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1Department of Psychology, 2Centre for Neuroscience, University of Alberta, Edmonton, Alberta, Canada
Submitted 11 August 2004; accepted in final form 8 October 2004
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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). The analysis of optic flow is important for the generation of optokinetic responses, such as optokinetic nystagmus and the optocollic reflex, which facilitate gaze stabilization (for review, see Ilg 1997; see also Carpenter 1988; Robinson 1981; birds, Gioanni 1988; Gioanni et al. 1981, 1983a, b). Gaze stabilization is important to prevent the degradation of visual acuity (Westheimer and McKee 1975) and enhance velocity discrimination (Nakayama 1981).
Numerous studies, using micro-stimulation, lesion, and electrophysiological methods, have implicated nuclei in the accessory optic system (AOS) and pretectum in the analysis of optic flow and the generation of optokinetic responses (for reviews, see Grasse and Cynader 1990; Simpson 1984; Simpson et al. 1988). The AOS and pretectum are highly conserved, and homologous structures have been identified in mammalian and avian species (Fite 1985; McKenna and Wallman 1985; Weber 1985). The mammalian AOS consists of the medial, lateral, and dorsal terminal nuclei (MTN, LTN, and DTN, respectively), which are equivalent to the nucleus of the basal optic root (nBOR) in birds. Likewise the pretectal nucleus of the optic tract (NOT) of mammals is equivalent to the avian pretectal nucleus lentiformis mesencephali (LM) (for reviews, see Simpson 1984; Simpson et al. 1988).
Physiological recordings from the AOS and pretectum from numerous species have shown that neurons in these nuclei have large, contralateral receptive fields and exhibit direction-selectivity to large-field moving stimuli rich in visual texture (NOT: Collewijn 1975a, b; Distler and Hoffmann 1993; Hoffmann and Distler 1989; Hoffman and Schoppmann 1975, 1981; Hoffmann et al. 1988; Ilg and Hoffmann 1996; Klauer et al. 1990; Mustari and Fuchs 1990; Volchan et al. 1989; Yakushin et al. 2000; LM: Fan et al. 1995; Fite et al. 1989; Katte and Hoffmann 1980; McKenna and Wallman 1981, 1985; Winterson and Brauth 1985; Wylie and Frost 1996; MTN/LTN: Grasse and Cynader 1982; Grasse et al. 1984; Simpson et al. 1979; Soodak and Simpson 1988; nBOR, Ariel and Kogo 2001; Burns and Wallman 1981; Gioanni et al. 1984; Kogo et al. 1998, 2002; Morgan and Frost 1981; Rosenberg and Ariel 1990; Wylie and Frost 1990). Recent neurophysiological studies that used large-field sinusoidal gratings as stimuli showed that pretectal and AOS neurons show spatiotemporal tuning. This was first shown in the wallaby NOT (Ibbotson et al. 1994) and subsequently in the pigeon nBOR and LM (Crowder and Wylie 2001; Crowder et al. 2003a, b; Wolf-Oberhollenzer and Kirschfeld 1994; Wylie and Crowder 2000). These studies found that pretectal and AOS neurons fall into two groups based on the location of the peak (maximal) response in the spatiotemporal domain: slow cells were maximally sensitive to motion at low temporal frequency (TF < 1 Hz) and high spatial frequency (SF > 0.25 cycles/°, cpd), whereas fast cells were maximally sensitive to high TF (>1 Hz) and low SF (<0.25 cpd) sine wave gratings. Figure 1A depicts the fast and slow regions in the spatiotemporal domain. Ibbotson and Price (2001) noted that the spatiotemporal preferences of the fast and slow units in the pretectum of wallabies and pigeons were remarkably similar. We must caution that the fast/slow distinction is not so simplistic. It is not uncommon for a slow neuron to show a secondary peak in the fast region or a fast neuron to show a secondary peak in the slow region (Crowder and Wylie 2001; Crowder et al. 2003a; Ibbotson et al. 1994; Wylie and Crowder 2000). Such neurons likely receive inputs from fast and slow subunits.
