3D Simulations of tension generation in the cortex

We generated 3D simulations of a cortical network with three components: actin filaments, myosin minifilaments, and crosslinkers (Fig. 4a, Supplementary Fig. 5a). Actin filaments and myosin minifilaments are modelled as rigid rods with finite lengths l_a and l_m, respectively. Myosin minifilament heads interact with actin filaments through a spring-like interaction. Similarly, crosslinkers that attach two actin filaments are treated as short springs.

The simulation is initialized as N_f actin filaments are placed within a box of square surface (side width W) and seeding thickness h₀ (Fig. 4b, Supplementary Fig. 5b). Crosslinkers are introduced in the system with an actin binding probability p_x. Finally, myosin minifilaments initially bind to actin filaments in a straight, unstretched configuration.

After initialization, the simulation is updated in two stages at every step of iteration. In the first stage, myosin minifilaments bind, unbind, and bound minifilaments walk towards plus ends of actin filaments. In the second stage, the network configuration is mechanically relaxed.

The simulation is run for 200s and updated every 10^-3 s. Network surface tension is measured by slicing the network with a plane and calculating the total force F acting in the direction normal to that plane (Fig. 4avi). Tension is then calculated by dividing F by the width of the simulation box W. To obtain average steady-state tensions plotted in Figs. 4d and ​and5a,5a, tension values are averaged between t₀= 25 s and the total simulation time = 200 s.

To explore the relationship between actin filament length and tension in the network, varying actin filament lengths were used as input while keeping the mean actin density constant in the network, in accordance with experimental observations. A more complete description can be found in the Supplementary Note.