INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

As was established by early studies of silver-stained material (Lorente de Nó 1926; Poljak 1927) and since confirmed by modern neuroanatomical techniques (Fernández et al. 1988, 1995), afferents innervating the cristae differ in their axon diameters, terminal morphology, and the zones of the neuroepithelium they supply. When it became evident that fibers also differed in their discharge properties (Baird et al. 1988; Boyle and Highstein 1990; Goldberg and Fernández 1971; Honrubia et al. 1989; Lysakowski et al. 1995; Myers and Lewis 1990), the question arose as to the relation between the morphology and physiology of individual afferents. Taking advantage of the fact that fiber diameter was correlated with terminal morphology and crista location, the first attempts to study this question characterized the discharge properties of thick, medium-sized and thin axons. Axon caliber was estimated by measuring conduction velocities (Goldberg and Fernández 1977; Lysakowski et al. 1995; Yagi et al. 1977) or by labeling axons (Honrubia et al. 1989). More recently, intraaxonal labeling methods have been used to visualize not only the parent axons but also the peripheral terminations of physiologically characterized fibers. Such studies have now been done in fish (Boyle et al. 1991), frogs (Myers and Lewis 1990), and mammals (Baird et al. 1988).

In anamniotes (fish and amphibians), only type II hair cells are found in the cristae and other vestibular organs (Lysakowski 1996; Wersäll and Bagger-Sjöbäck 1974). Afferents in these animals, nevertheless, have diverse morphological and physiological properties related to their longitudinal position in the neuroepithelium. In describing the results, it is useful to recall that the crista is saddle-shaped, a narrow isthmus region at the center of the organ giving way to a broader region near either planum semilunatum. The innervation near the planum consists of thin axons terminating in relatively simple arbors, whereas fibers supplying the isthmus have thicker axons with more robust arbors (Boyle et al. 1991; Honrubia et al. 1989; Myers and Lewis 1990). By correlating terminal morphology and physiology (Boyle et al. 1991; Myers and Lewis 1990), it was found that the planum fibers are regularly discharging and have small gains and small phase leads re angular head velocity; in contrast, many of the isthmus fibers are irregularly discharging with large gains and large phase leads. A similar conclusion arises from a correlation between fiber size and physiological properties (Honrubia et al. 1989).

A different organization is seen in the mammalian crista. Both type I and type II hair cells are found throughout the neuroepithelium (Fernández et al. 1995; Lindeman 1969; Lysakowski and Goldberg 1997). Based on the size, shape, and spacing of hair cells (Fernández et al. 1995; Lindeman 1969; Lysakowski and Goldberg 1997), on the morphology of their synaptic inputs (Lysakowski and Goldberg 1997), and on the branching patterns of the afferents (Fernández et al. 1988, 1995), the neuroepithelium has been divided into three concentrically arranged zones. There is a central zone, occupying the apex of the crista except near the planum, successively surrounded by an intermediate and a peripheral zone. Extracellular labeling has been used to describe the afferent innervation (Fernández et al. 1988, 1995). Calyx units innervate type I hair cells in the central zone; bouton units supply type II hair cells in the peripheral zone; and dimorphic units provide a mixed innervation to both kinds of hair cells throughout the neuroepithelium.

The discharge characteristics of the various kinds of mammalian afferents have been determined by intraaxonal labeling (Baird et al. 1988). Calyx and bouton fibers are each relatively homogeneous in their behavior. In contrast, the physiological properties of dimorphic units vary with the zones in which they terminate. Dimorphic units in the central zone are irregularly discharging, and their gains and phase leads are large; in comparison, dimorphic units in the peripheral zone have a regular discharge, small gains, and small phase leads. Calyx units, although resembling central dimorphic units in their irregular discharge and large phase leads, have considerably smaller gains. Because of their thin axons, bouton afferents have been difficult to impale and label (Baird et al. 1988). Fortunately, such afferents can be recognized by their distinctively slow conduction velocities (Goldberg and Fernández 1977; Lysakowski et al. 1995; Yagi et al. 1977). Bouton units so identified resemble peripheral dimorphic units in discharge regularity, gain, and phase. The results for the peripheral zone emphasize the concentric organization of the mammalian crista because labeled units in this zone have similar discharge properties whether they are located at the apex of the organ near the planum or at the base of the organ, near the planum, or near the isthmus (Baird et al. 1988).

