Influence of the hypercycle on the error threshold: a stochastic approach

Area of Science:

• Theoretical Biology
• Complex Systems
• Statistical Physics

Background:

• The error threshold is crucial for maintaining information in systems like the hypercycle.
• Previous studies often used deterministic models, potentially overlooking the impact of fluctuations.
• Understanding fluctuations is key to explaining system stability and evolution.

Purpose of the Study:

• To investigate the role of stochastic fluctuations on the hypercycle's error threshold.
• To analyze the dynamics of a simplified hypercycle model using a stochastic approach.
• To compare stochastic findings with deterministic predictions.

Main Methods:

• Derivation of the master equation for a simplified hypercycle model.
• Calculation of the unique steady state, indicating system extinction.
• Gillespie simulation of the stochastic process to identify quasi-stationary states.

Main Results:

• The system's unique steady state implies extinction, but this state is reached over extremely long timescales.
• Quasi-stationary states, relevant for experimental timescales, were identified via simulation.
• The error threshold shifts to higher values of the quality factor (Q) in the presence of fluctuations.
• Information regarding fluctuations around these quasi-stationary states was obtained.

Conclusions:

• Stochastic effects and quasi-stationary states are critical for understanding hypercycle dynamics over relevant timescales.
• Fluctuations can stabilize the system by shifting the error threshold, contradicting purely deterministic extinction predictions.
• The study highlights the importance of stochastic simulations for accurately modeling complex biological systems.