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Forces between clustered stereocilia minimize friction in the ear on a subnanometre scale

Nature volume 474, pages 376–379 (2011)Cite this article

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Abstract

The detection of sound begins when energy derived from an acoustic stimulus deflects the hair bundles on top of hair cells1. As hair bundles move, the viscous friction between stereocilia and the surrounding liquid poses a fundamental physical challenge to the ear’s high sensitivity and sharp frequency selectivity. Part of the solution to this problem lies in the active process that uses energy for frequency-selective sound amplification2,3. Here we demonstrate that a complementary part of the solution involves the fluid–structure interaction between the liquid within the hair bundle and the stereocilia. Using force measurement on a dynamically scaled model, finite-element analysis, analytical estimation of hydrodynamic forces, stochastic simulation and high-resolution interferometric measurement of hair bundles, we characterize the origin and magnitude of the forces between individual stereocilia during small hair-bundle deflections. We find that the close apposition of stereocilia effectively immobilizes the liquid between them, which reduces the drag and suppresses the relative squeezing but not the sliding mode of stereociliary motion. The obliquely oriented tip links couple the mechanotransduction channels to this least dissipative coherent mode, whereas the elastic horizontal top connectors that stabilize the structure further reduce the drag. As measured from the distortion products associated with channel gating at physiological stimulation amplitudes of tens of nanometres, the balance of viscous and elastic forces in a hair bundle permits a relative mode of motion between adjacent stereocilia that encompasses only a fraction of a nanometre. A combination of high-resolution experiments and detailed numerical modelling of fluid–structure interactions reveals the physical principles behind the basic structural features of hair bundles and shows quantitatively how these organelles are adapted to the needs of sensitive mechanotransduction.

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Figure 1: Finite-element analysis of fluid–structure interactions in a hair bundle.
Figure 2: Fluid–structure interactions in a stochastic model.
Figure 3: Experimental verification of model predictions.

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Acknowledgements

We thank A. J. Hinterwirth for assistance in constructing the interferometer and B. Fabella for programming the experimental software; M. Fleischer for help with programming the fluid finite-element model; R. Gärtner and A. Voigt for discussions of the finite-element model and stochastic computations; M. Lenz for discussions of stochastic computations and the analytic derivation of fluid-mediated interactions; and O. Ahmad, D. Andor and M. O. Magnasco for discussions about data analysis. This research was funded by National Institutes of Health grant DC000241. Computational resources were provided by the Center for Information Services and High Performance Computing of the Technische Universität Dresden. J.B. was supported by grants Gr 1388/14 and Vo 899/6 from the Deutsche Forschungsgemeinschaft. A.S.K. was supported by the Howard Hughes Medical Institute, of which A.J.H. is an Investigator.

Author information

Authors and Affiliations

  1. Howard Hughes Medical Institute and Laboratory of Sensory Neuroscience, The Rockefeller University, 1230 York Avenue, New York, 10065, New York, USA

    Andrei S. Kozlov, Corstiaen P. C. Versteegh & A. J. Hudspeth

  2. Department of Mathematics, Institute of Scientific Computing, Technische Universität Dresden, 01062 Dresden, Germany

    Johannes Baumgart

  3. Institut Curie, Centre de Recherche, F-75005 Paris, France

    Thomas Risler

  4. UPMC Université Paris 06, UMR 168, F-75005 Paris, France

    Thomas Risler

  5. CNRS, UMR 168, F-75005 Paris, France

    Thomas Risler

  6. Experimental Zoology Group, Wageningen University, 6709 PG Wageningen, The Netherlands

    Corstiaen P. C. Versteegh

Authors
  1. Andrei S. Kozlov
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  2. Johannes Baumgart
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  3. Thomas Risler
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  4. Corstiaen P. C. Versteegh
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  5. A. J. Hudspeth
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Contributions

A.S.K. organized the collaboration, designed and performed the experiments, analysed data, and wrote most of the manuscript. J.B. developed the finite-element formulation and conducted the corresponding computations, implemented the stochastic modelling, derived analytic estimates of fluid-mediated interactions, wrote the corresponding Supplementary Information sections, analysed data and edited the manuscript. T.R. derived analytic estimates of fluid-mediated interactions, developed the stochastic models, implemented the data analysis, wrote the corresponding Supplementary Information sections and edited the manuscript. C.P.C.V. built the scaled model and performed the corresponding experiment. A.J.H. designed the experiments, performed the electron microscopy and edited the manuscript.

Corresponding author

Correspondence to A. J. Hudspeth.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-19 with legends, Supplementary Tables 1-2 and additional references. (PDF 12632 kb)

Supplementary Movie 1

This movie shows motion of a hair bundle without elastic links. Progressively more stereocilia are entrained with increasing frequency. (ZIP 26822 kb)

Supplementary Movie 2

This movie shows motion of a hair bundle with elastic top connectors. The bundle moves as a unit at all frequencies until inertia intervenes at frequencies above several kilohertz. (ZIP 26832 kb)

Supplementary Movie 3

This movie shows motion of a hair bundle with tip links. At low frequencies, only the stereocilia in the symmetry plane are deflected. The obliquely oriented tip links amplify the motion for the shorter stereocilia. As the frequency rises, more and more stereocilia are entrained. (ZIP 26831 kb)

Supplementary Movie 4

This movie shows motion of a hair bundle containing both tip links and top connectors. The bundle moves as a unit at all frequencies until inertia intervenes at frequencies above several kilohertz. (ZIP 26791 kb)

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Kozlov, A., Baumgart, J., Risler, T. et al. Forces between clustered stereocilia minimize friction in the ear on a subnanometre scale. Nature 474, 376–379 (2011). https://doi.org/10.1038/nature10073

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