The turtle posterior crista shares features with the cristae of both mammals and anamniotes. As illustrated in Fig. 1, the turtle crista consists of two triangular-shaped hemicristae. Each hemicrista extends from the planum to a nonsensory torus found at the isthmus. Within each hemicrista, there is a central zone and a surrounding peripheral zone. Type I hair cells are confined to the central zone, which also contains a smaller number of type II hair cells (Brichta and Peterson 1994; Jørgensen 1974; Lysakowski 1996). The type I hair cells are innervated by calyx and dimorphic fibers; the type II hair cells, by dimorphic and bouton fibers (Brichta and Peterson 1994). Only type II hair cells and bouton fibers are found in the peripheral zone (Brichta and Peterson 1994; Jørgensen 1974; Lysakowski 1996). Similar to the longitudinal gradient in axon size and terminal arbors described in anamniotes (Boyle et al. 1991; Honrubia et al. 1989; Myers and Lewis 1990), bouton fibers ending near the planum have thin axons and sparse terminal arbors, whereas those terminating in the remainder of the organ, including the portion near the nonsensory torus, have thicker axons and can have more robust arbors (Brichta and Peterson 1994). Bouton fibers in midportions of the hemicrista are similar in their morphology whether they innervate the central or peripheral zones.

View larger version (22K): [in this window] [in a new window]   Fig. 1. Hair cells and innervation patterns in the turtle posterior crista based on Brichta and Peterson (1994). Drawings of transverse (A) and longitudinal (B) sections are indicated by the vertical and horizontal lines in the inset, respectively. Organ includes two triangular-shaped hemicristae, which meet at the isthmus, where a nonsensory torus is found. Each hemicrista extends to the planum semilunatum and is divided into a central zone (CZ) surrounded by a peripheral zone (PZ). Afferents include calyx (c), dimorphic (d) and bouton (b) fibers. CZ contains type I hair cells innervated by c and d fibers and fewer type II hair cells innervated by d and b fibers. Only type II hair cells innervated by b fibers are found in the PZ. b fibers are subdivided into b and b subtypes. Of the two, b fibers have smaller axons and soma areas and their terminal fields have fewer branches and fewer and smaller-sized bouton endings. b fibers are found throughout the hemicrista, whereas b fibers are concentrated near the torus.

The purpose of the present study was to determine the discharge properties of the various afferent groups in the turtle posterior crista. A specific hypothesis was that in their physiology turtle bouton fibers would show a longitudinal gradient similar to that described in anamniotes (Boyle et al. 1991; Honrubia et al. 1989; Myers and Lewis 1990), whereas calyx-bearing units in the turtle central zone would resemble the corresponding units of the mammalian central zone (Baird et al. 1988; Lysakowski et al. 1995). The hypothesis led to three predictions: 1) bouton units near the planum would be regularly discharging and have low gains and phases; those near the torus would be irregular and have high gains and phases; and those in midportions of the hemicrista would have intermediate properties whether they innervated the central or peripheral zones. 2) Turtle calyx-bearing units should resemble one another in their discharge regularity and phase, but calyx units should have distinctively lower gains than dimorphic units. And 3) the gains and phases of turtle calyx-bearing units should fall between those of bouton units located near the planum and near the isthmus. This last prediction was based on a comparison of bouton units in the anamniote crista with centrally located calyx and dimorphic units in the mammalian crista.

The discharge properties of turtle afferents were studied in a half-head preparation. Intraaxonal labeling was used to relate the physiology of individual afferents with the morphology and locations of their terminal trees. Impaled units were tested with rotations at a single sinusoidal frequency (0.3 Hz), chosen because preliminary studies indicated that variations between units in gain and phase were largest there. Even with this limited testing, bouton and calyx-bearing afferents were distinctive. On the other hand, calyx and dimorphic units were so similar that they had to be placed in a single calyx-bearing class. For either bouton or calyx-bearing units, discharge properties varied with longitudinal position in a hemicrista. Data from labeled units were used to develop statistical formulas from which the morphological classes and longitudinal positions of extracellularly recorded units could be inferred.

