., Fajardo, A.: Reaction networks and evolutionary game theory. J. Math. Biol. 68(1–2), 181–206 (2014)
Veloz, T., Razeto-Barry, P.: Reaction networks as a language for systemic modeling: fundamentals and examples. Systems 5(1), 11 (2017a)
Veloz, T., Razeto-Barry, P.: Reaction networks as a language for systemic modeling: on the study of structural changes. Systems 5(2), 30 (2017b)
Veloz, T., Ramos, R., Maldonado, P., Moisset, P.: Reaction networks as a tool for representing and analyzing ecological networks (2018, in preparation)
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Veloz, T., Bassi, A., Maldonado, P., Razeto, P. (2019). On the Existence of Synergies and the Separability of Closed Reaction Networks. In: Chaves, M., Martins, M. (eds) Molecular Logic and Computational Synthetic Biology. MLCSB 2018. Lecture Notes in Computer Science(), vol 11415. Springer, Cham. https://doi.org/10.1007/978-3-030-19432-1_7
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