Bursting noise in gene expression dynamics: linking microscopic and mesoscopic models

Area of Science:

• Systems Biology
• Computational Biology
• Biomathematics

Background:

• Gene regulatory networks exhibit stochastic fluctuations, known as noise.
• The dynamics of short-lived messenger RNA (mRNA) lead to bursts in protein production.
• Conventional mathematical models may not accurately represent this bursting phenomenon.

Purpose of the Study:

• To investigate the propagation of bursting noise across different mathematical modeling levels.
• To compare the efficacy of diffusion approximations versus a piecewise deterministic Markov process (PDMP) model in capturing bursting noise.
• To analyze the performance of the PDMP model in biologically relevant parameter ranges.

Main Methods:

• Mathematical modeling of gene regulatory networks.
• Application and comparison of diffusion approximation models.
• Implementation and analysis of a piecewise deterministic Markov process (PDMP) model.
• Development of analytical methods for calculating stationary distribution and switching frequencies.

Main Results:

• Diffusion approximations can fail to accurately capture bursting noise in gene regulatory networks.
• The piecewise deterministic Markov process (PDMP) model demonstrates superior performance in capturing bursting noise compared to diffusion approximations.
• The PDMP model is effective within biologically relevant parameter regimes.

Conclusions:

• The PDMP model offers a more accurate representation of bursting noise in gene regulatory networks than traditional diffusion approximations.
• This study provides a framework for embedding the PDMP model within existing modeling approaches.
• Analytical methods are presented for characterizing the PDMP model's behavior, including its stationary distribution and switching frequencies.