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; Simpson et al. 1988; birds, Brecha et al. 1980; Clarke 1977). In birds, there are two inputs from the LM and nBOR to the VbC: an indirect climbing fiber (CF) pathway through the medial column of the inferior olive (mcIO) (Arends and Voogd 1989; Brecha et al. 1980; Clarke 1977; Gamlin and Cohen 1988; Lau et al. 1998; Wylie et al. 1999; Crowder et al. 2000; Winship and Wylie 2001, 2003; Wylie 2001) and a direct mossy fiber (MF) pathway that is mainly restricted to folium IXcd (Brecha and Karten 1979; Brecha et al. 1980; Brauth and Karten 1977; Clarke 1977; Gamlin and Cohen 1988; Wylie and Linkenhoker 1996; Wylie et al. 1997). The CF pathway to the VbC exists in mammals (for reviews, see Simpson 1984; Simpson et al. 1988). The complex spike activity (CSA) of VbC Purkinje cells, which reflects CF input (Thach 1967), is direction selective for particular patterns of optic flow (Graf et al. 1988; Kano et al. 1990; Kusonoki et al. 1990; Simpson et al. 1981; Wylie and Frost 1993, 1999; Wylie et al. 1998). The MF pathway has also been reported in turtles and fish (Fan et al. 1993; Finger and Karten 1978; Reiner and Karten 1978) but not in several mammalian species (Blanks et al. 1983; Giolli et al. 1984; Kawasaki and Sato 1980). Winfield et al. (1978) reported a direct MF pathway from the MTN to the VbC in the chinchilla, although this finding has been contested (Giolli et al. 1984). In this study, in effort to determine whether the fast or slow cells in the AOS and pretectum feed the MF and CF pathways to the VbC, we recorded the responses of units in the granular layer of folium IXcd and the CSA of VbC Purkinje cells to sine wave gratings of varying TF and SF. |
METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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The methods reported herein conform to the guidelines established by the Canadian Council on Animal Care and approved by the Biosciences Animal Care and Policy Committee at the University of Alberta. Silver King pigeons (obtained from a local supplier) were anesthetized using an intramuscular ketamine (65 mg/kg) and xylazine (8 mg/kg) mixture. Depth of anesthesia was monitored via toe pinch and supplemental doses were administered as necessary. Body temperature was maintained via a thermal probe and heating pad (Fine Science Tools). The pigeons were placed in a stereotaxic apparatus with ear bars and beak adapter such that the orientation of the head conformed to the atlas of Karten and Hodos (1967). Sufficient bone and dura was removed to allow access to the VbC. Glass micropipettes with tip diameters of 4–5 µm filled with 2 M NaCl were used for the extracellular recordings. Micropipettes were advanced through the VbC via an hydraulic microdrive (Frederick Haer). The extracellular signal was amplified, filtered, and fed to a data acquisition unit [Cambridge Electronic Designs (CED) 1401plus]. The data were analyzed off-line using Spike2 for Windows (CED). This included spike sorting and the construction of peristimulus time histograms (PSTHs).
Stimuli and stimulus presentation
The procedures for stimulus construction and presentation were essentially identical to those described in previous studies from this lab that examined the spatiotemporal tuning of nBOR and LM units (Crowder et al. 2003a, b, 2004; Wylie and Crowder 2000). All stimuli were generated by a VSGThree (Cambridge Research Systems) graphics computer and back-projected (InFocus LP750) onto a screen measuring 90 x 75° (width x height) that was positioned in the most responsive area of the receptive field. On identification and isolation of the CSA of P cells or a GL unit, the direction preference and approximate receptive field boundaries were qualitatively determined by moving a large (90 x 90°) hand-held visual stimulus, consisting of black bars, squiggles, and dots on a white background, throughout the visual field. Subsequently, spatiotemporal tuning was quantified using 36–42 combinations of sine-wave gratings of varying SF (0.03–2 cpd) and TF (0.03–24 cycles per second, Hz) moving in the preferred and anti-preferred direction for that unit. The contrast of the sine wave gratings was 0.95 [(luminanceMAX – luminanceMIN)/(luminanceMAX + luminanceMIN)] and the mean luminance was 65 cd/m2. The refresh rate was 80 Hz. Each sweep for a particular SF/TF combination consisted of 4 s of motion in the preferred direction, a 3-s pause, 4 s of motion in the anti-preferred direction, followed by a 4-s pause. During the pauses, the stimulus was a uniform gray of the standard mean luminance. Firing rates were averaged over 2–12 sweeps, and mean firing rates for motion in the preferred and anti-preferred direction were computed over the entire 4-s motion segment. For CSA, the firing rate is typically very low, thus we tried to obtain as many sweeps as possible (
12) for each SF/TF combination. This was generally not a problem as the units are not difficult to hold for long periods of time. For GL units, the firing rate is higher (
10-fold), but the units were extremely difficult to isolate and hold for long durations. We required a minimum of two sweeps, assuming the unit was well isolated.
