The turtle posterior crista consists of two hemicristae. Each hemicrista extends from the planum semilunatum to the nonsensory torus and includes a central zone (CZ) surrounded by a peripheral zone (PZ). Type I and type II hair cells are found in the CZ and are innervated by calyx, dimorphic and bouton afferents. Only type II hair cells and bouton fibers are found in the PZ. Units were intraaxonally labeled in a half-head preparation. Bouton (B) units could be near the planum (BP), near the torus (BT), or in midportions of a hemicrista, including the PZ and CZ. Discharge properties of B units vary with longitudinal position in a hemicrista but not with morphological features of their peripheral terminations. BP units are regularly discharging and have small gains and small phase leads re angular head velocity. BT units are irregular and have large gains and large phase leads. BM units have intermediate properties. Calyx (C) and dimorphic (D) units have similar discharge properties and were placed into a single calyx-bearing (CD) category. While having an irregular discharge resembling BT units, CD units have gains and phases similar to those of BM units. Rather than any single discharge property, it is the relation between discharge regularity and either gain or phase that makes CD units distinctive. Multivariate statistical formulas were developed to infer a unit's morphological class (B or CD) and longitudinal position solely from its discharge properties. To verify the use of the formulas, discharge properties were compared for units recorded intraaxonally or extracellularly in the half-head or extracellularly in intact animals. Most B units have background rates of 10–30 spikes/s. The CD category was separated into CD-high and CD-low units with background rates above or below 5 spikes/s, respectively. CD-low units have lower gains and phases and are located nearer the planum than CD-high units. In their response dynamics over a frequency range from 0.01–3 Hz, BP units conform to an overdamped torsion-pendulum model. Other units show departures from the model, including high-frequency gain increases and phase leads. The longitudinal gradient in the physiology of turtle B units resembles a similar gradient in the anamniote crista. In many respects, turtle CD units have discharge properties resembling those of calyx-bearing units in the mammalian central zone.
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.
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. And3) 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).
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 MΩ 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 MΩ 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.
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(t̄) =a(t̄) · cv*b(t̄), relating the cv to the mean interval, t̄. cv* can be viewed as a parameter that varies from unit to unit but does not vary with (t̄). In contrast,a(t̄) andb(t̄) vary witht̄ in an manner identical for all units. Values of a(t̄) andb(t̄) were obtained by fitting data from 28 posterior-canal units, where sinusoidal head rotations were used to vary t̄ 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.2 A, 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 t̄ fell outside the normalization range (Fig. 2 B), we used the rotation responses of the unit, selecting near-stationary data with a t̄ as close as possible to 50 ms.
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, βij =ai (cv*ij)b, between the galvanic sensitivity (βij) and cv*ij, where the subscripts refer to thejth unit in the ith animal. To estimate the sensitivity factor for each animal (ai ), as well as the exponent (b) for all animals, an analysis of covariance was run between the logarithmic transforms of βij 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, β*ij = βij/ai .
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 units—total bouton area, mean bouton area, and number of terminal branches—were 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.
To develop an empirical formula distinguishing calyx-bearing (CD) and bouton (B) units, we used discriminant analysis. Three variables–x 1 = log10(cv*), x 2 = log10(gain), andx 3 = phase–were measured for every labeled fiber; the gain (in spikes · s−1/deg · s−1) 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 = (x 1,x 2,x 3). The coefficients definingg(x) were chosen so that units withg(x) > 0 and g(x) < 0 were assigned, respectively, to the B and CD groups (see Fig.7 C).
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, wheres is the pooled intragroup SD obtained from labeled B and CD units. We calculated the mean normalized scores,ḡ CD/s andḡ B/s. To simplify matters, the two means were adjusted so they were symmetrically disposed about zero, i.e., z̄ CD = −(‖ḡ CD‖ + ‖ḡ B‖)/2s andz̄ B = (‖ḡ CD‖ + ‖ḡ 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 −z̄ CD) andp(z/B) = N(z −z̄ 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) andp(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., Equation 1Similarly, when z > 0, we use the conditional probability that the unit, which is assigned to the B class, actually belongs to the CD class, Equation 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.
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.
The locations of all labeled units in the neuroepithelium are shown in Fig. 3 A. A large proportion (37/54 = 69%) of the units were located in the medial hemicrista. As expected, calyx-bearing units were only found in the central zone. Three bouton units were also centrally located. The remaining 20 bouton units were distributed in the peripheral zone with a higher concentration near the torus than near the planum or in midportions of the crista. Terminal fields are illustrated by photomontages in Fig.4 and by drawings in Fig.5.
The terminal trees of dimorphic units were compact and contained one (n = 14, Figs. 4 C and 5, C andD) or two calyx endings (n = 4, Fig. 5,E and F) and from one (Fig. 5 E) to 31 bouton endings (Figs. 4 C and 5 C). Most (15/18) dimorphic units had fewer than four bouton endings. Calyx endings were found at the ends of thick processes, either the parent axon or thick secondary branches; some of the endings were simple (Fig. 5,C, E, and F), but most (18/22) were complex (Fig. 5, D and E), supplying two to five hair cells. Bouton endings were located on or at the ends of thinner branches that emerged from the parent axon (Fig. 5, C, D,and F) or from the base or sides of calyx endings (Fig. 5,C and E).
Bouton units had extensive terminal trees. There were a variety of branching patterns. The parent axon could run undivided through the neuroepithelium (Figs. 4 A and 5, J andL) or it could divide one or more times into relatively thick secondary branches (Fig. 5, H, I, andK). Neither the parent axon nor the thicker branches contained boutons. En passant and terminal boutons were found on thin, usually short, collaterals arising from the axon and its branches and on longer continuations of the branches. The continuations were thin and usually arose at branch points. In a few instances, the parent axon, almost immediately on crossing the basement membrane, gave way to thin, bouton-containing branches (Fig. 5 G). Bouton endings could be round or oval and their long axes ranged from <1 to >5 μm. Quite often, an elongated terminal arbor was placed eccentrically with respect to the point at which the parent axon entered the neuroepithelium (Fig. 5, J and L). Receptive-field shapes are illustrated in Fig. 3, B andC. Arbors were restricted to the central or peripheral zones. In only one instance did an arbor extend a branch from one hemicrista to the other. The long axes of the terminal fields ranged from 65 (Fig. 5 G) to 145 μm (Fig. 5 L). Calculated terminal-field diameters (see methods) ranged from 40 to 80 μm. By comparison, the long axis of each hemicrista is 450 μm.
