A Quasi-Stationary Distribution Bound for Fault Analysis in Gene Regulatory Networks

Area of Science:

• Synthetic biology
• Systems biology
• Biophysics

Background:

• Stochastic fluctuations in gene regulatory networks (GRNs) create unpredictability, hindering the design of robust synthetic systems.
• Multi-stable GRNs, essential for biosensors and logic gates, are prone to unintended state transitions due to inherent noise.
• Limited tools exist for characterizing probability distributions around stable states in these complex biological systems.

Purpose of the Study:

• To develop a mathematical framework for analyzing multi-stable GRNs.
• To provide quantitative design principles for enhancing the stability of synthetic toggle switches.
• To assess the reliability of GRN-based biosensors by calculating error rates.

Main Methods:

• Utilized continuous-time Markov chains (CTMCs) to model the dynamics of multi-stable GRNs.
• Employed quasi-stationary distributions to analyze the behavior of systems near stable states.
• Applied the framework to existing literature examples and simulated biosensor population dynamics.

Main Results:

• Developed a broadly applicable mathematical framework for analyzing multi-stable systems with connected state spaces.
• Identified critical parameter thresholds dictating the transition from frequent stochastic switching to long-term stability (hours vs. years/decades).
• Calculated upper bounds for false positive/negative rates in population-level biosensor dynamics.

Conclusions:

• The proposed framework offers quantitative design principles for robust toggle switch construction.
• The method aligns with experimental observations and provides predictive power for synthetic GRN stability.
• This work enhances the reliability of GRN-based synthetic biology applications, including biosensors and logic gates.