| dc.description.abstract | This thesis reports theoretical studies on the experimentally observed geometrical trajectories of Listeria monocytogenes.
The intracellular bacterium Listeria monocytogenes utilizes its specific surface protein to activate actin polymerization inside the host cell.
The polymerizing actin network pushes Listeria forward, and leaves a cometlike actin tail behind the bacterium.
Experiments of Listeria-type actin-based motility have observed fascinating geometrical trajectories such as straight lines, circles, S-shaped curves, and translating figure eights.
Based on the experimental observations, we constructed a phenomenological model for Listeria-type motion of a disk (in two dimensions) and a bead (in three dimensions).
In our model, the actin density and force per filament on the disk surface
are influenced by the translation and self-rotation of the disk,
which in turn is induced by the asymmetric distributions of those densities.
We show that this feedback can destabilize a straight trajectory,
leading to the geometrical trajectories observed in experiments
through bifurcations in the distributions of actin density and force per filament.
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.
To mimic the nonuniform distribution of functionalized protein on Listeria surface,
we have also studied the motion of a disk whose surface is half coated and half clean. We show that a half-coated disk also undergoes similar symmetry-breaking bifurcations when the straight trajectory loses its 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.
In addition, for a bead moving in a three-dimensional environment,
we find that the instability mechanism for the transition from a straight trajectory to a curved trajectory is the same as that for a disk in a two-dimensional environment. Despite this similarity, the couplings between bead self-rotation and the evolution of actin density and force per filament are found to give the bead more rich dynamics.
For example, different from the disk motion confined to a plane,
a bead in three dimensions is able to move along trajectories with nonzero torsion such as helical trajectories. | en_US |