Figure S4.

In support of Fig. 4: Temporal analysis of de novo biogenesis. (A) Scatter plot of observed inter-event time between the first four de novo biogenesis events in the GFP–Plk4 reporter fly line. Note that the fly line overexpresses two copies of Plk4, one of which is tagged with GFP. This higher expression level is a possible explanation for the slightly shorter time until the first de novo event. Horizontal lines and error bars represent median and interquartile range, respectively (n = 9). (B) Scatter plot of observed inter-event time between the first four de novo biogenesis events in the Asl–mCherry reporter fly line overexpressing Plk4. Horizontal lines and error bars represent median and interquartile range, respectively (n = 10). (C) Estimation of the mean centriole biogenesis times at the highest Plk4 concentration (1, in blue) and at the lowest Plk4 overexpression (0.16, in orange) by maximum likelihood estimation fitting of a simple exponential model to data shown in Fig. 4 C. (D) Estimation of the waiting time until the first de novo event and inter-event time between the first and subsequent de novo events, at high (1, in blue) and the lowest (0.16, in orange) concentration of Plk4, after fitting data shown in Fig. 4 C. (E) Model of Plk4 autoactivation and dephosphorylation based on data from (Lopes et al., 2015). Plk4 trans-autophosphorylates to become fully active, transitioning from an enzyme with basal activity, B form, to an activated form phosphorylated on its T-loop residue, A* form. Highly phosphorylated Plk4, A** form, is also active but is targeted for degradation (Cunha-Ferreira et al., 2013; Guderian et al., 2010; Holland et al., 2012; Klebba et al., 2013). Dark arrows indicate the forward phosphorylation reaction flux, while red arrows indicate the reverse dephosphorylation flux catalyzed by a putative counteracting phosphatase. The leftmost dark arrow marks the synthesized Plk4 that enters the system, while the dashed lines refer to Plk4 degradation. Green arrows depict the Plk4 forms that catalyze the forward flux. (F) A nonlinear balance between phosphorylation and dephosphorylation activities generates a Plk4 critical threshold, as a function of its concentration. Therefore, total concentration (active and inactive) of Plk4 in cells likely affects the timing at which a critical concentration threshold is overcome and triggers centriole assembly (Lopes et al., 2015). (G) Fitting of Plk4 autoactivation and dephosphorylation model to data measured in explants at different Plk4 concentrations. The gray gradient represents different concentrations of Plk4. The different concentrations were prepared experimentally by mixing the cytoplasm from high overexpression eggs (taken as the unit 1, black) with cytoplasm from WT eggs, in different proportions such that the dilutions are 0.5, 0.33, and 0.16 relative concentrations. The dots are the relative frequency of explants containing at least one de novo formed centriole for the different concentrations of Plk4: 1 (n = 56), 0.5 (n = 62), 0.33 (n = 39), and 0.16 (n = 25). The lines are the solution of the model of Plk4 trans-autophosphorylation. The continuous lines are the solution of the ordinary differential equation model, and the staircase lines are the results of stochastic simulations under the same parameter settings. The Plk4 activity in the higher concentration (denoted K) was adjusted, whereas the activities in the dilutions were set in relative terms (0.16 K, 0.33 K, and 0.5K). The modeling and simulations, as well as the remaining parameters and values, are described in the Materials and methods (Statistics and mathematical modeling). Notice that as Plk4 concentration decreases, so does the number of explants where centriole biogenesis occurs within 40 min of time-lapse recording.