In their extracellular labeling study, Brichta and Peterson (1994) separated fibers into alpha and beta categories based on a multivariate analysis of several morphological variables. Of the two categories, alpha fibers had smaller axons and somas; their terminal fields had fewer terminal branches and fewer and smaller bouton endings. The same multivariate procedure was applied to the 17 bouton fibers of the present sample in which complete data were available. Examples of the two classes are illustrated in Fig. 5 (alpha: Fig. 5,G–I; beta: Fig. 5, J–L). Of the 17 fibers, 5 were classified as alpha and 12 as beta. Locations of the two groups are indicated in Fig. 3, B and C. InBrichta and Peterson's (1994) study, alpha fibers were found throughout each hemicrista, whereas beta fibers were restricted to the half of the hemicrista nearer the torus. Our study makes clear that at least some beta fibers are located near the planum (see, for example, Fig. 5 L).
Table 1 summarizes data for calyx, dimorphic, and bouton fibers. For statistical purposes, we sometimes combined calyx (C) and dimorphic (D) fibers into a single CD group. In the table, B fibers were divided by their longitudinal positions into those near the torus (BT), those near the planum (BP), and those in midportions of the hemicrista (BM), including the central zone (see Fig. 3 B). CD fibers had larger axons (range: 1.7–4.1 μm) than B fibers (range: 1.2–3.6 μm). D units contacted fewer type I hair cells than C units and many fewer bouton endings than B units. There was a statistically significant correlation between the longitudinal position of B fibers and their axon diameters (r = −0.51, P < 0.05). In other respects, including terminal-field size and number of boutons, BT, BM, and BP units were similar.
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. 6 B) and calyx-bearing axons (Fig.6 C).
Five other differences between the two samples are summarized in Table2. 1) B units made up a larger fraction of the extracellular than of the intraaxonal sample.2) As compared with the intraaxonal sample, the extracellular sample had a higher proportion of BP units and a lower proportion of BT units. 3) Alpha fibers made up a majority of the extracellular sample but a minority of the intraaxonal sample.4) Almost half the extracellular C units innervated one or two type I hair cells, whereas all 11 intraaxonal C units innervated three or more such hair cells. And 5) there were proportionately more D units with large numbers of bouton endings in the extracellular than in the intraaxonal sample. Mean axon diameters, calculated for each morphological category from the extracellular sample, are presented in the second column of Table 2. For each of the five differences, the category of units underrepresented in the intraaxonal sample had the smaller mean diameter. This suggests that some, if not all, of the bias in the intraaxonal sample is related to the difficulty in impaling small axons.
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.
B-high units range from regular (cv* ≈ 0.20) to irregular (cv* ≈ 1.0). For these units, there is a strong power-law relation between gain and cv* (Fig. 7 A) and a strong semilogarithmic relation between phase and cv* (Fig. 7 B). There are only three B-low units; their cv*s range from 0.23 to 0.66, and their gains and phases tend to be slightly lower than those of B-high units of comparable discharge regularity.
CD-high units are irregularly discharging with most of them having cv*s between 0.6 and 0.8. Gains and phases are lower than those of B-high units with similar cv*s. CD-low units are also irregular and have even lower gains and phases. We wished to ascertain whether C and D units differed. Many discharge properties vary with longitudinal position in the neuroepithelium. To separate the effects of background discharge and morphological class, we did a two-way multivariate analysis of covariance (ANCOVA) with background rate (high-rate vs. low-rate) and morphological class (C vs. D) as the categorical variables and position as the covariate. Dependent variables were background rate, cv*, gain and phase; cv* and gain were log transformed. C and D units resembled each other in their background discharge, cv* and phase. The only significant difference was in gain (P < 0.05) with C units having an estimated mean gain 1.7 times that of D units. This is precisely opposite from the difference in gains predicted in theintroduction. Location had a significant effect on gain (P < 0.001) and phase (P < 0.01); CD units closer to the planum had lower values of gain and phase than those nearer the torus. Background rate had an independent effect on gain (P < 0.001) but not on phase (P> 0.8). Presumably reflecting the combined effects of background rate and location, there is a fourfold difference between the mean gains of CD-low and CD-high units (Table 3).
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 variables—x 1 = log10 (cv*), x 2= log10 (gain), andx 3 = 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 eliminatingx 2 orx 3.
Two-dimensional discriminant curves separating B and CD units are drawn in Fig. 7, A and B. Separate curves are presented for high-rate and low-rate units, respectively. Any point located to the right and below the appropriate curve is assigned to the CD class; otherwise it is categorized as a B unit. The two-dimensionalx 1,x 2 (Fig. 7 A) andx 1,x 3 curves (Fig. 7 B) misassign six and nine units, respectively. When all three variables are used, there are only three misclassified units. These are enclosed by squares in Fig. 7, A and B, and include one B-high and two CD-high points located near the curves separating B and CD units. In addition to the three units misclassified by the original discriminant functions, the jack-knife procedure misclassified two CD-low units and these are marked by arrows in Fig. 7, A andB. The proportion of units misclassified by the jack-knife procedure is 5/54 (9.3%).
