Minimality in Reflexive and Stoichiometric Autocatalysis
Abstract
Autocatalysis, the ability of a chemical subsystem to sustain its own constituents when supplied with sufficient food molecules, has been closely related to the origin of life on Earth. Emerging from Wilhelm Ostwald's considerations about an explicit autocatalytic reaction, different notions of autocatalysis have been developed over the years. The two most prominent are reflexively autocatalytic F-generated sets (RAFs) and stoichiometric autocatalysis. After having shown that each RAFs is, under reasonable conditions, in general stoichiometrically autocatalytic, we examine here the relationship between the two notions of minimality: irreducible RAFs and autocatalytic cores. To this end, we overcome the obstacle that RAFs and stoichiometric autocatalysis have been formalized in distinct systems of chemical reactions, i.e., catalytic reaction systems (CRS) and chemical reaction networks (CRNs), respectively. We show that reactions in a CRS constitute equivalence classes of reactions of the corresponding CRNs w.r.t. their specific catalyzations. Using the fact that CRN and CRS can be canonically identified whenever each CRS reaction is associated with a single catalyzation, we demonstrate that the Kőnig graph of a monocatalyzed, irreducible RAF is composed of strong blocks devoid of food and waste species that are separated by reaction vertices, each of which contains an autocatalytic core. In fact, a single irreducible RAF can, in general, contain exponentially many autocatalytic cores.
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BibTeX
@misc{golnik2026minimality,
title = {{Minimality in Reflexive and Stoichiometric Autocatalysis}},
author = {Richard Golnik and Thomas Gatter and Wim Hordijk and Peter F. Stadler and Nicola Vassena},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23602},
eprint = {2609.23602},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23602},
}
RIS
TY - UNPB
TI - Minimality in Reflexive and Stoichiometric Autocatalysis
AU - Richard Golnik
AU - Thomas Gatter
AU - Wim Hordijk
AU - Peter F. Stadler
AU - Nicola Vassena
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23602
UR - https://arxiv.org/abs/2609.23602
AB - Autocatalysis, the ability of a chemical subsystem to sustain its own constituents when supplied with sufficient food molecules, has been closely related to the origin of life on Earth. Emerging from Wilhelm Ostwald's considerations about an explicit autocatalytic reaction, different notions of autocatalysis have been developed over the years. The two most prominent are reflexively autocatalytic F-generated sets (RAFs) and stoichiometric autocatalysis. After having shown that each RAFs is, under reasonable conditions, in general stoichiometrically autocatalytic, we examine here the relationship between the two notions of minimality: irreducible RAFs and autocatalytic cores. To this end, we overcome the obstacle that RAFs and stoichiometric autocatalysis have been formalized in distinct systems of chemical reactions, i.e., catalytic reaction systems (CRS) and chemical reaction networks (CRNs), respectively. We show that reactions in a CRS constitute equivalence classes of reactions of the corresponding CRNs w.r.t. their specific catalyzations. Using the fact that CRN and CRS can be canonically identified whenever each CRS reaction is associated with a single catalyzation, we demonstrate that the Kőnig graph of a monocatalyzed, irreducible RAF is composed of strong blocks devoid of food and waste species that are separated by reaction vertices, each of which contains an autocatalytic core. In fact, a single irreducible RAF can, in general, contain exponentially many autocatalytic cores.
ER -