Research ArticleBIOPHYSICS

Self-organized stress patterns drive state transitions in actin cortices

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Science Advances  06 Jun 2018:
Vol. 4, no. 6, eaar2847
DOI: 10.1126/sciadv.aar2847
  • Fig. 1 Dynamic model actin cortices.

    Quasi-2D actin networks were generated by encapsulating Xenopus egg extract in water-in-oil emulsion droplets and confining actin polymerization to the interface. (A) Equatorial cross section of flattened droplets. Simultaneous confocal imaging of Bodipy-conjugated ActA (green, left) and rhodamine-labeled actin (magenta, right). Amphiphilic Bodipy-ActA localizes to the water-oil interface and catalyzes the formation of a quasi-2D dynamic actin network by local activation of Arp2/3. (B) Top: Schematic of the experiment. Cortical dynamics are tracked near the flat bottom surface of the droplet. There is continuous turnover between the thin polymeric actin layer and actin monomers in the bulk (arrows). Bottom: Zoomed-in schematic of the essential components of the cortex. IR fluorescent SWNTs are inserted as probes of cortex dynamics.

  • Fig. 2 Signatures of distinct steady states.

    Network percolation can be induced by increasing cross-linker density (α-actinin). Three distinct steady states can be identified on the basis of qualitative differences in collective network dynamics imaged in the bottom cortical layer in the droplets. (A) Low cross-linking (0 to 1.5 μM of added α-actinin; images shown, 1.5 μM). (B) Intermediate cross-linking (2 to 2.5 μM of added α-actinin; images shown, 2.5 μM). The colored patches delineate the particles that moved as clusters at time points gray (10 s), red (100 s), and yellow (200 s; movie S2). (C) High cross-linking (3 to 4 μM of added α-actinin; images shown, 3 μM). (A to C) Top left: Fluorescence image of inserted SWNT probes. Top right: Confocal image of the actin distribution. Bottom: Individual SWNTs were tracked in 200-s-long movies with 2000 frames (movies S1 to S4). Tracks of individual SWNTs color-coded for progression in time. In the high-connectivity state, the fraction of SWNTs that were accumulated in the cap has not been tracked because of the high density. Scale bar, 20 μm.

  • Fig. 3 Collective dynamics and fluctuations.

    Steady states differ in the degree of order and correlation of probe particle velocities. (A) Normalized velocity fluctuation autocorrelation is plotted as a function of lag time for different α-actinin concentrations evaluated in a 5 × 5 coarse-grained grid for 200-s movies, averaged over all grid points. (B) Dynamic order parameter calculated from the averaged velocity directional persistence as a function of α-actinin concentration. (C) An actin density–based structural order parameter showing the fraction of phase-separated cortices as a function of cross-linker concentration (0 to 4 μM of added α-actinin), inferred from images of actin fluorescence. (D) The normalized velocity-velocity fluctuation cross-correlation at zero lag time is plotted as a function of probe distances for different α-actinin concentrations (symbols). Data are fitted with single exponentials (lines). (E) Characteristic correlation lengths from fits in (D) as a function of α-actinin concentrations. Error bars represent 95% confidence interval. (F) Susceptibility of cluster motion to stress fluctuations quantified from the amplitude of the velocity-velocity fluctuation correlation taken at R = 5 μm, plotted as a function of α-actinin concentration. Error bars correspond to SDs.

  • Fig. 4 Order and symmetries in the stress patterns.

    Increasing cross-linker density leads to increasing order and breaking of symmetries in the arrangement of stress generators. (A to C) Directional velocity-velocity correlation maps the degree of order and shows breaking of symmetry for increasing α-actinin concentrations. For each concentration, the colors portray the average alignment of pairs of probe velocities, as a function of the distance and angle between them [(A), inset]. At low cross-linking [1 μM; (A)], there is no appreciable correlation. At intermediate connectivity [2.5 μM; (B)], the map shows enhanced correlations, distributed anisotropically, primarily along the front-back axis, signifying the emergence of nematic polar order and the breaking of rotational symmetry. At high connectivity [3 μM; (C)], the converging network flow leads to an asymmetry between top and bottom, indicating the appearance of centrosymmetric polar order and the breaking of translational symmetry. (D to F) Schematic illustration of the conceptual model for cortex dynamics as a function of connectivity. At low connectivity (D), the network is not mechanically connected, so myosin cannot generate long-range forces, and the network fluctuates randomly. At intermediate connectivity (E), the network reaches the mechanical percolation threshold. Myosin-generated stresses can propagate over larger distances, leading to the formation of rigid clusters, which move in a divergence-free manner. The interplay between stresses and network rearrangement lead to local nematic ordering of the force-generating myosin minifilaments. At high connectivity (F), the network self-organizes into a single large cap with persistent converging flow of clusters into the cap and polar ordering of the myosin force dipoles.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/6/eaar2847/DC1

    Simulations

    fig. S1. Actin turnover.

    fig. S2. Control experiments with myosin-immunodepleted extracts.

    fig. S3. Curl field of intermediate cross-link regime.

    fig. S4. Divergence field of high cross-link regime.

    fig. S5. Cortex at steady state.

    fig. S6. Velocity correlation.

    fig. S7. Symmetry breaking of cortices with addition of cross-linker.

    fig. S8. Simulations.

    fig. S9. Density current maps.

    fig. S10. Cluster size development with time.

    fig. S11. Order and symmetries in the stress patterns of the high cross-link concentration.

    movie S1. Motion of SWNTs in the cortex at low connectivity (1.5 μM of added α-actinin).

    movie S2. Motion of SWNTs in the cortex at intermediate connectivity (2.5 μM of added α-actinin).

    movie S3. Motion of SWNTs in the cortex at intermediate connectivity (2.5 μM of added α-actinin).

    movie S4. Motion of SWNTs in the cortex at high connectivity (3.0 μM of added α-actinin).

    movie S5. Rhodamine-labeled actin cortices at high connectivity (3.0 μM of added α-actinin) phase-separate and form a large cap, which extend over a substantial fraction of the droplet surface.

  • Supplementary Materials

    This PDF file includes:

    • Simulations
    • fig. S1. Actin turnover.
    • fig. S2. Control experiments with myosin-immunodepleted extracts.
    • fig. S3. Curl field of intermediate cross-link regime.
    • fig. S4. Divergence field of high cross-link regime.
    • fig. S5. Cortex at steady state.
    • fig. S6. Velocity correlation.
    • fig. S7. Symmetry breaking of cortices with addition of cross-linker.
    • fig. S8. Simulations.
    • fig. S9. Density current maps.
    • fig. S10. Cluster size development with time.
    • fig. S11. Order and symmetries in the stress patterns of the high cross-link concentration.
    • Legends for movies S1 to S5

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.avi format). Motion of SWNTs in the cortex at low connectivity (1.5 μM of added α-actinin).
    • movie S2 (.avi format). Motion of SWNTs in the cortex at intermediate connectivity (2.5 μM of added α-actinin).
    • movie S3 (.avi format). Motion of SWNTs in the cortex at intermediate connectivity (2.5 μM of added α-actinin).
    • movie S4 (.avi format). Motion of SWNTs in the cortex at high connectivity (3.0 μM of added α-actinin).
    • movie S5 (.mp4 format). Rhodamine-labeled actin cortices at high connectivity (3.0 μM of added α-actinin) phase-separate and form a large cap, which extend over a substantial fraction of the droplet surface.

    Files in this Data Supplement:

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