Can VEGFC Form Turing Patterns in the Zebrafish Embryo?

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.

Experimental visually-guided investigation of sub-structures in three-dimensional Turing-like patterns

“…A particular, well-studied example in this context is the zebrafish, see Figure 1. Studies have connected genes (Asai et al (1999)), chemical properties (Wertheim and Roose (2019)), and cell-network interactions (Nakamasu et al (2009)) to the formation of Turing patterns within the zebrafish. Recently, researchers revealed how mechanical stresses can lead to tissue anisotropies and thus morphogen gradients in the formation of Turing patterns, causing the characteristic stripes of a common zebrafish, see Hiscock and Megason (2015).…”

A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions

“…The presence of these layers in the neighborhood of the boundary of the domain engenders steep gradients in the solution $$$ u $$$ whenever the perturbation parameter $$$ \varepsilon \to 0 $$$. These type of problems form an essential basis for several physical, biological and chemical processes including pattern formation [2], morphogenesis [3], animal coats and skin pigmentation [4], ecological invasions [5], spread of epidemics [6], tumor growth [7], blood clotting [8], wound healing [9], regulation of lymphangiogenesis [10], gas liquid interactions in chemical engineering [11], traveling wave oscillations [12], nerve propagations [13], to analyze the spreading of biological populations with the co‐existence problem of competing and co‐operating species, combustion theory [14].…”

In Situ Wide-Field Visualization of Palladium Hydrogenation

“…Although our study was focused on real time visualization of hydrogenation in metal membranes using local wrinkles, our methods of retrieving stress states using wide-field optical scatterometric means in real time can be applied to a more general class of reaction-diffusion systems 34 , where the induced surface instability generates various surface patterns, as previously reported in chemical traveling waves 35 , electrodeposition 36,37 , and biological systems 38 . Because the wrinkles and folds can be easily imposed on these material systems over large areas at low cost, we expect such simple and elegant geometric effect on enhanced reflection can provide deep physical insight of monitoring strain evolution associated with the host material (such as thin solid electrolyte interphases in the lithium battery) during diffusion-reaction at real time.…”