Figure 6.
Branching and Annihilating Random Walks Can Reproduce Quantitatively the 3D Kidney Topology
(A) Schematic of kidney morphogenesis as a stochastic branching process where active tips (red) either elongate, branch, or stop contributing to branching via nephron differentiation (yellow).
(B) Reconstructions of murine kidney at E13, E15, E16, and E18 (left to right) with generation number of segments color coded in blue.
(C) Typical output of numerical simulations of BARW model at corresponding time points.
(D) Experimental versus theoretical tip termination probability as a function of generation for mammary gland (purple) and kidney (green), using the radius of termination R′a = 0.25 as the only fitting parameter.
(E) The model predicts a self-organized zone of active tips growing at the periphery of the kidney, followed spatially by a domain of tip termination, reminiscent of the nephrogenic zone observed in vivo.
(F) Tree representation of a E17 kidney branching topology (top, green) and the output of the theory at the corresponding time point (bottom, black). Error bars represent mean and SEM.