Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns

Abstract The meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation. In this paper, we found that the meshwork pattern is formed by four kinds of stalk behaviours: stalk extens...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Shan Guo, Ming-zhu Sun, Xin Zhao
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/cd849d5c225c45e8aa98ce80826a1c78
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:cd849d5c225c45e8aa98ce80826a1c78
record_format	dspace
spelling	oai:doaj.org-article:cd849d5c225c45e8aa98ce80826a1c782021-12-02T13:20:04ZWavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns10.1038/s41598-021-84313-72045-2322https://doaj.org/article/cd849d5c225c45e8aa98ce80826a1c782021-03-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-84313-7https://doaj.org/toc/2045-2322Abstract The meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation. In this paper, we found that the meshwork pattern is formed by four kinds of stalk behaviours: stalk extension, tip bifurcation, side branching and tip fusion. The Turing-type pattern underlying the meshwork pattern is a Turing spot pattern, which indicates that the Turing instability of the spot pattern promotes activator peak formation and then guides the formation of meshwork patterns. Then, we found that the Turing wavelength decreased in turn from tip bifurcation to side branching to tip fusion via statistical evaluation. Through the functional relationship between the Turing wavelength and model parameters ( $$\upvarepsilon ,{ \rho }_{A}$$ ε , ρ A and $${\rho }_{H}$$ ρ H ), we found that parameters $$\upvarepsilon $$ ε and $${\rho }_{H}$$ ρ H had monotonic effects on the Turing wavelength and that parameter $${\rho }_{A}$$ ρ A had nonmonotonic effects. Furthermore, we performed simulations of local meshwork pattern formation under variable model parameter values. The simulation results verified the corresponding relationship between the Turing wavelength and stalk behaviours and the functional relationship between the Turing wavelength and model parameters. The simulation results showed that the Turing wavelength regulated the meshwork pattern and that the small Turing wavelength facilitated dense meshwork pattern formation. Our work provides novel insight into and understanding of the formation of meshwork patterns. We believe that studies associated with network morphogenesis can benefit from our work.Shan GuoMing-zhu SunXin ZhaoNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-14 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Shan Guo Ming-zhu Sun Xin Zhao Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns
description	Abstract The meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation. In this paper, we found that the meshwork pattern is formed by four kinds of stalk behaviours: stalk extension, tip bifurcation, side branching and tip fusion. The Turing-type pattern underlying the meshwork pattern is a Turing spot pattern, which indicates that the Turing instability of the spot pattern promotes activator peak formation and then guides the formation of meshwork patterns. Then, we found that the Turing wavelength decreased in turn from tip bifurcation to side branching to tip fusion via statistical evaluation. Through the functional relationship between the Turing wavelength and model parameters ( $$\upvarepsilon ,{ \rho }_{A}$$ ε , ρ A and $${\rho }_{H}$$ ρ H ), we found that parameters $$\upvarepsilon $$ ε and $${\rho }_{H}$$ ρ H had monotonic effects on the Turing wavelength and that parameter $${\rho }_{A}$$ ρ A had nonmonotonic effects. Furthermore, we performed simulations of local meshwork pattern formation under variable model parameter values. The simulation results verified the corresponding relationship between the Turing wavelength and stalk behaviours and the functional relationship between the Turing wavelength and model parameters. The simulation results showed that the Turing wavelength regulated the meshwork pattern and that the small Turing wavelength facilitated dense meshwork pattern formation. Our work provides novel insight into and understanding of the formation of meshwork patterns. We believe that studies associated with network morphogenesis can benefit from our work.
format	article
author	Shan Guo Ming-zhu Sun Xin Zhao
author_facet	Shan Guo Ming-zhu Sun Xin Zhao
author_sort	Shan Guo
title	Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns
title_short	Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns
title_full	Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns
title_fullStr	Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns
title_full_unstemmed	Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns
title_sort	wavelength of a turing-type mechanism regulates the morphogenesis of meshwork patterns
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/cd849d5c225c45e8aa98ce80826a1c78
work_keys_str_mv	AT shanguo wavelengthofaturingtypemechanismregulatesthemorphogenesisofmeshworkpatterns AT mingzhusun wavelengthofaturingtypemechanismregulatesthemorphogenesisofmeshworkpatterns AT xinzhao wavelengthofaturingtypemechanismregulatesthemorphogenesisofmeshworkpatterns
_version_	1718393239113826304

Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns

Ejemplares similares