Introduction to Cochlear Micromechanics

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Sensory cells in the inner ear are called hair cells. This slide (from A.J. Hudspeth, Science, 230:745-752, 1985) shows a light microscopic image of a hair cell that has been isolated from the tissues that normally surround it. Hair cells convert mechanical stimulations of the microscopic sensory hairs that project from their apical surface into an electrical signal. This hair cell is about 30 micrometers long and the hair bundle is about 5 micrometers wide. To put these dimensions into perspective, let's compare the size of this hair cell to something more familiar.
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This cover of Scientific American shows a scanning electron micrograph of an ant. The ant is holding a tiny microfabricated gear, and the point of the cover is that we can now fabricate mechanical parts that are small compared to ants. To illustrate the size of a hair cell, I have electronically pasted the image of the hair cell onto the microfabricated gear. You will have to zoom in to see it.
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Hair cells are small. But hair cells are themselves complex micromechanical systems whose function relies on an array of even smaller mechanical parts. Displacements of hair bundles generate electrical responses in hair cells via mechanically sensitive ion channels in the cell membrane.
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Ion channels are proteins that are integral parts of the membranes of all cells. Most of the cell's membrane is lipid and acts as a chemical and electrical barrier between the inside and outside of the cell. Ion channels have pores that act as conduits for ionic currents to pass through the membrane.

The state of conduction of an ion channel can be modulated by external stimuli. For example, some ion channels have chemical binding sites, and their state of ionic conduction depends on whether the binding site is occupied. Such ion channels act as chemical sensors. They underlie sensory functions ranging from olfaction to the detection of neurotransmitters. Many ion channels are sensitive to other stimuli, such as voltage. The mechanically-sensitive ion-channels in hair cells are sensitive to mechanical stress.

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Mechanical stress is transmitted to ion channels in hair cells via tiny filaments that connect neighboring hairs in a hair bundle. The left panel shows a transmission electron micrograph (from A.J. Hudspeth and P.G. Gillespie, Neuron, 12:1-9, 1994) of two adjacent hairs in one hair cell and the tiny tip link that connects them. The hairs are about 500 nm in diameter and tip links are on the order of 2 nm in diameter.
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Displacements of the hair bundle modulate the mechanical stress in the tip links and that stress is transmitted to ion channels, as illustrated in the attached animation. These trap doors represent highly simplified models of ion channels, which are actually complex molecules built out of thousands of amino acids. Nevertheless, these complex molecules can exist in a number of stable states, and this cartoon accurately depicts the fact that mechanical stress modulates the state of conduction of ion channels.
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Each hair cell is micromachine that is constructed from hundreds of much smaller components (e.g. ion channels and tip links). But hair cells do not operate in isolation. Hair cells are part of a larger system: the inner ear. Thus the inner ear represents VERY LARGE SCALE INTEGRATION of hundreds of thousands of biological microelectromechanical devices.

The inner ear performs some very remarkable signal processing. For example, the inner ear can detect motions of the eardrum on the order of a PICOMETERS -- i.e., much smaller than the diameter of a hydrogen atom. Furthermore, the inner ear performs a frequency analysis of low level sounds, and that analysis is very frequency selective. In bats, the quality of tuning of inner ear structures can exceed 800! And the Q of 800 is not achieved in a vacuum; it is not even achieved in air; it is achieved UNDER WATER! We are interested to understand how hair cells and other structures in the inner ear are organized to obtain these remarkable signal processing properties.

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Hair cells are organized in a tissue that separates two fluid-filled compartments of the inner ear. The mechanically sensitive hair bundles project into a gelatinous structure called the tectorial membrane. Sound induces motions of the stapes, the last of the three middle ear bones, so that the stapes moves in a piston-like fashion that modulates the pressures in the inner ear fluids. The sound-induced pressures deform the inner ear tissues and thereby displace the hair bundles of hair cells, as illustrated in the the attached video.

This type of a model has been investigated for more than twenty years, and no one has yet been able to account for the remarkable signal processing properties of the ear using such a model. There has been a wide range of theories for why these models are inadequate. For example, for my doctoral thesis, I studied the effects of hydrodynamic forces on hair bundles and showed that hair bundles can exhibit a mechanical resonance. Another important theory is that the tectorial membrane could resonate. In the video, the displacements of all of the moving structures had similar magnitudes and identical phases. However, if the tectorial membrane were resonant, then its displacement and phase would depend on frequency, and at resonance, the displacements of the tectorial membrane would far exceed those of other structures.

Further progress in understanding cochlear mechanics depends not only on developing new theories but also on testing theories with direct observations.

