Speaker
Description
In recent years, there have been a few uses of the word ‘core’ in the context of chemical reaction networks, all related to some idea of minimality. Based on stoichiometric considerations alone (i.e. no dynamics nor kinetic considerations involved), Alex Blokhuis with co-authors identified autocatalytic cores as minimal structures carrying autocatalysis, a fundamental biochemical concept related to self-amplification. To effectively connect stoichiometric intuitions to dynamical conclusions, I introduced with Peter Stadler the framework of parameter-rich kinetics, which allows disentangling parametric dependence from the structural analysis of the Jacobian matrix. Widely used kinetics in biochemistry, such as Michaelis–Menten or generalized mass action, are naturally parameter-rich. Within this framework, we investigated minimal stoichiometric structures whose presence guarantees the possibility of dynamical instability (that is, the capacity for a locally unstable steady state). Since the autocatalytic cores sensu Blokhuis form a strict subset of these structures, we named them unstable cores. Finally, with both Peter Stadler and Alex Blokhuis, we addressed periodic oscillations, introducing the concept of oscillatory cores, i.e. minimal structures that guarantee periodic oscillations in any network containing them, again under parameter-rich kinetics. In this talk, I will give an overview of these and related results.
Bibliography
@article{blokhuis_universal_2020,
title = {Universal motifs and the diversity of autocatalytic systems},
volume = {117},
issn = {0027-8424, 1091-6490},
url = {https://www.pnas.org/doi/full/10.1073/pnas.2013527117},
doi = {10.1073/pnas.2013527117},
language = {en},
number = {41},
urldate = {2026-03-18},
journal = {Proceedings of the National Academy of Sciences},
author = {Blokhuis, Alex and Lacoste, David and Nghe, Philippe},
month = oct,
year = {2020},
pages = {25230--25236},
}
@article{vassena_unstable_2024,
title = {Unstable cores are the source of instability in chemical
reaction networks},
volume = {480},
issn = {1364-5021, 1471-2946},
url = {https://doi.org/10.1098/rspa.2023.0694},
doi = {10.1098/rspa.2023.0694},
language = {en},
number = {2285},
urldate = {2026-03-18},
journal = {Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences},
author = {Vassena, Nicola and Stadler, Peter F.},
month = mar,
year = {2024},
pages = {20230694},
}
@misc{blokhuis_stoichiometric_2025,
title = {Stoichiometric recipes for periodic oscillations in reaction
networks},
url = {https://arxiv.org/abs/2508.15273},
doi = {10.48550/arXiv.2508.15273},
urldate = {2026-03-18},
publisher = {arXiv},
author = {Blokhuis, Alexander and Stadler, Peter F. and Vassena, Nicola},
month = oct,
year = {2025},
note = {arXiv:2508.15273},
keywords = {Quantitative Biology - Molecular Networks, Mathematics -
Dynamical Systems},
}
