Generic algebraic conditions for the occurrence of switch-like behavior of a chemical kinetic system of the hypoxia pathway

Weakly reversible chemical reaction networks with zero deficiency associated with mass-action kinetics admit, within each positive stoichiometric compatibility class, one positive steady state which is locally asymptotically stable and this irrespective of the values of the kinetics constants. Netwo...

Full description

Saved in:
Bibliographic Details
Published in:Journal of biological physics Vol. 50; no. 1; pp. 29 - 53
Main Author: Vanhaelen, Quentin
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.03.2024
Springer Nature B.V
Subjects:
Biochemistry
Biological and Medical Physics
Biophysics
Chemical reactions
Complex Fluids and Microfluidics
Complex Systems
Humans
Hypoxia
Kinetics
Models, Biological
Neurosciences
Physics
Physics and Astronomy
Soft and Granular Matter
74G05
Switch-like behavior
Extreme currents
Mass-action kinetics
34C23
34A34
34D30
74H60
Chemical reaction network
Convex coordinates
Steady state
ISSN:0092-0606, 1573-0689, 1573-0689
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Weakly reversible chemical reaction networks with zero deficiency associated with mass-action kinetics admit, within each positive stoichiometric compatibility class, one positive steady state which is locally asymptotically stable and this irrespective of the values of the kinetics constants. Networks which do not enjoy these structural properties potentially exhibit more diverse dynamical behaviors. In this article, we consider a chemical reaction network associated with mass-action kinetics which is not weakly reversible and has a deficiency larger than one. The chemical reactions are at most bimolecular, but inflow and outflow reactions are present. Our results are as follows. We establish the existence of positive steady-state solutions and obtain their analytic expressions in the concentration space and in convex coordinates. We show that the system fulfills necessary conditions for a saddle-node and for a bifurcation into a saddle and a node. We apply a constructive approach to obtain a set of numerical values for the state variables and kinetic parameters, not reported previously, such that the reduced Jacobian is characterized by a zero eigenvalue with all other eigenvalues having negative real parts. The bifurcation diagram confirms the presence of the switch-like behavior.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
content type line 23
ISSN:0092-0606
1573-0689
1573-0689
DOI:10.1007/s10867-023-09647-x