To verify the use of the statistical formulas, we first compared the discharge properties in units recorded intraaxonally or extracellularly in the half-head or extracellularly in intact animals. The formulas were then used in the half-head to relate the inferred morphological class and longitudinal position of each extracellularly recorded unit with its other physiological properties. One such property, the response dynamics over a broad frequency range, is considered in this paper. Other properties are studied in the next paper (Brichta and Goldberg 2000).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Preparation and recording

We used red-eared turtles [Pseudemys (Trachemys) scripta elegans] of both sexes. Animals weighed 200-400 g and had carapace lengths of 11-14 cm. Experiments were done at room temperature (21-23°C). On the basis of a previously published procedure (Crawford and Fettiplace 1980), the animal was decapitated, the head was split in the midsagittal plane, and the two half-heads were placed in a turtle Ringer solution. One half-brain was blocked at the levels of the trigeminal nerve rostrally and the glossopharyngeal nerve caudally. To expose the dorsal surface of the posterior division of the VIIIth nerve, including the fibers innervating the posterior crista, we pivoted the brain stem 90° about the VIIth and VIIIth nerves. After removal from Ringer solution, the half-head was placed on its lateral surface in a recording chamber and a moist gas mixture (95% O₂-5% CO₂) was passed continually over the tissue. The chamber was bolted to the superstructure of a rotating device whose motion was controlled by a velocity servomechanism (Inland 823, Pittsburgh, PA).

To gauge the influence of in vitro conditions, we also studied intact animals anesthetized with pentobarbital sodium (10 mg/kg im). The skin, hyoid cartilage, and soft tissue under the mandible were reflected to expose the tongue, glottis, and trachea. The animal was then intubated and respired with compressed air. Artificial respiration mimicked natural breathing patterns with nonventilatory periods followed by breathing episodes (Burggren 1975; Frankel et al. 1969). To accomplish this, we built a three-phase respirator (Hasan 1986). A breathing episode consisted of 10 breaths, each including an 8-s expiration followed by a 5-s inspiration with the tidal volume adjusted to 15 ml/kg. After the 10th inspiration, there was a 10-min apneic period. The procedure resulted in a heart rate of 30-40/min and an expired pCO₂ of 3-4%. Analysis of blood drawn from the femoral artery and measured at 37°C gave a pH of 7.35-7.45, a p0₂ of 15-30%, and a pCO₂ of 4-8%, values that are close to normal (Frankel et al. 1969).

In intact animals, both divisions of the eighth nerve were exposed by drilling through the hard palate with a dental burr. Care was taken not to disturb the blood supply in and around the nerve. The animal was placed in a supine position on the superstructure with the head clamped inside a recording chamber.

In both the half-head and intact preparations, recording microelectrodes were advanced by a screw-micrometer drive attached to the top of the chamber. For extracellular recordings, microelectrodes were filled with 3 M NaCl (20-40 M impedance). Intraaxonal labeling was done with beveled microelectrodes containing 4% biocytin (Molecular Probes, Eugene OR) in 0.5 M KCl and 0.05 M Tris (pH = 7.4; 40-80 M impedance). Recordings were made from the posterior division of the VIIIth nerve proximal to its ganglion. Unless otherwise stated, data are from the half-head preparation.

Physiological testing

The posterior division of the VIIIth nerve supplies five organs. Fibers innervating the posterior crista and papilla neglecta responded to head rotations, while those supplying the other three organs did not (see RESULTS). Rotation-sensitive units were characterized as follows. The head was kept in a fixed position relative to the horizontal plane of rotation. For all units, a 5-s sample of background discharge was recorded, as was the response to a 0.3-Hz sinusoidal head rotation. In some extracellularly recorded units, responses to sinusoidal rotations at frequencies ranging from 0.01 to 3 Hz and spaced one-half decade apart were studied. Maximal head velocities were 320 deg/s for 0.01 and 0.03 Hz, 160 deg/s for 0.1 Hz, 80 deg/s for 0.3 Hz, 40 deg/s for 1.0 Hz, and 20 deg/s for 3.0 Hz; the number of cycles ranged from 4 at 0.01 Hz to 128 at 3.0 Hz. Phase histograms were viewed on-line to ensure that each unit was tested with rotation amplitudes in its linear range. Linearity was judged by a lack of harmonic distortion and, in spontaneously active units, an absence of inhibitory silencing. When in doubt, we continued halving the stimulus intensity until there was no consistent change in response gain or phase. In some especially sensitive fibers, this required testing at velocities approaching 1 deg/s. We used Fourier analysis to extract the fundamental component of the response. A similar analysis was done on the servo's table-velocity (tachometer) signal. Gains were obtained as the ratio of the response amplitude (in spikes/s) to the table-velocity amplitude (in deg/s). For the phase (in degrees), the table-velocity phase was subtracted from the response phase; positive phases correspond to the response leading table velocity. The effective posterior-canal plane was delineated in a previous paper (Brichta and Goldberg 1998a). In the half-head preparation, the effective plane deviated 45° from the rotation plane and the gains stated in the paper should be multiplied by to get their maximal values. For intact animals, the effective canal plane was 60° from the rotation plane, leading to a correction factor of 2.

