Fig. 2.

Steady-state network density and rearrangement timescales are set by two parameters. (A) Junction mobility and tubule spawning rate set the length and time scales ($\ell$, $\tau$ respectively). (B) Network length over time for nine separate simulations, each starting from an initially sparse honeycomb network enclosed in a circle of radius $15$ $\mathrm{\mu }$m. The steady-state network length is set by $\ell$ (color) and the time to reach steady state is set by $\tau$ (line style). Other parameters are $D={10}^{-5}\mathrm{\mu }{\text{m}}^2$/s and $v=1$ $\mathrm{\mu }$m/s. (C) Timescale to approach steady state, extracted via exponential fit of curves as in (B) is proportional to the intrinsic network timescale $\tau$. (D) The mean area of polygons in a liquid network is proportional to ${\ell }^2=b/k$. Mean polygon area in COS7 cells is indicated by the dotted blue line; the shaded region gives intercell SD ($N=7$ cells). Inset: illustration of polygon extraction, different colored regions correspond to individual polygons. (E) Measured spawning rates from 19 COS7 cells, with mean and intercell SD of $8.5\pm 0.8\times {10}^{-3}\mathrm{\mu }{\text{m}}^{-1}{\text{s}}^{-1}$. Scatter data for (C and D) is from simulations with mobility ranging between 0.001 to 0.1 $\mathrm{\mu }\text{m}/\text{s}$ and spawning rate ranging between 0.0005 to 0.05 $\mathrm{\mu }{\text{m}}^{-1}{\text{s}}^{-1}$.