dorsal/arxiv
View SchemaPattern formation of reaction-diffusion system having self-determined flow in the amoeboid organism of Physarum plasmodium
| Authors | H. Yamada, T. Nakagaki, M. Ito |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9805004 |
| URL | https://arxiv.org/abs/patt-sol/9805004 |
| DOI | 10.1103/PhysRevE.59.1009 |
Abstract
The amoeboid organism, the plasmodium of Physarum polycephalum, behaves on the basis of spatio-temporal pattern formation by local contraction-oscillators. This biological system can be regarded as a reaction-diffusion system which has spatial interaction by active flow of protoplasmic sol in the cell. Paying attention to the physiological evidence that the flow is determined by contraction pattern in the plasmodium, a reaction-diffusion system having self-determined flow arises. Such a coupling of reaction-diffusion-advection is a characteristic of the biological system, and is expected to relate with control mechanism of amoeboid behaviours. Hence, we have studied effects of the self-determined flow on pattern formation of simple reaction-diffusion systems. By weakly nonlinear analysis near a trivial solution, the envelope dynamics follows the complex Ginzburg-Landau type equation just after bifurcation occurs at finite wave number. The flow term affects the nonlinear term of the equation through the critical wave number squared. Contrary to this, wave number isn't explicitly effective with lack of flow or constant flow. Thus, spatial size of pattern is especially important for regulating pattern formation in the plasmodium. On the other hand, the flow term is negligible in the vicinity of bifurcation at infinitely small wave number, and therefore the pattern formation by simple reaction-diffusion will also hold. A physiological role of pattern formation as above is discussed.
{
"annotation_id": "7e638ca0-a80d-4dad-9155-1b393bc20611",
"date_created": "2026-03-02T18:00:29.403000Z",
"date_modified": "2026-03-02T18:00:29.403000Z",
"file_hash": "2ba6321bc95718e4dae701de98c77c4fb025d13327f90171369a6cd609532463",
"private": false,
"record": {
"abstract": "The amoeboid organism, the plasmodium of Physarum polycephalum, behaves on\nthe basis of spatio-temporal pattern formation by local\ncontraction-oscillators. This biological system can be regarded as a\nreaction-diffusion system which has spatial interaction by active flow of\nprotoplasmic sol in the cell. Paying attention to the physiological evidence\nthat the flow is determined by contraction pattern in the plasmodium, a\nreaction-diffusion system having self-determined flow arises. Such a coupling\nof reaction-diffusion-advection is a characteristic of the biological system,\nand is expected to relate with control mechanism of amoeboid behaviours. Hence,\nwe have studied effects of the self-determined flow on pattern formation of\nsimple reaction-diffusion systems. By weakly nonlinear analysis near a trivial\nsolution, the envelope dynamics follows the complex Ginzburg-Landau type\nequation just after bifurcation occurs at finite wave number. The flow term\naffects the nonlinear term of the equation through the critical wave number\nsquared. Contrary to this, wave number isn\u0027t explicitly effective with lack of\nflow or constant flow. Thus, spatial size of pattern is especially important\nfor regulating pattern formation in the plasmodium. On the other hand, the flow\nterm is negligible in the vicinity of bifurcation at infinitely small wave\nnumber, and therefore the pattern formation by simple reaction-diffusion will\nalso hold. A physiological role of pattern formation as above is discussed.",
"arxiv_id": "patt-sol/9805004",
"authors": [
"H. Yamada",
"T. Nakagaki",
"M. Ito"
],
"categories": [
"patt-sol",
"nlin.PS",
"q-bio"
],
"doi": "10.1103/PhysRevE.59.1009",
"title": "Pattern formation of reaction-diffusion system having self-determined flow in the amoeboid organism of Physarum plasmodium",
"url": "https://arxiv.org/abs/patt-sol/9805004"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "c9f1a956-b801-4e99-a480-010e25c71a96",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}