On classes of reaction networks and their associated polynomial dynamical systems
- PDF / 4,627,921 Bytes
- 31 Pages / 439.37 x 666.142 pts Page_size
- 55 Downloads / 164 Views
On classes of reaction networks and their associated polynomial dynamical systems David F. Anderson1 · James D. Brunner2 · Gheorghe Craciun1,3 · Matthew D. Johnston4 Received: 16 April 2020 / Accepted: 30 May 2020 © Springer Nature Switzerland AG 2020
Abstract In the study of reaction networks and the polynomial dynamical systems that they generate, special classes of networks with important properties have been identified. These include reversible, weakly reversible, and, more recently, endotactic networks. While some inclusions between these network types are clear, such as the fact that all reversible networks are weakly reversible, other relationships are more complicated. Adding to this complexity is the possibility that inclusions be at the level of the dynamical systems generated by the networks rather than at the level of the networks themselves. We completely characterize the inclusions between reversible, weakly reversible, endotactic, and strongly endotactic network, as well as other less well studied network types. In particular, we show that every strongly endotactic network in two dimensions can be generated by an extremally weakly reversible network. We also introduce a new class of source-only networks, which is a computationally convenient property for networks to have, and show how this class relates to the above mentioned network types. Keywords Reaction networks · Polynomial dynamical systems * James D. Brunner [email protected] David F. Anderson [email protected] Gheorghe Craciun [email protected] Matthew D. Johnston [email protected] 1
Department of Mathematics, University of Wisconsin-Madison, Madison, USA
2
Division of Surgical Research, Department of Surgery, Mayo Clinic, Rochester, USA
3
Department of Biomolecular Chemistry, University of Wisconsin-Madison, Madison, USA
4
Department of Mathematics & Computer Science, Lawrence Technological University, Southfield, USA
13
Vol.:(0123456789)
Journal of Mathematical Chemistry
Mathematics Subject Classification 34C20 · 37N25 · 80A30 · 92C42 · 92C45
1 Introduction Chemical reaction networks model the behavior of sets of reactants, usually termed species, that interact at specified rates to form sets of products. Under simplifying assumptions such as (i) a well-mixed reaction vessel, (ii) a sufficiently large number of reactants, and (iii) mass action kinetics, the dynamics of the concentrations of the species can be modeled by a system of autonomous polynomial ordinary differential equations. Such systems are known as mass action systems. With the increased recent interest in systems biology, significant attention has been given to the question of how dynamical properties of a mass action system can be inferred from the structure of the network of interactions that it models. In particular, it is of great interest to identify network structures that inform the dynamics regardless of the choice of parameters for the model (which are often unknown, or only known up to order of magnitude). This is not a trivial e
Data Loading...
