Research ArticleCELL BIOLOGY

Actin kinetics shapes cortical network structure and mechanics

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Science Advances  22 Apr 2016:
Vol. 2, no. 4, e1501337
DOI: 10.1126/sciadv.1501337
  • Fig. 1 Dynamics of formin molecules in the cell cortex.

    (A) Individual CA-Diaph1-GFP molecules appear as dot-like structures in the cortex of HeLa and M2 cells. Individual molecules are indicated by arrows. Scale bar, 10 μm; scale bars in zooms, 2 μm. SM, single molecule. (B) Top: Cortical section with CA-Diaph1-GFP. Scale bar, 1 μm. Middle: Kymograph of the section’s fluorescence intensity. a.u., arbitrary unit. (B1 and B2) The section contains seemingly mobile molecules (B1) and immobile molecules (B2). Bottom: Trajectories of CA-Diaph1 molecules. (C) Schematic illustrating the effects of projection of the three-dimensional (3D) molecule trajectories onto the 2D plane of observation. (D) Scanning electron micrograph of the actin cortex of a HeLa cell. Actin filaments appear to be isotropically distributed. (E) Distributions of projected travel distances of CA-Diaph1-GFP in HeLa cells obtained from measurements of 3000 molecules (triangles) and from deconvolving the raw distribution, with the distributions obtained after formin inhibition and Rho-kinase inhibition, respectively (circles, Supplementary Materials). The red line is a fit of travel distances obtained from theoretical analysis of actin assembly and disassembly, projected into the focal plane. We determined ωoff,F = 0.12 s−1. Inset: Inferred distribution of filament lengths polymerized by individual formins in HeLa cells. The average length added by single formins is 3900 nm (M2 cells: 2500 nm).

  • Fig. 2 Dynamics of actin-GFP molecules in the cell cortex.

    (A) Individual actin-GFP molecules appear as dot-like structures in the cortex of HeLa and M2 cells. Arrows indicate individual molecules. (B to E) Distribution of actin-GFP molecule lifetimes in wild-type (wt) HeLa cells (B), after application of the formin inhibitor SMIFH2 (C), and after application of the Arp2/3 inhibitor CK666 (D). Circles, experimental values; triangles, values from single-filament simulation of the processes illustrated in (E). Red lines give an analytical approximation of the latter. Parameter values are ωoff,A = 0.23 s−1, koff = 29 sub s-1, and kon,0 = 28 sub s-1. Insets give a log-linear presentation of the data. (C and D) Insets: Data from untreated cells are given in gray for comparison. (E) Illustration of the molecular processes accounted for in the quantitative analysis of actin molecule dynamics. This included free and formin-mediated, barbed-end elongation at rates kon,0 and kon,F, release of an elongation factor from the barbed end at rate ωoff,F, release of a capping factor from the pointed end at rate ωoff,A, and filament pointed-end disassembly at rate koff. These processes capture the dynamics of filaments with free barbed ends, as well as the effects of formin-mediated elongation, Arp2/3-complex capping, and of factors involved in filament disassembly.

  • Fig. 3 Actin filament length distribution in the cell cortex.

    (A) Inferred filament length distributions for HeLa (red) and M2 cells (blue). Symbols, finite cortex simulations; lines, analytical approximations (Supplementary Materials). In HeLa cells, formin-nucleated filaments had an average length of 1200 nm (M2: 600 nm), whereas the average length of Arp2/3-nucleated filaments was 120 nm (M2: 60 nm). Parameter values are ron = 9 s−1 μM−1, ron,F = 45 s−1 μM−1, koff = 28 s−1, ωoff,F = 0.12 s−1, ωoff,A = 0.3 s−1, ctot = 80 μM, cform = 0.2 nM, and carp = 24 nM. (B) Scanning electron micrographs of the actin cortex of control HeLa cells (top), cells treated with the formin inhibitor SMIFH2 (middle), and cells treated with the Arp2/3 inhibitor CK666 (bottom), with (right) and without (left) dashed lines indicating complete actin filaments. In control cells, areas of long and highly oriented filaments were clearly visible. These could not be seen in SMIFH2-treated cells. In contrast, in CK666-treated cells, long and highly oriented filaments were visible but short ones were not. Scale bar, 500 nm. (C) Snapshots of stochastic simulations of actin cortex turnover. Scale bar, 10 μm. (D) Experimental FRAP curve for HeLa cells (main panel) and M2 cells (inset) averaged over 28 experiments. Red curves, simulation results; see the Supplementary Materials for parameter values. Experimental data points are indicated in gray. Bars, SDs.