This last ratio provides an estimate of the proportion of misclassified units in a sample of unlabeled units. In addition, we needed to evaluate the probability that single unlabeled cases would be misclassified. As a starting point, we tabulated the normalized z scores for labeled B and CD units (Fig. 7 C). Combining high and low groups, we calculated mean values,z̄ CD = −1.26 andz̄ B =1.26. The data were fit by normal distributions (Fig. 7 C, - - -) whose separation was statistically significant (t = 9.12, df = 52,P ≪ 0.001). Probabilities of misclassification were calculated according to Eqs. 1 and 2 inmethods (Fig. 7 D); reflecting the almost equal numbers of presumed B and CD units in the extracellular sample (see Table 3), p(B) and p(CD) were both set to 0.5. The misclassification probability is highest (P = 0.5) when z = 0 and declines logarithmically so thatP = 0.090 at ‖z‖ = 1 andP = 6.33 × 10−5 at ‖z‖ = 4.
DISCHARGE PROPERTIES AND LONGITUDINAL POSITION.
In Fig. 8, cv*, gain and phase are plotted versus normalized longitudinal position, ℓ. ℓ = 0 corresponds to the torus; ℓ = 1, to the planum. Gain (Fig.8 B) and phase (Fig. 8 C) are both strongly related to ℓ; 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 ℓ differed for B and CD units and separate regression lines are drawn in Fig.8 A for the two groups. The latter difference is not surprising as it forms the basis for the discriminant analysis described in the preceding section.
The results presented in Fig. 8 can be summarized as follows. First, B units near the torus have an irregular discharge and large gains and phases. In contrast, B units near the planum have a more regular discharge, together with low gains and phases. Second, the discharge properties of the three central B units (Fig. 8, symbols in squares) resemble those of peripheral B units located at the same longitudinal position in the hemicrista (Fig. 8, symbols not in squares). Third, CD-low units have a location in the central zone closer to the planum than do CD-high units. CD-low units also have lower gains and phases, but similar values of cv*. As shown in an ANCOVA described in the preceding text, the lower gains of CD-low units may reflect a joint dependence on location and background discharge, whereas the lower phases can be explained solely by the relative locations of CD-high and CD-low units. These conclusions are exemplified in Fig. 8, Band C. Consider the gains (Fig. 8 B). With one exception, the gains for CD-low units are below the regression line for all units, while most (13/18) of the CD-high gains are above this line. In contrast, both CD-high and -low phases are found in almost equal numbers to either side of the regression line in Fig. 8 C.
The strong relations in Fig. 8 imply that the longitudinal position of an unlabeled unit can be predicted from its physiological properties. Forward stepwise multiple regressions were used on labeled units to obtain separate prediction equations for CD and B units (see legend to Fig. 9 for details). As illustrated in Fig. 9, the predictions were accurate; the residual SD, expressed as a percentage of the total length of the hemicrista, was 8.8% for B units and 6.8% for CD units.
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.
For B units, the morphological features considered included longitudinal position, axon diameter, number of boutons, total bouton area, mean bouton area, number of terminal branches, and terminal-field diameter (Brichta and Peterson 1994). Background rate was unrelated to longitudinal position (P > 0.3) but was negatively related to the number of boutons (P < 0.02). Of the several independent variables, only longitudinal position was significantly related to log(cv*), log(gain), and phase (P < 0.001 in all cases).
Independent variables for CD units were longitudinal position, axon diameter, number of type I hair cells, and number of bouton endings. log(cv*) was not significantly related to any morphological feature. Each of the other three discharge properties was significantly related only to longitudinal position (P < 0.001 in all cases). The dependence of background rate on position is consistent with the observation that CD-low units have locations nearer the planum than CD-high units. In addition, there was a suggestion that phase was related negatively to the number of type I hair cells (P = 0.054) and positively related to the number of bouton endings (P = 0.082).
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.
The assignment of extracellular units is illustrated in Fig.10, A and B,which shows the relations between gain and cv* and between phase and cv* for extracellular units identified as B or CD by discriminant functions. Comparisons with the intraaxonal sample (Fig. 7,A and B) showed that the relations for B units from the two samples were statistically indistinguishable. Because of the larger size of the extracellular sample, it provided more precise estimates of the regression coefficients. A power-law regression, gain = a(cv*)b, for extracellular B units gave a = 41.6 ± 3.5 spikes · s−1/deg · s−1 and b = 2.66 ± 0.08 (r = 0.89, P < 0.001). The semilogarithmic regression, phase = a + blog (cv*), for the same units provided a = 82.6 ± 4.2° and b = 97.9 ± 3.0° (r = 0.89, P < 0.001).
Table 3 compares statistics for the intraaxonal and extracellular B samples. Predicted locations of extracellular B units were used to assign them to the BT, BM, and BP categories. Comparisons based on all B units indicate that mean background rates, cv*, gain, and phase were slightly higher in the intraaxonal sample. As a results of these differences, there is a shift in the calculated normalized longitudinal position between the two samples. Mean values of the calculated position for B units are 0.426 ± 0.056 (intraaxonal) and 0.579 ± 0.020 (extracellular) (P < 0.05, 2-tailed t-test). The discrepancy in background rates may reflect the depolarization of impaled axons. Discrepancies in the other three variables and in longitudinal position are in directions that can be explained by a smaller proportion of thin axons in the intraaxonal sample than in the extracellular sample (Fig. 6 B).
Comparisons were also done for CD units (Table 3). Mean values of background discharge, gain and phase were statistically indistinguishable for the intraaxonal and extracellular samples. This was so for both CD-high and CD-low units. The small difference in cv* for CD-low units was of marginal statistical significance (P < 0.10). Two factors may contribute to the similarity in the extracellular and intraaxonal statistics for CD units. 1) CD units include relatively few of the thinnest axons (Fig. 6 C), which may reduce size-related sampling differences between intraaxonal and extracellular recording. And2) although our data are unclear on the matter, it is possible that the various discharge properties of CD units may be only weakly related to axon diameter.
