Intracellular pathogens such as Listeria monocytogenes and Rickettsia
rickettsii move within a host cell by polymerizing a comet-tail of actin fibers
that ultimately pushes the cell forward. This dense network of cross-linked
actin polymers typically exhibits a striking curvature that causes bacteria to
move in gently looping paths. Theoretically, tail curvature has been linked to
details of motility by considering force and torque balances from a finite
number of polymerizing filaments. Here we track beads coated with a prokaryotic
activator of actin polymerization in three dimensions to directly quantify the
curvature and torsion of bead motility paths. We find that bead paths are more
likely to have low rather than high curvature at any given time. Furthermore,
path curvature changes very slowly in time, with an autocorrelation decay time
of 200 seconds. Paths with a small radius of curvature, therefore, remain so
for an extended period resulting in loops when confined to two dimensions. When
allowed to explore a 3D space, path loops are less evident. Finally, we
quantify the torsion in the bead paths and show that beads do not exhibit a
significant left- or right-handed bias to their motion in 3D. These results
suggest that paths of actin-propelled objects may be attributed to slow changes
in curvature rather than a fixed torque