Mechanical Properties of the Basilar Papilla of Alligator Lizard

A. J. Aranyosi and D. M. Freeman

This poster was presented at the Twenty-Fourth Meeting of the Association for Research in Otolaryngology at St. Petersburg Beach, FL on February 6, 2001. The image below provides a link to a PDF file of the poster, suitable for printing. If you need a PDF viewer for Windows, MacOS, or Linux, please visit Adobe's web site.

Image of poster


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Introduction

Our group is studying cochlear micromechanics by measuring sound-induced motions of cochlear structures. These measurements allow us to obtain a better understanding of the mechanisms by which the remarkable signal-processing properties of the cochlea arise. The measurements also provide experimental data for testing and developing models of cochlear mechanics.


Drawing of alligator lizard cochlea


The alligator lizard cochlea (shown above) contains two regions: the apical tectorial region, in which hair bundles project into an overlying tectorial structure (bottom of 1/3 image), and the basal free-standing region, in which hair bundles project freely into endolymph (top of image). In the free-standing region, hair bundles vary in height from roughly 30 micrometers at the apical end, where best frequencies are near 1 kHz, to about 10 micrometers at the basal end, where best frequencies are near 4 kHz (Mulroy, 1974; Weiss et al, 1976).


Measurements of the motion of the basilar membrane using the Mossbauer technique (Peake and Ling, 1980) showed that the displacement of the basilar membrane is in phase along its length (i.e., there is no travelling wave) and has a frequency dependence matching that of the middle ear (i.e., the basilar membrane does not have sharp tuning). However, both auditory nerve fibers (Weiss et al, 1976) and hair cells (Holton and Weiss, 1983a; Baden-Kristensen and Weiss, 1983) are sharply tuned, with best frequencies varying with hair bundle height (Holton and Weiss, 1983b). Measurements of the motions of hair bundles show that the rotation of hair bundles in response to mechanical stimulation is frequency dependent, and that the best frequency varies with hair bundle height (Holton and Hudspeth, 1983; Frishkopf and DeRosier, 1983). These results led to models of alligator lizard cochlea micromechanics in which the frequency selectivity of hair cells is determined by the mechanics of the middle ear and of the hair bundles (Weiss and Leong, 1985; Freeman and Weiss, 1988, 1990). The basilar papilla was lumped in with the basilar membrane as having no significant frequency dependence.

These models of cochlear mechanics in the alligator lizard face two significant limitations. First, the models required an additional low-pass filter in order to match existing neural tuning curve data. The models predicted that this low-pass filter should be mechanical, but did not exist in the middle ear nor in the mechanical properties of the free-standing hair bundles. Second, the models treated hair bundle angular rotation as the relevant excitatory stimulus. We now know that tip-link stretch, which opens transduction channels (see Pickles and Corey, 1992 for review), depends on both angular rotation and the height of hair bundles. Since hair bundle height is graded with position in the alligator lizard cochlea, hair cells with taller hair bundles are more sensitive to angular rotation than those with shorter hair bundles. So in the context of the tip-link model of transduction, the models of alligator lizard mechanics require an increased sensitivity for high-CF hair cells with shorter hair bundles.

The present study examines the contribution of the basilar papilla to the mechanical properties of the alligator lizard cochlea. Previous studies (Aranyosi and Freeman, 2000; Frishkopf and DeRosier, 1983; Holton and Hudspeth, 1983) suggest that the mechanical properties of the basilar papilla are more complex than the simple rotational motion assumed in models. In this poster we show that the basilar papilla exhibits both a translational and a rotational mode of motion, and that both modes contribute to the excitatory motion of hair bundles. In addition, the rotational mode of motion provides both the low-pass filter and the increased sensitivity for short hair bundles required by the models.

Methods

See also Aranyosi and Freeman, ARO 2000.
Schematic of experiment chamber


To measure sound-induced motions, we isolate the cochlea and place it in an experimental chamber, schematized above. We clamp the cochlea between two fluid spaces. To simulate the in vivo fluid environment, an artificial endolymph is perfused through the apical space, and an artificial perilymph is perfused through the basal space. Sound pressures are generated in the basal fluid with a piezoelectric disk, and are calibrated with a hydrophone (Entran). We view the cochlea from above using a Zeiss Axioplan microscope with a 63x, 0.9 NA water-immersion objective. We use stroboscopic illumination to take pictures of the cochlea at different phases of the periodic sound stimulus. Images are taken with a 12-bit CCD camera (Dalsa CA-D7-1024A). The light source is a green LED (Nichia; ceneter wavelength 525 nm) which is strobed with a 1/8 duty cycle at the same frequency as the sound stimulus. The phase of the strobe signal relative to the sound stimulus determines the phase of motion at which the image is obtained (see the poster for more details).

