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Department of Biology, Brandeis University, Waltham, Massachusetts 02454
Submitted 16 May 2003; accepted in final form 30 June 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESACKNOWLEDGMENTSREFERENCES |
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; Stone 1983; Stone and Fukuda 1974), and parvocellular (P), magnocellular (M), and koniocellular (K) cells in primates (Irvin et al. 1986; Kaas et al. 1978). Each of these cell groups has unique anatomical and physiological properties, and the homological relationships among X, Y, and W cells and P, M, and K cells and how receptive field properties of these cell classes compare with LGN cells in other mammals remain unclear (Casagrande and Norton 1991; Norton et al. 1988; Shapley and Perry 1986).
X and P cells show sustained responses to constant stimulation (Dreher et al. 1976; Enroth-Cugell and Robson 1966) and have smaller receptive field sizes at a given retinal eccentricity compared with Y and M cells, respectively (Linsenmeier et al. 1982; Perry et al. 1984). Y and M cells show transient responses to constant stimulation (Dreher et al. 1976; Enroth-Cugell and Robson 1966) and have shorter latencies to stimulation than X and P cells (Dreher et al. 1976; Fukada 1971; Kaplan and Shapley 1982). On the basis of these and other similarities, some scientists have suggested that X and P cells and Y and M cells are instantiations of two functional pathways that are homologous across mammals (Casagrande and Norton 1991; Levitt et al. 2001; Norton et al. 1988; Rodieck and Brening 1983). However, P cells differ from M, X, and Y cells in that P cells show only modest increases in firing rate with increasing contrast, that is, they have low contrast gains, whereas M, X, and Y cells have large contrast gains (Benardete et al. 1992; Kaplan and Shapley 1982). In addition, P cells in trichromatic monkeys show red-green color opponency, whereas M, X, and Y cells do not show color opponency (Pearlman and Daw 1970; Wiesel and Hubel 1966). Moreover, all Y cells show nonlinear spatial summation across their receptive fields (Hochstein and Shapley 1976a), whereas only a small percentage of M cells show this type of nonlinearity (Kaplan and Shapley 1982). These and other differences have led other scientists to suggest that X and Y cells are closely related to linear and nonlinear M cells, respectively, and, in this view, P cells represent a fundamentally different pathway not found in carnivores (Kaplan and Shapley 1982; Shapley and Perry 1986). The W and K groups are heterogeneous, consisting of cells with long latencies, cells with sluggish or variable responses, blue-ON cells, and other cells that have not been well characterized (Irvin et al. 1986; Martin et al. 1997; Stone and Fukuda 1974).
To better understand the functional and homological relationships among mammalian LGN cells, we have characterized the receptive field properties and laminar organization of neurons in LGN of a highly visual rodent, the gray squirrel. Comparative studies of receptive field properties across different mammals can identify which properties are common to all or most mammals and which are unique to particular species (Casagrande and Kaas 1994; Kaas et al. 1972; Kahn et al. 2000). Because each species has unique behavioral characteristics, understanding the relationship between an animal's behavioral characteristics and its neuronal properties can shed light on the function of these neuronal properties. In addition, understanding the relationship between LGN neurons in monkeys, which are very similar to those in humans, and LGN neurons in carnivores and rodents is of particular importance given that carnivores and rodents are more frequently used to study synaptic and cellular principles underlying visual function.
Previous studies of LGN in rat (Fukuda 1977; Gabriel et al. 1996; Hale et al. 1979) and chipmunk (Morigiwa et al. 1988) have identified three groups of neurons as determined by latency to optic chiasm stimulation or receptive field properties. However, studies in these animals have examined only a few receptive field properties (Fukuda 1977; Hale et al. 1979; Lennie and Perry 1981) or used qualitative methods for classification (Morigiwa et al. 1988). To identify functionally distinct neuron classes and to compare these classes across different animals, it is necessary to measure many different receptive field properties for each cell (Bullier and Norton 1979a; Irvin et al. 1986; Kirby and Wilson 1986; Rodieck and Brening 1983; Stone 1983) because properties that distinguish LGN neurons in one species may not distinguish LGN neurons in another species and because homologous neuron groups could differ in a few properties and nonhomologous neuron groups could have a few properties in common. Measurements of many LGN cell receptive field properties have been made in the nocturnal opossum and rabbit and diurnal tree shrew, but the properties of LGN cell groups in these animals do not strongly implicate either of the hypotheses above regarding the relationship between X, Y, and W cells and P, M, and K cells. Cell groups in opossum closely resemble the X, Y, and W cells of the cat (Kirby and Wilson 1986). In rabbit, there are sustained and transient center-surround cells and other cells resembling W or K cells, but, unlike carnivores or primates, all or most of these sustained and transient neurons show nonlinear spatial summation (Swadlow and Weyand 1985). Although studies in tree shrew have shown this mammal has a class of small-celled neurons resembling the W or K group of carnivores and primates (Diamond et al. 1993; Holdefer et al. 1995), studies of the larger LGN cells are equivocal. One early study of these cells reported X-like and Y-like cells (Sherman et al. 1975), but a later study that measured many receptive field properties did not find properties that identified groups among the larger cells besides ON and OFF cells (Holdefer et al. 1995). Thus it seems important to characterize many receptive field properties of LGN neurons in another diurnal species.