The coefficient of variation (cv) normalized to a standard mean interval provides a measure of discharge regularity (Goldberg et al. 1984). As a standard interval, we chose 50 ms because it corresponds to the average background rate of 20 spikes/s found for a large population of nonsilent units from the turtle posterior crista (Fig. 11). To convert the cv of a steady-state sample to its normalized value, cv*, we used a power-law regression, cv() = a() · cv*^b(), relating the cv to the mean interval, . cv* can be viewed as a parameter that varies from unit to unit but does not vary with (). In contrast, a() and b() vary with in an manner identical for all units. Values of a() and b() were obtained by fitting data from 28 posterior-canal units, where sinusoidal head rotations were used to vary between 20 and 100 ms. The details of the calculations are presented elsewhere (Goldberg et al. 1984). Data were selected near the peaks and troughs of responses, where discharge was nearly stationary. Relations for nine individual units are shown in Fig. 2A, along with the relations for constant values of cv* between 0.1 and 1.0. Whenever possible, the cv* of a unit was calculated from its background discharge. When the background fell outside the normalization range (Fig. 2B), we used the rotation responses of the unit, selecting near-stationary data with a as close as possible to 50 ms.

View larger version (17K): [in this window] [in a new window]   Fig. 2. Discharge regularity of afferents innervating the turtle posterior crista can be measured by a coefficient of variation (cv). A: cv is plotted as a function of the mean interval, , for 9 fibers (dotted lines). In each case, cv increases with . To remove the influence of , power-law regressions, cv() = a()cv*b(), were run on a sample of 28 units to determine the coefficients, a() and b(), needed to relate cv() and with cv*, the cv at  = 50 ms, as a parameter. Thick lines are the cv vs. relations for values of cv* ranging from 0.1 to 1.0. Note that the curves for individual units almost parallel the thick lines. cv* is a measure of discharge regularity independent of . B: relation between cv and , from the background activity for 510 extracellularly recorded units. For another 57 units,  > 1,000 ms. For 403 units, the background discharge had a mean interval within the normalization range of 20-100 ms and could be used to determine cv*. For another 164 units in the extracellular sample, activity during sinusoidal head rotations was used.

Galvanic sensitivity of individual units was tested in three half-head preparations. A chlorided silver wire was placed near the posterior ampullary nerve as it exited the ampulla, and a second chlorided silver wire was placed in the nasal cavity. Polarity is stated as that of the ampullary electrode. The resting discharge measured in the immediately preceding 5-s period was subtracted from the discharge rate averaged over the last 2.5 s of a 5-s 50-µA cathodal (excitatory) current step. Data were fit by a power-law relation, _ij = a_i(cv*_ij)^b, between the galvanic sensitivity (_ij) and cv*_ij, where the subscripts refer to the jth unit in the ith animal. To estimate the sensitivity factor for each animal (a_i), as well as the exponent (b) for all animals, an analysis of covariance was run between the logarithmic transforms of _ij and cv*_ij. It was verified that there was no statistically significant difference between the exponents from different animals. To eliminate interanimal differences in sensitivity, which are likely to reflect electrode placement and other technical factors, we calculated a normalized galvanic sensitivity, *_ij = _ij/a_i.

Intracellular labeling

After physiological testing, impaled axons were injected iontophoretically with biocytin. Currents were 5 nA alternating every 500 ms between anodal and cathodal pulses. These were interrupted every 30 s to measure the resting potential and the size of the action potential. Injections, which were started only if the resting potential was more negative than 25 mV and the action potential exceeded 5 mV, continued for a total of 10 min or until the resting potential fell below 10 mV or the action potential fell below 1 mV. Only one posterior-canal afferent was injected in each preparation. Two to 12 h later the tissue was fixed in 0.1 M phosphate buffer (pH 7.4) containing 2.5% paraformaldehyde and 2.5% glutaraldehyde. The skull was removed and the remaining block, consisting of the labyrinth, the VIIIth nerve and the attached brain stem, was handled en toto. The block was placed in a phosphate-buffered 30% sucrose solution until it sank and was then embedded in 12% gelatin and cut into 40-µm frozen serial sections. Biocytin labeling was demonstrated by treating sections with an avidin-biotinylated horseradish peroxidase procedure (ABC kit, Vector Laboratories, Burlingame, CA) with diaminobenzidine (DAB) as the chromogen. Sections were rinsed, mounted, dehydrated, and cover-slipped.

