Computational Model for Cell Morphodynamics

We develop a computational model, based on the phase-field method, for cell morphodynamics and apply it to fish keratocytes. Our model incorporates the membrane bending force and the surface tension and enforces a constant area. Furthermore, it implements a cross-linked actin filament field and an actin bundle field that are responsible for the protrusion and retraction forces, respectively. We show that our model predicts steady state cell shapes with a wide range of aspect ratios, depending on system parameters. Furthermore, we find that the dependence of the cell speed on this aspect ratio matches experimentally observed data.

Figure 1

(a) Snapshots of the numerical evolution of a cell shape. The resulting distributions of $V$ and $W$ are shown in (b) and (c), respectively.

Figure 2

Snapshots of three steady state solutions of our model for $a=0.069{\mathrm{s}}^{-1}$ (a), $a=0.084{\mathrm{s}}^{-1}$ (b), and $a=0.107{\mathrm{s}}^{-1}$ (c). The corresponding aspect ratios and cell speeds are $S=1.41$ and $v=0.12\mu \mathrm{m}/\mathrm{s}$, $S=1.92$ and $v=0.19\mu \mathrm{m}/\mathrm{s}$, and $S=2.79$ and $v=0.27\mu \mathrm{m}/\mathrm{s}$. (d) Cell speed as a function of the aspect ratio. The solid line is our simulation result, the dots are experimental results from 11, and the dashed curve is the prediction from the simple model in 11. The three circles correspond to (a), (b), and (c).