In addition to being useful animals for comparative studies of the mammalian visual system (e.g., Kaas et al. 1972), squirrels may be an excellent preparation for studying synaptic and cellular mechanisms underlying neuronal processing and disease in the human visual system (Jacobs et al. 2002; Paolini and Sereno 1998). Many tree and ground squirrels are diurnal, have good color vision (Anderson and Jacobs 1972; Blakeslee et al. 1988; Jacobs 1976), and have cone-dominated retinas (West and Dowling 1975), similar to the primate fovea. Rodents offer many technical advantages for studying the synaptic and cellular mechanisms underlying processing in the nervous system because they are suitable for a wide variety of experimental techniques including brain slice physiology, whole animal physiology, behavioral studies, and molecular studies. Although the squirrel's large and highly elaborated visual brain structures have received considerable attention from neuroanatomists (Gould 1984; Harting and Huerta 1983; Kaas, Guillery, and Allman 1972; Kaas, Hall, and Diamond 1972; Kaas et al. 1989; Robson and Hall 1975, 1976, 1977), a major barrier to using these animals for studying synaptic and cellular principles of vision is a lack of knowledge about receptive field properties and laminar organization in the LGN. A goal of this study was to provide a thorough description of these neurons to support such studies.
On the basis of receptive field properties and laminar organization, we identified three groups of cells in squirrel LGN, called X-like, Y-like, and W-like. X-like cells are sustained, show center-surround organization, and are almost exclusively linear in spatial summation. Y-like cells are transient, have short response latencies, show center-surround organization, and can show either linear or nonlinear spatial summation. W-like cells are a heterogeneous group of cells that show variable response latencies and peak responses, and can show linear or nonlinear spatial summation. Our data are consistent with the idea that all mammals have three basic classes of LGN neurons, one showing reliable, sustained responses and center-surround organization; another showing transient but reliable responses, short latencies, and center-surround organization; and a third, highly variable and heterogeneous class of cells. Other properties such as dependency of receptive field size on eccentricity, linearity of spatial summation, and contrast gain appear to vary from species to species. When considered with evidence from anatomical and gene expression studies, our data are consistent with the hypothesis that X and P, Y and M, and W and K cells are homologous neuron classes.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESACKNOWLEDGMENTSREFERENCES |
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Fifteen adult gray squirrels (Sciurus carolinensis) weighing 475-700 g were trapped locally. Animals were sprayed to remove fleas and ticks (Adams Flea and Tick Mist, Memphis, TN) and temporarily housed with food and water up to 1 wk before an experiment.
Animals were initially anesthetized with a mixture of ketamine and acepromazine maleate (90 mg/ml ketamine, 0.91 mg/ml acepromazine maleate, 0.5 ml/kg initial dose, intramuscularly). A femoral vein was canulated (0.6-mm tube) for later administration of paralytic, and a tracheostomy (3-mm tube) was performed to permit artificial respiration and for administration of supplemental isoflurane anesthesia for the remainder of the experiment (0.5-2.0% isoflurane in 50/50 oxygen/nitrous oxide). Respiration was provided by a rodent ventilator (Harvard Instruments, South Natick, MA) with 5-ml stroke volume operating at 35-85 strokes/min, adjusted to keep end tidal CO2, measured with a Tidal Wave capnograph (Novametrix, Wallingford, CT), to be 4%. The animal was mounted in a custom rodent stereotaxic frame specifically designed not to obstruct frontal vision. An incision was made in the scalp and the skin reflected to expose the skull. Two leads were attached to a front and hind paw to monitor heart rate, and leads were attached to two screws inserted into the skull to monitor the electroencephalogram (EEG). A third screw was inserted in the skull for electrical grounding. Heart rate and EEG were recorded and displayed continuously. Rectal temperature was monitored and maintained at 38°C by a heating pad (FHC, Bowdoinham, ME). Pupils were dilated with 1% atropine sulfate, contact lenses (plano, 8.0 mm diameter, radius of curvature 5.0, 5.25, or 5.5 mm; Platt Contact Lens, Mt. Vernon, OH) were inserted to prevent drying, and eyelids were held open with loose sutures. Consistent with prior reports (McCourt and Jacobs 1984a), we found the eyes of these animals to be highly emmitropic, with the vast majority of animals within 1 diopter of focus and all animals within 2 diopters. In practice we found adjusting focus unnecessary because these animals have a large depth of focus (see Green et al. 1980) and tests with lenses over a few diopters did not affect receptive field size as measured by reverse correlation. An artificial pupil was not used because we were interested in the visual field with the largest LGN representation, which is in front of the animal and about 70° from each lens's axial line. In every experiment we could easily identify distinct receptive field centers and surrounds, and we recorded similar receptive field center sizes and spatial frequency preferences in one animal for which we did not dilate the eyes.
A small craniotomy was performed above the LGN (2 to 6.5 mm lateral from bregma and 0 to 5 mm posterior to bregma), the dura resected, and the surface of the brain digitally photographed for charting electrode penetration locations (Nikon Coolpix 995, Nikon, Melville, NY). Warm artificial cerebrospinal fluid was used to keep the brain moist, and 3% agar in lactated ringer's solution was used to protect the brain and minimize pulsations during the electrode penetrations. Next, infusion of paralytic (10 mg/ml gallamine triethoiodide, 0.5 ml/h) was begun to suppress spontaneous eye movements. After paralysis, we took great care to monitor the heart rate and EEG to ensure adequate anesthesia, and isoflurane concentration was increased if spindle activity disappeared on the EEG or if the heart rate increased in response to a toe pinch. Typically, 1% isoflurane was required to maintain this level of anesthesia. Finally, after the paralysis had taken effect, we charted the location of the nasal bulb of each optic streak.