Quantification and illustration of spatiotemporal tuning
To graphically illustrate tuning in the spatiotemporal domain, for each unit, a contour plot of the mean firing rate as a function of SF and TF was made using Sigma Plot. TF and SF were plotted on the ordinate and abscissa, respectively, and firing rate (minus spontaneous rate) was plotted on the z axis. The location of maximal excitation was referred to as the primary peak of the contour plot. A peak of lesser magnitude was termed a secondary peak. Concluding that a contour plot contained a single peak versus two peaks was somewhat subjective (see contour plots in Figs. 1B, 2, and 3). To be classified as a secondary peak, it had to be clearly separable from the background activity and distinct from the primary peak by visual inspection, and a consistent response of >40% the magnitude of the primary peak was necessary. (The contour plots shown in Figs. 1B and 3C are representative in this regard).
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is ln (TF), 
is the angle of the Gaussian, (x, y) is the location of the peak of the Gaussian, 
x and y are the spread of the Gaussian in the u' and ' dimensions, respectively, and P is a constant reflecting the spontaneous activity of the cell. x, y, x, y, , and P were optimized to minimize the sum of the mean error between the actual and G values using the solver function in Microsoft Excel. Not all of the data points from the contour plots were necessarily included in the Gaussian fits. In cases where there were two peaks in the contour plot, the points corresponding to each peak were fit separately (e.g., see Fig. 3, C and D). In addition, for some contour plots with single peaks spurious values distant from the peak were omitted (e.g., Fig. 2, A and B, and C and D).
To determine whether the CSA and GL primary peaks were located in the fast or slow regions of the spatiotemporal domain, we first used a hierarchical cluster analysis to divide a group of 118 cells from previous studies of LM and nBOR (Crowder and Wylie 2001; Crowder et al. 2003a, b; Wylie and Crowder 2000) into two groups based on the SF (x) and TF (y) of their primary peaks. (These are plotted in Fig. 4C). Post hoc inspection of the classification showed that the two largest clusters corresponded to fast and slow cells. We then determined a linear discriminant function to discriminate fast from slow cells using the cluster analysis results as a training set. The discriminant function was then used to calculate the posterior probabilities of fast or slow memberships for GL units and the CSA of P cells recorded in the present study. All analyses were conducted in R (Ihaka and Gentleman 1996). We used the hclust() function from the "stats" library, with the "Ward's" method, to perform the cluster analysis. The lda() function of the MASS library (Venables and Ripley 2002) was used for the linear discriminant analysis.