There is a small size-related bias favoring the inclusion of thin B axons in the extracellular sample. Thin axons are regularly discharging and have low gains and phases. To explore how this might affect the discrimination between B and CD units, we used the extracellular gain versus cv* and phase versus cv* regressions to determine how the discrimination scores of B units would change with discharge regularity. Scores increased from a minimum of 8.7 at cv* = 0.5 to reach 110 at cv* = 0.1 and 27 at cv* = 1.0. From these calculations, a shift in the extracellular sample toward more regular B units should be accompanied by an increase in scores. There should be no effect on CD scores. Both predictions were confirmed. In particular, the extracellular, as compared with intraaxonal, scores for B units showed a statistically significant increase (P < 0.01), whereas the corresponding change for CD units was not significant (P > 0.2) (t-tests, unequal variances). The results indicate that discrimination should be easier in the extracellular sample.
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 (seemethods). “Very insensitive” units, presumably of the CD-low variety, were found in vivo. The results suggest that invitro 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 extracellular sample are described.
The mean value for B units is 20.0 ± 0.6 spikes/s and that for CD units is 16.7 ± 0.9 spikes/s. Although the mean rates for the two groups are similar, the distributions differ (Fig.11). Rates for B units are almost symmetrically distributed about a mode just above 20 spikes/s. The CD distribution, in contrast, is positively skewed with many of its units having no background discharge. Silent units make up a larger proportion of CD units (42/279, 15.1%) than of B units (7/288, 2.4%).
Multiple-regression equations were used to predict the normalized longitudinal positions of extracellular B and CD units (Fig.12 A). The distribution for B units has two peaks, one at 0.3 and the other near 1.0. The trough between 0.4 and 0.8, which corresponds to the position of the central zone, may be explained by the small size of the peripheral zone in this range and the large proportion of CD units in the central zone (Fig. 1). Consistent with this interpretation, it is in this range that CD units are placed (Fig. 12 A).
One feature of the B-unit distribution undoubtedly reflects a bias in the intraaxonal sample. There were only three intraaxonal B units near the planum (Figs. 3 A and 8). They had longitudinal positions between 0.9 and 1.0, together with relatively low values of cv*, gain, and phase. Many of the extracellular B units had even lower values of cv*, gain, and phase (Fig. 10). Such values lead to predicted locations >1.0, i.e., outside the neuroepithelium. A simple explanation is that the intraaxonal units near the planum are not representative of all the units found there, many of which have very thin axons (Brichta and Peterson 1994).
Figure 12 B compares the predicted locations of CD-high and CD-low units. As was the case for the intraaxonal sample (Figs. 8 and9), the extracellular CD-low units have a location nearer the planum than do CD-high units. The finding is not a statistical artifact as the background discharge was not used to predict CD locations.
B units can be regular or irregular, whereas almost all CD units are irregular (Fig. 12 C). There is a small, but statistically significant difference in mean values of cv* for CD-high and CD-low units (t test, P < 0.001; Fig.12 D and Table 3).
GAIN AND PHASE.
There are two peaks in the gain (Fig. 12 E) and phase (Fig.12 G) distributions for extracellular B units. The gain peaks are at 0.5 and 10–20 spikes · s−1/deg · s−1, the phase peaks, at 0–10° and 50–60°. The separate peaks are related to longitudinal position. This can be seen in Table 3 in which the B units are divided into BT, BM, and BP categories. BT units have an average gain >50 times that of BP units. There is a large difference in phase for the two groups. BM units have intermediate values of gain and phase. The differences are not a statistical artifact of the fact that gains and phases were used in calculating the presumed locations. Large regional differences still were observed when gains or phases were removed from the location calculation.
Gains are much lower for CD-low, as compared with CD-high, units (Fig.12 F). CD-low phases fall at the lower end of the range for CD-high units (Fig. 12 H). On average, there is a fourfold difference in gains and a 10–15° difference in phases for the two CD groups (Table 3). As suggested by an ANCOVA done on the intraaxonal sample (see preceding text), the gain difference may reflect a joint dependence on background rate and longitudinal position, whereas the phase difference can be explained entirely by a dependence on position.
We divided our CD units into high and low populations based on whether their background rates were <5 or >5 spikes/s. To study the influence of background rate in more detail, we did regressions between the background discharge of our extracellular CD-high units and each of three variables—cv*, gain, and phase (Fig.13). All three regressions were positive, and two of them were statistically significant (cv*,P < 0.02; gain, P ≪ 0.001; phase,P > 0.1). To determine whether CD-low units were distinctive, we compared their actual values with predictions from the CD-high regressions; actual values of cv*, gain, and phase were significantly lower than predictions (paired t-tests: cv*,P < 0.01; gain and phase, P ≪ 0.001). Separate comparisons for silent and nonsilent CD-low units indicated that cv* was distinctive for silent (P < 0.002) but not for nonsilent units (P > 0.6), gain was distinctive for both CD-low groups (P < 0.001), and phase was significantly distinctive for silent units (P ≪ 0.001) and marginally distinctive for nonsilent units (P < 0.10). Mean values for the various groups are presented in Table 3.
Responses to externally applied 50-μA currents are illustrated in Fig. 14, A and B, for two units recorded consecutively from one animal. Cathodal currents increase discharge and anodal currents decrease it. The top unit (Fig.14 A) is irregular (cv* = 0.65), whereas the bottom unit is regular (cv* = 0.13). For the irregular unit, cathodal currents result in a response of ≈55 spikes/s, whereas anodal currents abolish firing. Smaller, ≈2.5 spikes/s responses are seen in the cathodal and anodal responses of the regular unit.
Figure 14 C plots normalized galvanic responses (β*) versus discharge regularity (cv*) for 25 units obtained in a single preparation and for 24 units obtained in two other preparations. An ANCOVA was used to eliminate interanimal variability and to estimate the exponent (b) in the power-law relation, β* = cv*b (see methods). The exponent, based on all 49 units, was b =1.02 ± 0.22. Of the 49 units, 39 were B units and 10 were CD units. To see if the two groups differed in their galvanic responses, we first fit a separate regression to the B units, β* = a · cv*b, which gave a = 0.47 ± 0.06 and b = 0.50 ± 0.24. These parameters were used to calculate a ratio between the actual and predicted β* for all units. Mean ratios, 1.01 ± 0.13 for the B units and 2.76 ± 0.60 for the CD units, differed significantly (2-tailedt test, P < 0.001). The results imply that galvanic responses are 2.5–3 times larger in CD than in B units.
