(A–D) Simulation results of the model with different ATML1 auto-induction strengths show different qualitative behaviors. Simulations with different feedback strengths and different ATML1 basal production rates that lead to similar percentages of giant cells in the tissue (7 to 9%) are shown. Histograms of ATML1 concentrations (left), ATML1 time traces for cells becoming giant cells (middle left), ROC analysis (middle right) and percentages of cells with the different ploidies. Boxplots are obtained from five simulations with different initial conditions (middle right and right panels). The stronger is the feedback, the higher is the CV for the ATML1 concentrations. No feedback or a weak feedback give rise to a unimodal distribution of ATML1 concentrations (A–C), while a stronger feedback can give rise to a bimodal distribution (D). For no feedback (A) or weaker feedback (B), small and fast fluctuations drive the singling out of cells for endoreduplication. Stronger feedback strengths make larger fluctuations appear, whose time-scales are larger (C–D). This makes the ATML1 peak levels at 2C equivalent to 4C levels. In these cases, the AUC values are also high at 2C, which does not correspond to the experimental data. Similar fractions of giant cells are produced by all four induction strengths (A–D). Color codes of the time traces are as in Figure 7—figure supplement 1. The red lines and shaded bands in the time traces represent the predicted ATML1 soft threshold ΘA* and its error, respectively (Materials and methods). Feedback auto-induction strengths and basal production rates for the different panels are (A) VA = 0, PA = 1.41, (B) VA = 1.25, PA = 1.14, (C) VA = 1.75, PA = 1.01 and (D) VA = 2.5, PA = 0.88, respectively. Left and right panels in (B) are also shown in Figure 7, and the AUCs panel in (B) is shown in Figure 7—figure supplement 3. Other parameter values are described in Table 1. (E–F) QPCR results testing feedback strength of ATML1 induction on endogenous ATML1 48 hr after application of 10 µM, 1 µM or 0.1 µM estradiol (inducing agent) compared to mock treated inflorescences. Endogenous ATML1 transcript levels increase approximately 1.5-fold within 48 hr after ATML1 is induced with 10 µM estradiol as compared to mock-treated plants. To put this fold change in context, we examined the 10 µM estradiol induction of other genes downstream of ATML1 including CER5 (2.3-fold), FDH (1.6-fold), PDF2 (1.5-fold) and PDF1 (1.2-fold). Note that these downstream genes are induced with very similar fold changes as the endogenous ATML1. CER5, FDH, and PDF1 do not encode transcription factors and therefore cannot act in a feedback loop. This suggests that the feedback of ATML1 on itself is not activating ATML1 further than other targets at the 48 hr time point. The transgene was induced about 700-fold by 10 µM estradiol (F). Induction with 0.1 µM or 1 µM estradiol produced intermediate levels of induction and activation of downstream genes, also consistent with a weak positive feedback loop. Wilcoxon 1-tailed tests were performed between the corresponding mock treated and estradiol treated plants. p-value ≤ 0.05 marked with *. Associated with Figure 7.