Figure 3. Stiffness gradients of the gating springs and of the stereociliary pivots.

Stiffness (A) of the contribution of the gating springs (${\mathrm{{\rm K}}}_{\mathrm{G}\mathrm{S}}=r{\mathrm{{\rm K}}}_{\mathrm{H}\mathrm{B}}$), (B) of a hair bundle after tip-link disruption, corresponding to the contribution of the stereociliary pivots (${\mathrm{{\rm K}}}_{\mathrm{S}\mathrm{P}}=\left(1-r\right){\mathrm{{\rm K}}}_{\mathrm{H}\mathrm{B}}$), (C) of a single stereociliary pivot ($\mathrm{\kappa }={\mathrm{{\rm K}}}_{\mathrm{S}\mathrm{P}}{h}^2/N_{\mathrm{S}\mathrm{P}}$), and (D) of a single gating spring (${\displaystyle k_{\mathrm{G}\mathrm{S}}={\mathrm{K}}_{\mathrm{G}\mathrm{S}}/({\gamma }^2{N}_{\mathrm{T}\mathrm{L}})}$) as a function of the characteristic frequency (CF) for inner (white disks) and outer (black disks) hair cells. These stiffnesses were calculated from measured values of the hair-bundle stiffness ${\mathrm{{\rm K}}}_{\mathrm{H}\mathrm{B}}$ (Figure 2), the amplitude ratio $1-r$ of hair-bundle movements before and after tip-link disruption (Figure 3—figure supplement 1), the hair-bundle height $h$ and the number of stereocilia $N_{\mathrm{S}\mathrm{P}}$ (Figure 3—figure supplement 2), and the average number $N_{\mathrm{T}\mathrm{L}}$ of intact tip links (Figure 3—figure supplement 3). Each data point is the mean ± SEM; SEMs were calculated as described in the Materials and methods.

Figure 3—figure supplement 1. Gating-spring contribution to the hair-bundle stiffness.

We measured the amplitude of the hair-bundle movement evoked by a sinusoidal fluid-jet stimulus before (amplitude $X_1$) and after (amplitude $X_2$) application of EDTA iontophoresis (see an example in Figure 4A of the main text). The ratio $r=\left(X_2-X_1\right)/X_2$ is here plotted as a function of characteristic frequency (CF) for inner (white disks) and outer (black disks) hair cells. Because EDTA disrupted the tip links, the ratio $r={\mathrm{{\rm K}}}_{\mathrm{G}\mathrm{S}}/{\mathrm{{\rm K}}}_{\mathrm{H}\mathrm{B}}$ quantifies the contribution ${\mathrm{{\rm K}}}_{\mathrm{G}\mathrm{S}}$ of the gating springs to the stiffness ${\mathrm{{\rm K}}}_{\mathrm{H}\mathrm{B}}$ of an intact bundle; the complementary ratio, $1-r={\mathrm{{\rm K}}}_{\mathrm{S}\mathrm{P}}/{\mathrm{{\rm K}}}_{\mathrm{H}\mathrm{B}}$, represents the relative contribution of the stereociliary pivots, of stiffness ${\mathrm{{\rm K}}}_{\mathrm{S}\mathrm{P}}$. Error bars correspond to mean values ± SEM, with the number of cells indicated on the figure. These experiments were performed in low-Ca²⁺ saline.

Figure 3—figure supplement 2. Hair-bundle morphology along the tonotopic axis.

We used electron microscopy to count the number of stereocilia in a hair bundle. To avoid dehydration artefacts, we used instead optical microscopy to measure the width and height of the hair bundle. To measure width, the hair bundle was visualized from above (Figure 1). To measure height, the hair bundle was visualized from the side after it had been pushed against the apical surface of the hair cell with a glass rod. (A) Electron micrographs of typical outer (top row) and inner (bottom row) hair cells at cochlear locations corresponding to characteristic frequencies indicated on the figure. Tension in the tip links results in stereociliary tips with a prolate shape, which is also indicative of tip-link orientation. Scale bars: 1 µm. The height ${\displaystyle h}$ (B), width ${\displaystyle W}$ (C), geometrical gain ${\displaystyle \gamma }$ (D), and number of stereocilia $N_{\mathrm{S}\mathrm{P}}$ (E) of a hair bundle are plotted as a function of the characteristic frequency (CF) for inner (white disks) and outer (black disks) hair cells. In panel (C), the inset shows a schematic top view of a hair bundle and indicates how the bundle’s width was measured. The geometrical gain was calculated as the ratio of the interstereociliary spacing and the hair-bundle height, assuming an interstereociliary spacing of 462 nm for all outer hair cells and 420 nm for all inner hair cells. The error bars in (B), (C) and (E) represent standard errors of the means with numbers of cells indicated between brackets; in (D), error bars are calculated as described in the Materials and methods.

Figure 3—figure supplement 3. Transduction currents and number of intact tip links along the tonotopic axis.

A large mechanical stimulus (top; fluid-jet voltage command) was applied to the hair bundle to estimate the magnitude of the transduction current (bottom) at saturation in inner hair cells (A) and outer hair cells (B) along the tonotopic axis of the cochlea. Maximal current (C) and estimated number $N_{\mathrm{T}\mathrm{L}}$ of tip links ((D); see Materials and methods) are plotted as a function of the characteristic frequency (CF) for inner (white disks) and outer (black disks) hair cells. Error bars correspond to mean values ± SEM, with n = 10 cells for all data points. In panels (A and B), the hair cell’s characteristic frequency is indicated above each recording; the frequency of stimulation was 60 Hz. In these experiments, the hair cells were immersed in standard saline at a Ca²⁺ concentration of 1.5 mM.