title: A mathematical model for adaptive transport network in path finding by true slime mold.
abstract: 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.
authors.affiliation: Department of Mathematical and Life Sciences, Hiroshima University, Higashi Hiroshima 739-8526, Japan. tero@topology.coe.hokudai.ac.jp
authors.forename: Atsushi
authors.initials: A
authors.lastname: Tero
authors.forename: Ryo
authors.initials: R
authors.lastname: Kobayashi
authors.forename: Toshiyuki
authors.initials: T
authors.lastname: Nakagaki
mesh_terms: D000222:Adaptation, Physiological / Q000502:physiology; D000818:Animals; D001522:Behavior, Animal / Q000502:physiology; D001692:Biological Transport / Q000502:physiology; D005246:Feedback / Q000502:physiology; D008124:Locomotion / Q000502:physiology; D008433:Mathematics; D008954:Models, Biological; D016839:Physarum polycephalum / Q000502:physiology*; D015398:Signal Transduction / Q000502:physiology