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 action 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 dynamical behaviour. 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 superlinear growth and oscillations.
%0 Journal Article
%1 vassena2024unstable
%A Vassena, Nicola
%A Stadler, Peter F.
%D 2024
%J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
%K imported
%N 2285
%P 20230694
%R 10.1098/rspa.2023.0694
%T Unstable cores are the source of instability in chemical reaction networks
%U https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2023.0694
%V 480
%X 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 action 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 dynamical behaviour. 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 superlinear growth and oscillations.
@article{vassena2024unstable,
abstract = {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 action 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 dynamical behaviour. 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 superlinear growth and oscillations.},
added-at = {2024-10-02T13:52:45.000+0200},
author = {Vassena, Nicola and Stadler, Peter F.},
biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/20a6b7e4b7e6bfb5163f1c0b0914fd6a4/scadsfct},
doi = {10.1098/rspa.2023.0694},
eprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2023.0694},
interhash = {4129a16e5066ac53dc58f5f779f244a1},
intrahash = {0a6b7e4b7e6bfb5163f1c0b0914fd6a4},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
keywords = {imported},
number = 2285,
pages = 20230694,
timestamp = {2024-10-02T13:52:45.000+0200},
title = {Unstable cores are the source of instability in chemical reaction networks},
url = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2023.0694},
volume = 480,
year = 2024
}
