Tonotopy of the mammalian cochlea is associated with stiffness and tension gradients of the hair cell’s tip-link complex

Frequency analysis of sound by the cochlea relies on sharp frequency tuning of mechanosensory hair cells along a tonotopic axis. To clarify the underlying biophysical mechanism, we have investigated the micromechanical properties of the hair cell’s mechanoreceptive hair bundle in the rat cochlea. We studied both inner and outer hair cells, which send nervous signals to the brain and amplify cochlear vibrations, respectively. We find that tonotopy is associated with gradients of stiffness and resting mechanical tension, with steeper gradients for outer hair cells, emphasizing the division of labor between the two hair-cell types. We demonstrate that tension in the tip links that convey force to the mechano-electrical transduction channels increases at reduced Ca2+. Finally, we reveal tonotopic gradients in stiffness and tension at the level of a single tip link. We conclude that intrinsic mechanical gradients of the tip-link complex help specify the characteristic frequency of the hair cell.

respectively. We find that tonotopy is associated with gradients of stiffness and resting 23 mechanical tension, with steeper gradients for outer hair cells, emphasizing the division of 24 labor between the two hair-cell types. We demonstrate that tension in the tip links that 25 convey force to the mechano-electrical transduction channels increases at reduced Ca 2+ . 26 Finally, we reveal tonotopic gradients in stiffness and tension at the level of a single tip link. 27 We conclude that intrinsic mechanical gradients of the tip-link complex help specify the 28 characteristic frequency of the hair cell. 29 30 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint The cochlea -the auditory organ of the inner ear-is endowed with a few thousands of 32 mechanosensory hair cells that are each tuned to detect a characteristic sound frequency 33 (Fettiplace and Kim, 2014). Different frequencies are detected by different cells, which are 34 spatially distributed in the organ according to a frequency -or tonotopic-map (Lewis et al.,35 1982; Greenwood, 1990; Viberg and Canlon, 2004). Despite its critical importance for 36 frequency analysis of complex sound stimuli, determining the mechanism that specifies the 37 characteristic frequency of a given hair cell remains a major challenge of auditory physiology. 38 Although certainly not the only determinant of hair-cell tuning (Fettiplace and Fuchs,39 1999), we focus here on the contribution of the hair bundle, the cohesive tuft of cylindrical 40 processes called stereocilia that protrude from the apical surface of each hair cell. The hair 41 bundle works as the mechanical antenna of the hair cell (Hudspeth, 1989). Sound evokes 42 hair-bundle deflections, which modulate tension in oblique proteinaceous tip links (Pickles et (Corey and Hudspeth, 1983;Ricci et al., 1998;Fettiplace and Kim, 51 2014), which is thought to stabilize the closed state of the transduction channels (Hacohen et 52 al., 1989;Cheung and Corey, 2006). Tip-link tension has been estimated at ~8 pN in the 53 bullfrog's sacculus (Jaramillo and Hudspeth, 1993) but, to our knowledge, there has been no 54 such report in the mammalian cochlea. 55 Adaptation continuously resets the mechanosensitive channels to a sensitive operating 56 point when static deflections of the hair bundle threaten to saturate mechanoelectrical 57 transduction (Eatock, 2000). Most of the available evidence indicates that movements by The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint 6 forming each tip link (Kazmierczak et al., 2007). From the increased magnitude of the hair-130 bundle response to a given mechanical stimulus (see an example in Fig. 4A), we found that 131 the gating springs contributed up to 50% of the total hair-bundle stiffness Κ HB . Averaging 132 over all inner and outer hair cells that we tested, the relative contribution of the gating springs outer hair cells displayed a gradient of gating-spring stiffness Κ GS = Κ HB (Fig. 3A).

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When immersing the hair cells in low-Ca 2+ saline, the negative movement was always 235 followed by tip-link disruption and could thus not be observed twice with the same hair 236 bundle. However, in six different preparations for which the hair bundle was immersed in 237 saline with a higher Ca 2+ concentration (500 µM) than usual (20 µM), we were able to 238 preserve the integrity of the tip links and demonstrate that the negative movements could be 239 reversible (Fig. 6D). Under such conditions, we observed that the absolute magnitude and the 240 speed of the negative movement increased with the magnitude of the iontophoretic current.

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Notably, the hair bundle reached a new steady-state position when the iontophoretic step was 242 long enough (Fig. 6E), suggesting that resting tension in the tip links could be modulated by 243 the extracellular Ca 2+ concentration, with higher tensions at lower Ca 2+ concentrations.

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Tonotopy of the mammalian cochlea is known to be associated with gradients of hair-bundle 246 morphology (Wright, 1984;Lim, 1986;Roth and Bruns, 1992;Tilney et al., 1992), as well as  in stiffness ratio between the two extreme cochlear locations that we were able to probe, we 261 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint roughly estimate that the measured stiffness ratios (Fig. 2E) were 51% and 66% larger than 262 those expected from morphology for outer and inner hair cells, respectively. We interpret this 263 result as the consequence of intrinsic gradients of the single gating-spring stiffness (Fig. 3D).