Recording, data acquisition, and stimulation
To aid placement of recording electrodes and histological reconstruction, we initially mapped the LGN with several penetrations using low-impedance microelectrodes (1 M
; WPI, Sarasota, FL). We mapped responses to handheld stimuli while monitoring neuronal activity on a loudspeaker. As we gained experience, we could identify the LGN layers qualitatively because the vast majority of sites in layers 1 and 2 gave very sustained responses to light and the vast majority of sites in layers 3a, 3b, and 3c gave very transient responses to light. In addition, the background activity of cells in layers 3a, 3b, and 3c sometimes drifted from low to high over periods of 10 to 30 s, but this was never observed in layers 1 and 2. We then used high-impedance microelectrodes (3-7 M; Thomas Recording, Giessen, Germany) to record well-isolated single units. The recording electrodes were coated with di-I so the tracts could be easily visualized histologically (DiCarlo et al. 1996; Snodderly and Gur 1995). Signals were amplified x10,000 with a headstage and amplifier (A-M Systems, Carlsborg, WA), and sampled digitally with a Ni-DAQ PCIMIO-6071E acquisition card (National Instruments, Austin, TX). Action potentials were isolated using a custom-developed multiple-window discriminator using Matlab (The MathWorks, Natick, MA).
Visual stimulation was provided by an Apple Macintosh PowerMac 7500 and a 900SL CRT (Samsung), gamma-corrected using ColorVision Spyder (Pantone, Carlstadt, NJ). Custom stimulation software was developed using Matlab and the Psychophysics Toolbox (Brainard 1997; Pelli 1997), and stimuli were shown at a refresh rate of 120 Hz.
Experimental protocol
After isolating a cell and mapping the receptive field using handheld stimuli, a white-noise grid was presented, and we computed the reverse correlation of the spike output and the stimulus to find the precise center of the receptive field. The white-noise grid was 16 x 16 with 0.7° blocks, and every 67 ms each grid pixel randomly assumed a value of white or black, similar to Citron et al. (1981). We then presented (in pseudorandom order) spots of varying diameter centered on the receptive field, 500 ms on, 500 ms off, to estimate the center region size and to see whether the cell showed a center-surround organization. If the reverse correlation above indicated the cell was an ON cell, we showed a white spot on a black background, and we used a black spot on a white background for an OFF cell. Spontaneous activity was assessed by interleaving blank trials. Each spot was presented 10 times, and when the optimal diameter was determined, a spot of that diameter was presented 40 additional times to accurately measure the response time course.
We obtained measures of peak firing rate, initial and peak latency, maintained firing rate, and transient time constant from the mean response to this spot stimulus. We binned the responses into 1-ms increments. The peak latency (PL) was defined as the bin with the greatest number of spikes, and the peak firing rate (PR) was taken to be the mean rate in a 3-ms window centered on the peak latency. The initial latency (IL) was defined as the first bin with a spike count greater than or equal to one-half the maximum, although this measurement was too noisy for a few cells (18) with a maximum firing rate <60 Hz and the initial latency was taken to be the peak latency for these cells. The maintained firing rate (MR) was defined as the mean firing rate in an interval between 300 and 350 ms after the peak latency time. The transient time constant 
trans, a measure of transience, was defined such that MR = PR exp(-325 ms/trans). This time constant is larger for more sustained cells and smaller for transient cells.
Next, we assessed orientation selectivity by showing drifting gratings with different orientations. We used a spatial frequency of 0.1 cycles/deg and a temporal frequency of 4 Hz, which we found to drive virtually all cells in our sample. Only a small handful of cells showed some orientation selectivity, and all cells showed much less orientation selectivity than we have found in preliminary studies of primary visual cortex in this animal. We will not consider orientation further in this report, but the remaining gratings were run at the optimal orientation for each cell.
We assessed spatial frequency tuning by showing gratings of varying spatial frequencies (0.05-1.6 cpd), and assessed temporal frequency by showing gratings of varying temporal frequencies (0.5-32 Hz). We then ran gratings of varying contrast (0-100%) for temporal frequencies of 1, 4, and 8 Hz. For both the temporal frequency test and contrast test, we used the optimal spatial frequency. We analyzed the modulated response of the neuron to each grating at the fundamental stimulus frequency (F1 component) and fit the contrast F1 responses with the Naka-Rushton function R(c) = Rmc/(b + c) (Naka and Rushton 1966). In this equation, b is the contrast for which the cell fires at half its saturating rate and Rm is the saturating firing rate, which is proportional to the firing rate at 100% contrast. Contrast gain for each response curve was defined as Rm/b. Fit parameters were chosen to minimize squared error between individual data points and the fit. For all contrast response curves we also computed C50, the linearly interpolated contrast that evoked half the maximum response.