Sinusoidal head rotations were presented in half-decade steps over the frequency range, 0.01–3 Hz. Rotation amplitude was adjusted to stay within the linear range of each unit. Bode plots are shown for individual BP, BT, CD-high, and CD-low units (Fig.15, A–G). Of the CD-low units, only those with some background discharge could be studied because silent units did not respond to the maximal rotation amplitudes possible at the higher frequencies. Mean gains and phases for the other groups are shown in Fig. 15, D andH.
BP units encode near angular head velocity at frequencies >0.1 Hz (Fig. 15, A and E), where gains are nearly constant and phases are close to zero. Except for phase leads slightly greater than expected at the lowest frequencies, data for BP units conform to a first-order torsion-pendulum model (Oman et al. 1987; Steinhausen 1931) with an average (±SD) time constant of 2.7 ± 0.9 s (thick lines, Fig. 15,A and E).
BT units are more dynamic than BP units. In the frequency range from 0.01–0.3 Hz, BT gains (Fig. 15, B and D) increase with a 5- to 10-fold greater slope than BP gains (Fig. 15,A and D) and phase curves for BT units (Fig. 15,F and H) are displaced upward from those of BP units by almost 50° (Fig. 15, E and H). From their gain slopes between 0.1 and 1 Hz (4.0-fold per decade) and their phases at 0.3 Hz (60–70°), BT units encode slightly closer to angular acceleration than to angular velocity. The dynamic effects seen in BT units are not maintained at frequencies >0.3 Hz. Unlike other units, BT units do not reach a constant phase and a constant gain slope at higher frequencies. Rather the phase continues to decline up to 3 Hz where it approaches near-zero values. The gain slope declines from 5.9-fold per decade between 0.1 and 0.3 Hz to 1.8-fold per decade between 1 and 3 Hz.
CD-high units show more variability in their gains and phases (Fig. 15,C and G) than either BP or BT units. The mean CD-high gain and phase curves (Fig. 15, D and H) lie close to the mean curves for BM units. The longitudinal locations of CD-high and BM units overlap. The 0.3-Hz gains and phases of CD-high units resemble those of B units located at the same longitudinal position (Fig. 8, B and C). The similarity in the CD-high and BM curves of Fig. 15, D and H,implies that the resemblance extends to other frequencies.
The four CD-low units (Fig. 15, C and G) resemble CD-high units in the shapes of their gain and phase curves. All four CD-low phase curves fall near the lower end of the CD-high range, but this is true for only two of the four CD-low gain curves. Many other, silent CD-low units did not respond to the small-amplitude rotations we could produce at the higher frequencies and so could not be included in the analysis. For this reason, CD-low mean gain and phase curves are not included in Fig. 15, D and H.
Functional organization of the turtle posterior crista
Previous studies suggested that there were similar spatial gradients in the morphology of bouton afferents innervating the cristae of turtles (Brichta and Peterson 1994), frogs (Honrubia et al. 1989; Myers and Lewis 1990), and fish (Boyle et al. 1991). On the basis of this similarity, we hypothesized that turtle B fibers would show longitudinal gradients in afferent discharge properties resembling those found in anamniotes (Boyle et al. 1991;Honrubia et al. 1989; Myers and Lewis 1990). The hypothesis was confirmed. In the turtle crista, bouton (BP) units terminating near the planum have a more regular discharge, smaller rotational gains, and smaller rotational phases than do bouton (BT) fibers ending near the torus. BM units, supplying midportions of the hemicrista, are intermediate in all three respects. Furthermore BM units had similar discharge properties whether they innervated the central (CZ) or peripheral zones (PZ). A similar functional organization is seen in the anterior and horizontal cristae of turtles (Igic and Brichta 1997; unpublished data).
We also predicted that in their physiology CD units, restricted to the turtle CZ, would resemble the comparable units in the mammalian CZ. The latter prediction was only partly confirmed. As is the case for centrally located mammalian calyx (C) and dimorphic (D) units (Baird et al. 1988; Lysakowski et al. 1995), turtle CD units are irregularly discharging and have gains and phase leads that are intermediate between those of turtle BP and BT units. Despite the basic similarity between calyx-bearing CZ units in the mammals and turtles, there are two obvious differences. First, in mammals, centrally located C and D units differ in their rotational phases and gains, with the C units having slightly larger phases and considerably lower gains. This may be contrasted with the situation in the turtle where C and D units have similar gains and phases. We shall return to this topic in a later section (seeDeterminants of response gain). Second, turtle CD units can be divided into those with low and high background rates. In contrast, almost all mammalian afferents have an appreciable background rate. In the turtle, CD-low units have considerably lower rotational gains than CD-high units. Low rotational gains may help to extend the range of angular head velocities that can be linearly encoded (Baird et al. 1988; Brichta and Goldberg 2000). In this respect, CD-low units in turtles may serve the same function as do C units in mammals.
A comparison of the crista in anamniotes, turtles, and mammals has led to speculations concerning the evolution of the vertebrate crista (Goldberg and Brichta 1998). In particular, it has been suggested that the presumed transformation of the crista from a longitudinal organization in anamniotes (Boyle et al. 1991; Honrubia et al. 1989; Myers and Lewis 1990) to a partly concentric organization in turtles is related to the presence of type I hair cells in the turtle CZ (Brichta and Peterson 1994; Jørgensen 1974; Lysakowski 1996) and that the presumed transformation to a fully concentric organization in mammals is related to the distribution of type I hair cells throughout the mammalian neuroepithelium (Fernández et al. 1995;Lindeman 1969; Lysakowski and Goldberg 1997). Although the proposed scheme provides a useful framework, there are indications that it may be overly simplified. One such indication is the early finding in the guitarfish of a transverse variation in afferent physiology (O'Leary and Dunn 1976;O'Leary et al. 1974).
