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


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.


  1. Hudspeth, A. J. How the ear’s works work. Nature 341, 397–404 (1989)

    Article  CAS  ADS  Google Scholar 

  2. Hudspeth, A. J. Making an effort to listen: mechanical amplification in the ear. Neuron 59, 530–545 (2008)

    Article  CAS  Google Scholar 

  3. Hudspeth, A. J., Jülicher, F. & Martin, P. A critique of the critical cochlea: Hopf—a bifurcation—is better than none. J. Neurophysiol. 104, 1219–1229 (2010)

    Article  CAS  Google Scholar 

  4. Stokes, G. G. On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 1–86 (1850)

    ADS  Google Scholar 

  5. Batchelor, G. K. An Introduction to Fluid Dynamics 353–364 (Cambridge University Press, 2000)

    Book  Google Scholar 

  6. Tamada, K. & Fujikawa, H. The steady two-dimensional flow of viscous liquid at low Reynolds numbers passing through an infinite row of equal parallel circular cylinders. Q. J. Mech. Appl. Math. 10, 425–432 (1957)

    Article  Google Scholar 

  7. Yeom, J., Agonafer, D. D., Han, J.-H. & Shannon, M. A. Low Reynolds number flow across an array of cylindrical microposts in a microchannel and figure-of-merit analysis of micropost-filled microreactors. J. Micromech. Microeng. 19 10.1088/0960-1317/19/6/065025 (2009)

  8. Denk, W., Webb, W. W. & Hudspeth, A. J. Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer. Proc. Natl Acad. Sci. USA 86, 5371–5375 (1989)

    Article  CAS  ADS  Google Scholar 

  9. Perrin, F. Mouvement brownien d’un ellipsoïde (I). Dispersion diélectrique pour des molécules ellipsoïdales. J. Phys. Radium 5, 497–511 (1934)

    Article  CAS  Google Scholar 

  10. Broersma, S. Viscous force and torque constant for a cylinder. J. Chem. Phys. 74, 6989–6990 (1981)

    Article  ADS  Google Scholar 

  11. Kozlov, A. S., Risler, T. & Hudspeth, A. J. Coherent motion of stereocilia assures the concerted gating of hair-cell transduction channels. Nature Neurosci. 10, 87–92 (2007)

    Article  CAS  Google Scholar 

  12. Pickles, J. O. A model for the mechanics of the stereociliar bundle on acousticolateral hair cells. Hear. Res. 68, 159–172 (1993)

    Article  CAS  Google Scholar 

  13. Cotton, J. & Grant, W. Computational models of hair cell bundle mechanics: II. Simplified bundle models. Hear. Res. 197, 105–111 (2004)

    Article  Google Scholar 

  14. Karavitaki, K. D. & Corey, D. P. Sliding adhesion confers coherent motion to hair cell stereocilia and parallel gating to transduction channels. J. Neurosci. 30, 9051–9063 (2010)

    Article  CAS  Google Scholar 

  15. Martin, P., Mehta, A. D. & Hudspeth, A. J. Negative hair-bundle stiffness betrays a mechanism for mechanical amplification by the hair cell. Proc. Natl Acad. Sci. USA 97, 12026–12031 (2000)

    Article  CAS  ADS  Google Scholar 

  16. Verpy, E. et al. Stereocilin connects outer hair cells stereocilia to one another and to the tectorial membrane. J. Comp. Neurol. 519, 194–210 (2011)

    Article  CAS  Google Scholar 

  17. Howard, J. & Hudspeth, A. J. Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog’s saccular hair cell. Neuron 1, 189–199 (1988)

    Article  CAS  Google Scholar 

  18. Jaramillo, F., Markin, V. S. & Hudspeth, A. J. Auditory illusions and the single hair cell. Nature 364, 527–529 (1993)

    Article  CAS  ADS  Google Scholar 

  19. Neugebauer, D. C. & Thurm, U. Surface charges of the membrane and cell adhesion substances determine the structural integrity of hair bundles from the inner ear of fish. Cell Tissue Res. 249, 199–207 (1987)

    Article  Google Scholar 

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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.

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Authors and Affiliations



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).

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