Finally, we assessed linearity of spatial summation by showing stationary sinusoidal gratings at different spatial phases (following Hochstein and Shapley 1976a). The gratings were modulated in time sinusoidally (counterphase). For each phase, we computed the ratio of the response at twice the stimulus temporal frequency to the response at the stimulus frequency (F2/F1), and took the average of this ratio at all phases weighted by the number of spikes at each phase (F0) to be our index of linearity. Weighting by the number of spikes discounts phases with very few spikes, which is important because the F2/F1 ratio is very noisy for these phases. A linearity index value >1 represents a substantial nonlinearity, and we label such cells nonlinear. Because Y cells in the cat demonstrate their nonlinearity at higher spatial frequencies (Hochstein and Shapley 1976a), we used gratings at many spatial frequencies. We initially showed counterphase gratings at the optimal spatial frequency, and we presented gratings at increasing spatial frequencies until the linearity measure was >1 or the cell no longer responded to the gratings. Thus our F2/F1 linearity index represents an upper bound for linear cells and a lower bound for nonlinear cells.
Multivariate analysis
We divided our cells into three groups as described in the text. To visualize the differences among properties of cells in these groups, we employed Fisher linear discriminate analysis (LDA) and projected the data onto its canonical variates (Fisher 1936; Mardia et al. 1979). The canonical variate projection is a linear projection that maximizes the ratio of the between-groups sum of squares to the within-groups sum of squares. We computed the multivariate "between-groups" sums of squares and products matrix B and the "within-groups" sum of squares and products matrix W as follows
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The canonical variates are the eigenvectors of inv(W)B, and the eigenvalues corresponding to these eigenvectors indicate the amount of between-group variation that is explained by each component. This procedure is analogous to principal-component analysis, except that LDA uses grouped data.
Statistical methods
We used Bartlett's method to evaluate the homogeneity of variance of each property across the groups. Variances were significantly different across several properties, so a multivariate rank test (Choi and Marden 1997) was used for multivariate group comparisons. Comparisons of individual properties were made using a one-way ANOVA test when variances were deemed homogeneous by Bartlett's test and using the Kruskal-Wallis (K-W) rank test when they were not. Post hoc tests were made using a modified t-test for ANOVA tests and the Mann-Whitney U test for K-W tests. For categorical frequency analysis, such as for center-surround organization or linearity, we employed 
2 tests. 
was 0.05 for all tests.
Histology
After the experiment, the animal was given a large dose of ketamine/acepromazine or sodium thiopental, and transcardially perfused with 0.1 M phosphate-buffered solution (PBS) followed by 4% paraformaldehyde. The brain was stored in a jar containing 4% paraformaldehyde, and, before sectioning, moved into successive jars of 10, 20, and 30% sucrose in 0.1 M PBS until it sank. The brain was blocked into 3- to 5-mm coronal chunks, covered in TissueTek OTC compound (Sakura, Torrance, CA), and flash frozen to -20°C in a slurry of dry ice and isopentane. Slices (50 µm) were cut on a CM3050 cryostat (Leica, Nussloch, Germany) and left to dry overnight on slides. Staining was accomplished by soaking sections in 0.1 M PBS for 40 min, rinsing in 0.1% Triton X-100 (Sigma, St. Louis, MO) for 10 min, rinsing twice in 0.1 M PBS for 5 min, and incubating in 5% NeuroTrace 500/525 green fluorescent Nissl stain (Molecular Probes, Eugene, OR) in 0.1 M PBS for 20 min. Slides were then washed three times in 0.1 M PBS (20 min, 2 x 5 min) and cover-slipped with Fluromount G media (Electron Microscopy Sciences, Ft. Washington, PA). Under fluorescent light, the bright red electrode tracts were easily observed among the green cell bodies (see Fig. 1B).
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We used these tracts in combination with physiologically observed eye dominance changes, measurements from our manipulators, and the charted location of our mapping penetrations to identify the layer of each recorded cell. In every case, the information in the histological sections agreed with our mapping penetrations. The boundaries between layers 3a, 3b, and 3c are not observable in a Nissl stain (see Fig. 1A), and we had hoped to rely on eye dominance and mapping data to be able to classify each cell exactly. Layer 3b is easily recognized because it receives ipsilateral input, and we had planned to distinguish cells in layers 3a and 3c by electrode location relative to layer 3b. As we gained experience, we realized that our mapping penetrations might occasionally miss the thin layer 3b, so when we did not specifically find layer 3b we labeled layer 3a or 3c cells as "3a or 3c."" We observed similar properties across layers 3a, 3b, 3c, and "3a or 3c" neurons and grouped them for most analyses (see RESULTS).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESACKNOWLEDGMENTSREFERENCES |
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), as shown in Fig. 1. Layers 1, 3a, and 3c receive input from the contralateral eye, whereas layers 2 and 3b receive input from the ipsilateral eye. The layers are arranged from rostromedial to caudolateral, with layer 1 being the most rostral and medial layer, and layer 3c being the most caudal and lateral, bordering the optic tract. As in other mammals, cells in the left LGN encode information about the right visual hemifield and vice versa, although the binocular region of each hemifield in squirrels is only about 30° (Kaas et al. 1972). The binocular region is the most highly represented space in the LGN and primary visual cortex (Kaas et al. 1972), and we primarily recorded cells in that region. Our goal was to sketch a wide variety of receptive field properties of each cell using several computer-controlled stimuli. After isolating a unit for study, we first ran a white-noise stimulus and correlated the response of the neuron with the stimulus to precisely locate the receptive field center and to determine whether the center region responded to light increments (ON) or decrements (OFF), as in Fig. 2A. We then showed spots of light of appropriate sign (ON or OFF) and varying size on a background of opposite sign to measure the size of the center region and to see whether the cell contained an inhibitory surround (see Fig. 2B). Next, we showed many presentations of a spot of light exactly covering the center region to characterize the response of the cell to stimulation in the center region (see Fig. 2C). We measured initial and peak response latencies, peak and maintained firing rates, transience, and response reliability from this response. Finally, we characterized linearity of spatial summation, spatial and temporal frequency responses, and contrast responses using sinusoidal gratings.
