Fig. 4: Self-organized structures reproduced by agent-based model simulation.

a Schematics of the simulation model, including actin filaments (blue) and two types of connectors: crosslinkers (yellow) and motors (red). See Supplementary Notes for details. b Steady-state solutions for different conditions. Each column refers to different numbers of cross-linkers: Low (L), moderate (M), and High (H) from left to right. Each of the four rows refers to no anisotropy and no motor (blue circle, “1”); with anisotropy and no motor (orange triangle, “2”); no anisotropy with motors (yellow square, “3”); and with anisotropy and motors (red diamond, “4”). See Supplementary Table 3 for detail information. In each condition, the snapshot (left), the filament density distribution (middle), and the binarized filament density distribution (right) are displayed. The actin pattern that meets the criterion of circumferential cable formation is marked by a red frame (4-M). c Characterization of the clusters. The median orientation and average major length are quantified using the binarized filament density distribution (“OrientationJ analysis” and “Cluster analysis“). Each data point corresponds to the simulation condition in (b). For comparison, the results of the experiments at stages 15 and 16 are also plotted (gray). d, e Spatial displacement of actin clusters in x and y directions, ∆x (µm) and ∆y (µm), respectively. The mean value of |∆y| divided by mean value of |∆x| is displayed in blue in (d), and the magnitude is statistically analyzed with two-sided Student’s t test in (e). P = 0.511 in 1-M (n = 1461), P = 0.0485 in 2-M (n = 1134), or P = 0.00714 in 4-M (n = 152). n indicates number of clusters’ motion appeared in a simulation. ^∗P < 0.05, ^∗∗P < 0.01. Boxplots represent median plus minima and maxima with lower and upper quantiles. f Formation of actin cables for the simulation condition (4-M) in (b). The actin pattern starting from a uniform distribution was characterized by the dominant direction and connectivity (“OrientationJ analysis”). The filament density distributions at t = 0, 4, 40 s are displayed at the bottom. Source data are provided as a Source Data file.