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    Area of Science:

    • Systems Biology
    • Computational Biology
    • Biophysics

    Background:

    • Gene regulatory networks (GRNs) govern cellular processes through complex interactions.
    • Stochasticity in GRNs arises from low molecule numbers and reaction rate differences.
    • The feed-forward loop (FFL) is a fundamental and prevalent motif in gene regulation.

    Purpose of the Study:

    • To compute the exact steady-state probability landscape of stochastic FFLs.
    • To investigate FFL behavior under varying regulation intensities and slow promoter binding.
    • To define and analyze stochastic sensitivity in FFLs.

    Main Methods:

    • Accurate Chemical Master Equation (dCME) for direct computation of steady-state probability landscapes.
    • Analysis of FFL dynamics under conditions of slow promoter binding.
    • Development of a novel stochastic sensitivity metric.

    Main Results:

    • FFLs exhibit diverse multistabilities in their probability landscapes under specific conditions (e.g., slow promoter binding).
    • Stochastic sensitivity was defined to quantify the response of FFL probability distributions to parameter perturbations.
    • Gene expression changes in FFLs demonstrate sensitivity to system parameters and multistability states.

    Conclusions:

    • The Accurate Chemical Master Equation is effective for characterizing stochastic FFLs.
    • FFLs display complex behaviors like multistability and parameter sensitivity, crucial for cellular function.
    • Stochastic sensitivity provides a new framework for understanding GRN robustness and adaptability.