Effective Markovian Dynamics Method for Solving Non-Markovian Dynamics of Stochastic Gene Expression
1University of Electronic Science and Technology of China, School of Mathematical Sciences, Chengdu 611731, China.
Physical Review Letters
|August 12, 2025
Summary
This study introduces an effective Markovian dynamics (EMD) method to solve complex gene expression models with nonexponential protein degradation. The new approach simplifies non-Markovian dynamics, enabling analytical solutions for previously intractable models.
Area of Science:
- Systems Biology
- Molecular Biology
- Biophysics
Background:
- Over 10% of proteins exhibit nonexponential degradation, complicating gene expression modeling.
- Stochastic dynamics of nonexponentially degraded proteins are non-Markovian and difficult to solve analytically.
Purpose of the Study:
- To develop a method for solving gene expression models with nonexponential protein decay.
- To enable analytical solutions for non-Markovian gene expression dynamics.
Main Methods:
- Developed an effective Markovian dynamics (EMD) method.
- Converted non-Markovian models into effective Markovian ones.
- Analytically solved gene expression models with nonexponential or delayed protein decay.
Main Results:
- The EMD method yields identical mRNA and protein distributions to non-Markovian models.
- Successfully solved classical gene expression models with previously unknown exact distributions.
- Explained the lower mRNA-protein correlation in nonexponentially degraded proteins.
Conclusions:
- The EMD method provides a powerful tool for analyzing complex gene expression systems.
- Predicts enhanced bimodality in gene expression with delayed protein degradation.
- Offers new insights into protein degradation kinetics and gene expression variability.
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