Critical slowing down in biochemical networks with feedback

Area of Science:

• Biophysics
• Systems Biology
• Statistical Mechanics

Background:

• Systems exhibit critical slowing down near bifurcation points, characterized by diverging response times.
• Stochastic biochemical feedback models are crucial for understanding cellular dynamics.
• The mean-field Ising universality class provides a framework for analyzing critical phenomena.

Purpose of the Study:

• Investigate critical slowing down in well-mixed stochastic models of biochemical feedback.
• Analyze system responses to sudden parameter changes (quenches) and continuous perturbations.
• Quantify critical slowing down in biological systems, specifically T cells.

Main Methods:

• Exploit a mapping to the mean-field Ising universality class.
• Analyze responses to sudden quenches and continuous parameter driving.
• Apply the Kibble-Zurek scaling to predict hysteresis in cellular responses.

Main Results:

• Demonstrated that the studied models exhibit the Kibble-Zurek collapse under continuous driving.
• Showcased predictable scaling of hysteresis in cellular responses to gradual perturbations.
• Quantified critical slowing down in T cells, relating drug addition to a parameter quench.

Conclusions:

• The findings elucidate the tradeoff between response precision and speed in biological systems.
• The study provides a theoretical framework for understanding critical slowing down in cellular processes.
• The mapping to the Ising universality class offers a powerful tool for analyzing complex biological dynamics.