Date of this Version
Bulletin of Mathematical Biology DOI: 10.1007/s11538-018-00560-2 Page 1-59
This paper is concerned with a late stage of lymphangiogenesis in the trunk of the zebrafish embryo. At 48 hours pos-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 throacic duct, dorsal longitudinal lymphatic vessel, and parachordal lymphatic vessel. This paper deals wit hthe 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. Futhermore, this control mechanism must ensure that the VEGFC patterns are useful for lymphangiogenesis: stationary, steep gradients, and resonably fast forming. Generally, the combination of a patterning species, a matrix protein, and a remodelly species is a new patterning mechanism.