Hydrodynamics of Cellular Cortical Flows and the Formation of Contractile Rings

We propose a mechanism for the formation of contractile rings and the apparition of a flow in the cortical layer of cells undergoing cytokinesis at the end of cell division or during the healing of a wound in the cortex of Xenopus eggs. We generalize the hydrodynamic active gel theory along the lines of thin shell theory of continuum elasticity to describe the cell cortex. As in liquid crystal physics, the flow couples to the orientation of the actin filaments. The cortical flow is driven by an increased density of myosin motors in the cortex, and orients the filaments to form the ring.

Figure 1

Velocity and order parameter as a function of $r$ for the in-plane contractile ring in Xenopus egg cortex ($\frac{\tilde{\zeta }\Delta \mu a}{\eta }=1$, $\frac{\tilde{\zeta }\Delta \mu }{\tilde{K}}=0.3$, $\frac{a}{r_0}=0.2$, ${\beta }_1=2$, and ${\beta }_2=\eta$). Inset: schematic of filament alignment.

Figure 2

Velocity and order parameter as a function of $x$ for a cylindrical cell submitted to an excess myosin activity in a central stripe. Inset : schematic of filament alignment.