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Sustained and transient responses to light
Responses of six LGN cells to light in the center region are shown in Fig. 3A. The stimulus screen alternated each 500 ms between background and a spot of light of appropriate sign, ON (44.1% of cells) or OFF (55.9%), that exactly covered the center region of the cell. Note that each cell shows a large initial transient response, but the cells in layers 1 and 2 have a substantial maintained discharge throughout the stimulus presentation, whereas the cells in layers 3a, 3b, and 3c show very transient responses. The mean responses of all cells in layers 1 and 2 and layers 3a, 3b, and 3c are shown in Fig. 3B. The mean response of layer 1 and 2 cells 500 ms poststimulus is about 30 Hz, whereas the spontaneous activity near time 0 is about 3 Hz. The mean response of layer 3a, 3b, and 3c cells 500 ms poststimulus is only about 6 Hz, whereas the spontaneous activity near time 0 is around 2 Hz.
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We assessed response transience by two measures, maintained firing rate and transience time constant. Maintained firing rate is plotted in Fig. 3C. Layer 1 and 2 cells had relatively high maintained firing rates (36.9 ± 4.0 and 23.8 ± 2.7 Hz), whereas layers 3a, 3b, and 3c had relatively low maintained rates (8.9 ± 3.2, 8.7 ± 2.9, and 1.6 ± 0.5 Hz, respectively). The differences in maintained firing rate among the layers are highly significant (K-W, P < 1e-16). Layers 1 and 2 had slightly different maintained rates (U test, P = 0.012), but the differences among layers 3a, 3b, and 3c were not statistically significant (K-W, P = 0.19). The maintained firing rate in layer 1 and 2 cells combined is significantly greater than the rate observed in layer 3a, 3b, and 3c cells combined (K-W, P < 1e-16). Figure 3D shows a histogram of maintained firing rate for layer 1 and 2 cells and layer 3a, 3b, and 3c cells. Note that very few cells in layers 3a, 3b, and 3c show substantial maintained firing.
The change in firing rate between the peak rate (PR) and the maintained rate (MR) was quantified by a time constant trans. Larger values of trans indicate a slower decline in firing rate during the stimulus and less transience, and vice versa. Layer 1 and 2 cells had trans values of 144 ± 9 and 136 ± 13 ms, whereas layer 3a, 3b, and 3c cells had smaller values (88 ± 18, 79 ± 19, and 56 ± 12 ms, respectively). The differences among the layers are significant (ANOVA, P = 7.3e-7), but there are no significant differences between layers 1 and 2 (mod t-test, P = 0.1798) or among layers 3a, 3b, and 3c (ANOVA, P = 0.3064).
By both measures of transience, maintained firing rate and transience time constant, layer 1 and 2 cells showed more sustained activity and cells in layers 3a, 3b, and 3c showed more transient activity. That layers 1 and 2 showed largely sustained activity and layers 3a, 3b, and 3c showed largely transient activity was plainly evident in our initial mapping using low-impedance electrodes and handheld stimuli, and this quality can be used to quickly and reliably distinguish these layers in mapping.
Center-surround organization
We examined whether each cell had a center-surround receptive field organization by stimulating the center of each cell's receptive field with spots of light of varying diameter. Center-surround cells, 10 of which are shown in Fig. 4A, responded maximally at a particular diameter and then showed reduced firing when the spot was enlarged. Other cells, 11 of which are shown in Fig. 4B, either did not show a reduction as spot size increased or showed no clear maximum. The classification of cells as "center-surround" or "noncenter-surround" was made manually by the experimenter based on the shape of the curve as well as the variance of the responses for each cell. Center-surround cells with low firing rates could be easily distinguished from noncenter-surround cells because center-surround cells had much smaller coefficients of variation (see Fig. 4C).
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The fraction of cells in each layer that showed center-surround organization is plotted in Fig. 4F. Some 49 of 50 layer 1 cells (98%) and 37 of 40 layer 2 cells (93%) showed center-surround organization, whereas only 11 of 21 layer 3a cells (52%), 15 of 18 layer 3b cells (83%), and 11 of 16 layer 3c cells (69%) were center-surround. The frequencies of center-surround cells among all the layers were significantly different (2, P = 7.8e-6), although there were no significant differences in center-surround cell frequencies between layer 1 cells and layer 2 cells (2, P = 0.2084) or among layer 3a, 3b, and 3c cells (2, P = 0.1200).
Response latency
We recorded the initial latency for each cell, which was defined as the first poststimulus time bin to reach half the maximum firing rate. The initial latencies for all cells in each layer are shown in Fig. 5. The layer 1 and layer 2 cell initial latencies were tightly clustered between 20 and 40 ms. The layer 3a, 3b, and 3c cell latencies were more variable, and many cells had latencies between 15 and 35 ms, whereas others had longer, more scattered latencies. As shown in Fig. 5, many but not all of these long latency cells also lacked center-surround organization. The differences in initial latency distribution across the layers are highly significant (K-W, P = 0.0019). Excluding the one long latency outlier, the mean initial latencies for layer 1 and layer 2 cells were 21.2 ± 0.8 and 23.7 ± 0.9 ms, respectively, whereas the mean latencies of layers 3a, 3b, and 3c were 73.8 ± 19, 42.5 ± 7, and 36.0 ± 9 ms, respectively.
