Constraints on Active Processes in Cochlear Hair Cells

In the cochlea, an organ responsible for mammalian hearing, sound waves are transduced into surface waves propagating along the basilar membrane. Due to the spatially varying stiffness of this membrane, frequency modes are peaked at a particular resonant position, with infinitely strong resonance in an idealized limit without friction. However, the real cochlea has dissipation too large to explain the sharply peaked frequency responses observed in hearing. Active processes in hair cells counter this dissipation throughout the cochlea, but the exact form of these active processes remains an open question. Here, we present a model with feedback where dissipation is cancelled at each location for the resonant frequency mode. While this mechanism ensures that there exists a spatial mode that is nearly infinitely peaked, it does not prevent the existence of other delocalized unstable modes. Numerically, we find that active processes must be fast compared to the resonant frequency. Otherwise, when active process strength is increased, a delocalized mode becomes unstable before sharply peaking. By considering the spectrum of the dynamics near the resonant position, we identify conditions for the active process to be viable.