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 (IT) 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.
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.
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.
Raw data (symbols) showing the height of the tallest stereocilia for cochlear hair cells from mouse [2], [44], human [2], [44], guinea pig [45], mustached bat [46], chick [47], alligator lizard [1], [13], [48] and the basilar papilla of turtle [49]. 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.
Table 1.
Model coefficients and parameters.
Table 2.
Nominal Physical Parameters.