Self-straining of actively crosslinked microtubule networks

Article metrics


Cytoskeletal networks are foundational examples of active matter and central to self-organized structures in the cell. In vivo, these networks are active and densely crosslinked. Relating their large-scale dynamics to the properties of their constituents remains an unsolved problem. Here, we study an in vitro active gel made from aligned microtubules and XCTK2 kinesin motors. Using photobleaching, we demonstrate that the gel’s aligned microtubules, driven by motors, continually slide past each other at a speed independent of the local microtubule polarity and motor concentration. This phenomenon is also observed, and remains unexplained, in spindles. We derive a general framework for coarse graining microtubule gels crosslinked by molecular motors from microscopic considerations. Using microtubule–microtubule coupling through a force–velocity relationship for kinesin, this theory naturally explains the experimental results: motors generate an active strain rate in regions of changing polarity, which allows microtubules of opposite polarities to slide past each other without stressing the material.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Bleaching of aligned active gels reveals microtubule sliding speed.
Fig. 2: Microtubule sliding speed is independent of polarity and motor concentration.
Fig. 3: Sketch of the microscopic model.

Data availability

Figures 1 and 2 are based on microscopy data. The raw data are available from the authors upon reasonable request.


  1. 1.

    Marchetti, M. C. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).

  2. 2.

    Needleman, D. & Dogic, Z. Active matter at the interface between materials science and cell biology. Nat. Rev. Mater. 2, 17048 (2017).

  3. 3.

    Alberts, B. et al. Molecular Biology of the Cell 4th edn (Garland, 2002).

  4. 4.

    Kruse, K., Joanny, J.-F., Jülicher, F., Prost, J. & Sekimoto, K. Generic theory of active polar gels: a paradigm for cytoskeletal dynamics. Eur. Phys. J. E 16, 5–16 (2005).

  5. 5.

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

  6. 6.

    Jülicher, F., Grill, S. W. & Salbreux, G. Hydrodynamic theory of active matter. Rep. Prog. Phys. 81, 076601 (2018).

  7. 7.

    Bray, D. Cell Movements: From Molecules to Motility 2nd edn (Garland, 2001).

  8. 8.

    Naganathan, S. R. et al. Morphogenetic degeneracies in the actomyosin cortex. elife 7, e37677 (2018).

  9. 9.

    Roostalu, J., Rickman, J., Thomas, C., Nédélec, F. & Surrey, T. Determinants of polar versus nematic organization in networks of dynamic microtubules and mitotic motors. Cell 175, 796–808 (2018).

  10. 10.

    Foster, P. J., Fürthauer, S., Shelley, M. J. & Needleman, D. J. From cytoskeletal assemblies to living materials. Curr. Opin. Cell Biol. 56, 109–114 (2019).

  11. 11.

    Mitchison, T. J. Mechanism and function of poleward flux in Xenopus extract meiotic spindles. Phil. Trans. R. Soc. Lond. B 360, 623–629 (2005).

  12. 12.

    Burbank, K. S., Mitchison, T. J. & Fisher, D. S. Slide-and-cluster models for spindle assembly. Curr. Biol. 17, 1373–1383 (2007).

  13. 13.

    Yang, G., Cameron, L. A., Maddox, P. S., Salmon, E. D. & Danuser, G. Regional variation of microtubule flux reveals microtubule organization in the metaphase meiotic spindle. J. Cell Biol. 182, 631–639 (2008).

  14. 14.

    Fürthauer, S., Strempel, M., Grill, S. W. & Jülicher, F. Active chiral fluids. Eur. Phys. J. E 35, 1–13 (2012).

  15. 15.

    Thampi, S. P., Golestanian, R. & Yeomans, J. M. Velocity correlations in an active nematic. Phys. Rev. Lett. 111, 118101 (2013).

  16. 16.

    Salbreux, G., Prost, J. & Joanny, J.-F. Hydrodynamics of cellular cortical flows and the formation of contractile rings. Phys. Rev. Lett. 103, 058102 (2009).

  17. 17.

    Mayer, M., Depken, M., Bois, J. S., Jülicher, F. & Grill, S. W. Anisotropies in cortical tension reveal the physical basis of polarizing cortical flows. Nature 467, 617–621 (2010).

  18. 18.

    Naganathan, S. R., Fürthauer, S., Nishikawa, M., Jülicher, F. & Grill, S. W. Active torque generation by the actomyosin cell cortex drives left–right symmetry breaking. elife 3, e04165 (2014).

  19. 19.

    Brugués, J. & Needleman, D. Physical basis of spindle self-organization. Proc. Natl Acad. Sci. USA 111, 18496–18500 (2014).

  20. 20.

    Kruse, K. & Jülicher, F. Actively contracting bundles of polar filaments. Phys. Rev. Lett. 85, 1778–1781 (2000).

  21. 21.

    Aranson, I. S. & Tsimring, L. S. Pattern formation of microtubules and motors: inelastic interaction of polar rods. Phys. Rev. E 71, 050901 (2005).

