Multiscale modeling of mechanotransduction in the utricle.

We review recent progress in using numerical models to relate utricular hair bundle and otoconial membrane (OM) structure to the functional requirements imposed by natural behavior in turtles. The head movements section reviews the evolution of experimental attempts to understand vestibular system function with emphasis on turtles, including data showing that accelerations occurring during natural head movements achieve higher magnitudes and frequencies than previously assumed. The structure section reviews quantitative anatomical data documenting topographical variation in the structures underlying macromechanical and micromechanical responses of the turtle utricle to head movement: hair bundles, OM, and bundle-OM coupling. The macromechanics section reviews macromechanical models that incorporate realistic anatomical and mechanical parameters and reveal that the system is significantly underdamped, contrary to previous assumptions. The micromechanics: hair bundle motion and met currents section reviews work based on micromechanical models, which demonstrates that topographical variation in the structure of hair bundles and OM, and their mode of coupling, result in regional specializations for signaling of low frequency (or static) head position and high frequency head accelerations. We conclude that computational models based on empirical data are especially promising for investigating mechanotransduction in this challenging sensorimotor system.

Utricular afferents: morphology of peripheral terminals.

The utricle provides critical information about spatiotemporal properties of head movement. It comprises multiple subdivisions whose functional roles are poorly understood. We previously identified four subdivisions in turtle utricle, based on hair bundle structure and mechanics, otoconial membrane structure and hair bundle coupling, and immunoreactivity to calcium-binding proteins. Here we ask whether these macular subdivisions are innervated by distinctive populations of afferents to help us understand the role each subdivision plays in signaling head movements. We quantified the morphology of 173 afferents and identified six afferent classes, which differ in structure and macular locus. Calyceal and dimorphic afferents innervate one striolar band. Bouton afferents innervate a second striolar band; they have elongated terminals and the thickest processes and axons of all bouton units. Bouton afferents in lateral (LES) and medial (MES) extrastriolae have small-diameter axons but differ in collecting area, bouton number, and hair cell contacts (LES >> MES). A fourth, distinctive population of bouton afferents supplies the juxtastriola. These results, combined with our earlier findings on utricular hair cells and the otoconial membrane, suggest the hypotheses that MES and calyceal afferents encode head movement direction with high spatial resolution and that MES afferents are well suited to signal three-dimensional head orientation and striolar afferents to signal head movement onset.

Steady-state stiffness of utricular hair cells depends on macular location and hair bundle structure.

Spatial and temporal properties of head movement are encoded by vestibular hair cells in the inner ear. One of the most striking features of these receptors is the orderly structural variation in their mechanoreceptive hair bundles, but the functional significance of this diversity is poorly understood. We tested the hypothesis that hair bundle structure is a significant contributor to hair bundle mechanics by comparing structure and steady-state stiffness of 73 hair bundles at varying locations on the utricular macula. Our first major finding is that stiffness of utricular hair bundles varies systematically with macular locus. Stiffness values are highest in the striola, near the line of hair bundle polarity reversal, and decline exponentially toward the medial extrastriola. Striolar bundles are significantly more stiff than those in medial (median: 8.9 µN/m) and lateral (2.0 µN/m) extrastriolae. Within the striola, bundle stiffness is greatest in zone 2 (106.4 µN/m), a band of type II hair cells, and significantly less in zone 3 (30.6 µN/m), which contains the only type I hair cells in the macula. Bathing bundles in media that break interciliary links produced changes in bundle stiffness with predictable time course and magnitude, suggesting that links were intact in our standard media and contributed normally to bundle stiffness during measurements. Our second major finding is that bundle structure is a significant predictor of steady-state stiffness: the heights of kinocilia and the tallest stereocilia are the most important determinants of bundle stiffness. Our results suggest 1) a functional interpretation of bundle height variability in vertebrate vestibular organs, 2) a role for the striola in detecting onset of head movement, and 3) the hypothesis that differences in bundle stiffness contribute to diversity in afferent response dynamics.

Architecture of the mouse utricle: macular organization and hair bundle heights.

