Reachability, persistence, and constructive chemical reaction networks (part II): a formalism for species composition in chemical reaction network theory and application to persistence
- 100 Downloads
Chemical Reaction Network Theory uses mathematics to study systems of reactions and infer their properties from their structure. At the onset is an abstract definition of a chemical reaction network which is very general and is pertinent beyond chemistry, e.g. in modeling interactions of microscopic and macroscopic living species. This allows the theory to provide widely applicable theorems. It also results in that the idea of chemical composition is mostly used implicitly in examples to illustrate theorems, not explicitly to establish new properties. In this paper we propose a formalism for species composition in a way that generalizes the idea of atomic composition—for instance, elementary species will extend the idea of atoms. We envision that this formalism could lead to more theorems on classes of networks that are of interest in biochemistry. Toward that prospect, we prove that if there is no isomerism among elementary species, and if a newly formalized and widely applicable reversibility condition holds, then a reaction network is vacuously persistent: no species will tend to extinction if all species are implicitly present at initial time. This paper is the second in a series of three articles. The first paper studies vacuous persistence and the third one probes a class of enzymatic networks.
KeywordsChemical reaction network Species composition Constructive network Vacuous persistence Reachability
Mathematics Subject Classification (2010)92C42 92C45 34D05
- 1.D. Angeli, P. De Leenheer, E.D. Sontag, A Petri net approach to persistence analysis in chemical reaction networks, in Biology and Control Theory: Current Challenges, ed. by I. Queinnec, S. Tarbouriech, G. Garcia, S.-I. Niculescu. Lecture Notes in Control and Information Sciences, vol. 357 (Springer, Berlin, 2007), pp. 181–216. doi: 10.1007/978-3-540-71988-5
- 4.G. Gnacadja, Reachability, persistence, and constructive chemical reaction networks (part I): reachability approach to the persistence of chemical reaction networks. J. Math. Chem. (2011). doi: 10.1007/s10910-011-9894-4
- 5.G. Gnacadja, Reachability, persistence, and construtive chemical reaction networks (part III): a mathematical formalism for binary enzymatic network and application to persistence. J. Math. Chem. (2011). doi: 10.1007/s10910-011-9895-3