Plasmodial vein networks of the slime mold Physarum polycephalum form regular graphs

Werner Baumgarten1, Tetsuo Ueda, Marcus J B Hauser

  • 1Institut für Experimentelle Physik, Abteilung Biophysik, Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany.

Insights

The Physarum polycephalum slime mold forms a unique biological transport network with regular, degree-3 nodes. This vein network

Area of Science:

  • * Biological network formation and analysis.
  • * Morphological studies of Physarum polycephalum.

Background:

  • * Biological transportation networks exhibit diverse structures.
  • * Real-world networks often display small-world or scale-free properties.
  • * The Physarum polycephalum plasmodium serves as a model for biological network development.

Purpose of the Study:

  • * To analyze the morphology of the Physarum polycephalum vein network during its extension.
  • * To compare its network topology to other biological and artificial transportation systems.
  • * To investigate the distribution of vein segment properties and their evolution.

Main Methods:

  • * Morphological analysis of the developing Physarum polycephalum vein network.
  • * Topological characterization of the network graph.
  • * Statistical analysis of vein segment lengths, widths, and areas.

Main Results:

  • * The Physarum polycephalum vein network forms a regular graph with exclusively degree-3 nodes.
  • * This structure contrasts with typical small-world or scale-free networks.
  • * Vein segment lengths and areas follow exponential distributions, while widths are log-normally distributed.
  • * These distributions remain robust throughout network evolution, despite changes in exponents due to coarsening.

Conclusions:

  • * The Physarum vein network represents a distinct class of biological transport systems.
  • * Its complexity is determined by the statistical weighting of its components.
  • * The observed distributions are maintained during network development and coarsening.

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