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Further emphasizing mechanical regulation at the level of the tip-link complex, we also 265 observed that the rotational stiffness of a single stereocilium was nearly uniform across the 266 cochlear locations that we tested, especially in outer hair cells (Fig. 3C). Stiffness gradients 267 of hair bundles with disrupted tip links are thus entirely determined by morphology, in 268 contradistinction to intact hair bundles.   Gummer et al., 1996). The resonance frequency C = � ⁄ of a spring-mass system is 292 given by the square root of the system's stiffness divided by the mass ; it thus increases 293 with stiffness, but relatively slowly. Assuming for simplicity that the bundle's mass remains 294 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint nearly the same along the tonotopic axis (Tilney and Tilney, 1988), two orders of magnitude 295 in frequency must be produced by a 10,000-fold increase in stiffness, corresponding to much 296 steeper gradients than those reported here. 297 Alternatively, it has been proposed that the hair bundle could actively resonate with sound 298 as the result of spontaneous oscillations (Martin et al., 2001;Hudspeth, 2008). Within this 299 framework, the characteristic frequency is set by the frequency of the oscillator, which is The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint basal cochlear locations, there are more motors or that each motor exerts higher forces than 328 near the apex. Notably, the tip links of inner-hair-cell bundles were found to bear less tension 329 than those of outer hair cell ( Fig. 5B-C). This property qualitatively makes sense, for the 330 open probability of the transduction channels is thought to be smaller in inner hair cells than 331 in outer hair cells (Russell and Sellick, 1983). There is also no, or only a weak, gradient of  The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint 13 hypothesis, it has recently been suggested that the number of TMC1-dependent transduction 361 channels increases by ~2.5-fold in outer hair cells but shows nearly no gradient in inner hair 362 cells from the apex to the base of the mouse cochlea (Beurg et al., 2018). If each channel 363 were associated with its own gating spring, the number of transduction channels per tip link 364 would directly control the effective stiffness of the tip-link complex. This mechanism could 365 contribute to the stiffness gradients reported here (Fig. 3D). However, for outer hair cells, we 366 found that the stiffness of the tip-link complex increased by ~3-fold over a region spanning 367 only 20% of the cochlear tonotopic axis (Fig. 3D), whereas the conductance associated with a   The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint is dominated by gating forces (Howard and Hudspeth, 1988) so that the resting tension in the 395 tip links is nearly the same before and after application of the stimulus. In the other regime 396 (our study), Ca 2+ -evoked changes of the resting tension in the tip links (Fig. 6) dominate 397 gating forces. In the chicken cochlea, depolarization of the hair cell was reported to evoke 398 negative movements of the hair bundle (Beurg et al., 2013), a directionality in agreement with 399 that found here (Fig. 4A). In addition, it has been shown in the bullfrog's sacculus (Tinevez       The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint Iontophoresis of a Ca 2+ Chelator. We used iontophoresis to apply the calcium chelator 461 EDTA in the vicinity of a hair bundle (Fig. 1B)    For stiffness measurements, we measured hair-bundle movements evoked by 100-ms force 488 steps ( Fig. 2; see the force-calibration procedure below). We observed that the hair bundle 489 responded to a force step with a fast deflection in the direction of the stimulus followed by a 490 slower movement in the same direction; this mechanical creep was strongly reduced upon tip-491 link disruption by EDTA treatment (Figure 2-figure supplement 4). Over the duration of the 492 step, the deflection of the hair bundle increased by 12-22% in the direction of the applied 493 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint step. The bundle displacement was measured 5-10 ms after the onset of the step stimulus; the  To estimate max , we measured the force � ≅ 6 F � applied by the same jet on a 527 calibrated glass fiber, whose longitudinal axis was oriented perpendicularly to that of the The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint transduction channels per transducing stereocilium (Beurg et al., 2006). In outer hair cells, 589 there is no direct estimate of 1 . However, the unitary current was shown to increase (Beurg sufficient to achieve a signal-to-noise ratio of 1-1.5, with 80% power at a 5% significance 620 level. We performed a one-way ANOVA to assay statistical significance of the measured 621 author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint 21 mean-value variation of a given property, e.g. the hair-bundle stiffness, between the different 622 cochlear locations for inner (IHC) or outer (OHC) hair cells. We also used two-tailed         The hair bundles were exposed to 20-µM Ca 2+ . In B, the dashed line indicates the current for 732 which the transduction channels are all closed. 733 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint   The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint 30 were immersed in a saline containing 500-µM Ca 2+ ; this higher Ca 2+ concentration preserved 769 the integrity of the tip links upon EDTA iontophoresis.

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The following table supplement is available for figure 6: 771 The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/497222 doi: bioRxiv preprint