### 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.

Original language | English |
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Pages (from-to) | 553-564 |

Number of pages | 12 |

Journal | Journal of Theoretical Biology |

Volume | 244 |

Issue number | 4 |

DOIs | |

Publication status | Published - Feb 21 2007 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Medicine(all)
- Modelling and Simulation
- Immunology and Microbiology(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

*Journal of Theoretical Biology*,

*244*(4), 553-564. https://doi.org/10.1016/j.jtbi.2006.07.015

**A mathematical model for adaptive transport network in path finding by true slime mold.** / Tero, Atsushi; Kobayashi, Ryo; Nakagaki, Toshiyuki.

Research output: Contribution to journal › Article

*Journal of Theoretical Biology*, vol. 244, no. 4, pp. 553-564. https://doi.org/10.1016/j.jtbi.2006.07.015

}

TY - JOUR

T1 - A mathematical model for adaptive transport network in path finding by true slime mold

AU - Tero, Atsushi

AU - Kobayashi, Ryo

AU - Nakagaki, Toshiyuki

PY - 2007/2/21

Y1 - 2007/2/21

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33846443614&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846443614&partnerID=8YFLogxK

U2 - 10.1016/j.jtbi.2006.07.015

DO - 10.1016/j.jtbi.2006.07.015

M3 - Article

C2 - 17069858

AN - SCOPUS:33846443614

VL - 244

SP - 553

EP - 564

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

IS - 4

ER -