Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Solid friction between soft filaments


Any macroscopic deformation of a filamentous bundle is necessarily accompanied by local sliding and/or stretching of the constituent filaments1,2. Yet the nature of the sliding friction between two aligned filaments interacting through multiple contacts remains largely unexplored. Here, by directly measuring the sliding forces between two bundled F-actin filaments, we show that these frictional forces are unexpectedly large, scale logarithmically with sliding velocity as in solid-like friction, and exhibit complex dependence on the filaments’ overlap length. We also show that a reduction of the frictional force by orders of magnitude, associated with a transition from solid-like friction to Stokes’s drag, can be induced by coating F-actin with polymeric brushes. Furthermore, we observe similar transitions in filamentous microtubules and bacterial flagella. Our findings demonstrate how altering a filament’s elasticity, structure and interactions can be used to engineer interfilament friction and thus tune the properties of fibrous composite materials.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Single-molecule experiments reveal frictional interactions between a pair of sliding F-actin filaments.
Figure 2: 1D–Frenkel–Kontorova model accounts for the essential features of interfilament sliding friction.
Figure 3: Interfilament sliding friction depends on relative filament polarity.
Figure 4: Filament surface structure controls the transition from solid to hydrodynamic friction.
Figure 5: Sliding dynamics of microtubules and bacterial flagella.


  1. 1

    Vigolo, B. et al. Macroscopic fibres and ribbons of oriented carbon nanotubes. Science 290, 1331–1334 (2000).

    CAS  Article  Google Scholar 

  2. 2

    Sanchez, T., Chen, D. T. N., DeCamp, S. J., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012).

    CAS  Article  Google Scholar 

  3. 3

    Kozlov, A. S., Baumgart, J., Risler, T., Versteegh, C. P. C. & Hudspeth, A. J. Forces between clustered stereocilia minimize friction in the ear on a subnanometre scale. Nature 474, 376–379 (2011).

    CAS  Article  Google Scholar 

  4. 4

    Claessens, M., Bathe, M., Frey, E. & Bausch, A. R. Actin-binding proteins sensitively mediate F-actin bundle stiffness. Nature Mater. 5, 748–753 (2006).

    CAS  Article  Google Scholar 

  5. 5

    Heussinger, C., Bathe, M. & Frey, E. Statistical mechanics of semiflexible bundles of wormlike polymer chains. Phys. Rev. Lett. 99, 048101 (2007)

    Article  Google Scholar 

  6. 6

    Zimmerman, S. B. & Minton, A. P. Macromolecular crowding—biochemical, biophysical and physiological consequences. Annu. Rev. Biophys. Biomol. Struct. 22, 27–65 (1993).

    CAS  Article  Google Scholar 

  7. 7

    Rau, D. C., Lee, B. & Parsegian, V. A. Measurement of the repulsive force between poly-electrolyte molecules in ionic solution—hydration forces between parallel DNA double helices. Proc. Natl Acad. Sci. USA 81, 2621–2625 (1984).

    CAS  Article  Google Scholar 

  8. 8

    Vanossi, A., Manini, N., Urbakh, M., Zapperi, S. & Tosatti, E. Colloquium: Modeling friction: From nanoscale to mesoscale. Rev. Mod. Phys. 85, 529–552 (2013).

    CAS  Article  Google Scholar 

  9. 9

    Braun, O. M. & Kivshar, Y. S. Nonlinear dynamics of the Frenkel–Kontorova model. Phys. Rep. 306, 1–108 (1998).

    Article  Google Scholar 

  10. 10

    Merkel, R., Nassoy, P., Leung, A., Ritchie, K. & Evans, E. Energy landscapes of receptor–ligand bonds explored with dynamic force spectroscopy. Nature 397, 50–53 (1999).

    CAS  Article  Google Scholar 

  11. 11

    Gnecco, E. et al. Velocity dependence of atomic friction. Phys. Rev. Lett. 84, 1172–1175 (2000).

    CAS  Article  Google Scholar 

  12. 12

    Muser, M. H., Urbakh, M. & Robbins, M. O. in Advances in Chemical Physics Vol. 126 (eds Prigogine, I. & Rice, S. A.) 187–272 (John Wiley, 2003).

    Book  Google Scholar 

  13. 13

    Suda, H. Origin of friction derived from rupture dynamics. Langmuir 17, 6045–6047 (2001).

    CAS  Article  Google Scholar 

  14. 14

    Holmes, K. C., Popp, D., Gebhard, W. & Kabsch, W. Atomic model of the actin filament. Nature 347, 44–49 (1990).

    CAS  Article  Google Scholar 

  15. 15

    Kojima, H., Ishijima, A. & Yanagida, T. Direct measurement of stifness of single actin-filaments with and without topomyosin by in-vitro nanomanipulation. Proc. Natl Acad. Sci. USA 91, 12962–12966 (1994).

    CAS  Article  Google Scholar 

  16. 16

    Lau, A. W. C., Prasad, A. & Dogic, Z. Condensation of isolated semi-flexible filaments driven by depletion interactions. Europhys. Lett. 87, 48006 (2009).