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We have developed an experimental method to test theories of cochlear micromechanics. We mount the inner ear of a lizard in an experimental chamber, so that we can stimulate it with sound while observing its motion with a microscope. We are interested in motions at audio frequencies. Therefore we use stroboscopic illumination and we record the resulting images using a CCD camera.
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This slide shows an image taken with our system. The drawing represents a cross sectional view of the cochlea. The cluster of hair cells rests on the basilar membrane, and are surmounted by a gelatinous tectorial membrane. We view the cochlea in the direction indicated by the arrow, and the focal plane of the microscope is indicated by the dashed line. The left panel shows the image seen at this focal plane, which is through the top of the tectorial membrane.
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By changing the focal plane of the microscope, different parts of the cochlea become visible, a property called optical sectioning. At this plane of section, one can see the tips of several hair bundles. The edge of the tectorial membrane can also be seen, especially at the right margin of the image.
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At this plane of section, the bases of several hair bundles can be seen, as well as the right boundary of the tectorial membrane. In general, we record sufficiently many images to characterize all of the structures in the inner ear, as shown in the attached video.
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We are interested in the motions that result in response audio frequency stimulation. Therefore we use stroboscopic illumination to obtain a sequence of images, each locked to a different stimulus phase. The vertical arrow in the inset indicates the phase at which the corresponding image was acquired. The attached video shows a slow motion video sequence of the motions of the bases of several hair cells. The sequence consists of images acquired at 8 phases of the stimulus period.
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We can repeat these measurements at other planes of focus. This image and the associated video show the tips of several hair bundles. Thus, by combining stroboscopic illumination with optical sectioning, we obtain information about the motions of all structures in the field of view.
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Even after magnification by a light microscope, the sound-induced motions of inner ear structures are small -- much smaller than the pixel spacing of a modern CCD camera. Nevertheless, images obtained during subpixel displacements still contain information about motion, which is illustrated in this figure and in the associated video. The squares represent the pixels of our camera. The circle represents a target moving horizontally. The bar graphs at the bottom of the figure indicate the brightnesses of the row of pixels indicated by the arrow. Even though the circle translates less than a pixel, its motion modulates pixel brightnesses. We use algorithms from computer vision to make quantitative estimates of the displacement of the circle from the changes in pixel brightness.
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To test the system, we built a microscopic target whose motions could be measured by an independent method. We then used the computer microvision system to determine the motion and compared the results from the video images with the independent method. Measurement errors are on the order of 14 nm: less than 3 percent of the wavelength of the light used to obtain the image.
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These two images and the associated video illustrate the motions of the tectorial membrane (left) and hair bundles (right) that result from a moderately loud (92 dB SPL) sound source. The 513 Hz frequency was chosen to match the most sensitive frequency for these hair cells.

These images are the first images of the motions of hair bundles and their overlying tectorial membrane. They are the first measurements that allow direct tests of previous theories of cochlear mechanics. These images clearly indicate that the tectorial membrane is NOT moving more than the hair bundles. The tectorial membrane is in fact moving much less. Thus these measurements do not support the notion that the tectorial membrane is a resonant structure. This result should be regarded as preliminary until sufficiently many control experiments have been done to eliminate the possibility of experimental error. However, to date, we have repeated this experiment with 12 different lizard ears, and we have never seen resonance of the tectorial membrane.

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We can electronically zoom in to look at mechanics at the level of individual cells.
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The left part of this slide shows a schematic drawing of a hair bundle and overlying tectorial membrane. The right panels show images from different planes of section that have been stacked up to produce a 3D image of a hair bundle. By showing such 3D images as a function of time, the associated video can convey a qualitative idea of the 3D motions of a hair bundle.
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We can apply our computer vision algorithms to obtain quantitative motion estimates. This slide and the associated video shows motion estimates for each of the six panels in the previous slide. The waveforms show the displacements of the associated images as a function of time. As we saw previously, motion of the tectorial membrane is smaller than that of the hair bundles. Motion of the hair bundles is about 0.5 micrometers peak-to-peak and that of the top of the tectorial membrane is about 0.18 micrometers. However, the quantitative estimates also reveal a systematic change in phase. The top of the tectorial membrane lags the base of the hair cell by nearly 90 degrees. This change of phase through the tectorial membrane has not previously been suggested. It represents a new mode of motion: a mode that hadn't been conceived before these measurements.
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The quantitative motion estimates allow other interesting manipulations. For example, we can shift each of the images to compensate for the motion at the base of the hair bundle. The resulting images and associated video show motions relative to the base, i.e., in a frame of reference attached to the hair cell. When we estimate motions of these images with our computer vision algorithms, the motions at the base are greatly reduced. Now we can use the peak-to-peak motions near the tip of the hair bundle to estimate the angular displacement of the hair bundle. The plane near the tip is 6 micrometers above the plane near the base, and the motions near the tip are about 0.3 micrometers peak-to-peak. Therefore, the angular displacement is about 3 degrees peak-to-peak.
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We can zoom in even more to investigate the motions between sensory hairs within a bundle.
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This slide and the associated video shows a section through the center part of the hair bundle. Translations of the images result both because the base is translating and because the bundle is rotating. In addition to the translation, there also appears to be a modulation of the distance between the individual sensory hairs.
We can use our motion estimation algorithm to estimate the motion of the right edge of the hair bundle and then shift the images to compensate for that motion. The resulting images and associated video show relative motions between sensory hairs. For example, the distance between the hairs near the center of the bundle changes as the bundle translates and rotates. Changes in distance between sensory hairs are important because they affect the stress in tip links.
Previously, it was thought that sensory hairs remain parallel as the bundle rotates, as was shown in the previous animation. This conception was based on experiments in which bundles were displaced with tiny glass fibers or with a water jet and observed with a microscope. In hindsight, it is not difficult to imagine how results are different for dynamic stimuli. The tip links provide elastic connections between hairs. But the surrounding fluid provides viscous drag. Thus it is not surprising that motions of shorter hairs lag those of longer hairs. But this relation was not suspected previously.
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These studies show how video microscopy can be applied to gain insights into cochlear micromechanics at the level of single sensory hairs, at the level of hair bundles, and for the entire inner ear (see video).