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://urldefense.com/v3/https://pnas.org/doi/full/10.1073/pnas.2013527117;!!DZ3fjg!7968kARyfdkFu6rjI62n7fG2Qtsj3gpDJYfIycVWKtNPUZPtwa5qYwKB8VVjMOdubCm0raevNWBUm0b-j_mVGZz7JKqpsF7CR1o$ },
doi = {10.1073/pnas.2013527117},
abstract = {Significance
Autocatalysis, the ability of chemical systems to make
more of themselves, is a hallmark of living systems, as it underlies
metabolism, reproduction, and evolution. Here, we present a unified
theory of autocatalysis based on stoichiometry. This allows us to
identify essential motifs of autocatalytic networks, namely,
autocatalytic cores, which come in five categories. In these networks,
internal catalytic cycles are found to favor growth. The stoichiometry
approach furthermore reveals that diverse autocatalytic networks can
be formed with multiple compartments. Overall, these findings suggest
that autocatalysis is a richer and more abundant phenomenon than
previously thought.
,
Autocatalysis is essential for the origin of life and
chemical evolution. However, the lack of a unified framework so far
prevents a systematic study of autocatalysis. Here, we derive, from
basic principles, general stoichiometric conditions for catalysis and
autocatalysis in chemical reaction networks. This allows for a
classification of minimal autocatalytic motifs called cores. While all
known autocatalytic systems indeed contain minimal motifs, the
classification also reveals hitherto unidentified motifs. We further
examine conditions for kinetic viability of such networks, which
depends on the autocatalytic motifs they contain and is notably
increased by internal catalytic cycles. Finally, we show how this
framework extends the range of conceivable autocatalytic systems, by
applying our stoichiometric and kinetic analysis to autocatalysis
emerging from coupled compartments. The unified approach to
autocatalysis presented in this work lays a foundation toward the
building of a systems-level theory of chemical evolution.},
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://urldefense.com/v3/__https://royalsocietypublishing.org/doi/10.1098/rspa.2023.0694__;!!DZ3fjg!7968kARyfdkFu6rjI62n7fG2Qtsj3gpDJYfIycVWKtNPUZPtwa5qYwKB8VVjMOdubCm0raevNWBUm0b-j_mVGZz7JKqpuvN30us$ },
doi = {10.1098/rspa.2023.0694},
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.},
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://urldefense.com/v3/http://arxiv.org/abs/2508.15273;!!DZ3fjg!7968kARyfdkFu6rjI62n7fG2Qtsj3gpDJYfIycVWKtNPUZPtwa5qYwKB8VVjMOdubCm0raevNWBUm0b-j_mVGZz7JKqpDCS0H18$ },
doi = {10.48550/arXiv.2508.15273},
abstract = {Oscillatory chemical reactions are functional components
in a variety of biological contexts. In chemistry, the construction
and identification of even rudimentary oscillators remain elusive and
lack a general framework. Using parameter-rich kinetics - a
methodology enabling the disentanglement of parametric dependencies
from structural analysis - we investigate the stoichiometry of
chemical oscillators. We introduce the concept of oscillatory cores:
minimal subnetworks that guarantee the potential for oscillations in
any reaction network containing them. These cores fall into two
classes, depending on whether they involve positive or negative
feedback. In particular, the latter class unveils a family of
oscillators - yet to be synthesized - that require a minimum number of
reaction steps to exhibit oscillations, a phenomenon we refer to as
the principle of length. We identify several mechanisms through which
catalysis promotes oscillations: (I) furnishing instability (e.g.
autocatalysis), (II) lifting dependencies, (III) lowering length
thresholds. Notwithstanding this mechanistic ubiquity, we show that
oscillators can also be realized without employing any catalysis. Our
results highlight branches of chemistry where oscillators are likely
to arise by chance, suggest new strategies for their design, and point
to novel classes of oscillators yet to be realized experimentally.},
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},
}
