DOI: 10.5061/dryad.4mw6m90h4
title: Data from: 3D morphology of an outer-hair-cell hair bundle increases its displacement and dynamic range

description: 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.
description: <strong>Sample preparation </strong>
 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.
 <strong>Microscopy </strong>
 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. <strong>Pivot-point coordinates
 </strong> 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 (&lt; 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.
description: # Data from: 3D Morphology of an Outer-Hair-Cell Hair Bundle Increases Its
 Displacement and Dynamic Range #### Zhu3DOHB
 [https://doi.org/10.5061/dryad.4mw6m90h4](https://doi.org/10.5061/dryad.4mw6m90h4) * Fluorescence z-stack stored in lif file. * z-stack analysis output in jpg and xlsx files. * xlsx input to PivotPointAnalysis.nb for analysis. * nb files contain mathematical modeling code. * Numerical results of the mathematical modeling are in the mx files. ## Description of the data and file structure lif file contains z-stack of fluorescence data. Open with Leica Application Suite or ImageJ. JPEG output from ImageJ of one z-slice. xlsx file of putative pivot points output from ImageJ. Open with Excel. ## Code/Software * Mathematica 13: PivotPointAnalysis.nb code imports data from xlsx file and analyses pivot points. * Mathematica 13: IdenticalColumnsOHB.nb code for Identical Columns Mathematical Model. Results stored in IdenticalColumnsOHB*.mx file, which can be loaded at start of nb file.\ * Mathematica 13: ParallelColumnsOHB.nb code for Identical Columns Mathematical Model. Results stored in ParallelColumnsOHB*.mx file, which can be loaded at start of nb file. * Mathematica 13: 3DOHB.nb code for Identical Columns Mathematical Model. Results stored in 3DOHB*.mx file, which can be loaded at start of nb file.