Aggregation for Computing Multi-Modal Stationary Distributions in 1-D Gene Regulatory Networks

Area of Science:

• Computational Biology
• Biophysics
• Biomathematics

Background:

• Stochastic gene regulatory network modeling often uses multi-modal birth-death processes.
• Large state spaces in these models lead to numerical precision issues when computing stationary distributions.
• Existing methods struggle with probability values exceeding standard computational limits.

Purpose of the Study:

• To develop robust algorithms for computing stationary distributions and mean first passage times in large-scale multi-modal birth-death processes.
• To address numerical limitations encountered in Chemical Master Equation (CME) based models.
• To enable accurate analysis of complex biological systems, such as gene regulatory networks.

Main Methods:

• Proposed aggregation-based, three-stage algorithms.
• Analysis of reduced-size subsystems in isolation.
• Consideration of transitions between aggregated subsystems.

Main Results:

• Successfully overcame numerical problems in computing stationary distributions and mean first passage times.
• Demonstrated the effectiveness of aggregation for handling large state spaces.
• Applied algorithms to accurately determine the parameter range for the bimodal behavior of the lac operon in E. coli.

Conclusions:

• Aggregation-based algorithms provide a viable solution for numerical challenges in stochastic modeling.
• The methods enable precise characterization of multi-modal dynamics in biological systems.
• Accurate computational analysis of gene regulatory networks like the lac operon is now feasible.