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Structure formation in active networks

Abstract

Structure formation and constant reorganization of the actin cytoskeleton are key requirements for the function of living cells. Here we show that a minimal reconstituted system consisting of actin filaments, crosslinking molecules and molecular-motor filaments exhibits a generic mechanism of structure formation, characterized by a broad distribution of cluster sizes. We demonstrate that the growth of the structures depends on the intricate balance between crosslinker-induced stabilization and simultaneous destabilization by molecular motors, a mechanism analogous to nucleation and growth in passive systems. We also show that the intricate interplay between force generation, coarsening and connectivity is responsible for the highly dynamic process of structure formation in this heterogeneous active gel, and that these competing mechanisms result in anomalous transport, reminiscent of intracellular dynamics.

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Figure 1: Effect of κ on actin/fascin/myosin network structure.
Figure 2: Dynamics of actin/fascin/myosin networks.
Figure 3: Time evolution of the cluster-size distribution.
Figure 4: Dynamics of small, medium and large clusters.
Figure 5: Dependence of the mean run length on the cluster size.
Figure 6: Mean square displacement.
Figure 7: Dynamics and coarsening behaviour in the simulations.

References

  1. 1

    LeGoff, L., Amblard, F. & Furst, E. Motor-driven dynamics in actin-myosin networks. Phys. Rev. Lett. 88, 18101 (2002).

    Article  Google Scholar 

  2. 2

    Kruse, K., Joanny, J-F., Juelicher, F., Prost, J. & Sekimoto, K. Asters, vortices, and rotating spirals in active gels of polar filaments. Phys. Rev. Lett. 92, 78101 (2004).

    CAS  Article  Google Scholar 

  3. 3

    Joanny, J-F., Juelicher, F., Kruse, K. & Prost, J. Hydrodynamic theory for multi-component active polar gels. New. J. Phys. 9, 422 (2007).

    Article  Google Scholar 

  4. 4

    Lau, A., Hoffman, B., Davies, A., Crocker, J. & Lubensky, T. Microrheology, stress fluctuations, and active behaviour of living cells. Phys. Rev. Lett. 91, 198101 (2003).

    CAS  Article  Google Scholar 

  5. 5

    Joanny, J-F. & Prost, J. Active gels as a description of the actin-myosin cytoskeleton. HFSP J. 3, 94–104 (2009).

    CAS  Article  Google Scholar 

  6. 6

    Fletcher, D. A. & Geissler, P. L. Active biological materials. Annu. Rev. Phys. Chem. 60, 469–486 (2009).

    CAS  Article  Google Scholar 

  7. 7

    Guerin, T., Prost, J., Martin, P. & Joanny, J-F. Coordination and collective properties of molecular motors: Theory. Curr. Opin. Cell. Biol. 22, 14–20 (2010).

    CAS  Article  Google Scholar 

  8. 8

    Kane, R. E. Interconversion of structural and contractile actin gels by insertion of myosin during assembly. J. Cell. Biol. 97, 1745–1752 (1983).

    CAS  Article  Google Scholar 

  9. 9

    Janson, L. W., Kolega, J. & Taylor, D. L. Modulation of contraction by gelation/solation in a reconstituted motile model. J. Cell. Biol. 114, 1005–1015 (1991).

    CAS  Article  Google Scholar 

  10. 10

    Liverpool, T. B., Marchetti, M. C., Joanny, J-F. & Prost, J. Mechanical response of active gels. Epl-Europhys. Lett. 85, 18007 (2009).

    Article  Google Scholar 

  11. 11

    Koenderink, G. H. et al. Liquids and structural glasses special feature: An active biopolymer network controlled by molecular motors. Proc. Natl Acad. Sci. USA 106, 15192–15197 (2009).

    CAS  Article  Google Scholar 

  12. 12

    Bendix, P. M. et al. A quantitative analysis of contractility in active cytoskeletal protein networks. Biophys. J. 94, 3126–3136 (2008).

    CAS  Article  Google Scholar 

  13. 13

    Backouche, F., Haviv, L., Groswasser, D. & Bernheim-Groswasser, A. Active gels: Dynamics of patterning and self-organization. Phys. Biol. 3, 264–273 (2006).

    CAS  Article  Google Scholar 

  14. 14

    Smith, D. et al. Molecular motor-induced instabilities and cross linkers determine biopolymer organization. Biophys. J. 93, 4445–4452 (2007).

    CAS  Article  Google Scholar 

  15. 15

    Claessens, M. M. A. E., Semmrich, C., Ramos, L. & Bausch, A. R. Helical twist controls the thickness of F-actin bundles. Proc. Natl Acad. Sci. USA 105, 8819–8822 (2008).

    CAS  Article  Google Scholar 

  16. 16

    Lieleg, O., Claessens, M. M. A. E., Luan, Y. & Bausch, A. R. Transient binding and dissipation in cross-linked actin networks. Phys. Rev. Lett. 101, 108101 (2008).