  22. 22.

    Liverpool, T. B. & Marchetti, M. C. Bridging the microscopic and the hydrodynamic in active filament solutions. Europhys. Lett. 69, 846–852 (2005).

  23. 23.

    Liverpool, T. B. & Marchetti, M. C. in Cell Motility (ed. Lenz, P.) 177–206 (Springer, 2008).

  24. 24.

    Saintillan, D. & Shelley, M. J. Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. Phys. Rev. Lett. 100, 178103 (2008).

  25. 25.

    Saintillan, D. & Shelley, M. J. Instabilities, pattern formation and mixing in active suspensions. Phys. Fluids 20, 123304 (2008).

  26. 26.

    Saintillan, D. & Shelley, M. J. Active suspensions and their nonlinear models. C. R. Phys. 14, 497–517 (2013).

  27. 27.

    Foster, P. J., Fürthauer, S., Shelley, M. J. & Needleman, D. J. Active contraction of microtubule networks. eLife 4, e10837 (2015).

  28. 28.

    Gao, T., Blackwell, R., Glaser, M. A., Betterton, M. D. & Shelley, M. J. Multiscale polar theory of microtubule and motor-protein assemblies. Phys. Rev. Lett. 114, 048101 (2015).

  29. 29.

    Heidenreich, S., Dunkel, J., Klapp, S. H. L. & Bär, M. Hydrodynamic length-scale selection in microswimmer suspensions. Phys. Rev. E 94, 020601 (2016).

  30. 30.

    Maryshev, I., Marenduzzo, D., Goryachev, A. B. & Morozov, A. Kinetic theory of pattern formation in mixtures of microtubules and molecular motors. Phys. Rev. E 97, 022412 (2018).

  31. 31.

    Broedersz, C. P. & MacKintosh, F. C. Modeling semiflexible polymer networks. Rev. Mod. Phys. 86, 995 (2014).

  32. 32.

    Ronceray, P. & Lenz, M. Connecting local active forces to macroscopic stress in elastic media. Soft Matter 11, 1597–1605 (2015).

  33. 33.

    Ronceray, P., Broedersz, C. P. & Lenz, M. Fiber networks amplify active stress. Proc. Natl Acad. Sci. USA 113, 2827–2832 (2016).

  34. 34.

    Belmonte, J. M., Leptin, M. & Nédélec, F. A theory that predicts behaviors of disordered cytoskeletal networks. Mol. Syst. Biol. 13, 941 (2017).

  35. 35.

    Foster, P. J., Yan, W., Fürthauer, S., Shelley, M. J. & Needleman, D. J. Connecting macroscopic dynamics with microscopic properties in active microtubule network contraction. New J. Phys. 19, 125011 (2017).

  36. 36.

    Hentrich, C. & Surrey, T. Microtubule organization by the antagonistic mitotic motors kinesin-5 and kinesin-14. J. Cell Biol. 189, 465–480 (2010).

  37. 37.

    Yu, C.-H. et al. Measuring microtubule polarity in spindles with second-harmonic generation. Biophys. J. 106, 1578–1587 (2014).

  38. 38.

    Brugués, J., Nuzzo, V., Mazur, E. & Needleman, D. J. Nucleation and transport organize microtubules in metaphase spindles. Cell 149, 554–564 (2012).

  39. 39.

    Kapitein, L. C. et al. The bipolar mitotic kinesin Eg5 moves on both microtubules that it crosslinks. Nature 435, 114–118 (2005).

  40. 40.

    Tan, R., Foster, P. J., Needleman, D. J. & McKenney, R. J. Cooperative accumulation of dynein–dynactin at microtubule minus-ends drives microtubule network reorganization. Dev. Cell 44, 233–247 (2018).

Download references


C.E.W. acknowledges support by NIH R35GM122482. D.J.N. acknowledges the Kavli Institute for Bionano Science and Technology at Harvard University and National Science Foundation grants PHY-1305254, PHY-0847188, DMR-0820484 and DBI-0959721. P.J.F. acknowledges support from the Gordon and Betty Moore Foundation for support as a Physics of Living Systems Fellow through grant no. GBMF4513. M.J.S. acknowledges support from National Science Foundation grants DMR-0820341 (NYU MRSEC), DMS-1463962 and DMS-1620331. Z.D. acknowledges support from NSF MRSEC DMR-1420382.

Author information

S.F., M.J.S. and D.J.N. developed the theory. B.L., P.J.F., S.C.E.-M., C.-H.Y., C.E.W. and Z.D. performed experiments and provided materials. S.F., B.L., D.J.N. and M.J.S. wrote the paper with input from all authors.

Correspondence to Sebastian Fürthauer.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information: Nature Physics thanks Karin John, Gijsje Koenderink and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Information, Figs. 1–4 and refs. 1–17.

Reporting Summary

Supplementary Video 1

Fluorescent microtubule material with 0.4 µM XCTK2.

Supplementary Video 2

Fluorescent microtubule material with 0.75 µM XCTK2.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark