Linear mapping approximation of gene regulatory networks with stochastic dynamics

Area of Science:

• Systems Biology
• Computational Biology
• Molecular Biology

Background:

• Stochastic gene expression models are often analytically intractable due to protein-DNA binding reactions.
• Accurate modeling of gene expression is crucial for understanding cellular processes.

Purpose of the Study:

• To develop a novel approximation method for simplifying models of stochastic gene expression with protein-DNA binding.
• To enable analytic or semi-analytic solutions for protein number distributions.

Main Methods:

• The linear-mapping approximation combines conditional mean-field approximation and the Magnus expansion.
• The method maps systems with protein-promoter interactions to equivalent systems without binding reactions.
• Stochastic simulations were used to validate the accuracy of the approximation.

Main Results:

• The linear-mapping approximation provides accurate time-dependent and steady-state protein number distributions.
• The method effectively captures dynamics in auto- and mutual-regulated gene networks across different timescales.
• The approach was applied to analyze first-passage time, fluctuation sensitivity, and stochastic bifurcation diagrams.

Conclusions:

• The linear-mapping approximation offers a powerful tool for analyzing complex stochastic gene expression systems.
• This method simplifies intractable models, facilitating deeper insights into gene regulation.
• The approach is versatile, applicable to various network architectures and dynamic properties.