Image of lizard cochlea


The image above shows a typical image obtained with our system. In the upper left hand corner is a representation of our imaging setup; the cochlea is viewed from above (in the direction of the arrow), and the microscope is focused so that we are seeing structures in the focal plane indicated by the red line. The focal depth, or "thickness" of the image is highly dependent on the numerical aperture (NA) of the imaging system; our NA is about 0.9, which gives us a focal depth of less than 1 micrometer.

Movie of lizard cochlea in motion


By taking pictures at several phases of the sound stimulus and viewing them in sequence, we can generate a movie showing the cochlea in motion. Such a movie is shown above. The motion of cochlear structures is difficult to interpret from a single such movie, since structures are moving perpendicular to the image plane (i.e., in and out of focus).

Image of lizard cochlea at a
different focal plane


To solve this problem, we take images at several planes of focus. The movie above shows motions at another plane of focus (again indicated by the red line). By taking a series of such images at closely-spaced focal planes (typically 1 micrometer spacing) we obtain a three-dimensional image of the cochlea in motion.

Creating a 3D image from a stack
of 2D images


We can create a three-dimensional image by stacking together a series of two-dimensional images, as shown above. A series of such images at different phases of the sound stimulus provides information about three-dimensional motions.

Reslicing 3D images to
provide different 2D views


By reslicing the three-dimensional images in an arbitrary direction, we can view any desired cross-section of the data set. The image above illustrates reslicing the three-dimensional image in the xz plane (outlined in cyan) to create a virtual cross-sectional image.

Reconstructed cross-sectional
movie of lizard cochlea in motion


Animating cross-sectional images taken at different phases of the sound stimulus gives us movies like the one above. Each image in the movie was generated by reslicing 80 images taken at a 1 micrometer spacing. The large circular structure in the center of the image is the basilar papilla. Near the upper right are three hair bundles. Motion of the papilla in this plane depends on position; for example, the abneural side (to the right) moves more than the neural side (to the left).

The resolution in the vertical axis is determined by the axial resolution of the microscope, which for this image was near 1 micrometer. The resolution in the horizontal axis is determined by the horizontal resolution of the microscope, about 300 nanometers for this image. The thickness of the image is equal to the horizontal resolution of 300 nm; thus we do not see a horizontal view of the entire hair bundle, but a thin slice through a few stereocilia, similar to the view obtained in a TEM image.

Results and Discussion

Plot of elliptical
trajectories of motion in the xz plane


The figure above shows trajectories of motion for four locations on the body of the basilar papilla. The image in the background shows the papilla (note that the neural and abneural sides are reversed relative to the previous view; that is, the abneural side is now on the left). The circles show the position of each measured location at each of eight phases of the 5 kHz sound stimulus; the red circles indicate the location at phase 0. Note that at each location, the papilla moves in an elliptical pattern. In this plot the displacements have been exaggerated by a factor of 5 relative to the positions of structures. This exaggeration was done to make the elliptical trajectories more evident.

Elliptical motion of the papilla cannot result from the simple rotation assumed by models of the alligator lizard cochlea; the trajectories resulting from pure rotation are simple arcs. However, multiple modes of motion can give rise to elliptical trajectories. For example, two translational modes that are out of phase with each other, or one translational and one rotational mode, can generate elliptical motions. To determine the combination of modes that best describes our measurements, we fit a three-mode model to the data using a least-squares algorithm. The three modes were

  1. Translation in the transverse direction (the z axis)
  2. Translation in the lateral direction (the x axis)
  3. Rotation about the longitudinal axis (i.e., in the plane of the cross-section shown above). The center of rotation was also fit, and was assumed to move due to the translational modes of motion.
The magnitude and phase of each mode were fit, as well as the x and z coordinates of the center of rotation, for a total of eight degrees of freedom for fitting 64 data points (x and z position for 4 locations for each of 8 phases). The best fit for these data (shown as black lines in the plot above) had 1.77 micrometers peak translation in the transverse direction, 1.96 degrees rotation about the point indicated by the red "X" above, and only 7 nanometers translation in the lateral direction. Since the small lateral motion was in phase with the transverse motion, we treated the lateral and transverse components as a single mode, giving us a 2-mode fit with 6 degrees of freedom. The rms error of the fit was 0.175 micrometers.

Animation of the 
translational component of motion


How does each mode affect the mechanics of the cochlea? To answer this question we need to first consider the modes separately. The animation above illustrates the translational mode of motion, and its effect on hair bundle excitation (for asymptotically high frequencies of motion). In the alligator lizard cochlea, free-standing hair bundles presumably rotate due to viscous and inertial forces applied by the fluid in the direction of hair bundle excitation (Freeman and Weiss, 1988, 1990). Because the direction of hair bundle excitation changes with lateral position in this cochlea, the excitatory motion generated by the translational mode of motion can vary over a wide range for a given cross section. In the animation above, the hair bundle in the center of the papilla receives no excitatory stimulus while the hair bundles on the sides are deflected. Thus if the translational mode of motion were present alone, hair cells would exhibit a large range of sensitivities to sound.

