title: Intermediates, catalysts, persistence, and boundary steady states.
abstract: For dynamical systems arising from chemical reaction networks, persistence is the property that each species concentration remains positively bounded away from zero, as long as species concentrations were all positive in the beginning. We describe two graphical procedures for simplifying reaction networks without breaking known necessary or sufficient conditions for persistence, by iteratively removing so-called intermediates and catalysts from the network. The procedures are easy to apply and, in many cases, lead to highly simplified network structures, such as monomolecular networks. For specific classes of reaction networks, we show that these conditions for persistence are equivalent to one another. Furthermore, they can also be characterized by easily checkable strong connectivity properties of a related graph. In particular, this is the case for (conservative) monomolecular networks, as well as cascades of a large class of post-translational modification systems (of which the MAPK cascade and the n-site futile cycle are prominent examples). Since one of the aforementioned sufficient conditions for persistence precludes the existence of boundary steady states, our method also provides a graphical tool to check for that.
authors.affiliation: Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.
authors.forename: Michael
authors.initials: M
authors.lastname: Marcondes de Freitas
authors.affiliation: Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.
authors.forename: Elisenda
authors.initials: E
authors.lastname: Feliu
authors.affiliation: Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark. wiuf@math.ku.dk.
authors.forename: Carsten
authors.identifier: 0000-0002-1302-4445
authors.initials: C
authors.lastname: Wiuf
mesh_terms: D001669:Biochemical Phenomena / Q000502:physiology*; D002623:Chemistry Techniques, Analytical / Q000379:methods*; D020935:MAP Kinase Signaling System / Q000502:physiology; D011499:Protein Processing, Post-Translational / Q000502:physiology
keywords: Boundary steady states; Catalysts; Intermediates; Model reduction; Persistence; Post-translational modification; Reaction network theory