  • Fig. 4 Turnover time is decoupled from network structure in the finite cortex simulations.

    (A and B) The actin concentration controls the length of cortical filaments in HeLa cells but not their turnover times. (C) The length of cortical formin-nucleated filaments is independent of the rate ωoff,A at which an Arp2/3 complex detaches from a filament. (D) The turnover rate ωd,1 of Arp2/3-nucleated filaments obtained from FRAP measurements increases with ωoff,A. (E) The length of Arp2/3-nucleated cortical filaments is independent of the rate ωoff,F at which a formin molecule detaches from a filament. (F) The turnover rate ωd,2 of formin-nucleated filaments obtained from FRAP measurements increases with ωoff,F. Parameter values: ron,0 = 9 s−1 μM−1, ron,F = 45 s−1 μM−1, koff = 28 s−1, ωoff,F = 0.12 s−1, ωoff,A = 0.3 s−1, ctot = 80 μM, cform = 0.2 nM, and carp = 24 nM.

  • Fig. 5 AFM measurements of cortex elasticity.

    (A) Schematic of an AFM cantilever indenting a cell adhered to a coverslip (left). Using a small tip and restricting the analysis to shallow indentation depths allows characterization of actin cortex elasticity (right). (B) Representative force indentation curves on HeLa cells subjected to different drug perturbations. Using a Hertz contact mechanics model, the elastic modulus was estimated by fitting the force indentation curves up to 500 nm. Inset: Zoom showing curve fitting up to 150-nm indentation. (C) Elasticity of the cell cortex under different experimental conditions. Error bars, SEMs.

  • Table 1 Summary of parameters of filament growth kinetics inferred from FSM experiments and single-molecule simulations compared with values in vitro from the literature for CA-Diaph1 and actin molecules.

    In the fourth column, cT is the concentration of ATP-actin.

    ExperimentHeLa cells in vivoM2 cells in vivoReported values in vitroSource
    kon,F (sub/s)
    kon,0 (sub/s)
    ωoff,F (1/s)
    ωoff,A (1/s)
    koff (1/s)
    136 ± 14
    28 ± 2
    0.12 ± 0.02
    0.23 ± 0.02
    29 ± 3
    102 ± 10
    21 ± 2
    0.15 ± 0.02
    1.1 ± 0.1
    23 ± 2
    46.9 × cT
    11.6, 6.5–9.5, 9.1–10.9 × cT
    ≲10−3
    1.23
    6.25–20, 4.7–51.6
    (17)
    (17, 33, 66)
    (17, 67, 68)
    (47)
    (66, 69, 70)
  • Table 2 Summary of FRAP and molecule fitting parameters in vivo in comparison with the finite cortex simulation results in silico in HeLa and M2 cells.

    The finite cortex simulations reproduce well the FRAP data in vivo based on the measured molecule growth kinetics. f1 and f2 denote the relative abundances of Arp2/3- and formin-nucleated filaments, respectively, whereas ωd,1 and ωd,2 are the turnover rates of the two respective filament populations.

    ExperimentHeLa cellsM2 cells
    In vivoIn silicoIn vivoIn silico
    f1 (rel.)
    f2 (rel.)
    ωd,1 (1/s)
    ωd,2 (1/s)
    0.8 ± 0.08
    0.2 ± 0.02
    0.3 ± 0.1
    0.02 ± 0.01
    0.83 ± 0.005
    0.17 ± 0.005
    0.28 ± 0.003
    0.02 ± 0.001
    0.75 ± 0.08
    0.25 ± 0.03
    1 ± 0.2
    0.04 ± 0.01
    0.76 ± 0.01
    0.24 ± 0.01
    0.87 ± 0.01
    0.045 ± 0.004
    kon,F (sub/s)
    kon,0 (sub/s)
    ωoff,F (1/s)
    ωoff,A (1/s)
    koff (1/s)
    136 ± 14
    28 ± 2
    0.12 ± 0.02
    0.23 ± 0.02
    29 ± 3
    134 ± 13
    27 ± 3
    0.12 ± 0.02
    0.3 ± 0.02
    28 ± 3
    102 ± 10
    21 ± 2
    0.15 ± 0.02
    1.1 ± 0.1
    23 ± 2
    100 ± 10
    22 ± 2
    0.15 ± 0.02
    1.2 ± 0.1
    24 ± 2