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In addition to providing the location of the spatiotemporal peak, the Gaussian function was also used to evaluate velocity tuning (velocity = TF/SF) following the procedure used by Priebe et al. (2003) [a variant of a method devised by Levitt et al. (1994)]. Units showing velocity tuning would have a value approaching 45°. When plotted on a contour plot, the peak of a unit tuned to velocity is elongated and oriented such that it has a slope of 
1 on log–log axes. This contrasts with a unit that shows "spatiotemporal independence," i.e., it responds maximally to a given TF irrespective of the SF. Such a unit would have a nonoriented peak in the contour plot (i.e., approaching 0 or 90°). To evaluate whether a unit showed velocity tuning as opposed to spatiotemporal independence, the primary peak for each unit was fit to a 2-D Gaussian as described in the preceding text but with constrained to either 45 ° to provide the velocity-tuned prediction or to 0°/90° to provide the independent prediction. We then computed the partial correlation of the actual response with the velocity or independent prediction using the following equations
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The statistical significance of Rvel and Rind was calculated by performing a Fisher Z-transform on the correlation coefficients {Zf = 1/2xln[(1 + R)/(1 – R)]}, and then calculating the difference between these z scores (Papoulis 1990)
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1.65 and Rvel was significantly >0. Likewise cells were categorized as independent if zdiff –1.65 and Rind was significantly >0. Cells not meeting these criteria were termed unclassifiable (1.65 > zdiff > –1.65). The conventional criterion probability of 0.1 was used (Crow et al. 1960). This criterion has been justified by the fact that this method is not a true test for statistical significance, but a convenient way to reduce data (see Gizzi et al. 1990; Movshon et al. 1985; Scannell et al. 1996). Histology
In some cases, dye spots were made at recording sites in the granular layer via iontophoretic injection of pontamine sky blue. At the end of these experiments, animals were given a lethal overdose of pentobarbital sodium (100 mg/kg) and immediately perfused with ice-cold saline followed by 4% paraformaldehyde in phosphate buffer (PB). The brains were extracted and postfixed (4% paraformaldehyde in PB with 30% sucrose) for 2–12 h and then placed in 30% sucrose solution in PB for 12–24 h. Frozen coronal sections (40 µm thick) through VbC were collected and mounted onto gelatin-coated slides. Sections were counterstained with neutral red and light microscopy was used to localize dye spots.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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1 spikes/s [0.98 ± 0.11 (SE) spikes/s]. Visually sensitive GL units were extremely difficult to isolate and hold but were easily distinguished from CSA by a much higher spontaneous rate (26.10 ± 3.68 spikes/s). The dye spots made at GL recording sites were all located in the granular layer of folia IXc,d. As expected, in response to the battery of drifting sine wave gratings, CSA and visual GL units showed clear spatiotemporal tuning. Spatiotemporal tuning of GL units
Consistent with previous studies, only a fraction (<10%) of the GL units were modulated by optic flow stimuli (Fan et al. 1993; Waespe et al. 1981). Moreover, consistent with Wylie et al. (1993), we found that the visual GL units had monocular receptive fields in either the ipsilateral (n = 11) or contralateral (n = 6) visual field and showed directional tuning to large-field stimuli. Different direction preferences (similar to those in LM and nBOR) were observed, but GL units with dissimilar direction selectivity did not have any apparent differences with respect to spatiotemporal tuning.
Figure 1B shows a contour plot illustrating the spatiotemporal tuning of a GL unit. This unit had a primary peak in the fast zone, and a slightly smaller secondary peak in the slow zone. Based on the best-fit Gaussian, the primary peak was localized to SF = 0.10 cpd, TF = 13.47 Hz and the secondary peak was located at SF = 1.0 cpd, TF = 0.28 Hz. PSTHs on the right show the unit's modulation during stimulation in the preferred and antipreferred direction for gratings of three different SF–TF combinations during a single sweep. The first 4 s show response to movement in the preferred direction, followed by a 3-s pause, 4 s of motion in the anti-preferred direction, and another 3-s pause. Clear excitation and inhibition to motion in the preferred and anti-preferred direction, respectively, are seen for PSTHs in the primary peak (SF = 0.125 cpd, TF = 16 Hz) and secondary peak (SF = 1 cpd, TF = 0.5 Hz), although this modulation is clearly greater for the primary peak. Considerably less modulation is seen outside these peaks (i.e., SF = 0.25 cpd, TF = 2 Hz). Evident in the PSTHs, the responses included both transient and steady-state components. (This was the also the case for CSA). Transients and other temporal factors have been extensively analyzed in previous studies of spatiotemporal tuning in the AOS and pretectum (Ibbotson et al. 1994; Price and Ibbotson 2002; Wolf-Oberhollenzer and Kirschfeld 1994) and will not be analyzed further in this paper.
