Multi-scale Simulation Of Early Ureter Branching During Kidney Morphogenesis

Morphogenesis is a biological process that allows tissues or organs to develop their shapes by controlling the spatial distribution of cells during embryonic development.The tree-like branch is a very common structure in nature,which not only constitutes the shape of a variety of plants,but also constitutes the basic structure of many organs in animals.However,the principle of branch morphogenesis is still unclear.In particular,the tips of the ureter during kidney morphogenesis all located on the outer surface of kidney.Inside,there is no branch intersecting with each other.How is it generated?This article focuses on the morphogenesis of kidney,and its main body is organized and presented as following:First,the ligand-receptor-based Turing model shows that all nearby tips and ducts will affect the concentration of the ligand-receptor complex on the surface of any growing branch of ureter.This mechanism causes repulsion between the branches,and the elongation direction and the bifurcation plane will deflect in the direction of the least repulsion.In addition,the different branch structures of ureter and lung trachea can be regard as the result of different positions where the ligands are produced.For growth or bifurcation,it is determined by the geometric relationship of the surrounding branches.Based on this conclusion,we have created a coarse-grained model and defined "simulation by repulsive effect"(RE).For each step in the growth,we calculate the vector sum of the repulsion of the surrounding branches,which determined the deflection direction of the branch and the plane where bifurcation angle lies.We also compare it with another algorithm "simulation by random walk"(RW).It can be seen from the experimental comparison results that only RE simulation can avoid the early branch crossing,so that most of the tips are distributed on the surface of the kidney.In addition,some geometric parameters in the RE simulation also match the experimental data,so it can reflect the growth of the real kidney.On the contrary,the randomness of the RW simulation resulted in a large number of termination tips in the early stage,which is quite different from the experimental result.Therefore,the branch structure of ureter grows through a certain rule,rather than randomness as the dominant factor.In order to verify the reliability of the simulation,we performed a parameter sensitivity analysis on the attenuation coefficient and the scale factor.It was found that the size of the parameter value determines the degree of matching between the simulation result and the actual kidney,and there is a suitable interval to match the real kidney.Finally,it is found that the projection rejection vector in each generation will decrease gradually during the growth process,which can be used as a calculation method for bifurcation in discrete simulation.If we assumed that the vector will branch once it is less than a certain threshold,and perform the discrete simulation again,the resulting parameters are basically the same as before.