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Solid friction between soft filaments

Nature Materials volume 14, pages 583–588 (2015)Cite this article

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Abstract

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.

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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.

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Acknowledgements

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).

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Authors and Affiliations

  1. Martin Fisher School of Physics, Brandeis University, 415 South Street Waltham, Massachusetts 02454, USA,

    Andrew Ward, Feodor Hilitski, Walter Schwenger & Zvonimir Dogic

  2. Graduate Program in Biophysics and Structural Biology, Brandeis University, 415 South Street Waltham, Massachusetts 02454, USA,

    David Welch

  3. Department of Physics, Florida Atlantic University, 777 Glades Road Boca Raton, Florida 33431, USA,

    A. W. C. Lau

  4. Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, 2300 RA Leiden, The Netherlands

    Vincenzo Vitelli

  5. School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, Massachusetts 02138, USA

    L. Mahadevan

  6. Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA

    L. Mahadevan

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Contributions

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.

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Correspondence to Zvonimir Dogic.

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The authors declare no competing financial interests.

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Ward, A., Hilitski, F., Schwenger, W. et al. Solid friction between soft filaments. Nature Mater 14, 583–588 (2015). https://doi.org/10.1038/nmat4222

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