Figure 2 shows the contour plots of the spatiotemporal tuning of two additional GL units. The unit in Fig. 2A showed a single peak in the fast region. Figure 2B shows the plot of the normalized best-fit Gaussian for this unit. The peak was located at SF = 0.06 cpd, TF = 2.03 Hz. Figure 2, C and D, shows the contour plot and normalized best-fit Gaussian, respectively, for a GL unit with a single peak in the slow zone (SF = 1.0 cpd, TF = 0.03 Hz). Eight (47.1%) GL units had a single peak in the contour plot (as in Fig. 2), whereas nine of the GL units (52.9%) had secondary peaks in their contour plots (as in Fig. 1B). Secondary peaks were always located in the opposite spatiotemporal domain and had a magnitude, on average, 73.4% the size of the primary peak (range, 43.4–98.5%).
Figure 4A plots the locations of the primary peaks of all 17 GL units as determined from the best-fit Gaussians. As described in METHODS, the locations of the peaks were assigned to either the fast or slow regions based on previous data of spatiotemporal tuning of LM and nBOR neurons (Crowder and Wylie 2001; Crowder et al. 2003a, b; Wylie and Crowder 2000). In Fig. 4C the primary peaks of nBOR and LM neurons is plotted along with data from the current study. Eight (47.1%) GL units were classified as fast cells (low SFs/high TFs; mean = 0.13 cpd/8.24 Hz), whereas nine (52.9%) GL units were slow cells (high SFs/low TFs; mean = 0.68 cpd/0.30 Hz; see also Table 1). The clustering into fast (white diamonds) and slow (gray diamonds) groups can be clearly seen in Fig. 4A (see also Fig. 4C).
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Previous studies in pigeons have shown that VbC Purkinje cells have binocular, virtually panoramic receptive fields, and the CSA responds best to optic flow patterns resulting from self-translation or self-rotation along/about a particular axis in three-dimensional space (Wylie and Frost 1993, 1999; Wylie et al. 1998). Based on the orientation of the preferred axis of rotation/translation, there are two classes of rotation neurons and four classes of translation neurons. Rotation-sensitive neurons in VbC respond best to optic flow rotating about either the vertical axis (VA) or an axis orientated 45° contralateral to the midline in the horizontal plane (45° c azimuth). Translation-sensitive neurons respond best to translational optic flow moving upward or downward along the VA, forward along an axis at 45° c azimuth or backward along an axis orientated at 45° ipsilateral azimuth. In the present study, all six classes were represented in the sample of 39 units (24 rotation neurons, and 15 translation neurons). The different groups did not differ with respect to spatiotemporal tuning, thus they have all been grouped together.
Figure 3 shows representative contour plots and best-fit Gaussians for the CSA of two Purkinje cells. In Fig. 3, A and B, a cell with a single peak in the slow domain of the contour plot is illustrated. From the best-fit Gaussian, the peak was located at SF = 0.66 cpd, TF = 0.18 Hz. In Fig. 3, C and D, a cell with a primary peak in the slow zone and a secondary peak in the fast zone is shown. From the best-fit Gaussian the primary peak was located at 0.77 cpd/0.10 Hz and the secondary peak was located at 0.11 cpd/18.0 Hz. Of the 39 CSA recordings, 11 (28.2%) of the contour plots showed a single peak, whereas 28 (71.8%) showed a secondary peak as well. On average, the secondary peak was 69.8% (range, 51.2–97.9%) the size of the primary peak. For two of these units, the magnitude of the secondary peak was >90% of the primary peak, making the assignment of primary and secondary peak more problematic.
