Directionality of stripes formed by anisotropic reaction-diffusion models

Hiroto Shoji, Yoh Iwasa, Atushi Mochizuki, Shigeru Kondo

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

Turing mechanism explains the formation of striped patterns in a uniform field in which two substances interact locally and diffuse randomly. In a twin paper, to explain the directionality of stripes on fish skin in closely related species, we studied the effect of anisotropic diffusion of the two substances on the direction of stripes, in the cases in which both substances have high diffusivity in the same direction. In this paper, we study the direction of stripes in more general situations in which the diffusive direction may differ between the two substances. We derive a formula for the direction of stripes, based on a heuristic argument of unstable modes of deviation from the uniform steady state. We confirm the accuracy of the formula by computer simulations. When the diffusive direction is different between two substances, the directions of stripes in the spatial pattern change smoothly with the magnitude of anisotropy of two substances. When the diffusive direction of the two substances is the same, the stripes are formed either parallel or perpendicular to the common diffusive direction, depending on the relative magnitude of the anisotropy. The transition between these two phases occurs sharply.

Original languageEnglish
Pages (from-to)549-561
Number of pages13
JournalJournal of Theoretical Biology
Volume214
Issue number4
DOIs
Publication statusPublished - Jan 1 2002

Fingerprint

Reaction-diffusion Model
computer simulation
diffusivity
Anisotropy
Fish
Skin
Computer simulation
fish skin
Direction compound
Anisotropic Diffusion
Spatial Pattern
Turing
Diffusivity
Computer Simulation
Perpendicular
Fishes
Deviation
Unstable
Heuristics

All Science Journal Classification (ASJC) codes

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

Cite this

Directionality of stripes formed by anisotropic reaction-diffusion models. / Shoji, Hiroto; Iwasa, Yoh; Mochizuki, Atushi; Kondo, Shigeru.

In: Journal of Theoretical Biology, Vol. 214, No. 4, 01.01.2002, p. 549-561.

Research output: Contribution to journalArticle

Shoji, Hiroto ; Iwasa, Yoh ; Mochizuki, Atushi ; Kondo, Shigeru. / Directionality of stripes formed by anisotropic reaction-diffusion models. In: Journal of Theoretical Biology. 2002 ; Vol. 214, No. 4. pp. 549-561.
@article{600f89afecea4732935387c0a1bf097f,
title = "Directionality of stripes formed by anisotropic reaction-diffusion models",
abstract = "Turing mechanism explains the formation of striped patterns in a uniform field in which two substances interact locally and diffuse randomly. In a twin paper, to explain the directionality of stripes on fish skin in closely related species, we studied the effect of anisotropic diffusion of the two substances on the direction of stripes, in the cases in which both substances have high diffusivity in the same direction. In this paper, we study the direction of stripes in more general situations in which the diffusive direction may differ between the two substances. We derive a formula for the direction of stripes, based on a heuristic argument of unstable modes of deviation from the uniform steady state. We confirm the accuracy of the formula by computer simulations. When the diffusive direction is different between two substances, the directions of stripes in the spatial pattern change smoothly with the magnitude of anisotropy of two substances. When the diffusive direction of the two substances is the same, the stripes are formed either parallel or perpendicular to the common diffusive direction, depending on the relative magnitude of the anisotropy. The transition between these two phases occurs sharply.",
author = "Hiroto Shoji and Yoh Iwasa and Atushi Mochizuki and Shigeru Kondo",
year = "2002",
month = "1",
day = "1",
doi = "10.1006/jtbi.2001.2480",
language = "English",
volume = "214",
pages = "549--561",
journal = "Journal of Theoretical Biology",
issn = "0022-5193",
publisher = "Academic Press Inc.",
number = "4",

}

TY - JOUR

T1 - Directionality of stripes formed by anisotropic reaction-diffusion models

AU - Shoji, Hiroto

AU - Iwasa, Yoh

AU - Mochizuki, Atushi

AU - Kondo, Shigeru

PY - 2002/1/1

Y1 - 2002/1/1

N2 - Turing mechanism explains the formation of striped patterns in a uniform field in which two substances interact locally and diffuse randomly. In a twin paper, to explain the directionality of stripes on fish skin in closely related species, we studied the effect of anisotropic diffusion of the two substances on the direction of stripes, in the cases in which both substances have high diffusivity in the same direction. In this paper, we study the direction of stripes in more general situations in which the diffusive direction may differ between the two substances. We derive a formula for the direction of stripes, based on a heuristic argument of unstable modes of deviation from the uniform steady state. We confirm the accuracy of the formula by computer simulations. When the diffusive direction is different between two substances, the directions of stripes in the spatial pattern change smoothly with the magnitude of anisotropy of two substances. When the diffusive direction of the two substances is the same, the stripes are formed either parallel or perpendicular to the common diffusive direction, depending on the relative magnitude of the anisotropy. The transition between these two phases occurs sharply.

AB - Turing mechanism explains the formation of striped patterns in a uniform field in which two substances interact locally and diffuse randomly. In a twin paper, to explain the directionality of stripes on fish skin in closely related species, we studied the effect of anisotropic diffusion of the two substances on the direction of stripes, in the cases in which both substances have high diffusivity in the same direction. In this paper, we study the direction of stripes in more general situations in which the diffusive direction may differ between the two substances. We derive a formula for the direction of stripes, based on a heuristic argument of unstable modes of deviation from the uniform steady state. We confirm the accuracy of the formula by computer simulations. When the diffusive direction is different between two substances, the directions of stripes in the spatial pattern change smoothly with the magnitude of anisotropy of two substances. When the diffusive direction of the two substances is the same, the stripes are formed either parallel or perpendicular to the common diffusive direction, depending on the relative magnitude of the anisotropy. The transition between these two phases occurs sharply.

UR - http://www.scopus.com/inward/record.url?scp=0036349926&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036349926&partnerID=8YFLogxK

U2 - 10.1006/jtbi.2001.2480

DO - 10.1006/jtbi.2001.2480

M3 - Article

C2 - 11851367

AN - SCOPUS:0036349926

VL - 214

SP - 549

EP - 561

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

IS - 4

ER -