force measurements on a scaled hair - bundle model respected the physiological character of the liquid flow .
the finite - element method provided approximate solutions to partial differential equations reflecting the hair bundle 's geometry .
the velocity variable of the liquid was substituted by the time derivative of the displacement ; fluid pressure was approximated by linear shape functions and the displacements of liquid and solid by quadratic ones .
the hydrodynamic forces between stereocilia were estimated analytically by solving the stefan - reynolds equations under the lubrication approximation , which is valid when the gaps between adjacent stereocilia are much smaller than their diameter .
stochastic simulations based on these results were performed for a system of linearly coupled dynamic variables following a langevin description with gaussian white noise at room temperature .
the integration procedure was validated by choosing time steps small enough to assure that the results were independent of the increment .
we tested the effects of inertia and of the estimated top - connecter stiffness and confirmed the validity of our conclusions for mammalian hair bundles .
dual - beam differential interferometry was used to record stereociliary motions with sub - nanometre spatial and sub - millisecond temporal resolution .
fourier analysis of the records was performed with the multitaper method to obtain coherence spectra as well as stiffness and drag coefficients .
these results were used to verify the predictions of the numerical model and to measure directly the relative mode of motion between stereocilia .
 the detection of sound begins when energy derived from an acoustic stimulus deflects the hair bundles atop hair cells1 . 
 as hair bundles move , the viscous friction between stereocilia and the surrounding liquid poses a fundamental physical challenge to the earfs 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 stereocilia and the liquid within the hair bundle . 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 . 
Methods Summary
Supplementary Material