Material was examined with a ×100 oil-immersion, planapochromatic objective under bright-field illumination. Peripheral arborizations of labeled afferents were reconstructed from serial sections with the aid of a drawing tube (total magnification ×1,650). In most cases, the posterior crista was sectioned so that the entire terminal field of a labeled unit was contained in one to three sections. A terminal field was judged to be complete when it was darkly labeled and each of its processes ended either as a terminal bouton or as a calyx ending.

The approximate center of the terminal field was taken as the location of the unit. To determine the average diameter of the parent axon immediately below the neuroepithelium, we measured the area of the axon's silhouette over a length >100 µm and then divided by the length (Liberman and Oliver 1984). For bouton units, an irregular polygon was drawn that included all of the terminal branches; an approximate terminal-field diameter was calculated as the square root of the polygon's area. Other morphological features of bouton unitstotal bouton area, mean bouton area, and number of terminal brancheswere measured as described by Brichta and Peterson (1994). For calyx and dimorphic units, the numbers of calyx and bouton endings, when present, were counted separately, as was the number of type I hair cells enclosed by each calyx ending. Calyx endings were called "simple" if they innervated a single hair cell or "complex" if they innervated two or more hair cells.

Discriminant analysis

To develop an empirical formula distinguishing calyx-bearing (CD) and bouton (B) units, we used discriminant analysis. Three variables-x₁ = log₁₀(cv*), x₂ = log₁₀(gain), and x₃ = phase-were measured for every labeled fiber; the gain (in spikes · s¹/deg · s¹) and phase (in degrees) came from the responses to 0.3-Hz sinusoidal head rotations. Because the covariance matrices for CD and B units were unequal, a quadratic (rather than a linear) discriminant function was calculated (Morrison 1990). The discriminant score, g(x), is a function of the vector, x = (x₁, x₂, x₃). The coefficients defining g(x) were chosen so that units with g(x) > 0 and g(x) < 0 were assigned, respectively, to the B and CD groups (see Fig. 7C).

The probability of misclassification is indicated by the proportion of known (labeled) units that were assigned to the wrong category. A more accurate procedure is provided by the "jack-knife" method. Here, a unit is removed from the sample, a revised discriminant function is calculated and used to classify the removed unit. The procedure is repeated for each unit and leads to a second estimate of the proportion of misclassified units. Because each removed unit does not contribute to the function used to classify it, the jack-knife simulates the procedure used when a new unit is classified.

The larger the magnitude of g(x), the more reliable the classification. The probability that an individual case would be misclassified is related to the normalized score, z = g(x)/s, where s is the pooled intragroup SD obtained from labeled B and CD units. We calculated the mean normalized scores, _CD/s and _B/s. To simplify matters, the two means were adjusted so they were symmetrically disposed about zero, i.e., _CD = (|_CD| + |_B|)/2s and _B = (|_CD| + |_B|)/2s. We assumed that the z scores were distributed normally for either morphological class, in which case the conditional probabilities, p(z/CD) = N(z  _CD) and p(z/B) = N(z  _B), where N is the standardized normal probability density function. In the rest of the derivation, we use standard relations between the joint and conditional probabilities for two events, x and y: p(x, y) = p(y/x) p(x) = p(x/y) p(y). The unconditional probability, p(z) = p(z, CD) + p(z, B) = p(z/CD) p(CD) + p(z/B) p(B). p(B) and p(CD) can be taken from the relative proportions of B and CD units in a particular sample. When z < 0, a unit will be assigned to the CD group. The misclassification probability is the conditional probability that the unit actually belongs to the B group, i.e.,

(1)

Similarly, when z > 0, we use the conditional probability that the unit, which is assigned to the B class, actually belongs to the CD class,

(2)

Equations 1 and 2 are examples of Bayes theorem (Bernstein et al. 1988).