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Response variability
We assessed variability of firing in each cell by computing the coefficient of variation of the peak firing rate. Three sample cells with different variabilities are shown in Fig. 6. Histograms showing response variabilities for layers 1 and 2 and layers 3a, 3b, and 3c are shown in Fig. 6B. Note that the vast majority of cells in layers 1 and 2 were quite reliable and had peak firing rate coefficients of variation (CV) <0.9. Many neurons in layer 3a, 3b, and 3c also had CV values of 0.9 or less, but many other cells in these layers showed more variable responses. Many of these layer 3 cells with variable responses lack center-surround organization and show long latencies to visual stimulation (data not shown).
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Grouping and multivariate analysis
In examining the properties of squirrel LGN cells, we noticed that the layer 1 and 2 cells and the layer 3 cells seemed to have different properties. The layer 1 and 2 cells showed much more sustained activity than the layer 3 cells (Fig. 3), were almost all center-surround (Fig. 4), had latencies that clustered fairly tightly between 20 and 40 ms (Fig. 5), and showed low response variability (Fig. 6). The layer 3 cells were generally transient (Fig. 3) and many lacked a center-surround organization (Fig. 4), but several showed short latencies clustering between 15 and 35 ms and had reliable peak responses, whereas others had highly variable latencies and highly variable peak responses (Figs. 5 and 6). Thus we divided the data into three groups as follows.
We pooled all layer 1 and 2 cells that had initial latencies <50 ms, center-surround organization, and peak firing rate CV <0.9 into a group we termed X-like because they share some properties with cells in carnivores, rodents, and tree shrews called X cells (see following text). This group contains 76 of 90 layer 1 and 2 cells recorded. We divided the remaining cells into two groups. Layer 3 cells with center-surround organization, initial latencies <40 ms, and peak firing rate CV <0.9 were grouped together and called Y-like cells because they share some properties with cells in carnivores, rodents, and tree shrews called Y cells. In addition to latency, center-surround organization, and peak response variability, the Y-like cells differ from other layer 3 cells in terms of peak firing rate (see following text) and center size (see following text), suggesting these cells are distinct from other layer 3 cells. All other layer 3 cells, noncenter-surround neurons from all layers, and cells from all layers with peak firing rate CV values >0.9 were lumped together in a group called W-like cells. The W-like group certainly contains more than one class of neuron, but we grouped these neurons together because they remind us of the heterogeneous W cell group in the cat and koniocellular cell group in the monkey (Hendry and Reid 2000; Irvin et al. 1986; Stone 1983; Stone and Fukuda 1974).
Table 1 shows a comparison of the means of these three cell groups for eight receptive field properties. The X-like cells were the most sustained and had higher maintained firing rates and larger trans than Y-like cells and W-like cells. The Y-like cells were the most transient and had the shortest latencies of all the groups, but did not differ significantly from X-like cells in peak firing rate, F2/F1 linearity index (see METHODS), center size, or peak response CV. Although different latency criteria were used to classify X-like and Y-like cells (initial latency <50 and 40 ms, respectively), Y-like cells still showed significantly shorter latencies than X-like cells if the same criterion (50 ms) was used (U test, P = 5.3e-10). Compared with both X-like and Y-like cells, the W-like cells had significantly lower peak firing rates, longer response latencies, larger receptive fields, and higher response variability.
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To visualize the amount of overlap or separation in these eight properties among the three cell groups, we projected the data onto their canonical variates. The canonical variate projection is a linear projection that maximizes the ratio of the between-groups sum of squares to the within-groups sum of squares. This projection for grouped data is analogous to the principal-component projection for ungrouped data. As described in METHODS, the canonical variates are the eigenvectors of inv(W)B, and the corresponding eigenvalue indicates the amount of variance explained by each variate.
We made a canonical variate projection for the X-like, Y-like, and W-like cells using the following properties: F2/F1 linearity (LN), peak latency (PL), spontaneous firing rate (SR), maintained firing rate (MR), transience time constant (trans), peak firing rate (PR), receptive field center size (CS), and peak response CV. Because the number of nonzero eigenvalues is at most min(N, G - 1), where N is the number of parameters used and G is the number of groups, there were two eigenvectors with nonzero eigenvalues: 
1 = 1.8886 and 2 = 0.3621. We projected the data onto the canonical variate space using the computed eigenvectors X1 and X2
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To verify that these groups were significantly different from each other, we employed a multivariate rank test attributed to Choi and Marden (1997) that is an extension of the univariate Kruskal-Wallis test. A rank test was necessary because the assumptions of normality and equal variances for a traditional multivariate ANOVA were not met (see METHODS). We included six receptive field properties for each cell: F2/F1 linearity index, spontaneous firing rate, maintained firing rate, transience time constant, peak firing rate, and receptive field center size. We excluded latency and peak firing CV from this analysis because these properties were used to divide the data into groups. The differences in distribution among these three groups were highly significant (P < 1e-16), and post hoc comparisons using the same test showed significant differences between X-like cells and Y-like cells (P = 3.0e-9), X-like cells and W-like cells (P < 1e-16), and Y-like cells and W-like cells (P = 1.1e-9).