Relation between morphology and physiology
In the turtle crista, the physiology of a bouton afferent is related to its longitudinal position. Longitudinal gradients in afferent morphology were described previously in an extracellular labeling study (Brichta and Peterson 1994) but were less evident in the present sample of intraaxonally labeled fibers. Some of the differences between the two studies can be ascribed to a bias in intraaxonal labeling toward larger diameter fibers. Possibly reflecting such a bias, there was little difference in the morphology of intraaxonally labeled BP, BT, and BM units. Despite the similarity in their morphology, the three subclasses of intraaxonally labeled B units differed in their physiology. This suggests that morphological features other than longitudinal position are unimportant in determining discharge properties. The conclusion was confirmed by a statistical analysis of the structural correlates of the cv*, gain, and phase of B units. Each of these discharge properties was related to longitudinal position, but not to axon diameter, number of boutons, or terminal branching patterns. A similar result held for CD units. All CD units were irregularly discharging, and their cv*s were unrelated to any measured morphological variable, including longitudinal position. In addition, the background discharge, gain, and phase were related to longitudinal position but not to axon diameter, the number of type I hair cells, or the number of bouton endings.
Perhaps the strongest evidence that discharge properties are unrelated to branching patterns comes from a comparison of B and CD units. Despite their distinctive terminal trees, CD units cannot be distinguished from B units by any single physiological variable, including gain, phase, or cv*. The gain and phase of CD units overlap those of BM units, whereas the cv* of CD and BT units resemble each other. In a previous study of intraaxonally labeled fibers in the lizard horizontal crista, Schessel et al. (1991)suggested that C units in lizards had a distinctively irregular discharge, but only one B unit was labeled and the cv's of C and D units were not corrected for differences in mean interval. In any case, our study indicates that discharge regularity, by itself, cannot be used to classify units into B, C, and D groups. Furthermore our results do not support the suggestion, made by Boyle et al. (1991), that response dynamics and dendritic branching patterns are causally related.
Determinants of response gain
There is a 200-fold variation in the gains of bouton afferents, with the gain at 0.3 Hz (g 0.3 Hz in spikes · s−1/deg · s−1) varying from 0.2 in the most regularly discharging BP units to 40 in the most irregularly discharging BT units. The results can be summarized by a power-law relation betweeng 0.3 Hz and cv* (Fig.16 A). On the basis of a previous analysis done in mammals (Baird et al. 1988;Goldberg et al. 1990), it can be supposed that there are at least two factors contributing to the relation. The first is the sensitivity of the postsynaptic spike encoder, which as measured by galvanic sensitivity (β*) increases with cv* (Goldberg et al. 1984; Smith and Goldberg 1986). The second is the influence of response dynamics. As we have shown elsewhere (Brichta and Goldberg 1998a), gain increases with sinusoidal frequency (f) according to a formula, gain ∝ (f/f 0)φ/90, where f 0 is a reference frequency and φ is the average phase lead (in degrees) over the frequency interval fromf 0 to f. Because of the semilogarithmic relation between φ and cv*, response dynamics will also contribute to the power-law relation between gain and cv*.
To estimate the relative contributions of the two factors, we started with the power-law relation for B units, g 0.3 Hz = 41.6 cv*2.66 (Fig. 16 A). To eliminate the influence of encoder sensitivity, we dividedg 0.3 Hz by the power law, β* = 0.47 cv*0.50 (Fig. 14 C, - - -), to giveg*0.3 Hz = 88.5 cv*2.16(Fig. 16 B). This left an exponent, b= 2.16, to be explained by response dynamics. The relation between (f/f 0)φ/90and cv* is closely fit by a power-law whose exponent increases with the ratio, (f/f 0). By substituting different values of the ratio, we found that the desired exponent of 2.16 was obtained when (f/f 0) = 125 or f 0 = 0.0024 Hz. The result was a flat relation between g*0.0024 Hz and cv* (Fig. 16 C). A 200-fold variation in gain corresponds to a 7.4-fold variation in cv*. The analysis suggests that of the 7.42.65 = 200 × variation ing 0.3 Hz, response dynamics makes a larger contribution (7.42.16 = 75X) than does encoder sensitivity (7.40.50 = 2.7X).
A similar analysis was done for CD-high and CD-low units. The value of g 0.3 Hz for each CD unit (Fig. 16 A) was divided by β* = 1.30cv*0.50 to give g*0.3 Hz (Fig. 16 B); the leading coefficient in the power law for β* was increased to reflect the finding that galvanic sensitivity was 2.75 times higher in CD than in B units. Because the Bode plots for CD-high units paralleled those for BM units (Fig. 15,D and H), we used the value off/f 0 = 125 gotten from B units to calculate g*0.0024 Hz =g*0.3 Hz/125(φ/90) for CD units (Fig. 16 C).
Mean values (in spikes · s−1/deg · s–1) of g*0.0024 Hz for the various extracellular groups were: 0.141 ± 0.006 (B), 0.039 ± 0.002 (CD-high), and 0.016 ± 0.002 (CD-low). Values for the three groups are in the ratio, 1:0.28:0.11.
As was done in mammals (Baird et al. 1988;Goldberg et al. 1990; Lysakowski et al. 1995), we wished to estimate the relative contributions of type I hair cells (w I) and bouton endings (w B) tog*f0,f 0 = 0.0024 Hz.g*f0 may be taken as a measure of the total synaptic input to all of an afferent's endings independent of encoder sensitivity and response dynamics. Encoder sensitivity and response dynamics are eliminated because the former reflects the channel properties of the nerve terminal (Smith and Goldberg 1986), whereas the latter is likely to reflect early stages in transduction (Highstein et al. 1996). As such, these two factors presumably are unrelated to the types and numbers of endings. w I was computed as the ratio between the mean values ofg*f0 and of the number of type I hair cells for 11 C units. Similarly,w B was taken as the ratio between the mean values of g*f0 and of the number of bouton endings for 20 B units. The weighting coefficients (in spikes · s−1/deg · s−1) were w I = 0.0084 ± 0.0020,w B = 0.0014 ± 0.0002 andw I:w B = 6.0 ± 1.7.
w I and w Bwere used to obtain predictions ofg*f0 for individual B, C, and D units. As can be seen in Fig.17, the agreement between actual and predicted values is only fair as judged by the correlation between the two variables (r = 0.42, df = 47,P < 0.01). In addition, the correlation within each group is poor. In calculating predicted responses, we took into account encoder sensitivity, response dynamics, and the numbers of type I hair cells and bouton endings. The poor correlations imply that there is considerable intragroup variability in the weighting coefficients, and, hence, that factors other than the three considered are important in determining rotational gains. A similar conclusion was reached in our studies in the chinchilla (Baird et al. 1988;Goldberg et al. 1990).
