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Can VEGFC Form Turing Patterns in the Zebrafish Embryo?

Wertheim, Kenneth Y.; Roose, Tiina


Tiina Roose


This paper is concerned with a late stage of lymphangiogenesis in the trunk of the zebrafish embryo. At 48 hours post-fertilisation (HPF), a pool of parachordal lymphangioblasts (PLs) lies in the horizontal myoseptum. Between 48 and 168 HPF, the PLs spread from the horizontal myoseptum to form the thoracic duct, dorsal longitudinal lymphatic vessel, and parachordal lymphatic vessel. This paper deals with the potential of vascular endothelial growth factor C (VEGFC) to guide the differentiation of PLs into the mature lymphatic endothelial cells that form the vessels. We built a mathematical model to describe the biochemical interactions between VEGFC, collagen I, and matrix metalloproteinase 2 (MMP2). We also carried out a linear stability analysis of the model and computer simulations of VEGFC patterning. The results suggest that VEGFC can form Turing patterns due to its relations with MMP2 and collagen I, but the zebrafish embryo needs a separate control mechanism to create the right physiological conditions. Furthermore, this control mechanism must ensure that the VEGFC patterns are useful for lymphangiogenesis: stationary, steep gradients, and reasonably fast forming. Generally, the combination of a patterning species, a matrix protein, and a remodelling species is a new patterning mechanism.


Wertheim, K. Y., & Roose, T. (2019). Can VEGFC Form Turing Patterns in the Zebrafish Embryo?. Bulletin of Mathematical Biology, 81(4), 1201-1237.

Journal Article Type Article
Acceptance Date Dec 11, 2018
Online Publication Date Jan 3, 2019
Publication Date Apr 15, 2019
Deposit Date Jan 23, 2023
Publicly Available Date Feb 1, 2023
Journal Bulletin of Mathematical Biology
Print ISSN 0092-8240
Electronic ISSN 1522-9602
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 81
Issue 4
Pages 1201-1237
Keywords Reaction–diffusion models; Turing patterns; Lymphangiogenesis; Zebrafish; VEGFC; MMP2; Collagen I
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© The Author(s) 2019.<br /> Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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