Figure 4B plots the locations of the primary peaks of the CSA of 39 P cells in this study. These are also plotted in Fig. 4C along with the GL units and the nBOR and LM data from previous studies (Crowder and Wylie 2001; Crowder et al. 2003a, b; Wylie and Crowder 2000). Using the linear discriminate function described previously, 38 (97.4%) of the CSA units were classified as slow units (mean = 0.67 cpd/0.35 Hz; Fig. 4A, 
), whereas one unit was classified as a fast unit (Fig. 4C, 
, primary peak at 0.10 cpd/0.55 Hz). This fast unit had a secondary peak of approximately equal magnitude (96.5%) located in the slow zone (0.42 cpd/0.43 Hz). Twenty seven of the 38 slow units had secondary peaks, and 25 of these were in the fast region.
Figure 5C shows the normalized average contour plots of spatiotemporal tuning for the CSA of all 39 P cells. The average plots clearly illustrate the dominance of slow spatiotemporal tuning in CSA, though the influence of secondary peaks in a subset of CSA (71.8%) is apparent with the smaller peak in the fast region. Note the similarity of the contour plots for the slow GL units and the CSA. Note also that the peaks for the slow GL units and CSA are sharper than that of the fast units, reflecting the fact that for the fast units the primary peaks are not as tightly clustered (Fig. 4A).
Velocity-like tuning
In Fig. 3A, note that peak for this unit is elongated and oriented such that it has a slope of 1 on a log–log axis. This suggests that the cell shows velocity tuning (velocity = TF/SF) to 0.25 °/s (see diagonal scale on the contour plot). As the response is not independent of SF, this has been more appropriately termed velocity-like tuning (Crowder et al. 2003a; Zanker et al. 1999). In the present study, many of the peaks that were in the slow zone were oriented such that they approached velocity-like tuning (e.g., Figs. 1B, 2C, and 3A). As described in METHODS, following Priebe et al. (2003), neurons were classified as velocity tuned, independent, or unclassified based on the partial correlations of the actual data for each unit to velocity and independent predictions. Using the criteria described in the methods, the CSA of 10 (26.3%) slow P cells showed velocity-like tuning, 5 (13.2%) showed independence, and 23 (60.5%) fell into the unclassified group. The single fast CSA was also unclassified. For the eight fast GL units, 4 (50%) showed SF/TF-independence, 1(12.5%) was velocity-tuned and three (37.5%) were in the unclassified group. For the nine slow GL units, all fell into the unclassified group.
Figure 6 shows a scatter plot of Rvel versus Rind for all units. For convenience, — has been added to provide an approximation of the divisions between velocity-tuned, unclassified, and independent regions. This line represents the statistical criteria separating these groups based on 24 points in the best-fit Gaussian. [The actual number of points in the best-fit Gaussians ranged from 12 to 42 (mean = 24), hence this line is an approximation between the divisions]. Note the CSA that showed velocity tuning in the top left () and the fast GL units that showed SF/TF-independence in the bottom right (
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Comparison with spatiotemporal tuning in the pretectum and AOS
Spatiotemporal tuning in the optokinetic system was originally demonstrated by Ibbotson et al. (1994), who recorded from the pretectum in wallabies. Subsequently, Wylie and Crowder (2000) showed strikingly similar results in the pretectal nucleus LM and the nBOR of the AOS in pigeons (Crowder and Wylie 2001; Crowder et al. 2003a, b; Wolf-Oberhollenzer and Kirschfeld 1994). The results from these previous studies closely parallel those in this study. Like CSA and GL units, LM and nBOR neurons had a primary peak located in either the fast or slow zone. In LM, fast units were more common than slow units (66 vs. 34%), but in nBOR, slow units were more common than fast units (75 vs. 25%). In the present study, we found that GL units included fast and slow units, whereas CSA was clearly tuned to slow gratings. Table 1 summarizes the mean preferred SF/TF combinations from studies of LM, nBOR, and the VbC of pigeons (Crowder and Wylie 2001; Crowder et al. 2003a; Wylie and Crowder 2000; present study). The average preferred SF/TF combinations for the slow units in LM and nBOR were 0.67 cpd/0.55 Hz and 0.53 cpd/0.30 Hz, respectively (Crowder and Wylie 2001; Crowder et al. 2003a; Wylie and Crowder 2000), which is quite close to the values for the slow GL units (0.68 cpd/0.30 Hz) and CSA (0.67 cpd/0.35 Hz) in the present study. Likewise, the average preferred SF/TF combinations for the fast units in LM and nBOR were 0.10 cpd/2.49 Hz and 0.08 cpd/2.84 Hz, respectively (Crowder et al. 2003a; Wylie and Crowder 2000), which is close to the values for the fast GL units (0.13 cpd/8.24 Hz) from the present study. In Fig. 4C, data from the current study of the VbC and previous studies of spatiotemporal tuning in LM and nBOR are collapsed onto a single plot: show the primary peak locations in the spatiotemporal domain of recordings of the CSA of P cells in VbC (n = 39; present study); 
show primary peak locations for GL units in VbC (n = 17; present study); 
show the primary peaks of LM units (n = 64) (Wylie and Crowder 2000); and the primary peaks of units from nBOR (n = 55) are represented by 
(Crowder and Wylie 2001; Crowder et al. 2003a). The fast and slow populations form distinct clusters. The distribution of primary peaks within the fast and slow regions is similar for LM, nBOR, and VbC units.
