Fig. 4.

The Twist1-Prrx1-TNC PFL functions as an internal bistable switch in regulating the proliferative signal of fibroblasts. The importance and functional implications of the Twist1-Prrx1-TNC PFL were demonstrated through mathematical simulations based on experimental data. a Schematic diagram of the Twist1-Prrx1-TNC PFL and the mathematical description of the loop (see Supplementary text for detailed explanations). b Ultrasensitive responses of the PFL to the varying doxycycline stimuli compared with cases in which feedback regulation was absent (V_TNC→Tw = 0). c Hysteretic responses of the three genes to the doxycycline stimulus. d Various profiles for the hysteretic TNC response to the doxycycline stimulation along with the increase of the feedback strength (V_TNC→Tw). e Irreversible hysteretic responses of the three genes to the doxycycline stimulus when the feedback strength is large (V_TNC→Tw = 80). f Phase diagram illustrating the irreversibility of TNC with respect to the feedback strength (V_TNC→Tw) and stability of Twist1 $\left(K_{\mathrm{Tw}}^{+}∕K_{\mathrm{Tw}}^{-}\right)$. ΔTNC denotes TNC^fin − TNCⁱⁿⁱ when doxycycline = 0 (left). Reversibility was characterized by TNC = 0 (irreversible, otherwise). The irreversibility of TNC can be categorized into two phases (center). Representative hysteretic curves for the corresponding phases are shown in the right panel