Autocatalytic cores in the diluted regime:classification and properties

TL;DR

This paper classifies and analyzes the properties of minimal autocatalytic networks in diluted regimes, establishing their equivalence in classification across stoichiometric and dynamical definitions, and examining their stationary regimes and robustness.

Contribution

It demonstrates that minimal autocatalytic networks in the dynamical regime follow the same classification as in the stoichiometric regime and proves the uniqueness of their stationary regimes.

Findings

Autocatalytic networks follow a unified classification in both stoichiometric and dynamical senses.

Stationary regimes are unique for all types except certain complex loops.

Results suggest robustness of stationary points under low-concentration perturbations.

Abstract

Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Autocatalysis was recently defined stoichiometrically for reaction networks; five types of minimal autocatalytic networks, termed autocatalytic cores were identified. A necessary and sufficient stoichiometric criterion was later established for dynamical autocatalysis in diluted regimes, ensuring a positive growth rate of autocatalytic species starting from infinitesimal concentrations, given that degradation rates are sufficiently low. Here, we show that minimal autocatalytic networks in the dynamical sense, in the diluted regime, follow the same classification as autocatalytic cores in the stoichiometric sense. We further prove the uniqueness of the stationary regimes of autocatalytic cores, with and without degradation, for all types, except types II with three catalytic loops or more. These results indicate that the stationary point is likely to be robust under perturbation at low concentrations. More complex behaviours are likely to arise by additional non-linear couplings between cores.