In the present study, we also found that the many of the contour plots of GL unit responses and CSA often included secondary peaks, almost always in the opposite region. This was also the case for many nBOR and LM neurons (Crowder and Wylie 2001; Crowder et al. 2003a; Wylie and Crowder 2000) and some NOT neurons in wallabies (Ibbotson et al. 1994).
Projections of fast and slow neurons in the AOS and pretectum to the VbC
Figure 7 shows a cartoon of the projections of the nBOR and LM to the VbC. There is an indirect CF pathway through the medial column of the inferior olive (mcIO) (Arends and Voogd 1989; Brecha et al. 1980; Clarke 1977; Crowder et al. 2000; Gamlin and Cohen 1988; Lau et al. 1998; Winship and Wylie 2001, 2003; Wylie 2001; Wylie et al. 1999) and a direct MF pathway that is restricted to folium IXcd (Brauth and Karten 1977; Brecha and Karten 1979; Brecha et al. 1980; Clarke 1977; Gamlin and Cohen 1988; Wylie and Linkenhoker 1996; Wylie et al. 1997). Our results suggest that the slow neurons in LM and nBOR make up the primary input to the CF pathway, whereas the MF pathway receives major inputs from fast and slow neurons in LM and nBOR. This is not to say that the CSA does not respond to fast gratings. Clearly many of the units have a secondary peaks in the fast region of the contour plot (Fig. 3C; see also Fig. 5C) as do many slow neurons in LM and nBOR (Crowder and Wylie 2001; Crowder et al. 2003a; Wylie and Crowder 2000), thus there is clearly an integration of fast and slow information in the CF pathway. Nonetheless we contend that the CF pathway receives input almost exclusively from cells in nBOR and LM that are maximally sensitive to slow gratings.
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; Simpson et al. 1988), a direct MF projection from the AOS and pretectum to the VbC has not been identified in mammals with the possible exception of a controversial MTN–VbC projection in the chinchilla (Winfield et al. 1978). However, there may be several indirect MF pathways from the pretectum and AOS to the VbC. Most of the MF input to the VbC arises in the vestibular nuclei and the prepositus hypoglossi (Ruigrok 2003; Voogd et al. 1996), but there are also projections originating in the reticular formation, the raphe nuclei, and neurons located within and around the medial longitudinal fasciculus (Blanks et al. 1983; Gerrits et al. 1984; Langer et al. 1985; Ruigrok 2003; Sato et al. 1983; for review, see Voogd et al. 1996). The NOT and the AOS project to many of these structures, including the vestibular nuclei, the medial and dorsolateral nuclei of the basilar pontine complex, the mesencephalic reticular formation, the prepositus hypoglossi, and the nucleus reticularis tegmenti pontis (Cazin et al. 1982; Giolli et al. 1984, 1985, 1988; Holstege and Collewijn 1982; Itoh 1977; Terasawa et al. 1979; Torigoe et al. 1986a, b; for review, see Simpson et al. 1988). Thus it is possible that optic-flow information reaches the VbC from the AOS and pretectum via an indirect MF pathway in mammalian species. It would be interesting to see if this information arises from fast and/or slow neurons. Function of fast and slow neurons
Ibbotson et al. (1994) described the potential role of the slow and fast NOT neurons in the generation and maintenance of OKN. The fast units would respond maximally when retinal slip velocity (RSV) is high, whereas the slow neurons would be involved when the RSV is low, such as providing the error signal when the OKN gain is high (see Ibbotson et al. 1994 and Wylie and Crowder 2000 for detailed discussions). From the findings of the present study, it follows that the MF inputs are involved when RSV is high and low, but the CF inputs are primarily involved when RSV is low. However, again we caution against such a stark simplification: the contour plots of many of the CSA recordings showed a secondary peak in the fast zone. Thus the CSA of these Purkinje cells would not be silent to fast optic flow stimuli.
