Supporting Information Analysis of Sprout Spatial Distribution and Simulation

In the simulation of Fig. 2d), the experimental size distribution of the microcarrier radius was collected (Fig. S2) as an estimate of pmf fR(r) and was resampled during simulation to generate the radii r. While the variation in the radius of the microcarrier r appeared too small to affect the number of sprouts ns, data was collected to ensure this independence (Fig. S3). The correlation between ns and r, nS and r , ns and ln(r) are respectively −0.067, −0.064, −0.072. These correlations are all insignificant, and in fact slightly negative, which further contradicts the notion that there may be more sprouts with greater surface area. Furthermore, regressions of ns on r,r, ln(r) also yield insignificant slopes. Thus, ns does not seem to depend on r in this assay, and the marginal probability mass function fNs(ns) can be used. Similarly, ns were generated by resampling the empirical distribution in Fig. 2a. Once ns was drawn, the location (θ, φ) of each sprout was drawn from fΘ(θ) = 1 2π and fΦ(φ) = 1 2 sinφ. The length of the sprout l was also resampled from the empirical data (Fig. S4). We chose to use the empirical distribution from the control experiment (The empirical distributions of ns and l in both control and +DAPT gave almost identical simulation results). A sprout was determined to be visible if it protruded from the edge of the circle in the 2D maximum intensity projection, namely if (l + r) sinφ > r. The distance between each visible pair of the i and j sprouts was then computed: di,j = r(min(|θi − θj |, 2π − |θi − θj |). Note that the distribution of di,j generated from this simulation is different from merely r · θ where r is distributed as the experimental distribution and θ distributed as U [0, π). This is because 1) the number of visible sprouts in a microcarrier