Hair cell bundles: flexoelectric motors of the inner ear

Abstract

Microvilli (stereocilia) projecting from the apex of hair cells in the inner ear are actively motile structures that feed energy into the vibration of the inner ear and enhance sensitivity to sound. The biophysical mechanism underlying the hair bundle motor is unknown. In this study, we examined a membrane flexoelectric origin for active movements in stereocilia and conclude that it is likely to be an important contributor to mechanical power output by hair bundles. We formulated a realistic biophysical model of stereocilia incorporating stereocilia dimensions, the known flexoelectric coefficient of lipid membranes, mechanical compliance, and fluid drag. Electrical power enters the stereocilia through displacement sensitive ion channels and, due to the small diameter of stereocilia, is converted to useful mechanical power output by flexoelectricity. This motor augments molecular motors associated with the mechanosensitive apparatus itself that have been described previously. The model reveals stereocilia to be highly efficient and fast flexoelectric motors that capture the energy in the extracellular electro-chemical potential of the inner ear to generate mechanical power output. The power analysis provides an explanation for the correlation between stereocilia height and the tonotopic organization of hearing organs. Further, results suggest that flexoelectricity may be essential to the exquisite sensitivity and frequency selectivity of non-mammalian hearing organs at high auditory frequencies, and may contribute to the "cochlear amplifier" in mammals.

Figure 1. Stereocilium flexoelectric biophysics.

a) As an excitatory force is applied the bundle deflects towards the tallest stereocilia and the tip link tension increases. Tip displacement causes the MET to open, current (I_T) to enter the stereocilia, thus leading to cable-like membrane depolarization. b–c) Through the membrane flexoelectric effect, depolarization compels a decrease in radius () and increase in height () under constant volume. Changes in length are accompanied by transverse motion due to the staircase gradient in stereocilia lengths and diagonal tip links. Deflections are resisted by actin stiffness and polymerization at the tip, the angular stiffness at the base, and fluid drag in the axial and transverse directions.

Figure 2. Flexoelectric Work Cycle.

During excitatory stimulation, the bundle is pushed towards the tallest stereocilium causing opening of the MET channel and an influx of depolarizing current. b) Under these conditions, flexoelectricity compels an increase in the curvature (decrease in the radius) and an isochoric increase in length resulting in an increase in the tip-link tension and bundle movement towards the applied bundle force. This is accompanied by MET adaptation and associated nonlinearities. d) As the stimulus moves in the inhibitory direction, hyperpolarizing MET current causes decreased stereocilium curvature, axial shortening, tip-link slackening, and further relaxation of the bundle in the direction of applied force.

Figure 3. Power Efficiency.

a) Taxonomy of power conversion for 6 µm long stereocilia showing peak efficiency of conversion at a specific best frequency (*). Input electrical MET power is lost to conductance of the soma and lost due to intrinsic mechanical properties of the stereocilia, including axial stiffness at low frequencies and entrained mass at high frequencies. Efficiency is further limited at high frequencies primarily by transverse viscous drag (light blue hatch). b) Peak conversion efficiency is tuned, with the optimum frequency (, *) increasing as the stereocilia becomes shorter (3 lengths shown). Efficiencies are predicted to be higher for axial motion (dashed curves, , **) vs. transverse motion (solid curves, *). c) Power output is also predicted to be tuned with peak power occurring at a specific frequency (solid curves, , ***). Tuning is reduced if axial length changes are not coupled to cause transverse bundle motion (dashed curves).

Figure 4. Universal phylogenetic law.

Raw data (symbols) showing the height of the tallest stereocilia for cochlear hair cells from mouse , , human , , guinea pig , mustached bat , chick , alligator lizard , , and the basilar papilla of turtle . Flexoelectric model predictions show the frequency of peak efficiency for stereocilia of different heights that impart power to accessory structures (e.g. TM) but lose power to the fluid, and for freestanding stereocilia that impart power to the fluid through viscous pumping alone.