Mathematical model for rhythmic protoplasmic movement in the true slime mold

Ryo Kobayashi, Atsushi Tero, Toshiyuki Nakagaki

Research output: Contribution to journalArticlepeer-review

86 Citations (Scopus)


The plasmodium of the true slime mold Physarum polycephalum is a large amoeboid organism that displays "smart" behavior such as chemotaxis and the ability to solve mazes and geometrical puzzles. These amoeboid behaviors are based on the dynamics of the viscoelastic protoplasm and its biochemical rhythms. By incorporating both these aspects, we constructed a mathematical model for the dynamics of the organism as a first step towards understanding the relation between protoplasmic movement and its unusual abilities. We tested the validity of the model by comparing it with physiological observation. Our model reproduces fundamental characteristics of the spatio-temporal pattern of the rhythmic movement: (1) the antiphase oscillation between frontal tip and rear when the front is freely extending; (2) the asynchronous oscillation pattern when the front is not freely extending; and (3) the formation of protoplasmic mounds over a longer time scale. Both our model and physiological observation suggest that cell stiffness plays a primary role in plasmodial behaviors, in contrast to the conventional theory of coupled oscillator systems.

Original languageEnglish
Pages (from-to)273-286
Number of pages14
JournalJournal of Mathematical Biology
Issue number2
Publication statusPublished - Aug 1 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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