Families of toric chemical reaction networks
- PDF / 653,392 Bytes
- 33 Pages / 439.37 x 666.142 pts Page_size
- 94 Downloads / 172 Views
Families of toric chemical reaction networks Michael F. Adamer1,2
· Martin Helmer3
Received: 9 December 2019 / Accepted: 23 July 2020 © The Author(s) 2020
Abstract We study families of chemical reaction networks whose positive steady states are toric, and therefore can be parameterized by monomials. Families are constructed algorithmically from a core network; we show that if a family member is multistationary, then so are all subsequent networks in the family. Further, we address the questions of model selection and experimental design for families by investigating the algebraic dependencies of the chemical concentrations using matroids. Given a family with toric steady states and a constant number of conservation relations, we construct a matroid that encodes important information regarding the steady state behaviour of the entire family. Among other things, this gives necessary conditions for the distinguishability of families of reaction networks with respect to a data set of measured chemical concentrations. We illustrate our results using multi-site phosphorylation networks. Keywords Families of reaction networks · Toric steady states · Model rejection · Matroid · Multistationarity
1 Introduction Many of the fundamental processes in biological cells can be described by a set of interlinked chemical reactions. Prominent examples of cellular processes regulated via biochemical interactions include immune response [1], cell signalling [2], cell death [3,4], and toxin formation [5]. For this reason the study of chemical reaction networks forms a central part of algebraic systems biology [6–10]. One approach focuses on the long term behaviour of networks by investigating their steady states and the relation of the number and stability of steady states to the network structure [10–12].
B
Michael F. Adamer [email protected]
1
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcliffe Observatory, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, UK
2
Max-Planck-Institut fur Mathematik in den Naturwissenschaften, Leipzig, Germany
3
Mathematical Sciences Institute, The Australian National University, Canberra, ACT, Australia
123
Journal of Mathematical Chemistry
In this paper we investigate the positive steady states for algorithmically constructed reaction networks, which we call families, for which the positive steady states may be parameterized by monomials (i.e. polynomials with a single term). Further, we use the algebraic dependencies of the variables representing the chemical concentrations to investigate experimental design and model identification for entire families. Families of networks are formally defined in Definition 3.2. To obtain an intuition for what could be described as a family, we introduce phosphorylation networks [12,13]. Phosphorylation is a vital signalling process in biochemistry and it is one of the most widely studied protein modifications. During phosphorylation a phosphoryl group (P O3− ) is added to an organic molecule which ac
Data Loading...
