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    This study introduces new algorithms to solve numerical issues in large gene network models. These methods accurately analyze multi-modal birth-death processes, like the lac operon, for better computational biology insights.

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    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.