    Article  Google Scholar 

  17. 17

    De Gennes, P. G. Maximum pull out force on DNA hybrids. C. R. Acad. Sci. IV 2, 1505–1508 (2001).

    CAS  Google Scholar 

  18. 18

    Hatch, K., Danilowicz, C., Coljee, V. & Prentiss, M. Demonstration that the shear force required to separate short double-stranded DNA does not increase significantly with sequence length for sequences longer than 25 base pairs. Phys. Rev. E 78, 011920 (2008).

    CAS  Article  Google Scholar 

  19. 19

    Bormuth, V., Varga, V., Howard, J. & Schaffer, E. Protein friction limits diffusive and directed movements of kinesin motors on microtubules. Science 325, 870–873 (2009).

    CAS  Article  Google Scholar 

  20. 20

    Choi, J. S. et al. Friction anisotropy-driven domain imaging on exfoliated monolayer graphene. Science 333, 607–610 (2011).

    CAS  Article  Google Scholar 

  21. 21

    Forth, S., Hsia, K-C., Shimamoto, Y. & Kapoor, T. M. Asymmetric friction of nonmotor MAPs can lead to their directional motion in active microtubule networks. Cell 157, 420–432 (2014).

    CAS  Article  Google Scholar 

  22. 22

    Li, G. L. & Tang, J. X. Diffusion of actin filaments within a thin layer between two walls. Phys. Rev. E 69, 061921 (2004).

    Article  Google Scholar 

  23. 23

    Sanchez, T., Welch, D., Nicastro, D. & Dogic, Z. Cilia-like beating of active microtubule bundles. Science 333, 456–459 (2011).

    CAS  Article  Google Scholar 

  24. 24

    Nogales, E., Wolf, S. G. & Downing, K. H. Structure of the αβ tubulin dimer by electron crystallography. Nature 391, 199–203 (1998).

    CAS  Article  Google Scholar 

  25. 25

    Klein, J., Kumacheva, E., Mahalu, D., Perahia, D. & Fetters, L. J. Reduction of frictional forces between solid-surfaces bearing polymer brushes. Nature 370, 634–636 (1994).

    CAS  Article  Google Scholar 

  26. 26

    Akbulut, M., Belman, N., Golan, Y. & Israelachvili, J. Frictional properties of confined nanorods. Adv. Mater. 18, 2589–2592 (2006).

    CAS  Article  Google Scholar 

  27. 27

    Mate, C. M., McClelland, G. M., Erlandsson, R. & Chiang, S. Atomic scale-friction of a tungsten tip on a graphite surface. Phys. Rev. Lett. 59, 1942–1945 (1987).

    CAS  Article  Google Scholar 

  28. 28

    Luan, B. Q. & Robbins, M. O. The breakdown of continuum models for mechanical contacts. Nature 435, 929–932 (2005).

    CAS  Article  Google Scholar 

  29. 29

    Yoshizawa, H., Chen, Y. L. & Israelachvili, J. Fundamental mechanism of interfacial friction. 1. Relation between adhesion and friction. J. Phys. Chem. 97, 4128–4140 (1993).

    CAS  Article  Google Scholar 

  30. 30

    Van Alsten, J. & Granick, S. Molecular tribometry of ultrathin liquid-films. Phys. Rev. Lett. 61, 2570–2573 (1988).

    CAS  Article  Google Scholar 

  31. 31

    Bohlein, T., Mikhael, J. & Bechinger, C. Observation of kinks and antikinks in colloidal monolayers driven across ordered surfaces. Nature Mater. 11, 126–130 (2012).

    CAS  Article  Google Scholar 

Download references


We acknowledge useful discussions with N. Upadhyaya, M. Hagan and R. Bruinsma. A.W., D.W. and W.S. were supported by National Science Foundation grants CMMI-1068566, NSF-MRI-0923057 and NSF-MRSEC-1206146. F.H. and Z.D. were supported by Department of Energy, Office of Basic Energy Sciences under Award DE-SC0010432TDD. V.V. acknowledges FOM and NWO for financial support. L.M. was supported by Harvard-NSF MRSEC and the MacArthur Foundation. We also acknowledge use of the Brandeis MRSEC optical microscopy facility (NSF-MRSEC-1206146).

Author information




A.W. and Z.D. conceived the experiments. A.W. measured actin sliding friction and performed computer simulations. F.H., A.W. and D.W. performed microtubule sliding experiments. W.S. performed flagella sliding dynamics. A.W.C.L. developed a preliminary theoretical model that explains the velocity dependence of sliding friction. L.M. and V.V. developed the theoretical model that explains the dependence of sliding friction on overlap length. A.W., V.V., L.M. and Z.D. wrote the manuscript. All authors revised the manuscript.

Corresponding author

Correspondence to Zvonimir Dogic.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 1271 kb)

Supplementary Information

Supplementary Movie 1 (AVI 15866 kb)

Supplementary Information

Supplementary Movie 2 (AVI 3519 kb)

Supplementary Information

Supplementary Movie 3 (AVI 7260 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ward, A., Hilitski, F., Schwenger, W. et al. Solid friction between soft filaments. Nature Mater 14, 583–588 (2015).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing