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Unstable cores are the source of instability in chemical reaction networks

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.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:90352
Date07 March 2024
CreatorsVassena, Nicola, Stadler, Peter F.
PublisherThe Royal Society
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/acceptedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess
Relation1471-2946, 10.1098/rspa.2023.0694

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