Curvature and torsion in growing actin networks

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

Spectroscopic measurements of the ion velocity distribution at the base of the fast solar wind

In situ measurements of the fast solar wind reveal non-thermal distributions of electrons, protons, and minor ions extending from 0.3 au to the heliopause. The physical mechanisms responsible for these non-thermal properties and the location where these properties originate remain open questions. Here, we present spectroscopic evidence, from extreme ultraviolet spectroscopy, that the velocity distribution functions (VDFs) of minor ions are already non-Gaussian at the base of the fast solar wind in a coronal hole, at altitudes of <1.1 R ⊙. Analysis of Fe, Si, and Mg spectral lines reveals a peaked line-shape core and broad wings that can be characterized by a kappa VDF. A kappa distribution fit gives very small kappa indices off-limb of κ ≈ 1.9–2.5, indicating either (a) ion populations far from thermal equilibrium, (b) fluid motions such as non-Gaussian turbulent fluctuations or non-uniform wave motions, or (c) some combination of both. These observations provide important empirical constraints for the source region of the fast solar wind and for the theoretical models of the different acceleration, heating, and energy deposition processes therein. To the best of our knowledge, this is the first time that the ion VDF in the fast solar wind has been probed so close to its source region. The findings are also a timely precursor to the upcoming 2018 launch of the Parker Solar Probe, which will provide the closest in situ measurements of the solar wind at approximately 0.04 au (8.5 solar radii)

Superattracting fixed points of quasiregular mappings

We investigate the rate of convergence of the iterates of an n-dimensional quasiregular mapping within the basin of attraction of a fixed point of high local index. A key tool is a refinement of a result that gives bounds on the distortion of the image of a small spherical shell. This result also has applications to the rate of growth of quasiregular mappings of polynomial type, and to the rate at which the iterates of such maps can escape to infinity

Genus 2 Cantor sets

We construct a geometrically self-similar Cantor set $X$ of genus $2$ in $\mathbb{R}^3$. This construction is the first for which the local genus is shown to be $2$ at every point of $X$. As an application, we construct, also for the first time, a uniformly quasiregular mapping $f:\mathbb{R}^3 \to \mathbb{R}^3$ for which the Julia set $J(f)$ is a genus $2$ Cantor set.Comment: 20 pages, 6 figure

Microscale Fluid Behavior during Cryo-EM Sample Blotting

Blotting has been the standard technique for preparing aqueous samples for single-particle electron cryo-microscopy for over three decades. This technique removes the excess solution from a transmission electron microscope grid by pressing absorbent filter paper against the specimen before vitrification. However, this standard technique produces vitreous ice with inconsistent thickness from specimen to specimen and from region to region within the same specimen, the reasons for which are not understood. Here, high-speed interference contrast microscopy is used to demonstrate that the irregular pattern of fibers in the filter paper imposes tortuous, highly variable boundaries during the removal of excess liquid from a flat, hydrophilic surface. As a result, aqueous films of nonuniform thickness are formed while the filter paper is pressed against the substrate. This pattern of nonuniform liquid thickness changes again after the filter paper is pulled away, but the thickness still does not become completely uniform. We suggest that similar topographical features of the liquid film are produced during the standard technique used to blot EM grids and that these manifest in nonuniform ice after vitrification. These observations suggest that alternative thinning techniques, which do not rely on direct contact between the filter paper and the grid, may result in more repeatable and uniform sample thicknesses

Do stiffness and asymmetries predict change of direction performance?

Change of direction speed (CODS) underpins performance in a wide range of sports but little is known about how stiffness and asymmetries affect CODS. Eighteen healthy males performed unilateral drop jumps to determine vertical, ankle, knee and hip stiffness, and a CODS test to evaluate left and right leg cutting performance during which ground reaction force data were sampled. A step-wise regression analysis was performed to ascertain the determinants of CODS time. A two-variable regression model explained 63% (R-2 = 0.63; P = 0.001) of CODS performance. The model included the mean vertical stiffness and jump height asymmetry determined during the drop jump. Faster athletes (n = 9) exhibited greater vertical stiffness (F = 12.40; P = 0.001) and less asymmetry in drop jump height (F = 6.02; P = 0.026) than slower athletes (n = 9); effect sizes were both "large" in magnitude. Results suggest that overall vertical stiffness and drop jump height asymmetry are the strongest predictors of CODS in a healthy, non-athletic population