Type II inputs to dimorphic units
The present results differ from those obtained in the chinchilla crista concerning the inputs from type II hair cells to D units. In the chinchilla, g*f0 was fivefold larger in D, as compared with C, units (Baird et al. 1988). Because both kinds of units contacted similar numbers of type I hair cells, it was presumed that the larger values ofg*f0 for D units could be explained by the additional bouton inputs they received. A linear model, g*f0 =n I w I +n B w B, was applied to C and D units to obtain aw I:w Bratio of 3:1. In the present study, we found that turtle C and D units had comparable values ofg*f0, a finding that is most easily explained were there a negligible type II input to turtle D units. The conclusion was verified when the same linear model was applied to turtle C and D units, giving an estimate ofw I identical to that stated in the preceding text (w I = 0.0084 ± 0.0020), but a near-zero estimate ofw B (−0.0017 ± 0.0013). The latter value may be contrasted with w B= 0.0014 ± 0.0002 obtained from turtle B units.
There are two differences between the turtle and chinchilla studies. The first concerns rotational frequencies. Turtle units were tested at 0.3 Hz; chinchilla units at 2 Hz. This is probably an unimportant difference. In particular, the Bode plots of Fig. 15, C andG, show that there is a high correlation between the gains at 0.3 and 3 Hz, implying that results would have been similar had we tested at the higher frequency. The second difference concernsf 0, the frequency at which dynamic effects on gain are assumed comparable for the various unit groups. In the chinchilla, response phases converged atf 0 = 0.2 Hz, whereas in the turtlef 0 was more than a 100-fold lower. The very low value of f 0 in turtles reflects the large range of phases seen in turtle B units at 0.3 Hz. It seems unlikely that the value of f 0, used in comparing B and CD units, also should be used when C and D units are compared. In fact, a regression betweeng*0.3 Hz and response phase suggests that the response dynamics of turtle C and D units would converge between 0.1 and 0.15 Hz. Using this higher value off 0 resulted in an increase in the relative value of w B, albeit one that was still not statistically distinguishable from zero.
There is no obvious functional advantage of a D unit making contact with type II hair cells and, yet, not receiving a significant input from them. At the same time, any of several mechanisms could be responsible for an ineffective input. So for example, a significant fraction of the bouton endings in the chinchilla crista lack afferent synapses (Lysakowski and Goldberg 1997), and the same conceivably could be true for the bouton endings of turtle D afferents. A second possibility is suggested by a recent survey of outwardly rectifying basolateral conductances in turtle crista hair cells (Brichta and Goldberg 1998b; Brichta et al. 1998). Many type II hair cells, including almost all those from the PZ and many of those from the CZ, have small, rapidly activating outward conductances. In contrast, a substantial proportion of type II hair cells from the CZ have larger, slowly activating conductances. The larger size of the conductances would lead to small receptor potentials, which in turn would make synaptic transmission from the hair cell less effective. Because the values ofg*f0 are similar for B units in the CZ and PZ, it might be supposed that hair cells with larger, slowly activating conductances preferentially synapse with D units. A third explanation can be offered. It is possible that the enlarged surface area of calyx endings would lower the input impedance of the postsynaptic terminal and, hence, the gains of both calyx and dimorphic units (Baird et al. 1988; Goldberg 1996). There were several reasons why the mechanism was thought not to operate in mammals (Goldberg 1996;Lysakowski et al. 1995). Evidence on this point is lacking in turtles. Fourth, there is a suggestion that differences in the response properties of calyx and dimorphic units in mammals may be related to differences in the intracellular machinery of the two kinds of afferents, rather than to differences in their synaptic inputs from type I and type II hair cells. In particular, calyx units in mammals are immunoreactive for the calcium-binding protein, calretinin, whereas dimorphic units are not (Desmadryl and Dechesne 1992). It is unclear whether calyx and dimorphic units in the turtle differ in this way (Monk and Peterson 1995).
In the present paper, we developed statistical procedures to infer the morphological type and location of an afferent solely from its discharge properties. This indirect approach was used to characterize the response dynamics of several groups of extracellularly recorded units. BP units had the simplest response dynamics, which could be approximated by a first-order torsion pendulum model. The same is also true of regularly discharging afferents in other species (Baird et al. 1988; Boyle and Highstein 1990;Goldberg and Fernández 1971;Honrubia et al. 1989). Because a torsion pendulum parallels the expected macromechanics of the semicircular canals (Oman et al. 1987; Steinhausen 1931), it is customary to presume that the transduction mechanisms following macromechanics do not greatly alter the response dynamics of such afferents.
Less regularly discharging afferents show high-frequency deviations from the torsion-pendulum model, and these can sometimes be described by a fractional (s k) operator,k > 0, which introduces a fixed phase lead, k · 90°, and a gain enhancement, (f/f 0)k, as frequency increases from f 0 tof (Baird et al. 1988; Boyle and Highstein 1990; Honrubia et al. 1989;Schneider and Anderson 1973). Ans k operator describes the deviations seen in our CD and in many of our BM units but not in our BT units. The latter units show a high-frequency decline in phase. A similar decline also was seen in afferents innervating the turtle papilla neglecta (Brichta and Goldberg 1998a) but not in acceleration afferents in the toadfish (Boyle and Highstein 1990). The cellular mechanisms responsible for the high-frequency phase decline are unknown.