Other statistical procedures were run in SYSTAT for the Macintosh. Unless otherwise stated, means are presented ±SE.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Organs innervated by rotation-sensitive units

Units encountered in the posterior division of the VIIIth nerve responded to sound, vibration, head tilt, a combination of vibration and head tilt, or head rotation. To determine which of these units innervated the posterior crista, we labeled 86 fibers. None of the auditory (n = 6), vibratory (n = 2), tilt-sensitive (n = 6), or tilt-plus-vibration-sensitive (n = 14) fibers was traced to the posterior crista or the papilla neglecta. Fifty-eight rotation-sensitive units were labeled, of which 54 innervated the posterior crista and 4 supplied the papilla neglecta.

As described elsewhere (Brichta and Goldberg 1998a), units innervating the posterior crista encoded between angular velocity and angular acceleration, whereas papilla neglecta units encoded between angular acceleration and angular jerk. The difference in coding properties was reflected in the phases of the response to 0.3-Hz sinusoidal head rotations, which ranged from 5 to 91° in labeled posterior-crista fibers and between 125 and 146° in labeled papilla-neglecta fibers. On the basis of these ranges, we assigned an extracellular unit to the posterior crista if its 0.3-Hz phase was 90° and to the papilla neglecta if it was 110°.

The properties of the papilla-neglecta units, which made up <10% of our extracellular sample, already have been described (Brichta and Goldberg 1998a). This and the companion paper (Brichta and Goldberg 2000) will only consider posterior-crista units.

Intraaxonally labeled units

MORPHOLOGY OF LABELED UNITS. Of the 54 labeled posterior- crista units, 23 were bouton units, 11 were calyx units, and 18 were dimorphic units. In addition, two calyx-bearing units were too faintly labeled to be assigned to the calyx or dimorphic categories. Terminal fields were labeled incompletely in five bouton units, and in one bouton unit, the terminal field was completely labeled but a labeled axon could not be found.

View larger version (41K): [in this window] [in a new window]   Fig. 3. A: locations of 54 intraaxonally labeled units. Two shaded circles denote calyx-bearing units that were too lightly labeled to determine whether they were calyx or dimorphic. Labels and hashmarks above the left (medial) hemicrista indiate boundaries for classifying bouton (B) units into BP (near planum), BM (midportions), or BT (near torus) categories. Locations and receptive-field shapes are shown for 12 bouton (beta) units (B) and 5 bouton (alpha) fibers (C). See Brichta and Peterson (1994) and Fig. 1 for the distinction between alpha and beta categories.

View larger version (164K): [in this window] [in a new window]   Fig. 4. Digital photomontages of 3 intraaxonally labeled afferents. Bouton unit (A), calyx unit (B), and dimorphic unit (C). Bouton unit is also drawn in Fig. 5L and the dimorphic unit in Fig. 5C. Three type I hair cells are enclosed by the calyx ending in B, but in this perspective, the part of the ending surrounding 1 of the hair cells obscures the rest of the ending. Bars, 20 µm.

View larger version (48K): [in this window] [in a new window]   Fig. 5. Reconstructions of intraaxonally labeled calyx (A and B), dimorphic (C-F), and bouton (G-L) fibers. Bouton fibers were classified as alpha (G-I) or beta (J-L). See Brichta and Peterson (1994) and Fig. 1 for the distinction between alpha and beta categories. *, parent axon in each example. Lower bar pertains to all reconstructions. Locations of the fibers are indicated in the inset (top right).

BIAS IN THE INTRAAXONAL SAMPLE. Large axons are easier to impale than small axons. This source of bias was evaluated in Fig. 6 by comparing diameters of the 54 intraaxonally labeled axons with 105 extracellularly labeled axons from a previous study (Brichta and Peterson 1994). As expected, the intraaxonal sample is missing the smallest axons seen in the extracellular sample and has proportionately more axons with diameters 2 µm. Similar biases are seen for bouton (Fig. 6B) and calyx-bearing axons (Fig. 6C).

View larger version (13K): [in this window] [in a new window]   Fig. 6. A: histograms comparing axon diameters of extracellularly labeled units (Brichta and Peterson 1994) and of the intraaxonally labeled units of the present study. Ordinate, proportion of units in each sample with stated diameter; bin size, 0.25 µm. Smallest diameter fibers seen in the extracellular sample are missing from the intraaxonal sample, and there are proportionately more thick fibers in the latter sample. Similar differences were seen when intraaxonal and extracellular samples of bouton (B) or calyx-bearing fibers (C) are compared.

