Pattern production through a chiral chasing mechanism

Woolley, Thomas E. ORCID: https://orcid.org/0000-0001-6225-5365 2017. Pattern production through a chiral chasing mechanism. Physical Review E 96 , 032401. 10.1103/PhysRevE.96.032401

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Abstract

Recent experiments on zebrafish pigmentation suggests that their typical black and white striped skin pattern is made up of a number of interacting chromatophore families. Specifically, two of these cell families have been shown to interact through a nonlocal chasing mechanism, which has previously been modeled using integro-differential equations. We extend this framework to include the experimentally observed fact that the cells often exhibit chiral movement, in that the cells chase, and run away, at angles different to the line connecting their centers. This framework is simplified through the use of multiple small limits leading to a coupled set of partial differential equations which are amenable to Fourier analysis. This analysis results in the production of dispersion relations and necessary conditions for a patterning instability to occur. Beyond the theoretical development and the production of new pattern planiforms we are able to corroborate the experimental hypothesis that the global pigmentation patterns can be dependent on the chirality of the chromatophores.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	American Physical Society
ISSN:	1539-3755
Date of First Compliant Deposit:	4 September 2017
Date of Acceptance:	10 August 2017
Last Modified:	17 Nov 2024 06:30
URI:	https://orca.cardiff.ac.uk/id/eprint/104230

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