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...
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| Vydáno v: | Journal of biological physics Ročník 50; číslo 1; s. 29 - 53 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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01.03.2024
Springer Nature B.V |
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| ISSN: | 0092-0606, 1573-0689, 1573-0689 |
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| Abstract | 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. |
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| AbstractList | 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. 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.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. |
| Author | Vanhaelen, Quentin |
| Author_xml | – sequence: 1 givenname: Quentin surname: Vanhaelen fullname: Vanhaelen, Quentin email: vanhaelen@insilicomedicine.com organization: Insilico Medicine Hong Kong Ltd |
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| Cites_doi | 10.1021/jp961573u 10.1016/j.aam.2004.04.003 10.1016/j.jprocont.2016.10.002 10.1137/10081722X 10.1016/j.jelechem.2004.11.011 10.3934/mbe.2020046 10.1007/BF00255665 10.1006/jsco.2001.0512 10.1091/mbc.e03-12-0897 10.1007/s11538-011-9685-x 10.1371/journal.pcbi.0030171 10.1007/BF00255664 10.1016/j.tcs.2014.07.032 10.1016/0009-2509(87)80099-4 10.1090/conm/286/04754 10.1073/pnas.0308265100 10.1016/0009-2509(88)87122-7 10.1016/j.mbs.2007.07.003 10.1002/9780470142622.ch1 |
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| Keywords | 74G05 Switch-like behavior Extreme currents Mass-action kinetics 34C23 34A34 34D30 74H60 Chemical reaction network Convex coordinates Steady state |
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| SubjectTerms | 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 |
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| Title | Generic algebraic conditions for the occurrence of switch-like behavior of a chemical kinetic system of the hypoxia pathway |
| URI | https://link.springer.com/article/10.1007/s10867-023-09647-x https://www.ncbi.nlm.nih.gov/pubmed/38127158 https://www.proquest.com/docview/2925773247 https://www.proquest.com/docview/2904571490 https://pubmed.ncbi.nlm.nih.gov/PMC10864246 |
| Volume | 50 |
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