Hair bundles are critical to mechanotransduction by vestibular hair cells, but quantitative data are lacking on vestibular bundles in mice or other mammals. Here we quantify bundle heights and their variation with macular locus and hair cell type in adult mouse utricular macula. We also determined that macular organization differs from previous reports. The utricle has approximately 3,600 hair cells, half on each side of the line of polarity reversal (LPR). A band of low hair cell density corresponds to a band of calretinin-positive calyces, i.e., the striola. The relation between the LPR and the striola differs from previous reports in two ways. First, the LPR lies lateral to the striola instead of bisecting it. Second, the LPR follows the striolar trajectory anteriorly, but posteriorly it veers from the edge of the striola to reach the posterior margin of the macula. Consequently, more utricular bundles are oriented mediolaterally than previously supposed. Three hair cell classes are distinguished in calretinin-stained material: type II hair cells, type ID hair cells contacting calretinin-negative (dimorphic) afferents, and type IC hair cells contacting calretinin-positive (calyceal) afferents. They differ significantly on most bundle measures. Type II bundles have short stereocilia. Type IC bundles have kinocilia and stereocilia of similar heights, i.e., KS ratios (ratio of kinocilium to stereocilia heights) approximately 1, unlike other receptor classes. In contrast to these class-specific differences, bundles show little regional variation except that KS ratios are lowest in the striola. These low KS ratios suggest that bundle stiffness is greater in the striola than in the extrastriola.

Layer thickness and curvature effects on otoconial membrane deformation in the utricle of the red-ear slider turtle: static and modal analysis.

Finite element models of otoconial membrane (OM) were developed to investigate the effects of three geometric variables on static and modal response of the OM: (1) curvature of the macular surface, (2) spatial variation in thicknesses of three OM layers, and (3) shape of the macular perimeter. A geometrically accurate model of a turtle utricle was constructed from confocal images. Modifying values for each variable formed variants of this model: modeling the macula surface as flat, OM layer thicknesses as spatially invariant, and the macular perimeter as a rectangle. Static tests were performed on each modified OM model, and the results were compared to determine the effects of each geometric variable on static mechanical gain (deflection per unit acceleration). Results indicate that all three geometric variables affect the magnitude and directional properties of OM static mechanical gain. In addition, through modal analysis, we determined the natural frequencies and displacement modes of each model, which illustrate the effects of the three geometric variables on OM dynamics. This study indicates the importance of considering three-dimensional OM geometry when attempting to understand responses of the OM and, therefore, the modulation of hair cell signals to accelerations during head movements.

Autocorrelation analysis of hair bundle structure in the utricle.

The ability of hair bundles to signal head movements and sounds depends significantly on their structure, but a quantitative picture of bundle structure has proved elusive. The problem is acute for vestibular organs because their hair bundles exhibit complex morphologies that vary with endorgan, hair cell type, and epithelial locus. Here we use autocorrelation analysis to quantify stereociliary arrays (the number, spacing, and distribution of stereocilia) on hair cells of the turtle utricle. Our first goal was to characterize zonal variation across the macula, from medial extrastriola, through striola, to lateral extrastriola. This is important because it may help explain zonal variation in response dynamics of utricular hair cells and afferents. We also use known differences in type I and II bundles to estimate array characteristics of these two hair cell types. Our second goal was to quantify variation in array orientation at single macular loci and use this to estimate directional tuning in utricular afferents. Our major findings are that, of the features measured, array width is the most distinctive feature of striolar bundles, and within the striola there are significant, negatively correlated gradients in stereocilia number and spacing that parallel gradients in bundle heights. Together with previous results on stereocilia number and bundle heights, our results support the hypothesis that striolar hair cells are specialized to signal high-frequency/acceleration head movements. Finally, there is substantial variation in bundle orientation at single macular loci that may help explain why utricular afferents respond to stimuli orthogonal to their preferred directions.

Hair bundle heights in the utricle: differences between macular locations and hair cell types.

Hair bundle structure is a major determinant of bundle mechanics and thus of a hair cell's ability to encode sound and head movement stimuli. Little quantitative information about bundle structure is available for vestibular organs. Here we characterize hair bundle heights in the utricle of a turtle, Trachemys scripta. We visualized bundles from the side using confocal images of utricular slices. We measured kinocilia and stereocilia heights and array length (distance from tall to short end of bundle), and we calculated a KS ratio (kinocilium height/height of the tallest stereocilia) and bundle slope (height fall-off from tall to short end of bundle). To ensure that our measurements reflect in vivo dimensions as closely as possible, we used fixed but undehydrated utricular slices, and we measured heights in three dimensions by tracing kinocilia and stereocilia through adjacent confocal sections. Bundle heights vary significantly with position on the utricular macula and with hair cell type. Type II hair cells are found throughout the macula. We identified four subgroups that differ in bundle structure: zone 1 (lateral extrastriola), striolar zone 2, striolar zone 3, and zone 4 (medial extrastriola). Type I hair cells are confined to striolar zone 3. They have taller stereocilia, longer arrays, lower KS ratios, and steeper slopes than do neighboring (zone 3) type II bundles. Models and experiments suggest that these location- and type-specific differences in bundle heights will yield parallel variations in bundle mechanics. Our data also raise the possibility that differences in bundle structure and mechanics will help explain location- and type-specific differences in the physiological profiles of utricular afferents, which have been reported in frogs and mammals.

