Fig. 5
A positive feedback regulates the interbud distance. a A ligand–receptor-based network motif (T1) and that with an additional positive feedback (in magenta) on ligand production; a detailed model description is provided in Supplementary Table 1: T5. b, c Branching patterns simulated on a growing domain with the standard ligand–receptor model, T1 (b), and c with the model T5 that harbours an additional positive feedback. The parameter values and model details are summarised in Supplementary Table 2. d, e Simulated concentration profile of ligand–receptors (rainbow colour code) and Gdnf expression (grey scale) for d the standard ligand–receptor-based model and e for the model T5 with an additional positive feedback. f The fraction of sampled parameter sets, Λ, which lead to the elongation mode of branching for the models T1 (black) and T5 (magenta). g Minimal deviation, Δ (Eq. (4)), between the growth field, E, extracted from the experimental data and the predicted spatial distribution of signalling strength C computed with either the complete ligand–receptor-based model (shown in Fig. 3a: T1) (black dots) or the model with an additional positive feedback (shown in a: T5) (magenta symbols). h The predicted optimal rate of WNT11 production (parameter b1, Supplementary Table 1: T5) is low in the first half, and high in the second half of the culture experiment. The red dashed line depicts the mean values. i The average minimal interbud distances in the time-lapse data of cultured ureteric buds are high in the first half, and low in the second half of the culture experiment. The red dashed line depicts the mean values
