Gene expression dynamics with stochastic bursts: Construction and exact results for a coarse-grained model

Area of Science:

• Systems Biology
• Theoretical Biology
• Computational Biology

Background:

• Gene expression often occurs in stochastic bursts, involving discrete messenger RNA (mRNA) and protein populations.
• Accurately modeling these dynamics is crucial for understanding cellular processes.
• Existing diffusion-type models often fail to capture the full complexity of bursty gene expression.

Purpose of the Study:

• To develop a theoretical framework for analyzing gene expression dynamics with stochastic bursts.
• To create a coarse-grained model that simplifies analysis while retaining accuracy.
• To provide accurate predictions for protein population dynamics under burst conditions.

Main Methods:

• Developed an individual-based model for joint mRNA and protein populations.
• Proposed an expanded master equation for the stochastic gene expression process.
• Derived closed-form expressions for stationary distributions and mean first-passage times.
• Validated the model using large-scale Monte Carlo simulations.

Main Results:

• The proposed coarse-grained model accurately describes protein population dynamics.
• The model fully accounts for the effects of discrete and fluctuating mRNA populations.
• Simulations demonstrate superior accuracy compared to commonly proposed diffusion-type models.

Conclusions:

• The new theoretical framework provides an accurate and simplified approach to modeling stochastic gene expression bursts.
• This method effectively captures the influence of mRNA dynamics on protein populations.
• The findings offer a more robust alternative to existing modeling techniques in systems biology.