Trajectories of Listeria-type motility in two dimensions.

Force generated by actin polymerization is essential in cell motility and the locomotion of organelles or bacteria such as Listeria monocytogenes. Both in vivo and in vitro experiments on actin-based motility have observed geometrical trajectories including straight lines, circles, S-shaped curves, and translating figure eights. This paper reports a phenomenological model of an actin-propelled disk in two dimensions that generates geometrical trajectories. Our model shows that when the evolutions of actin density and force per filament on the disk are strongly coupled to the disk self-rotation, it is possible for a straight trajectory to lose its stability. When the instability is due to a pitchfork bifurcation, the resulting trajectory is a circle; a straight trajectory can also lose stability through a Hopf bifurcation, and the resulting trajectory is an S-shaped curve. We also show that a half-coated disk, which mimics the distribution of functionalized proteins in Listeria, also undergoes similar symmetry-breaking bifurcations when the straight trajectory loses stability. For both a fully coated disk and a half-coated disk, when the trajectory is an S-shaped curve, the angular frequency of the disk self-rotation is different from that of the disk trajectory. However, for circular trajectories, these angular frequencies are different for a fully coated disk but the same for a half-coated disk.