Differences between stereocilia numbers on type I and type II vestibular hair cells.

A major outstanding goal of vestibular neuroscience is to understand the distinctive functional roles of type I and type II hair cells. One important question is whether these two hair cell types differ in bundle structure. To address this, we have developed methods to characterize stereocilia numbers on identified type I and type II hair cells in the utricle of a turtle, Trachemys scripta. Our data indicate that type I hair cells, which occur only in the striola, average 95.9 +/-16.73 (SD) stereocilia per bundle. In contrast, striolar type II hair cells have 59.9 +/- 8.98 stereocilia, and type II hair cells in the adjacent extrastriola average 44.8 +/- 10.82 stereocilia. Thus type I hair cells have the highest stereocilia counts in the utricle. These results provide the first direct evidence that type I hair cells have significantly more stereocilia than type II hair cells, and they suggest that the two hair cell types may differ in bundle mechanics and peak mechanoelectric transduction currents.

Kinocilia heights on utricular hair cells.

Kinocilium height is a critical determinant of any hair cell's response to head movement, but accurate measurements of kinocilia heights have been difficult to achieve. We have developed a method for measuring kinocilia heights that combines immunochemical staining with three-dimensional morphometry, and we have used this method to measure kinocilia in the utricle of a turtle, Pseudemys scripta. Our results suggest that kinocilium height varies with position on the utricular epithelium and that kinocilia in the striola are significantly shorter than kinocilia in other regions of the utricle.

Extrinsic Fabry-Perot interferometer for measuring the stiffness of ciliary bundles on hair cells.

We have developed an extrinsic Fabry-Perot interferometer (EFPI) to measure displacements of microscopic, living organelles in the inner ear. The EFPI is an optical phase-shifted instrument that can be used to measure nanometer displacements. The instrument transmits a coherent light signal to the end of a single glass optical fiber where the measurement is made. As the coherent light reaches the end of the fiber, part of this incident signal is reflected off the internal face of the fiber end (reference reflection) and part is transmitted through the end of the fiber. This transmitted light travels a short distance and is reflected off the surface whose displacement is to be measured (the target). This sensing reflection then reenters the fiber where it interferes with the reference reflection. The resulting interference signal then travels up the same optical fiber to a detector, where it is converted into a voltage that can be read from an oscilloscope. When the target moves, the phase relation between reference and sensing reflections changes, and the detector receives a modulated signal proportional to the target movement. Reflections of as little as 1% at both the sensor tip and target surfaces produce good results with this system. We use the EFPI in conjunction with fine glass whiskers to measure the stiffness (force per unit deflection) of stereociliary bundles on hair cells of the inner ear. The forces generated are in the tenths of picoNewton range and the displacements are tens of nanometers. Here we describe the EFPI and its development as a method for measuring displacements of microscopic organelles in a fluid medium. We also report experiments to validate the accuracy of the EFPI output and preliminary measurements of ciliary bundle stiffness in the posterior semicircular canal.

Differences in the brain stem terminations of large- and small-diameter vestibular primary afferents.

1. We visualized the central axons of 32 vestibular afferents from the posterior canal by extracellular application of horseradish peroxidase, reconstructed them in three dimensions, and quantified their morphology. Here we compare the descending limbs of central axons that differ in parent axon diameter. 2. The brain stem distribution of descending limb terminals (collaterals and associated varicosities) varies systematically with parent axon diameter. Large-diameter afferents concentrate their terminals in rostral regions of the medial/descending nuclei. As axon diameter decreases, there is a significant shift of terminal concentration toward the caudal vestibular complex and adjacent brain stem. 3. Rostral and caudal regions of the medial/descending nuclei have different labyrinthine, cerebellar, intrinsic, commissural, and spinal connections; they are believed to play different roles in head movement control. Our data help clarify the functions of large- and small-diameter afferents by showing that they contribute differentially to rostral and caudal vestibular complex.

