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    This study introduces influence networks with forces, offering a new way to model cell processes. These networks provide a hierarchy of semantics, aiding in building complex biological models and analyzing system attractors.

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    Area of Science:

    • Systems Biology
    • Computational Biology
    • Biochemistry

    Background:

    • Biochemical reaction networks are standard for modeling cell processes.
    • Influence diagrams are used for representing molecular interactions.
    • Bridging influence and reaction networks can enhance model building.

    Purpose of the Study:

    • Introduce a formalism of influence networks with forces.
    • Equip influence networks with a hierarchy of semantics (Boolean, Petri net, stochastic, differential).
    • Compare expressive power and analyze computational properties.

    Main Methods:

    • Formalism of influence networks with forces.
    • Hierarchy of discrete and continuous semantics.
    • Analysis of monotonicity properties.
    • Algorithm development for attractor computation.

    Main Results:

    • Influence networks have equivalent expressive power to reaction networks under differential semantics.
    • Influence networks are weaker than reaction networks under discrete semantics.
    • Developed a (positive) Boolean semantics and compared it with (negative) Boolean semantics.
    • Derived an algorithm to compute attractors in both positive and negative Boolean semantics.

    Conclusions:

    • Influence networks offer a valuable alternative for modeling biological systems.
    • The hierarchy of semantics provides flexibility in model analysis.
    • The developed algorithm aids in understanding system dynamics and attractors.