Animation of the 
rotational component of motion


A similar gradient exists for the rotational mode of motion. On the abneural side (left side of image), hair bundles are oriented to be maximally sensitive to the rotational mode of motion. On the neural side, hair bundles are oriented to be minimally sensitive to the rotational mode. In addition, because the neural hair bundles are closer to the center of rotation, the displacement magnitudes are smaller. Thus the rotational mode alone also generates a large range of sensitivities of hair cells.

However, because different hair cells are sensitive to different modes of motion, the overall range of sensitivities is reduced for the two-mode case. The range of sensitivities is determined by the relative magnitudes of the two modes, and by the phase difference between them (for abneural hair cells, which are sensitive to both modes of motion, the phase difference between the modes is significant).

Motion of the bases of
three hair bundles in the direction of hair bundle excitation


To estimate the range of sensitivities, we measured the motion of the bases of three hair bundles at 5 kHz, the same frequency used for the elliptical trajectories shown above. We then computed the component of motion in the direction of hair bundle excitation (shown by the arrows in the figure above). The sensitivities of these hair cells varied by about a factor of two, smaller than the variation expected for a single-mode motion of the papilla.

From measurements at a single frequency it is impossible to determine whether the translational and rotational modes are truly independent or simply part of a more complex mode. To resolve this issue, we need to compare the frequency and location dependence of the two modes. Because the modal fits are time-consuming, we took a first pass at separating the modes by comparing the lateral and transverse displacements of hair bundles on the neural side of the papilla. On the neural side, the rotational mode generates motion largely in the lateral direction, while the translational mode generates motion in the transverse direction. Thus by comparing motion in the two directions we can determine whether the two modes have similar or different frequency responses.

3-Dimensional motion of
the neural side of the papilla as a function of frequency and longitudinal
position


The figure above shows the magnitude of motion of the neural side of the papilla in three dimensions as a function of frequency (along the front axis) and distance from the basal end of the papilla (along the side axis). The lateral component of motion, on the left, provides information about the rotational mode. The transverse component, on the right, provides information about the translational mode (although the rotational mode also generates some motion in the transverse direction). The longitudinal component of motion is negligible.

From the plots above we can see that the rotational mode peaks near 5 kHz, and that this peak causes displacements that are largest at the basal end of the papilla. This peak is significantly smaller in the transverse direction, and is most likely due to the contribution of the rotational mode to the transverse motion. This peak increases the sensitivity of hair cells on the basal end, which have CFs near 4 kHz. This increased sensitivity compensates for the relatively lower sensitivity due to the shorter hair bundle length in these hair cells. By incorporating this increased sensitivity, models of cochlear function in the alligator lizard can be updated to include tip-link models of transduction.

Phase of lateral relative
to transverse motion on the neural side of the papilla


The above figure shows the phase of lateral motion relative to transverse motion as a function of frequency (front axis) and longitudinal position (side axis). At low frequencies the lateral and transverse components of motion are in phase with each other. As the frequency increases, the lateral comopnent increasingly lags the transverse component, reaching a peak lag of nearly 180 degrees at 10 kHz. The magnitude and phase plots in this and the previous figure, taken together, indicate that the rotational mode of motion is related to the translational mode by a second-order low-pass filter (the phase relationship indicates that the filter is low-pass rather than band-pass, which would start at +90 degrees). Thus the rotational mode may provide the additional low-pass filter needed by models of alligator lizard cochlear function.

In summary, we have shown that the basilar papilla of alligator lizard exhibits two simultaneous modes of motion. Both modes of motion play a role in the excitation of hair cells; the combintaion of modes allows all hair cells to have similar sensitivities. The resonant peak in the rotational mode of motion increases the sensitivities of high-CF hair cells, an increase which is required for incorporating the tip-link model of transduction into models of cochlear function in the alligator lizard. Finally, the low-pass filter between the translational and rotational modes of motion is likely to be the additional low-pass filter required by models.

Some new questions arise from these studies, however. How is it that the rotational mode of motion causes larger displacements at the basal end than at the apical end? Why do models need only a first-order low-pass filter, when we see a second-order filter? Since some hair cells are sensitive to only the translational mode and some to only the rotational mode, do these hair cells have different high-frequency slope? We plan to address these questions in future experimental and modeling studies.



Send comments to A.J. Aranyosi (aja at this university)



References

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