Autocatalytic cores in the diluted regime: classification and properties

Area of Science:

• Chemical Kinetics and Systems Biology
• Theoretical Chemistry
• Biochemistry

Background:

• Autocatalysis is fundamental to replication in chemical and biochemical systems.
• Minimal autocatalytic networks (autocatalytic cores) were previously classified stoichiometrically.
• A criterion for dynamical autocatalysis in dilute regimes was established, ensuring growth from low concentrations.

Purpose of the Study:

• To demonstrate that minimal autocatalytic networks in the dynamical sense align with the stoichiometric classification of autocatalytic cores.
• To investigate the uniqueness of stationary regimes for autocatalytic cores.
• To analyze the impact of degradation on stationary states and identify conditions for robustness.

Main Methods:

• Analysis of stoichiometric criteria for autocatalysis in diluted regimes.
• Mathematical modeling of reaction networks to determine dynamical behavior.
• Proof-based investigation of stationary state uniqueness for different autocatalytic core types.

Main Results:

• Minimal dynamical autocatalytic networks in dilute regimes follow the same classification as stoichiometric autocatalytic cores.
• The uniqueness of stationary regimes for autocatalytic cores is proven, both with and without degradation.
• An exception is noted for Type II autocatalytic cores with three or more catalytic loops, where uniqueness remains an open question.

Conclusions:

• The classification of minimal autocatalytic networks is consistent across dynamical and stoichiometric definitions in dilute regimes.
• Stationary points of autocatalytic cores are robust under perturbation at low concentrations.
• Complex behaviors beyond simple stationary states necessitate additional non-linear couplings.