In biochemical networks, complex dynamical features such as superlinear growth
and oscillations are classically considered a consequence of autocatalysis. For the
large class of parameter-rich kinetic models, which includes Generalized Mass Ac-
tion kinetics and Michaelis-Menten kinetics, we show that certain submatrices of
the stoichiometric matrix, so-called unstable cores, are sufficient for a reaction
network to admit instability and potentially give rise to such complex dynami-
cal behavior. The determinant of the submatrix distinguishes unstable-positive
feedbacks, with a single real-positive eigenvalue, and unstable-negative feedbacks
without real-positive eigenvalues. Autocatalytic cores turn out to be exactly the
unstable-positive feedbacks that are Metzler matrices. Thus there are sources of
dynamical instability in chemical networks that are unrelated to autocatalysis.
We use such intuition to design non-autocatalytic biochemical networks with su-
perlinear growth and oscillations.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:90352 |
| Date | 07 March 2024 |
| Creators | Vassena, Nicola, Stadler, Peter F. |
| Publisher | The Royal Society |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/acceptedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 1471-2946, 10.1098/rspa.2023.0694 |
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