Functional architecture of vestibular primary afferents from the posterior semicircular canal of a turtle, Pseudemys (Trachemys) scripta elegans.

Physiological studies in many vertebrates indicate that vestibular primary afferents are not a homogeneous population. Such data raise the question of what structural mechanisms underlie these physiological differences and what functional role is played by afferents of each type. We have begun to answer these questions by characterizing the architecture of 110 afferents innervating the posterior canal of Pseudemys scripta. We emphasize their spatial organization because experimental evidence suggests that afferent physiological properties exhibit significant spatial heterogeneity. The sensory surface of the posterior canal comprises paired, triangular hemicristae, which are innervated by two afferent types. Bouton afferents (66% of total afferents) are found over the entire sensory surface. They differ significantly in the shape and size of their collecting areas, number of boutons, soma size, and axon diameter; this morphological variation is systematically related to the afferent's spatial position. In addition, multivariate analyses suggest that bouton afferents may comprise two subtypes: alpha afferents have delicate processes and are found throughout the crista; beta afferents are more robust and are concentrated preferentially toward the canal center. Calyx-bearing afferents comprise two morphological subtypes: dimorphs (13% of total afferents) bear calyceal and bouton endings; calyceal afferents (21%) bear calyceal endings only. Both types occur exclusively in an elliptical region near the center of each hemicrista; their morphology varies with radial distance from the center of this elliptical region. Our data provide evidence that in Pseudemys: (1) the classical vestibular afferent types (bouton, calyx, dimorph) are structurally heterogeneous, and (2) their spatial sampling characteristics are highly structured and distinctive for each type. These spatial patterns may shed light on regional differences in physiological profiles of vestibular afferents, and they raise questions about the role of this spatial heterogeneity in signaling head movement.

Design and control of the head retractor muscle in a turtle, Pseudemys (Trachemys) scripta: II. Efferent innervation.

The head retractor muscle (RCCQ) of Pseudemys scripta is a useful model in which to study the mechanisms animals use to vary the force and timing of movement. Single fibers in this muscle differ significantly in attachments, length, diameter, taper characteristics, and histochemical properties, suggesting that they may be energetically and architecturally specialized for different roles in head movement. In the present paper, we report the peripheral and central efferent innervation of these diverse muscle cells, and we ask how the design of the neural apparatus is matched to the properties of its target muscle fibers. Three out of four bellies in RCCQ are supplied by multiple segmental nerves. The territories of these nerves are separated rostrocaudally within the muscle belly; thus, long muscle fibers cross the territories of two or more segmental nerves. Motor terminals in RCCQ resemble those on frog twitch muscles. Their sizes (length, bouton number) are correlated with the diameters of their target muscle fibers. Each muscle fiber bears 2-14 terminals evenly spaced (approx. 5 mm apart) along its length. Thus, single muscle fibers in RCCQ are multiterminally, and long fibers are multisegmentally innervated. Control experiments indicate that the axons in each segmental nerve arise from different motor neuron populations. Thus, short, in-series fibers are supplied by different motor neurons, and individual long fibers in RCCQ are polyneuronally innervated. These data help explain how long muscle fibers with relatively slow conduction speeds can generate rapid head movements, and they raise questions about the central mechanisms that coordinate the recruitment of RCCQ motor neurons.

Design and control of the head retractor muscle in a turtle, Pseudemys (Trachemys) scripta: I. Architecture and histochemistry of single muscle fibers.

We are using the head retractor muscle (RCCQ) of a turtle, Pseudemys scripta, to analyze the neuromuscular mechanisms by which organisms vary the force and timing of muscle contraction. Previously we demonstrated that RCCQ comprises three histochemically defined fiber types: fast glycolytic (Fg), fast oxidative glycolytic (FOG), and slow oxidative (SO). In the present paper we report the 1) architectural features of single muscle fibers in RCCQ, including their lengths, diameters, and taper characteristics, 2) histochemical profiles of single muscle fibers, and 3) quantitative relations between our architectural and histochemical variables. Single fibers in RCCQ exhibit an order of magnitude variation in length (4-60 mm). Approximately 40% span the full muscle. The remaining fibers generally attach to bone or tendon at one end, and the other end tapers intramuscularly; rarely a fiber may taper at both ends. The maximum (untapering) diameters of single fibers are bimodally distributed, forming two diameter classes. Fibers also vary in the percentage of their total length that tapers and in the shape of the tapering region. Large diameter muscle fibers generally are longer and have shorter, more blunted tapers than small diameter fibers. The large diameter fibers are almost all Fg types; these fibers have a median diameter of 59.3 microns, and they account for approximately 60% of total fibers in RCCQ. FOG and SO fibers generally have small diameters (median: 32.5 microns and 35.8 microns), and they typically account for 30% and 10% of total fibers. We use these relations to draw inferences about the attachments and architecture of glycolytic (Fg) and oxidative (FOG, SO) fiber types. Taken together, our data suggest that single muscle fibers in RCCQ may be architecturally as well as histochemically specialized to perform different roles in head retraction. In the accompanying paper we report the efferent innervation of these fibers and consider some of the neural control problems posed by these diverse fiber types.