Because the X-like, Y-like, and W-like cells overlap in their properties, it is difficult to be sure that we have divided the cells in the most parsimonious way. One might imagine an alternative classification for X-like and Y-like cells that divides short latency, center-surround cells from all layers into "sustained" and "transient" groups. In the cat, for example, transient Y cells are mixed with both X cells in the A laminae and W cells in the C laminae (Illing and Wassle 1981), and in the squirrel, the vast majority of neurons in layers 1 and 2 are sustained, although there are a handful of neurons that have low maintained firing rates (Fig. 3). To examine this possibility, we divided cells from layers 1 and 2 into two groups, those with maintained firing rates >10 Hz ("sustained"; n = 57) and those with maintained firing rates <10 Hz ("transient"; n = 16). A multivariate comparison of these groups using F2/F1 linearity index, spontaneous firing rate, peak firing rate, receptive field center size, and peak firing rate CV revealed no significant differences between these "sustained" and "transient" layer 1 and 2 cells (P = 0.0672). However, a multivariate comparison using the same parameters between the group of "transient" cells from layers 1 and 2 and the Y-like cells in layer 3 did reveal significant differences (P = 0.0167). Thus we favor dividing the cells into groups based on laminar location.
Receptive field center size
We examined the relationship between receptive field center size and eccentricity. Squirrels do not have an area centralis or fovea in the same manner as carnivores and primates, but instead possess an elongated horizontal streak with a high-density of photoreceptors (Long and Fisher 1983), and the density of photoreceptors remains very high over a large region. Therefore we considered the horizontal and vertical eccentricities separately. We defined the origin as an imaginary point directly in front of the animal and level with the eyes, located on average 69° nasal and 19° superior to the projection of the nasal bulb of the optic disk, and we corrected eccentricity measurements in each animal according to the deviation of its optic disk projections from this average.
Center size versus absolute horizontal and absolute vertical eccentricity for each cell group is plotted in Fig. 8, A-C. We considered the relationship between center size and eccentricity significant if the slope of a regression fit was significantly different from 0 with = 0.05 (F-test). Only two regressions were significant, and even those showed very small dependencies. X-like cell center sizes showed a slight dependency on vertical eccentricity (r2 = 0.1741) and W-like cells showed an even smaller though still significant dependency on horizontal eccentricity (r2 = 0.1184). Changing the definition of either the horizontal or vertical origin or considering total eccentricity did not significantly strengthen these regressions (data not shown). It is not surprising that squirrel LGN cells show little dependency on eccentricity because the density of photoreceptors in the retina remains at or close to its peak level over a region several square millimeters in area (Long and Fisher 1983).
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Because receptive field center sizes showed very little dependency on eccentricity for all three groups, we compared center sizes across cell groups without any correction for each cell's location in the visual field. The mean receptive field center sizes for all X-like cells, Y-like cells, and W-like cells are plotted in Fig. 8D. X-like cells had the smallest mean center sizes (1.54 ± 0.1°) compared with Y-like cells (1.94 ± 0.3°) and W-like cells (3.90 ± 0.4°), and the differences among the groups were significant (K-W, P = 4.6e-6). The differences between the X-like and Y-like cells were not significant (U test, P = 0.3188), although the differences between the X-like and W-like cells and the differences between the Y-like and W-like cells were significant (U test, P = 1.2e-6, P = 0.0037, respectively).
Linearity of spatial summation
We also examined the linearity of spatial summation in each neuron. In previously studied mammals, both linear and nonlinear spatial summation have been observed. In cat Y cells, this nonlinearity is attributed to small subunits of mixed signs present throughout the receptive field (Hochstein and Shapley 1976b). We measured the response of each neuron to stationary counterphase sinusoidal gratings presented at different spatial phases, and examined the ratio of the response of the cell at twice the stimulus temporal frequency (F2 component) to the response at the stimulus temporal frequency (F1 component). In the cat LGN, Y cells have F2/F1 ratios >1, whereas X cells have F2/F1 ratios <1 (Hochstein and Shapley 1976a). Because studies of cat Y cells have shown that the mixed subunits in those cells are more obvious at spatial frequencies higher than the cell's preferred spatial frequency (Hochstein and Shapley 1976a), we showed gratings at increasing multiples (1, 2, 3,...) of the cell's preferred spatial frequency until the cell no longer responded reliably to stimulation. We defined the F2/F1 linearity index to be a weighted average of the F2/F1 ratio among all phases for the highest spatial frequency to which the cell reliably responded. The average was weighted by the F0 response at each of these phases to discount phases with very few spikes because the F2/F1 ratio at these phases tended to be quite noisy.
Figure 9A1 shows the response of a "linear" cell to counterphase sinusoidal gratings of different spatial phases and spatial frequencies. The first and second panels show the phases eliciting the strongest and weakest responses for gratings at the optimal spatial frequency for the cell (0.2 cpd), whereas the third and fourth axes show the phases eliciting the strongest and weakest responses for gratings at four times the optimal spatial frequency (0.8 cpd). Note that the responses look fairly sinusoidal and occur at one phase of the stimulus. The F1 and F2 components for all phases and spatial frequencies are plotted in Fig. 9A2. The F2 component for this cell was much smaller than the F1 component, indicating the cell is highly linear, and the F2/F1 index for the cell is 0.26.
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Figure 9B1 shows the response of a "nonlinear" cell to the same stimuli as in Fig. 9A1. Note that the responses to the 0.8-cpd gratings occur at more than one phase of the stimulus, indicating a nonlinearity. The F1 and F2 components for all phases and spatial phases are plotted in Fig. 9B2, and it is clear that the F2 component becomes larger at higher spatial frequencies. This cell is modestly nonlinear, having an F2/F1 index of 1.73.