PHYSIOLOGY OF LABELED FIBERS. Figure 7 plots the gains and phases for 0.3-Hz sinusoidal head rotations versus cv* for the 54 labeled units. Units are separated by their morphological classes as well as by their background rates (high-rate, 5 spikes/s; low-rate, < 5 spikes/s). C and D units were placed into a single CD class because, as is described in the following text, the two kinds of units had similar discharge properties. Combining the terminology based on morphology with that based on background rates, we have B-high, B-low, CD-high, and CD-low categories.

View larger version (29K): [in this window] [in a new window]   Fig. 7. Discriminating between intraaxonally labeled B units and calyx-bearing or CD units (see key). Relation between gain and cv* (A) and between phase and cv* (B). Gain and phase are from responses to 0.3-Hz sinusoidal head rotations. cv*, coefficient of variation for a mean interval,  = 50 ms. Curves are quadratic discriminant functions separately calculated for B-high and CD-high units (background rate >5 spikes/s, ) and for B-low and CD-low units (background rate <5 spikes/s, - - -). Functions correctly discriminated 51 of 54 labeled units. Points for the 3 incorrectly discriminated units are enclosed in squares. Two other units (points marked by arrows) were misclassified in a jack-knife procedure (see text). Straight lines are a power-law regression (A) and a semilogarithmic relation (B) based on extracellularly recorded B units (Fig. 10, A and B). C: distribution of normalized discriminant (z) scores for four groups of intraaxonally labeled units (see key). Actual discriminant scores were divided by a pooled standard deviation, s = 14.7. Distributions for B and CD units were positioned so that their means were symmetrically disposed about 0. - - -, predicted numbers of B and CD units with stated z scores based on standardized normal distributions with means of 1.26 (B units) and 1.26 (CD units). , sum of calculated distributions for B and CD units. D: misclassification probabilities based on text Eqs. 1 and 2, the distributions illustrated in C, and the condition that B and CD units are encountered with equal probability.

DISCRIMINATION BETWEEN BOUTON AND CALYX-BEARING UNITS. B and CD units cannot be distinguished by any of the individual variables plotted in Fig. 7. CD units are irregular and have relatively small gains and phases. But they are neither the most irregular units nor do they have the smallest gains or phases. Rather it is the relationship between cv* and either gain or phase that makes CD units distinctive. In particular, CD units have larger cv*s than do B units with comparable values of gain and phase. Equivalently, when cv*s are equated, CD units have smaller gains and phases. To exploit this observation, we did a quadratic discriminant analysis involving three variablesx₁ = log₁₀ (cv*), x₂ = log₁₀ (gain), and x₃ = phase. Because of differences in gain and phase related to background discharge, a separate analysis was done for high-rate and low-rate groups. Since three-dimensional discriminant functions can be difficult to visualize, results are illustrated with the two-dimensional functions obtained by eliminating x₂ or x₃.

5

DISCHARGE PROPERTIES AND LONGITUDINAL POSITION. In Fig. 8, cv*, gain and phase are plotted versus normalized longitudinal position, .  = 0 corresponds to the torus;  = 1, to the planum. Gain (Fig. 8B) and phase (Fig. 8C) are both strongly related to ; because the relations are statistically indistinguishable for the B and CD groups, a single regression line is drawn for all units in each plot. In contrast, the relations between cv* and  differed for B and CD units and separate regression lines are drawn in Fig. 8A for the two groups. The latter difference is not surprising as it forms the basis for the discriminant analysis described in the preceding section.

View larger version (12K): [in this window] [in a new window]   Fig. 8. Comparisons for various populations of intraaxonally labeled B and CD units (see key) of the relations between normalized longitudinal position and other discharge characteristics, including cv* (A), gain (in spikes · s1/deg · s1) (B), and phase (C). cv*, coefficient of variation for a mean interval,  = 50 ms. Gain and phase are from responses to 0.3-Hz sinusoidal head rotations. Normalized location runs from 0 (torus) to 1 (planum) in each hemicrista. Units are classified as high- or low-rate depending on whether their background rates are greater or less than 5 spikes/s. Points in squares indicate 3 B units in the central zone. Single regression lines fit the data from all unit groups for gain and phase. Separate regression lines were needed for the cv*s of B and CD units.

