Mechanisms of branch tip fusion in meshwork patterns

Meshwork pattern is a significant pattern for the development of biological tissues and organs. The formation of meshwork pattern is facilitated by branch tip fusion. However, the mechanism of branch tip fusion is still unclear. In this paper, based on a reaction-diffusion model, we found that the local high concentration substrate guided the fusion of branch tips and provided the quantitative ranges of environmental conditions for branch tip fusion. Then we explored the Turing wavelengths underlying branch tip fusions. We found that the width of local high concentration substrate region did not influence the Turing wavelength of branch tip fusion and the width less than two Turing wavelengths promoted the fusion of branches. We also found that the increasing Co (production rate of substrate) reduced the Turing wavelength and potential of branch tip fusion. We believe that the molecular mechanism and Turing mechanism of branch tip fusion in this paper will be beneficial to the in-depth understanding of network morphogenesis.