Complex dynamics in a cross-catalytic self-replication mechanism.

Area of Science:

• Chemical kinetics
• Systems chemistry
• Biophysics

Background:

• Self-replicating systems are fundamental to understanding life's origins.
• Minimal models are crucial for dissecting complex biological phenomena.
• The R3C ligase ribozyme system serves as a known example of catalytic replication.

Purpose of the Study:

• To investigate the dynamics of a minimal two-template cross-catalytic self-replicating system.
• To explore complex dynamic behaviors beyond simple self-replication.
• To model phenomena such as bifurcations and oscillations in chemical systems.

Main Methods:

• Theoretical modeling of a two-template cross-catalytic system.
• Analysis of system dynamics using concepts from nonlinear dynamics.
• Identification of specific dynamic regimes like bifurcations and excitability.

Main Results:

• The minimal system exhibits significantly more complex dynamics than simpler self-replicating counterparts.
• Key nonlinear phenomena including Poincare-Andronov-Hopf bifurcation and canard transitions were observed.
• Hysteresis and excitability were identified, leading to birhythmicity between simple and complex oscillations.

Conclusions:

• Minimal cross-catalytic systems can display rich and complex dynamic behaviors.
• The studied system provides a simplified model for understanding complex oscillations in chemical and biological contexts.
• These findings contribute to the broader understanding of self-replication and emergent properties in chemical systems.