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Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold

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Title: Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold
Authors: Yamada, H. Browse this author
Nakagaki, T. Browse this author
Baker, R.E. Browse this author
Maini, P.K. Browse this author
Keywords: Dispersion relation
Reaction-diffusion-advection equation
Phase equation
Amoeboid movement
Issue Date: Jun-2007
Publisher: Springer Berlin / Heidelberg
Journal Title: Journal of Mathematical Biology
Volume: 54
Issue: 6
Start Page: 745
End Page: 760
Publisher DOI: 10.1007/s00285-006-0067-1
PMID: 17235581
Abstract: In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.
Rights: The original publication is available at
Type: article (author version)
Appears in Collections:電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 中垣 俊之

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