    CAS  Article  Google Scholar 

  17. 17

    Metzler, R. & Klafter, J. The random walk’s guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339, 1–77 (2000).

    CAS  Article  Google Scholar 

  18. 18

    Metzler, R. & Klafter, J. Accelerating Brownian motion: A fractional dynamics approach to fast diffusion. Europhys. Lett. 51, 492–498 (2000).

    CAS  Article  Google Scholar 

  19. 19

    Weitz, D. A. & Oliveria, M. Fractal structures formed by kinetic aggregation of aqueous gold colloids. Phys. Rev. Lett. 52, 1433–1436 (1984).

    CAS  Article  Google Scholar 

  20. 20

    Langer, J. S. Theory of spinodal decomposition in alloys. Ann. Phys. 65, 53–86 (1971).

    Article  Google Scholar 

  21. 21

    Viscek, T. & Family, F. Dynamic scaling for aggregation of clusters. Phys. Rev. Lett. 52, 1669–1672 (1984).

    Article  Google Scholar 

  22. 22

    Effler, J. C. et al. Mitosis-specific mechanosensing and contractile-protein redistribution control cell shape. Curr. Biol. 16, 1962–1967 (2006).

    CAS  Article  Google Scholar 

  23. 23

    Hoffman, B. D., Massiera, G., Citters, K. M. V. & Crocker, J. C. The consensus mechanics of cultured mammalian cells. Proc. Natl Acad. Sci. USA 103, 10259–10264 (2006).

    CAS  Article  Google Scholar 

  24. 24

    Gallet, F., Arcizet, D., Bohec, P. & Richert, A. Power spectrum of out-of-equilibrium forces in living cells: Amplitude and frequency dependence. Soft Matter 5, 2947–2953 (2009).

    CAS  Article  Google Scholar 

  25. 25

    Liverpool, T. B. & Marchetti, M. C. Instabilities of isotropic solutions of active polar filaments. Phys. Rev. Lett. 90, 138102 (2003).

    Article  Google Scholar 

  26. 26

    Aranson, I. S. & Tsimring, L. S. Pattern formation of microtubules and motors: Inelastic interaction of polar rods. Phys. Rev. E 71, 50901 (2005).

    Article  Google Scholar 

  27. 27

    Juelicher, F., Kruse, K., Prost, J. & Joanny, J-F. Active behaviour of the cytoskeleton. Phys. Rep. 449, 3–28 (2007).

    CAS  Article  Google Scholar 

  28. 28

    Schmoller, K. M., Lieleg, O. & Bausch, A. R. Structural and viscoelastic properties of actin/filamin networks: Cross-linked versus bundled networks. Biophys. J. 97, 83–89 (2009).

    CAS  Article  Google Scholar 

  29. 29

    Margossian, S. S. & Lowey, S. Preparation of myosin and its subfragments from rabbit skeletal muscle. Meth. Enzymol. 85, 55–71 (1982).

    CAS  Article  Google Scholar 

  30. 30

    Spudich, J. A. & Watt, S. The regulation of rabbit skeletal muscle contraction. I. Biochemical studies of the interaction of the tropomyosin-troponin complex with actin and the proteolytic fragments of myosin. J. Biol. Chem. 246, 4866–4871 (1971).

    CAS  Google Scholar 

  31. 31

    MacLean-Fletcher, S. & Pollard, T. D. Identification of a factor in conventional muscle actin preparations which inhibits actin filament self-association. Biochem. Biophys. Res. Commun. 96, 18–27 (1980).

    CAS  Article  Google Scholar 

  32. 32

    Vignjevic, D. et al. Formation of filopodia-like bundles in vitro from a dendritic network. J. Cell. Biol. 160, 951–962 (2003).

    CAS  Article  Google Scholar 

  33. 33

    Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Colloid. Interface Sci. 179, 298–310 (1996).

    CAS  Article  Google Scholar 

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Acknowledgements

We gratefully acknowledge technical support by M. Rusp, G. Chmel and K. Vogt. We gratefully acknowledge the financial support of the DFG in the framework of the SFB 863, and partial support in the framework of the German Excellence Initiative by the ‘Nanosystems Initiative Munich’ and the ‘Institute of Advanced Studies’ (TUM-IAS). S.K. and V.S. thank the ‘International Graduate School for Science and Engineering’. V.S. acknowledges support from the Elite Network of Bavaria by the graduate programme CompInt.

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S.K. and A.R.B. designed experiments, carried out and analysed experiments. V.S., S.K. and A.R.B. conceived, carried out and analysed the simulations and wrote the paper.

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Correspondence to Andreas R. Bausch.

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The authors declare no competing financial interests.

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Köhler, S., Schaller, V. & Bausch, A. Structure formation in active networks. Nature Mater 10, 462–468 (2011). https://doi.org/10.1038/nmat3009

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