A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are t hought to mediate amplification in the mammalian cochlea. In vertebrates th at lack these cells, and perhaps in mammals as well, active movements of ha ir bundles may underlie amplification. We have evaluated a mathematical mod el in which amplification stems from the activity of mechanoelectrical-tran sduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs an d exerts a negative force on the hair bundle. By enhancing bundle motion, t his force partially compensates for viscous damping by cochlear fluids. Lin ear stability analysis of a six-state kinetic model reveals Hopf bifurcatio ns for parameter values in the physiological range. These bifurcations sign al conditions under which the system's behavior changes from a damped oscil latory response to spontaneous limit-cycle oscillation. By varying the numb er of stereocilia in a bundle and the rate constant for Ca2+ binding, we ca lculate bifurcation frequencies spanning the observed range of auditory sen sitivity for a representative receptor organ, the chicken's cochlea. Simula tions using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transducti on channels occur universally in hair cells, this active-channel model desc ribes a mechanism of auditory amplification potentially applicable across s pecies and hair-cell types.