Links regulate deflection fluctuations in the sensory cells of hearing

In our ears, inner-hair-cell hair bundles (IHBs) convert sound-induced forces into electrical signals, which are ultimately transmitted to the brain. An IHB comprises filamentous stereocilia emanating from the inner-hair-cell apex. Stereocilium deflections promote ion-channel opening and closing, causing receptor currents. This process is limited by fluctuations in the deflections, which compete with the sound signal, limiting the threshold of hearing. Stereocilia are viscoelastic structures and are coupled by fluid and viscoelastic links. The stiffness and damping of the system's components constrain stereocilium deflections, but increasing damping increases thermal deflection fluctuations. Competition between the constraining forces and thermal forces determines the deflection fluctuations. To better understand the deflection fluctuations, we build a mathematical model that relates the IHB's mechanical properties to deflection fluctuations. We find that the coherency of neighboring stereocilium deflections is less than 0.75 at frequencies corresponding to the physiological range of sound frequencies. The coherency for pairs of stereocilia decreases exponentially with the distance between them and is approximately zero between stereocilia at the center and edge of the IHB. We determine how the deflection fluctuations depend on the stiffness and damping of the links. In the absence of stiff links between stereocilia, neighboring stereocilia are weakly or negatively correlated in the physiological frequency range. We show how the sign of the coherency between stereocilium pairs is determined by the eigendecomposition of the deflection power spectral density matrix. Increasing the number of stereocilia in the IHB decreases the coherency between stereocilium pairs. The model also predicts that the threshold of hearing corresponds to IHB stereocilium deflections owing to sound of < 1.5 nm and that links of physiological stiffness decrease the threshold of hearing by at least 10dB. Predictions of the mathematical model are experimentally testable using recently developed techniques.