Active zone organization and vesicle content scale with bouton size at a vertebrate central synapse.

A common observation in studies of neuronal structure is that axons differ in the size of their synaptic boutons. The significance of this size variation is unclear, in part because we do not know how the size of synaptic boutons is related to their internal organization. The present study has addressed this issue by using three-dimensional reconstruction of serial thin sections to examine the ultrastructure of synaptic boutons that vary in size. Our observations are based on complete or near-complete reconstructions of 53 synaptic boutons contacting large neurons in the ventromedial gray matter of the upper cervical spinal cord (probable neck motor neurons). We characterized bouton size in terms of volume and total area of membrane apposed to the motor neuron surface (apposition area). Boutons vary in apposition area by a factor of 40, and there is a significant positive correlation between our two measures of bouton size. In addition, bouton size is systematically related to four ultrastructural variables: 1) total active zone area, 2) number of active zones, 3) individual active zone area, and 4) number of synaptic vesicles. The correlations between these variables and both of our measures of bouton size are positive and significant. These data suggest that bouton size may be an index of ultrastructural features that are thought to influence transmitter storage and release.

Histochemical classification of neck and limb muscle fibers in a turtle, Pseudemys scripta: a study using microphotometry and cluster analysis techniques.

We have attempted to develop an objective, semiquantitative classification of fiber types in turtle neck and limb muscle using microphotometry and multivariate statistical techniques. We first stained serial sections for myosin adenosine triphosphatase (ATPase) (with acid and alkaline preincubation and without preincubation), NADH-diaphorase, and two glycolysis-associated markers, alpha-glycerophosphate dehydrogenase (alpha-GPDH) and glycogen phosphorylase A (GPA). This allowed us to characterize individual muscle fibers in terms of their contraction speed and metabolic properties. Next we used microphotometry to measure the optical density of the reaction product in each fiber, and we subjected the resulting optical density matrix to cluster and discriminant function analyses in order to assign fibers to groups (fiber types) and to determine which stains contribute most to the distinction between groups. As a control, we processed a well characterized mammalian muscle (rat sternomastoid) simultaneously. Our results suggest that both neck and limb muscle in Pseudemys can best be described as falling into three groups: 1) slow oxidative (SO) fibers; 2) fast oxidative glycolytic (FOG) fibers, with relatively high oxidative and glycolytic capacities; and 3) fast glycolytic (Fg) fibers, with low oxidative, low/intermediate alpha-GPDH, and high GPA activities. These three fiber types differ from like-named types in rat muscle both in the pH lability of their myosins and in their metabolic profiles.

Planar relations of semicircular canals in awake, resting turtles, Pseudemys scripta.

As part of a project aimed at elucidating mechanisms of vestibulocollic control in the red-eared turtle Pseudemys scripta, we have calculated the planar relations of its semicircular canals using principal-components analysis. This information is prerequisite to understanding the pattern of canal activation that is set up by head movement of any spatial form. In addition, we have developed a method for monitoring canal orientation in an awake, behaving animal, and we have used this technique to assess canal position in resting turtles. Our results indicate that ipsilateral canals in Pseudemys are not mutually orthogonal, nor are complementary canals precisely coplanar, although they approach this idealized condition more closely than do the canals of several other vertebrates for which quantitative data exist. One significant departure from the perfectly orthogonal configuration is that both verical canals are rotated slightly toward the frontal plane; thus, Pseudemys should be somewhat more sensitive to head roll than to head rotation in other planes. Radiographic analyses of awake, resting turtles indicate that the anterior interparietal suture is held aligned with the earth horizontal and midsagittal plane. The horizontal canal is pitched up (open anterior) 3-4 degrees relative to the earth horizontal.