Abstract
The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an active area of research. In this paper, we concentrate on two biologically relevant families of reaction networks that model multisite phosphorylation and dephosphorylation of a substrate at n sites. For small values of n, it had previously been shown that the parameter region of multistationarity is connected. Here, we extend these results and provide a proof that applies to all values of n. Our techniques are based on the study of the critical polynomial associated with these reaction networks together with polyhedral geometric conditions of the signed support of this polynomial.
| Original language | English |
|---|---|
| Article number | 144 |
| Journal | Bulletin of Mathematical Biology |
| Volume | 86 |
| Issue number | 12 |
| Number of pages | 45 |
| ISSN | 0092-8240 |
| DOIs | |
| Publication status | Published - 2024 |
Bibliographical note
Funding Information:The authors thank Elisenda Feliu for useful comments on the manuscript, which significantly improved its readability. NK was supported by Independent Research Fund of Denmark. MLT was supported by the European Union under the Grant Agreement no. 101044561, POSALG. Views and opinions expressed are those of the author(s) only and do not necessarily reflect those of the European Union or European Research Council (ERC). Neither the European Union nor ERC can be held responsible for them.
Publisher Copyright:
© The Author(s) 2024.
Keywords
- 52Bxx
- 92xx
- Connectivity
- Gale duality
- Newton polytope
- Phosphorylation networks
- Signed support