Liquid behavior of cross-linked actin bundles

Abstract

The actin cytoskeleton is a critical regulator of cytoplasmic architecture and mechanics, essential in a myriad of physiological processes. Here we demonstrate a liquid phase of actin filaments in the presence of the physiological cross-linker, filamin. Filamin condenses short actin filaments into spindle-shaped droplets, or tactoids, with shape dynamics consistent with a continuum model of anisotropic liquids. We find that cross-linker density controls the droplet shape and deformation timescales, consistent with a variable interfacial tension and viscosity. Near the liquid-solid transition, cross-linked actin bundles show behaviors reminiscent of fluid threads, including capillary instabilities and contraction. These data reveal a liquid droplet phase of actin, demixed from the surrounding solution and dominated by interfacial tension. These results suggest a mechanism to control organization, morphology, and dynamics of the actin cytoskeleton.

Keywords: actin; cytoskeleton; liquid crystal; phase separation.

Fig. 1.

Liquid droplets of cross-linked and short F-actin. (A) Fluorescence images of tetramethylrhodamine-labeled actin (TMR-actin) (1 mol % capping protein) before (actin only) and after addition of 10 mol % filamin (added at t = 0). (B) Tactoids are the shape of entropically formed liquid crystal droplets near the isotropic–nematic phase transition (Right). Here we observe tactoids induced by the addition of cross-linkers (Left). (C) Images of TMR-actin within a tactoid (1.5 mol % capping protein and 5 mol % filamin; Upper), with photobleaching occurring at t = 0 min. Average normalized TMR-actin intensity of the photobleached region over time (dashed line indicates exponential fit with τ_R = 880 s). (D) Phase diagram of solid, liquid, and gas phases of cross-linked actin. Black plus symbols are data where dispersed filaments are observed, blue filled circles are samples exhibiting tactoid droplets, dark blue open circles are samples with fluid bundles (Fig. 4), and black crosses are samples where space spanning networks are observed.

Fig. S1.

Fluorescence intensity after photobleaching data. The mean intensity, background subtracted and corrected for tactoid angle, is plotted for regions (Inset) on the bleached side (purple) and unbleached side (blue). As the fluorescence intensity of the tactoid on the bleached side increases, the intensity on the unbleached side decreases, indicating diffusive mixing of actin filaments.

Fig. 2.

Cross-linking regulates tactoid interfacial tension. (A) Tactoid (1.5 mol % capping protein) images, visualized with TMR-actin for filamin concentration from 2.5 to 15 mol %. Aspect ratio (black open circles) and ratio of anisotropic to isotropic interfacial tension, γ_A/γ_I (green diamonds), as a function of filamin concentration. (B) An arbitrary shaped liquid droplet with purely isotropic interfacial tension relaxes to an equilibrium shape of a sphere, whereas a droplet with purely anisotropic interfacial tension relaxes to an elongated, cylindrical equilibrium shape. (C) Model predictions of liquid droplet shape for varying isotropic and anisotropic interfacial tension ratios.

Fig. S2.

(A) Schematic of a homogeneous tactoid droplet defining the local surface normal $\widehat{\mathit{N}}$ and the nematic director field $\widehat{\mathit{n}}$. (B) Tactoid shape parameters: major axis (L), minor axis (r), radius (R), and the central angle ($\mathit{\alpha }$). (C) Dependence of the rescaled free energy, $\mathit{F}/{\mathit{\gamma }}_{\mathit{I}}{\mathit{V}}^{2/3}$, on the tactoid angle $\mathit{\alpha }$, at various values of the anchoring strength $\mathit{\omega }$. (D) Dependence of the droplet aspect ratio on the anchoring strength. Solid circles represent points obtained via numerical minimization of the free energy. Solid curves denote asymptotic scaling relations predicted by the continuum theory.

Fig. 3.

Cross-link density regulates interfacial tension and viscosity. (A) Fluorescence images of tactoid growth (1.5 mol % capping protein and 5 mol % filamin), visualized by TMR-actin. Average tactoid length (black closed circles) and aspect ratio (open squares) are shown as a function of time after filamin addition, and dashed line indicates a power law fit L ∼ t ^α, where α = 0.47 ± 0.01 for four datasets. Error bars represent $\pm 1$ SD. (B) Fluorescence images of tactoids (1 mol % capping protein and 10 mol % filamin) coalescence. Tactoid length, along the major axis, is shown as a function of time as two initially separate tactoids coalesce. Dashed line is an exponential fit. (C) Tactoid length, rescaled by the deformation length, as a function of time, rescaled by the characteristic relaxation time, for 14 coalescence events (1 mol % capping protein and 5 and 10 mol % filamin) collapses into a master curve. The solid line represents an exponential decay. (Inset) Linear scaling between relaxation time and deformation length from exponential fits of length relaxation. (D) The interfacial tension to viscosity ratio obtained from continuum model fits to the experimental data falls on the theoretically predicted curve for anisotropic droplets.

Fig. 4.

Interfacial tension drives instabilities and contraction in fluid F-actin bundles, visualized with TMR-actin. (A) Fluorescence images of an F-actin bundle (0.5 mol % capping protein and 10 mol % filamin) that exhibits instabilities that grow over time. (B) Fluorescence images of an F-actin bundle (0.25 mol % capping protein and 10 mol % filamin) that shortens over time. (C) Bundle length (0.25 mol % capping protein and 2.5 mol %, and 10 mol % filamin) as a function of time. (D) Bundle length, rescaled by the deformation length, as a function of time, rescaled by the characteristic relaxation time collapses on to a single master curve (0.25 mol % capping protein and 2.5, 5, and 10 mol % filamin). (E) Contractile strain increases with cross-linker concentration. Contrast is separately adjusted for prebundled actin images (A, 0′, 1′; B, 0′).

Fig. S3.

Schematic illustration of the geometry showing shape instability. The rod-like actin filaments are oriented along the z direction (long axis of the cylinder of initial radius ${\mathit{R}}_0$) in a homogeneous nematic configuration. The sinusoidal perturbation of wavelength $\mathit{\lambda }$ and amplitude u to the initial cylindrical geometry grows for $\mathit{\lambda }\ge \sqrt{1+\mathit{\omega }}\mathit{\hspace{0.17em}}\left(2\mathit{\pi }{\mathit{R}}_0\right)$, as the surface energy of the cylinder is reduced. As the capillary instability develops, liquid from the constricted regions have to flow into the bulging regions, thereby causing viscous dissipation.