Single Actin Bundle Rheology

Abstract

Bundled actin structures play an essential role in the mechanical response of the actin cytoskeleton in eukaryotic cells. Although responsible for crucial cellular processes, they are rarely investigated in comparison to single filaments and isotropic networks. Presenting a highly anisotropic structure, the determination of the mechanical properties of individual bundles was previously achieved through passive approaches observing bending deformations induced by thermal fluctuations. We present a new method to determine the bending stiffness of individual bundles, by measuring the decay of an actively induced oscillation. This approach allows us to systematically test anisotropic, bundled structures. Our experiments revealed that thin, depletion force-induced bundles behave as semiflexible polymers and obey the theoretical predictions determined by the wormlike chain model. Thickening an individual bundle by merging it with other bundles enabled us to study effects that are solely based on the number of involved filaments. These thicker bundles showed a frequency-dependent bending stiffness, a behavior that is inconsistent with the predictions of the wormlike chain model. We attribute this effect to internal processes and give a possible explanation with regard to the wormlike bundle theory.

Keywords: actin; biopolymers; bundles; dynamics; mechanical properties; optical tweezers; rheology.

Figure 1

(a) A 2-μm polystyrene bead coated with streptavidin is attached to an actin bundle enriched with biotinylated actin monomers. This bead is trapped by optical tweezers, and an oscillatory movement of the trap in the xy-plane induces oscillations in the bundle. The oscillation amplitudes subsequently decay when traveling through the bundle, a process which can be captured by fluorescence microscopy; (b) Fluorescence images of the experimental procedure. The 11 images represent half a period at a frequency of 0.7 Hz.

Figure 2

Hydrodynamic length and persistence length. Different colors and markers depict different individual bundles of varying thicknesses (blue dotted: thin bundle, blue circles: thick bundle, others: intermediate). (a) Regarding the frequency dependence of the hydrodynamic length, wiggling bundles with a bead attached to their ends revealed a power law exponent of −1/4; (b) which translated into a constant bending stiffness. Few bundles, however, also showed a softening behavior towards low frequencies.

Figure 3

Rheological response of a successively thickened bundle. (a) While comparably thin bundles (blue circles) obey the predictions determined by the wormlike chain model, thicker bundles (intermediate: red squares, thick: brown circles) deviated from the ${\mathit{\omega }}^{-\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{4}$}\right.}$-scaling, which translates into a frequency-dependent bending stiffness (b). With more and more bundles merged, the bending stiffness increased. At the same time, the bundles stiffened markedly for lower frequencies.

Figure 4

Stiffness scaling with the hydrodynamic length for increasing bundle diameters (thin bundles: blue circles, intermediate bundles: red squares, thick bundles: brown circles). For thickened bundles, the bending stiffness shows a scaling behavior with the excitation frequency. This scaling is more evident when looking at the bending stiffness with respect to the hydrodynamic length. While probing the bundle with different frequencies, the length scale on which the bundle was deformed changed. This translates into a higher bending stiffness for longer deformation modes.

Figure 5

Time lapse of the zipping process. Bundles were thickened by merging with other bundles. This was achieved by dragging the bundle with the optically trapped bead into the vicinity of another, freely floating bundle.

Figure 6

Wiggling bundle position data. Panel (a) shows the amplitude of the movement of the bundle contour in the y-direction with respect to its point along the bundle. The bead that is controllably deflected by the optical tweezers setup to induce oscillations is near position x = 27 µm, and is attached to one end of the bundle. Bundles that are not orthogonal to the oscillation direction were excluded from further analysis. Panel (b) shows the data after band passing. The first and last periods need to be excluded from ${\mathit{l}}_{\mathit{\omega }}$ -fitting because of the border effects of filtering