Curvature and torsion in growing actin networks

Abstract

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 s. 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 three-dimensional (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, possibly associated with filament debranching, rather than a fixed torque.

Figure 1

Example trajectories of 3D bead motion. Data are shown for a bead moving in the 2 μm (a) and 80 μm (b) chambers. The color scale denotes the z-position, the position along the microscope optical axis.

Figure 2

The calculated curvature (a) and torsion (b) as a function of time for the example trajectory shown in figure 1(b) from a bead moving in an 80 μm chamber. (b) Open shading denotes times during which the trajectory torsion is positive and thus moving with a right-handed component. Gray shading denotes left-handed sections. Note that the torsion crosses zero multiple times and thus the bead trajectory is not predominantly right or left handed.

Figure 3

(a) The 3D curvature probability distribution. The probability of measured curvatures for all beads using the 80 μm chambers is displayed (bars, n = 15). The curvature has been normalized by its RMS value from each run. For comparison, the distribution predicted by Rutenberg and Grant [21] is shown (red dotted line). (b) The normalized curvature distribution for all runs using the 2 μm chambers is displayed (n = 13). (c) Autocorrelation of the path curvature. The autocorrelation of the curvature as a function of path length for a single bead trajectory (open circles) and a fit of this data to a single exponential decay (red solid line).

Figure 4

(a) The torsion probability distribution. The torsion of measured curvatures for all beads using the 80 μm chambers is displayed (n = 15). (b) Box plot of the curvature distribution from each of the 15 individual beads whose data is compiled in (a). The three horizontal lines represent the 25th, 50th, and 75th percentiles of each set of torsions.