Autocatalytic networks with intermediates. I: Irreversible reactions

Area of Science:

• Biochemistry
• Chemical Kinetics
• Systems Biology

Background:

• Autocatalytic reaction networks are fundamental to understanding self-replication and the origin of life.
• Simple replicator dynamics model these systems but often oversimplify complex interactions.
• Template-dependent replication and specific catalysis are key features of biological and chemical systems.

Purpose of the Study:

• To analyze autocatalytic reaction networks by resolving trimolecular steps into consecutive irreversible reactions.
• To investigate the dynamics of competition and cooperative feedback in extended reaction networks.
• To compare the stability of fixed points and periodic orbits in these extended networks versus simple replicator dynamics.

Main Methods:

• Decomposition of trimolecular elementary steps into two consecutive irreversible reactions.
• Analysis of extreme cases: competition for common resources and hypercycle-like cooperative feedback.
• Mathematical modeling and stability analysis of the extended reaction networks.

Main Results:

• Extended network dynamics generally resemble simple replicator dynamics but exhibit significant differences.
• In cooperative feedback models, interior fixed points are asymptotically stable for any number of species.
• Simple replicator dynamics predict asymptotically stable periodic orbits for four or fewer species, and stable periodic orbits for more.

Conclusions:

• The resolution of trimolecular steps into simpler reactions reveals crucial differences in network stability.
• Cooperative feedback mechanisms in autocatalytic networks can lead to greater stability than previously modeled.
• These findings have implications for understanding the emergence and stability of complex chemical and biological systems.