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Pattern Formation in Polymerizing Actin Flocks: Spirals, Spots, and Waves without Nonlinear Chemistry

T. Le Goff, B. Liebchen, and D. Marenduzzo
Phys. Rev. Lett. 117, 238002 – Published 30 November 2016
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    Abstract

    We propose a model solely based on actin treadmilling and polymerization which describes many characteristic states of actin-wave formation: spots, spirals, and traveling waves. In our model, as in experiments on cells recovering motility following actin depolymerization, we choose an isotropic low-density initial condition; polymerization of actin filaments then raises the density towards the Onsager threshold where they align. We show that this alignment, in turn, destabilizes the isotropic phase and generically induces transient actin spots or spirals as part of the dynamical pathway towards a polarized phase which can either be uniform or consist of a series of actin-wave trains (flocks). Our results uncover a universal route to actin-wave formation in the absence of any system-specific nonlinear biochemistry, and it may help to understand the mechanism underlying the observation of actin spots and waves in vivo. They also suggest a minimal setup to design similar patterns in vitro.

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    • Received 5 August 2016

    DOI:https://doi.org/10.1103/PhysRevLett.117.238002

    © 2016 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Biological self-organizationBiomimetic & bio-inspired materialsClusteringCollective behaviorEmergence of patternsFlockingPattern formationSelf-organized systems
    Polymers & Soft MatterStatistical Physics & ThermodynamicsPhysics of Living Systems

    Authors & Affiliations

    T. Le Goff*, B. Liebchen†, and D. Marenduzzo

    • SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom

    • *Corresponding author. thomas.le-goff@ed.ac.uk
    • †Corresponding author. bliebche@staffmail.ed.ac.uk

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    Issue

    Vol. 117, Iss. 23 — 2 December 2016

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    • Figure 1
      Figure 1

      Representative snapshots for actin pattern formation as described in the main text. (a) Γ=1; (b) Γ=4.3; (c) Γ=10. Other parameters: r=1.1, D=5, and Γ2=0.075. The scale bar is 50.

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    • Figure 2
      Figure 2

      Snapshots of the evolution of the P field during the formation of spots for Γ=4.3, r=1.1, D=5, and Γ2=0.075, shown in Fig. 1.

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    • Figure 3
      Figure 3

      Real and imaginary parts of the dispersion relation of the uniform polarized phase (iii), for Γ=0, 2, 4, 6, 8, 10 (following the sense of the arrows), and with r=1.1, D=5, and Γ2=0.075.

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    • Figure 4
      Figure 4

      Phase diagram with curves resulting from the linear stability analysis. They are consistent with numerical simulations (see [29]) and correspond to D=5 and Γ2 equals 0.00075, 0.075, 0.1775, 0.3704, 3/8, 0.3754, and 0.4688 from bottom to top.

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