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On Computing Structural and Behavioral Complexities of Threshold Boolean Networks : Application to Biological

Urvan Christen1, Sergiu Ivanov2, Rémi Segretain1

  • 1CNRS, CHU Grenoble Alpes, Grenoble INP, TIMC-IMAG, Univ. Grenoble Alpes, 38000, Grenoble, France.

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Summary
This summary is machine-generated.

Threshold Boolean networks (TBNs) can exhibit simple behaviors despite complex structures. Our study reveals most TBNs are structurally complex, even when their dynamics are simple, using a novel complexity computation method.

Keywords:
Biological regulationComplexityThreshold Boolean networks

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Area of Science:

  • Systems biology
  • Computational biology
  • Network science

Background:

  • Threshold Boolean networks (TBNs) are used to model biological systems, such as gene regulatory networks.
  • Different TBNs can exhibit identical dynamic behaviors, making it challenging to infer network structure from function.
  • The complexity of these networks, both structural and behavioral, is a key area of investigation.

Purpose of the Study:

  • To investigate the relationship between structural and behavioral complexity in Threshold Boolean networks.
  • To determine if TBNs with simple dynamics are also structurally simple.
  • To develop a method for quantifying the structural complexity of TBNs.

Main Methods:

  • Developed a novel method to compute the structural complexity of TBNs.
  • Estimated the sizes of equivalence classes for the threshold Boolean functions within TBNs.
  • Computed both structural and behavioral complexities for various TBN models.

Main Results:

  • Most Threshold Boolean networks are found to be structurally complex.
  • This structural complexity persists even in TBNs that exhibit simple, predictable behaviors.
  • The developed method provides a quantitative measure for TBN structural complexity.

Conclusions:

  • A significant disconnect exists between the structural complexity and behavioral simplicity in many TBNs.
  • Understanding this structural complexity is crucial for accurate modeling of biological networks.
  • The new method offers a valuable tool for analyzing the complexity of TBNs in systems biology.