Abstract
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.
Highlights
We have previously proposed a mathematical model about lymphangiogenesis in the zebrafish embryo’s trunk (Wertheim and Roose 2017); it describes the biochemistryK
vascular endothelial growth factor C (VEGFC) and matrix metalloproteinase 2 (MMP2) can diffuse in the interstitial space, but their diffusion rates depend on the abundance of collagen I (Lutter and Makinen 2014)
VEGFC stimulates the production of MMP2, which degrades collagen I to suppress the positive feedback loop
Summary
The concentration dynamics of the vascular endothelial growth factor C (VEGFC), matrix metalloproteinase 2 (MMP2), tissue inhibitor of metalloproteinases 2 (TIMP2), and collagen I are described These dynamics are related to the lymphangiogenic events between 36 and 48 hours post-fertilisation (HPF).
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