In mammals, outer-hair-cell hair bundles (OHBs) transduce sound-induced forces into receptor currents and are required for the wide dynamic range and high sensitivity of hearing. OHBs differ conspicuously in morphology from other types of bundles. Here, we show that the 3D morphology of an OHB greatly impacts its mechanics and transduction. An OHB comprises rod-like stereocilia, which pivot on the surface of its sensory outer hair cell. Stereocilium pivot positions are arranged in columns and form a V shape. We measure the pivot positions (3D fluorescence microscopy z-slices in lif file, jpg of a single slice, pivot coordinates in xlsx file) and determine that OHB columns are far from parallel (Mathematica code). To calculate the consequences of an OHB’s V shape and far-from-parallel columns, we develop a mathematical model of an OHB that relates its pivot positions, 3D morphology, mechanics, and receptor current (Mathematica code). We find that the 3D morphology of the OHB can halve its stiffness, can double its damping coefficient, and cause stereocilium displacements driven by stimulus forces to differ substantially across the OHB. Stereocilium displacements drive the opening and closing of ion channels through which the receptor current flows. Owing to the stereocilium-displacement differences, the currents passing through the ion channels can peak versus the stimulus frequency and vary considerably across the OHB. Consequently, the receptor current peaks versus the stimulus frequency. Ultimately, the OHB’s 3D morphology can increase its receptor-current dynamic range more than twofold. Our findings imply that potential pivot-position changes owing to development, mutations, or location within the mammalian auditory organ might greatly alter OHB function.

Sample preparation

Sprague-Dawley rats of both sexes were sacrificed by decapitation using methods approved by the Stanford University Administration Panel on Laboratory Animal Care. The midapical turn (1-2 mm from the apex) of isolated organs of Corti were dissected from pups at postnatal day 10 (P10). Dissections were done in extracellular solution containing (in mM): 142 NaCl, 2 KCl, 2 CaCl2, 1 MgCl2, 10 HEPES, 6 Glucose, 2 Ascorbate/Pyruvate, 2 Creatine monohydrate, at pH 7.4 and a final osmolality of 304-307 mOsm. The tectorial membrane was slightly lifted using a needle tip and gently removed with a fine forceps. Each sample was then transferred to a dish containing fixative (4% paraformaldehyde in PBS) for 30 mins. The sample was washed three times, 5 min/wash, with PBS and permeabilized at room temperature in PBS containing 0.1% Triton X-100 for 20 mins. The sample was then blocked with 5% FBS (foetal bovine serum) in PBS for 1 h at room temperature. The sample was subsequently incubated with the primary TRIOBP rabbit polyclonal antibody (anti-TARA; 16124-1-AP Lot #6612; Proteintech) at 1:250 diluted in block overnight at 4 C with gentle rocking. The TRIOBP antibody detects TRIOBP-5 at the lower rootlet. After three washes with PBS, 5 min/wash, the Abberior STAR RED Anti-Rabbit IgG antibody at 1:500 was added to the sample, which was then incubated at room temperature with gentle rocking for 3 h. After three washes with PBS, 5 mins/wash, the sample was mounted in a closed chamber with glycerol mounting medium with DABCO (EMS) to ensure refractive index matching with the STED objective. The sample was held in place with single strands of dental floss while ensuring that OHBs were oriented vertically. A 100 um spacer was used in the closed chamber to ensure that the top coverslip (#1.5) was just above the OHBs but not touching them. The sample was protected from light until imaging.

Microscopy

Stimulated emission depletion (STED) images were acquired on a STELLARIS 8 Tau-STED microscope that was kindly made available by Leica Microsystems at their demo in the Wu Tsai Neurosciences Institute, Stanford University. STED was performed with an HC PL APO CS2 93x 1.3 NA glycerol immersion objective and SMD hybrid detectors. Emission depletion was accomplished with a 775 nm STED laser. The white light laser allowed for the choice of any wavelength between 470 nm and 670 nm for excitation. STAR RED was excited at 640 nm and the fluorescence emission was detected at 650-750 nm with 30% STED power in Tau-STED mode, which increased the resolution and eliminated uncorrelated background noise. Tau-STED parameters were set as follows: Tau-strength value 100, denoise value 50, and background suppression checked. The expected resolutions for the Tau-STED mode are 60-80 nm radially and 180-220 nm axially. STED z-stack images were recorded with a pixel size of 19 nm and a step size of 150 nm.

Pivot-point coordinates

Each 150 nm STED z-stack shows puncta at the rootlets of extant stereocilia or where stereocilia retracted during OHB development. To avoid including retracted stereocilia in our model, we identify the puncta in all of the z-stacks corresponding to three rows of stereocilia in a V-shape (this morphology is based on electron-microscopy observations). Like prior work using stereocilium tip positions, we identify stereocilium columns by linking puncta triplets starting at the notch (white lines). Puncta corresponding to the same rootlet are in several z-stacks. Using ImageJ 1.53t (National Institutes of Health) software and all the z-stacks, we find the 3D coordinates of each TRIOBP density's center for the extant stereocilia and defined these to be the pivot coordinates. After importing the pivot coordinates into Mathematica, we find that two principle components explain most of the variance in the coordinates (66% for component 1 and 33% for component 2). This implies that the pivots lie in a  at plane described by the first two principle components. We rotate the coordinates so that plane defined by the first two principle components aligns with the X and Y coordinates and so that the X axis aligns with the column formed by the three pivots below the notch in row 1. Because the variance in the Z coordinates around zero is small (< 1% of the coordinate variance), we set all the Z coordinates to zero (i.e., project the pivot positions into the XY-plane). This procedure enables us to define the hair-cell apex and the pivot point coordinates.