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Area of Science:

  • Network science
  • Control theory
  • Systems biology

Background:

  • Complex networks are often directed, requiring specialized analysis methods.
  • The Minimum Dominating Set (MDS) approach is effective for identifying control nodes but lacks speed for large directed networks.
  • Existing methods struggle with the scale and directed nature of real-world biological systems.

Purpose of the Study:

  • To develop a fast algorithm for applying the Minimum Dominating Set (MDS) approach to large-scale directed networks.
  • To identify critical control nodes in biological networks, including metabolic and signaling pathways.
  • To investigate the evolutionary conservation of control mechanisms in biological systems.

Main Methods:

  • Developed a novel algorithm utilizing efficient graph reduction for MDS identification in directed networks.
  • The algorithm achieves a 176-fold speed increase over existing methods.
  • Applied the algorithm to analyze metabolic pathways of 70 plant species and signaling pathways in model organisms.

Main Results:

  • The new algorithm significantly enhances computational speed and network size capacity (up to 65,000 nodes).
  • Identified functional pathways enriched with critical control molecules in plant and animal systems.
  • Demonstrated evolutionary conservation of most control categories from early plants to modern angiosperms.

Conclusions:

  • The developed algorithm provides an efficient tool for analyzing controllability in large-scale directed biological networks.
  • The findings highlight conserved regulatory principles across diverse plant lineages.
  • This work advances the application of network science and control theory to understand fundamental biological processes.