Fig. 7: Numerical simulations and the analytical solution of the tug-of-war model reproduce the two-state cluster positioning.

Both numerical simulations and the analytical solution Eq. (2) of the tug-of-war model (Fig. 6) reproduce the results of perturbation experiments (Fig. 5). (Top) In numerical simulations, the time averaged DC-ratio \((1/{T}_{0})\mathop{\int}\nolimits_{0}^{{T}_{0}}[d(t)/R]{\mathrm{{d}}}t\) (T0 = 1800 s) for each droplet was determined to statistically evaluate percolation dynamics, displayed as purple dots. (Bottom) Thereafter, the edge probability was determined from the DC-ratio, where a DC-ratio > 0.8 and <0.2 was classified as the “edge” and the “center”, respectively. a F-actin length L was changed with the fixed crosslinker concentration (C0 = 1 μM). Purple circles, blue triangles, and orange squares represent numerical simulations with L = 4 μm, L = 8 μm, and L = 12 μm, respectively. Solid curves are the corresponding analytical solutions. b Crosslinker concentration C0 was changed with the fixed F-actin length (L = 8 μm). Purple circles, blue triangles, and orange squares represent numerical simulations with C0 = 0.1 μM, C0 = 1 μM, and C0 = 10 μM, respectively. Solid curves are the corresponding analytical solutions. We defined different DC-ratio thresholds for the edge region from the experiments, because numerical simulations were performed for clusters without their finite volume, in which the centroid of the clusters is possible to reach the droplet boundary. For details, see Supplementary Note 4.