Fig. 6: Computational verification of the force-balance hypothesis.

a Schematic description of the computational model. The cell is modeled by the phase field variable \({{{{{\rm{\phi }}}}}}\) that takes on the value 1 inside the cell (beige area) and −1 outside with a smooth transition in the interface region whose thickness is proportional to the parameter \(\epsilon\). The cell membrane is implicitly defined as the region where \({{{{{\rm{\phi }}}}}}=0\) (green line). The microtubules (bleached red lines in the background) are not tracked individually but only through the orientation field \(P\), which gives the average microtubule direction at each point. The protrusive force of the microtubules is modeled by active stress in the direction of the orientation field (red arrows). The contractile myosin forces are modeled by the surface tension and bending forces (green arrows), which minimize the surface curvature and area. b Initially (at time t = 0), the cell is chosen to be elliptic with microtubules oriented in the P/D (x) direction. c Cell shape at steady state (time t = 5) for counteracting protrusive and contractile (surface tension) forces. The computational parameters were chosen as Fa = −1 and Ca = 0.1. For this choice of parameters, the cell approximately maintains its shape, indicating a force balance. d If the protrusive force is reduced (Fa = −10, Ca = 0.1), the cell is significantly shorter in the P/D direction at a steady state. e If the surface tension is reduced instead (Fa = −1, Ca = 1), the cell is significantly elongated at a steady state. The color bar shows the value of the phase-field parameter \({{{{{\rm{\phi }}}}}}\), and turquoise arrows represent the orientation field \(P\) (average microtubule orientation). The white line indicates the cell membrane (zero level set of \({{{{{\rm{\phi }}}}}}\)).