Figure 6.

Mathematical modeling of the effects of the BMP negative feedback loop on BMP1/Tolloid (Tld) activity. (A) Partial differential equation describing the temporal evolution of free Tld concentration. The terms accounting for the inhibition of Tld by BMP (reaction 10 in Supplemental Fig. 1) are boxed. The reactions involving Tld and their corresponding parameters are described in Supplemental Figure 2. (B) Schematic diagram of the negative feedback loop between Tld, BMP, and Chd, which regulates the D–V gradient of pSmad1 activity. (C,D) Effect of BMP negative feedback on the temporal evolution of free Tld concentration profile. D and V indicate the position of the dorsal and ventral sides. Each concentration profile is labeled from t0 (0 h) to t4 (2 h) to indicate their evolution over time. The arrows indicate the final level of free Tld on the ventral side without (C) or with (D) BMP4 feedback. Note that the model predicts that free (active) Tld is low in the dorsal midline due to the large amounts of Chd substrate secreted by the dorsal side (Supplemental Fig. 3).