A Mathematical Model for Adaptive Transport Network in Path Finding by True Slime Mold

J Theor Biol. 2007 Feb 21;244(4):553-64. doi: 10.1016/j.jtbi.2006.07.015. Epub 2006 Jul 24.


We describe here a mathematical model of the adaptive dynamics of a transport network of the true slime mold Physarum polycephalum, an amoeboid organism that exhibits path-finding behavior in a maze. This organism possesses a network of tubular elements, by means of which nutrients and signals circulate through the plasmodium. When the organism is put in a maze, the network changes its shape to connect two exits by the shortest path. This process of path-finding is attributed to an underlying physiological mechanism: a tube thickens as the flux through it increases. The experimental evidence for this is, however, only qualitative. We constructed a mathematical model of the general form of the tube dynamics. Our model contains a key parameter corresponding to the extent of the feedback regulation between the thickness of a tube and the flux through it. We demonstrate the dependence of the behavior of the model on this parameter.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adaptation, Physiological / physiology
  • Animals
  • Behavior, Animal / physiology
  • Biological Transport / physiology
  • Feedback / physiology
  • Locomotion / physiology
  • Mathematics
  • Models, Biological
  • Physarum polycephalum / physiology*
  • Signal Transduction / physiology