Measured and modeled motion of free-standing hair bundles in response to sound stimulation

Although there has been a long-standing debate about whether hair bundles can be mechanically resonant, existing measurements do not resolve the issue. To test the possibility of resonance, and to determine which fluid properties axe important for deflection of hair bundles, we have made detailed measurements of the sound-induced motion of free-standing hair bundles as a function of frequency. The measurements, which relate hair-bundle deflection 0 to reticular lamina velocity U-b, show a strong frequency dependence. At low frequencies, H(f) = theta/U-b is nearly independent of frequency, with a positive phase. At high frequencies, H(f) magnitude falls with frequency at -20 dB/decade, with a phase near -pi/2 radians. A 2D hydrodynamic model accurately predicts both magnitude and phase of H(f) with only a single free parameter. A low-pass filter model with two free parameters fits the magnitude of H(f), but predicts a larger phase lag than observed at low frequencies. These results are consistent with the idea that that both viscous and inertial fluid properties drive hair-bundle deflection at low frequencies, while inertial fluid properties drive deflection at high frequencies,