Emergent Lévy behavior in single-cell stochastic gene expression

Area of Science:

• Biophysics
• Systems Biology
• Computational Biology

Background:

• Single-cell gene expression exhibits inherent stochasticity.
• The chemical master equation models mRNA and protein copy number dynamics.
• Macroscopic limits are crucial for understanding emergent behaviors in gene expression.

Purpose of the Study:

• Establish new macroscopic limits for gene expression dynamics.
• Provide theoretical underpinnings for empirical models in stochastic gene expression.
• Analyze protein concentration distributions in autoregulatory gene networks.

Main Methods:

• Development of two macroscopic limits: Kurtz and Lévy.
• Application of the chemical master equation framework.
• Analytical calculation of protein concentration distributions.

Main Results:

• The Kurtz limit aligns with classical chemical kinetics.
• The Lévy limit validates an empirical equation from Friedman et al.
• Clarification of biochemical implications and applicability of macroscopic limits.
• Derivation of a comprehensive analytic expression for protein concentration distribution.

Conclusions:

• The study provides a robust theoretical framework for stochastic gene expression.
• The established macroscopic limits offer new insights into gene regulatory network behavior.
• Findings bridge the gap between theoretical models and empirical observations in population genetics.