Afferent responses to externally applied currents have been used to study the etiology of response dynamics. Currents have been applied to afferents by way of the perilymph (Ezure et al. 1983;Goldberg et al. 1982) or to hair cells by way of the endolymph (Highstein et al. 1996). The results imply that interunit differences in high-frequency response dynamics do not reflect later stages in transduction, including voltage-sensitive basolateral currents, the various stages of synaptic transmission, and the conversion of postsynaptic currents to spike frequency. Studies of solitary hair cells harvested from distinct regions of the turtle posterior crista are consistent with the conclusion (Brichta and Goldberg 1998b; Brichta et al. 1998). In particular, type II hair cells supplying BP and BT units show almost identical voltage responses to intracellularly injected sinusoidal currents in the frequency range of vestibular transduction. Moreover, responses are in phase with injected current. The conclusion may not extend to type I hair cells or to some central type II hair cells. Because of their slow kinetics, the basolateral currents obtained from these hair cells could contribute a significant fraction of the modest phase leads seen in CD units.
Multivariate statistical procedures have been used to classify neurons based on anatomical (Brichta and Peterson 1994;Matesz et al. 1995; Moschovakis et al. 1988) or physiological criteria (Frank et al. 1988; Leem et al. 1993; Pennartz et al. 1998). In the present study, a different approach was used. We first placed intraaxonally labeled neurons into morphological classes and then used a discriminant analysis to show that the classified neurons also could be distinguished by their physiological properties. The approach was used by Mason (1997) to determine that serotonergic neurons in the ventromedial medulla could be distinguished by their slow and steady background discharge. Similarly, calyx afferents innervating the chinchilla crista were distinctive in having an irregular discharge coupled with a small rotational gain (Baird et al. 1988). In the latter case, the classification rule defining calyx afferents was so simple that it was arrived at without the help of multivariate statistics.
There are two motives for determining the physiological properties distinguishing morphologically defined classes. The first motive can be expressed by two questions of theoretical interest: what is the minimal set of physiological properties that can distinguish two or more morphological classes? Does the minimal set represent one or more physiological mechanisms? There is no a priori reason why a single property should not suffice as a minimal set. In fact, the discriminant score defines a single property as a linear or quadratic combination of the measuring physiological variables. At the same time, the combination need not represent a single mechanism. This would appear to be the case for vestibular afferents, whether from mammals (Baird et al. 1988) or turtles (the present paper). To see this for turtle afferents, we need only consider the fact it is the relation between discharge regularity and either gain or phase that makes CD units distinctive. Discharge regularity (cv*) is likely to reflect postsynaptic mechanisms (Goldberg et al. 1984;Smith and Goldberg 1985). The ratio between gain and cv* is an estimate of the total synaptic input to the afferent and, as such, reflects presynaptic mechanisms (see Determinants of response gain). Response dynamics, including the phase at an individual frequency, is also likely to be determined presynaptically (see Response dynamics).
The second motive is more pragmatic. Data from intraaxonally labeled units can be used to develop statistical formulas that infer the morphological class and location of an extracellularly recorded unit from its physiological properties. In the present paper, the applicability of the formulas to extracellular units was confirmed by comparing the discharge properties of extracellular and intraaxonal samples. The indirect determination of the morphology and location of an extracellularly recorded afferent has several advantages. First, in our hands, only one labeled unit can be identified unambiguously in a single preparation, whereas many extracellular units can be recorded. Because the extracellular sample can be much larger than the labeled sample, a more reliable picture of morphophysiological relations emerges. Second, an extracellular sample is less biased because units with thin axons are recorded more readily extracellularly than intraaxonally. Third, although it is relatively easy to impale units, it remains a challenge to maintain intracellular contact for the long periods required to complete some physiological protocols.
Like all statistical predictions, the morphological classification and predicted location of an extracellularly recorded unit are subject to error. Based on the intraaxonally labeled sample, the probability of misclassification was estimated to be <10% and the error in predicting the location was 5–10% of the entire length of a hemicrista. As the method is used to study more discharge properties, several of them may prove useful in supplementing the three variables used in the original discriminant scheme. Consider, for example, the Bode plots shown in Fig. 15. In most BT units, phase continues to decline above 0.3 Hz (Fig. 15 F). This is not the case for most CD units (Fig. 15 G). In only 2/28 CD-high units, were there high-frequency phase declines overlapping those of BT units. From their z scores near 0.5, the units had a large misclassification probability (Fig. 7 D, P > 0.2), consistent with their being misclassified.
The present classification scheme requires the collection of a sample of background activity and the response to a single sinusoidal rotation at a frequency of 0.3 Hz. Typically, the classification protocol can be completed in 1 min. A similar situation occurs in mammals where the testing of crista units is confined to 2 Hz (Baird et al. 1988; Lysakowski et al. 1995). The classification error might be reduced by including several other variables in the discriminant analysis, but this would require a more complicated testing protocol. Our preference has been to keep the protocol simple and look for potentially misclassified units when studying a new discharge property. Potentially misclassified units are indicated by their having an atypical response in the new paradigm when compared with other, similarly classified units, together with a large misclassification probability as indicated by a near-zero discriminant score based on the original variables.
Drs. R. A. Eatock and A. Lysakowski made helpful comments on the manuscript. J. Joos and K. Dempsey helped in the preparation of histological material.
This research was supported by National Institute on Deafness and Other Communication Disorders Grant DC-02508 (J. M. Goldberg, principal investigator).
Present address of A. M. Brichta: Discipline of Anatomy, Medicine and Health Sciences, University of Newcastle, Callaghan, NSW 2308 Australia.
Address for reprint requests: J. M. Goldberg, Dept. of Neurobiology, Pharmacology and Physiology, University of Chicago, 947 E. 58th St., Chicago, IL 60637.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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