View larger version (15K): [in this window] [in a new window]   Fig. 9. Discharge properties can be used to predict the longitudinal position () of a unit. Separate forward stepwise regressions were run for B and CD units relating normalized longitudinal position, = constant + b0x0 + b1x1 + b2x2 + b3x3, where x0 = background rate (spikes/s), x1 = log10(cv*), x2 = log10(gain), and x3 = phase. Gain (spikes · s1/deg · s1) and phase (deg) are from responses to 0.3-Hz sinusoidal head rotations. Regression coefficients were constant = 0.829 ± 0.057, b0 = 0.00309 ± 0.00142, b2 = -0.359 ± 0.062, and b3 = 0.00386 ± 0.00162 for B units and constant = 0.786 ± 0.040, b2 = -0.137 ± 0.038, and b3 = 0.00486 ± 0.00111 for CD units. x1 was discarded in both regressions and x0 in the CD regression. The rms error for the two groups combined, expressed as a percentage of the total length of the hemicrista, was 8.0%.

DISCHARGE PROPERTIES AND OTHER MORPHOLOGICAL FEATURES. Each of the labeled units was characterized by several morphological features besides its longitudinal position. To investigate whether any of these other features was related to the unit's discharge properties, forward stepwise multiple regression was used separately on B and CD units. Dependent variables included the background rate as well as the three discharge properties considered in Fig. 8.

Relation between the discharge properties from various samples

In this section, we compare the physiology of the intraaxonally labeled and extracellularly recorded units from the half-head. The comparison is needed to determine if the multivariate equations, which are based on data from the intraaxonal sample, can be used to specify the morphological class and location of extracellular units. In addition, extracellular samples from the half-head and from intact animals are compared to gauge the effects of in vitro conditions on afferent discharge.

INTRAAXONAL VERSUS EXTRACELLULAR SAMPLES, HALF-HEAD. To be included in the extracellular sample, a unit had to be characterized in terms of its background discharge, its discharge regularity, and the gain and phase of its response to 0.3-Hz sinusoidal head rotations. The extracellular sample from the half-head comprised 567 units. Several other units, possibly as many as 5-10% of the sample, had to be discarded because they were silent at rest and were so insensitive that we were unable to drive them to rates needed to calculate a cv* or to determine their gains and phases. We labeled two such "very insensitive" units. They were C units with complex calyx endings.

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View larger version (35K): [in this window] [in a new window]   Fig. 10. Relations between gain or phase and the cv* are plotted for 567 units extracellularly recorded in isolated half-heads (A and B) and 40 units similarly recorded in intact, anesthetized animals (C and D). Note the similarity between the units recorded in the two kinds of preparations and between either group and units intraaxonally recorded in the half-head (Fig. 7, A and B). Gains (spikes · s1/deg · s1) and phases (deg) are from the responses to 0.3-Hz sinusoidal head rotations. cv*, coefficient of variation for a mean interval of 50 ms. Units are divided into presumed B and CD units, based on discriminant functions (curves) for high-rate () and low-rate (- - -) units, having background rates >5 and <5 spikes/s, respectively. Straight lines are a power-law fit between gain and cv* (A) and a semilogarithmic fit between phase and cv* (B) for the extracellular B units in the half-head preparation.

IN VITRO VERSUS IN VIVO EXTRACELLULAR SAMPLES. Forty units were obtained in eight intact turtles. The in vivo sample was classified by the discriminant analysis into B-high (n = 17), CD-high (n = 14), and CD-low (n = 9) units (Fig. 10, C and D); none of the units were B-low. There were no statistically significant differences between the intact and half-head preparations in the mean values of background rate, cv*, gain, or phase for B-high, CD-high, or CD-low units. Nor were there significant differences in the relations between cv* and gain or phase for B-high units from the two preparations. This was so even when gains were corrected for the angles between the plane of the posterior canal and the rotation plane (see METHODS). "Very insensitive" units, presumably of the CD-low variety, were found in vivo. The results suggest that in vitro conditions did not result in a deterioration of vestibular transduction.

Discharge properties of extracellular units from the half-head

Because of its larger size, the extracellular sample provides a more accurate picture of physiology than does the intraaxonal sample. In addition, the extracellular sample is likely to be less biased in recording from thin axons. In the following sections, discharge properties from the extracel