Velocity-like tuning versus spatiotemporal independence
In the present study, we found that many of the peaks in the slow zone were oriented such that they had a slope approximating one on log–log axes. That is, these units showed a peak response to a particular stimulus velocity (TF/SF), irrespective of the SF used. As the response maxima were dependent on SF, we (Crowder et al. 2003a) have previously called this velocity-like tuning (true velocity tuning would appear as a flattened ridge in the contour plot). Crowder et al. (2003a) concluded that the majority of the slow units in LM and nBOR showed velocity-like tuning, whereas the fast units were TF tuned (i.e., SF/TF-independent). However, Crowder et al. (2003a) did not provide a quantitative test in this regard, and one can infer from Priebe et al. (2003) that there is a danger in overstating the degree of velocity-like tuning. Thus we adopted the partial correlation outlined by Priebe et al. (2003) to compare velocity-tuned and SF/TF-independent predictions. The tendency of slow CSA to show velocity tuning is apparent in Fig. 6, but only 26% showed significant velocity tuning compared with the independence prediction; 13.1% showed significant SF/TF-independence, but most (60.5%) fell into the unclassified group, i.e., somewhere between velocity tuning and SF-TF-independence. Consistent with Crowder et al. (2003a), SF/TF-independence was more common with the fast GL units (50%). Following Zanker et al. (1999), Crowder et al. (2003a) argued that velocity-like tuning reflects the properties of an "unbalanced" Reichardt detector. Generally speaking, the more unbalanced the detector, the more the response approaches velocity tuning. Thus with respect to velocity tuning versus SF/TF-independence, the responses we observed suggest that the input units might vary with respect to the degree to which the detector is balanced.
GL units: granule cells or MF rosettes?
There is precious little data regarding the physiological properties of MF inputs to the granule cell layer, presumably because these cells are small and difficult to isolate and hold. In fact, it is unclear whether the GL units recorded in the present study represent MF rosettes or granule cells. This is not necessarily a critical issue for the present study, as recordings from either would allow us to determine if fast or slow units in the pretectum and AOS feed the MF pathway to the VbC. Fan et al. (1993) and Ariel and Fan (1993) recorded the visual responses of units in the GL in the turtle cerebellum using an in vitro preparation with eyes attached. Similar to pigeons (Wylie et al. 1993; present study), these units exhibited direction selectivity to large-field patterns but only respond to stimulation of the contralateral eye. Based on the following responses to stimulation of the nBOR, Ariel and Fan (1993) concluded that at least some (6/15) of the units they recorded were MF rosettes as opposed to granule cells. A recent study in rats using whole cell patch-clamp recordings showed that granule cells exhibited a low firing rate in vivo with the mean spontaneous firing rate in the absence of holding current being 0.5 ± 0.2 Hz (Chadderton et al. 2004). Based on this, it is likely that the GL units in the present study, which had high spontaneous rates (average = 26.10 ± 3.68 spikes/s), represent recordings from the MF rosettes in the granular layer.
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Address for reprint requests and other correspondence: D. R. Wong-Wylie, Dept. of Psychology, University of Alberta, Edmonton, Alberta, Canada T6G 2E9 (E-mail: dwylie{at}ualberta.ca)
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, slow GL units; 