Abstract
This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous work on the effect that removing or adding intermediates has on multistationarity, and also on methods to detect multistationarity for networks with a binomial steady-state ideal. In particular, we provide a new determinant criterion to decide whether a network is multistationary, which applies when the network obtained by removing intermediates has a binomial steady-state ideal. We apply this method to easily characterize which subsets of complexes are responsible for multistationarity; this is what we call the multistationarity structure of the network. We use our approach to compute the multistationarity structure of the n-site sequential distributive phosphorylation cycle for arbitrary n.
| Original language | English |
|---|---|
| Pages (from-to) | 2428–2462 |
| Number of pages | 35 |
| Journal | Bulletin of Mathematical Biology |
| Volume | 81 |
| DOIs | |
| Publication status | Published - 17 May 2019 |
| Externally published | Yes |
Bibliographical note
The final publication is available at Springer via http://dx.doi.org/10.1007/s11538-019-00612-1Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.
Keywords
- Binomial ideals
- Phosphorylation cycle
- Multistationarity
- Model reduction
- Determinant criterion
- Toric ideal