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/4/e1501337/DC1

    section SI. Supplementary materials, methods, and figures

    section SII. Determination of the formin-induced, barbed-end polymerization rate

    section SIII. Single-filament computations to determine effective molecular rates

    section SIV. Determination of filament length distribution in the subpopulations

    section SV. Filament severing

    section SVI. F-actin abundances in the actin cortex

    fig. S1. Experimental setup.

    fig. S2. Single-step photobleaching control by a temporal evolution of the molecule fluorescence intensity.

    fig. S3. (A and B) Lifetime distribution with average lifetime ωoff, F = 0:12 ± 0:1 of (A) Diaph1 (N = 1000 molecules) and of (B) CA-Diaph1 (N = 3000 molecules).

    fig. S4. Actin filament fractions depend on the cortical nucleator concentrations.

    fig. S5. Fraction Φ of immobile molecules as a function of the average filament length λ according to eq. S5 with p(ℓ) = exp(−ℓ/λ)/λ.

    fig. S6. Effects on molecule mobility.

    fig. S7. Illustration of monomer lifetimes during continuous filament growth.

    fig. S8. Simulated FRAP curves for scenarios including filament severing.

    table S1. Comparison between model parameters used in the finite cortex simulations and literature values.

    table S2. Parameter values used in the simulations of FRAP experiments.

    table S3. Parameter values for the two scenarios of filament severing.

    movie S1. Fluorescence imaging of cortical Diaph1-GFP in a HeLa cell corresponding to Fig. 1A.

    movie S2. Fluorescence imaging of cortical actin-GFP in an M2 cell.

    movie S3. Detail of fluorescence imaging of cortical Diaph1-GFP in a HeLa cell corresponding to Fig. 1B.

    movie S4. Cortex simulation of a FRAP/FLAP experiment in a HeLa cell.

    References (7173)

  • Supplementary Materials

    This PDF file includes:

    • section SI. Supplementary materials, methods, and figures
    • section SII. Determination of the formin-induced, barbed-end polymerization rate
    • section SIII. Single-filament computations to determine effective molecular rates
    • section SIV. Determination of filament length distribution in the subpopulations
    • section SV. Filament severing
    • section SVI. F-actin abundances in the actin cortex
    • fig. S1. Experimental setup.
    • fig. S2. Single-step photobleaching control by a temporal evolution of the molecule fluorescence intensity.
    • fig. S3. (A and B) Lifetime distribution with average lifetime ωoff, F = 0:12 ± 0:1
      of (A) Diaph1 (N = 1000 molecules) and of (B) CA-Diaph1 (N = 3000 molecules).
    • fig. S4. Actin filament fractions depend on the cortical nucleator concentrations.
    • fig. S5. Fraction Φ of immobile molecules as a function of the average filament length λ according to eq. S5 with p(ℓ) = exp(−ℓ/λ)/λ.
    • fig. S6. Effects on molecule mobility.
    • fig. S7. Illustration of monomer lifetimes during continuous filament growth.
    • fig. S8. Simulated FRAP curves for scenarios including filament severing.
    • table S1. Comparison between model parameters used in the finite cortex simulations and literature values.
    • table S2. Parameter values used in the simulations of FRAP experiments.
    • table S3. Parameter values for the two scenarios of filament severing.
    • References (71–73)

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.avi format). Fluorescence imaging of cortical Diaph1-GFP in a HeLa cell corresponding to Fig. 1A.
    • movie S2 (.avi format). Fluorescence imaging of cortical actin-GFP in an M2 cell.
    • movie S3 (.avi format). Detail of fluorescence imaging of cortical Diaph1-GFP in a HeLa cell corresponding to Fig. 1B.
    • movie S4 (.avi format). Cortex simulation of a FRAP/FLAP experiment in a HeLa cell.

    Files in this Data Supplement:

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