The data in Fig. 9B2 also indicate the importance of testing linearity with the F2/F1 ratio at many spatial frequencies (Hochstein and Shapley 1976a). Had we employed only a "null test" at the optimal spatial frequency by looking for a spatial phase that elicited no response for the 0.2-cpd gratings, we may have been misled into believing the cell was linear because the response at 150° was very weak and within the standard error for spontaneous activity of this cell. In addition, the F2/F1 index for the 0.2-cpd gratings was 0.53, indicating linear spatial summation, so it was important to test many spatial frequencies to reveal the nonlinearity in this cell.
The F2/F1 linearity indices for the X-like, Y-like, and W-like cell groups are plotted in Fig. 9C. X-like cells had a lower F2/F1 index (mean: 0.67 ± 0.04) than that of either the Y-like cells (mean: 0.79 ± 0.07) or the W-like cells (mean: 0.91 ± 0.09).
A histogram of the F2/F1 linearity index for all 146 cells tested in our study is shown in Fig. 8D. Most of the data appear to cluster between 0 and 1, and there are several outliers that have F2/F1 indices >1. In keeping with prior studies, we labeled cells with a linearity index <1 "linear" and those with a linearity index >1 "nonlinear."
Under this criterion, the vast majority of all neurons were linear (123/146, or 84%). 67 of 73 (92%) of X-like cells were linear, whereas Y-like cells (19 of 25 linear, or 76%) and W-like cells (36 of 47 linear, 77%) showed slightly lower rates of linearity. The differences among all groups were significant (2, P = 0.0400), and the X-like cells had a significantly lower frequency of nonlinear cells than Y-like cells (2, P = 0.0378) and W-like cells (2, P = 0.0199). The Y-like and W-like cells did not differ significantly in the percentage of nonlinear cells (2, P = 0.9548). The X-like cells that showed nonlinear spatial summation were not different from linear X-like cells in other parameters and showed sustained firing (data not shown), and there were no significant differences in maintained firing rate (K-W, P = 0.3562) or trans (ANOVA, P = 0.1206) between linear and nonlinear Y-like cells.
We noticed that the distribution of cells having F2/F1 linearity indices <1 in the histogram in Fig. 9D appeared slightly bimodal. We wondered whether cells with indices between 0.66 and 1 represented a different category of cell, and we checked to see whether cells in each group with F2/F1 indices in that range differed from cells with F2/F1 indices <0.66. However, we found no differences in peak latency, maintained firing rate, spontaneous firing rate, peak firing rate, center size, or trans among these subgroups (data not shown).
Spatial and temporal frequency properties
We sketched the spatial and temporal properties of squirrel LGN neurons with drifting sinusoidal gratings. The responses of cells to gratings of varying spatial frequency with a temporal frequency of 4 Hz are shown in Fig. 10. Figure 10A shows one example neuron from each group. The mean responses for all X-like, Y-like, and W-like cells are plotted in Fig. 10B. We computed the fraction of all cells in each group that showed statistically significant firing (compared with firing rates between stimuli using a t-test) for each spatial frequency, and the results are plotted in Fig. 10C. Note that the spatial frequency tuning for all the cell groups is rather broad. Finally, Fig. 10D shows a histogram of spatial frequencies that elicited the most spikes from each cell.
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The X-like cells had the highest spatial frequency preferences, with many cells preferring spatial frequencies of 0.2 or 0.4 cpd. The Y-like and W-like cells generally preferred lower spatial frequencies, with most cells preferring 0.1 or 0.2 cpd. Because we tested spatial frequency preferences at exponential intervals, we considered each spatial frequency a separate category in comparing the cell groups. The differences among the cell groups were statistically significant (2, P = 3.9e-7), and the X-like cells showed significantly higher spatial frequency preferences compared with Y-like and W-like cells (2, P = 4.5e-4, 2.1e-6). The differences between the Y-like and W-like cells were slightly significant (2, P = 0.0414).
We also examined temporal frequency responses to drifting gratings with optimal spatial frequency. The results of these recordings are displayed in Fig. 11. The format of Fig. 11 is the same as Fig. 10. Figure 11A shows temporal frequency response curves for one cell from each class, and Fig. 11B shows mean response curves for all X-like cells, Y-like cells, and W-like cells. The fraction of all cells in each group that showed statistically significant firing at each temporal frequency (compared with firing rates between stimuli) are plotted in Fig. 11C. Similar to the responses for spatial frequency, cells in all classes have relatively broad temporal frequency tuning. Histograms showing the optimal temporal frequency for each cell group are plotted in Fig. 11D. The X-like, Y-like, and W-like cells were not significantly different from each other (2, P = 0.1043).
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In pilot experiments, we noted that many squirrel LGN neurons could follow very fast temporal changes. We initially used a monitor refresh rate of 85 Hz, and several neurons would respond in a phase-locked fashion to 60-90% of refresh frames. However, no LGN neurons responded in a phase-locked fashion to the refresh rate of 120 Hz used in the study.
Contrast properties
Finally, we examined contrast response curves for squirrel LGN cells. We showed drifting sinusoidal gratings at the optimal spatial frequency at contrasts of 0, 2, 4, 16, 32, 64, and 100% and temporal frequencies of 1, 4, and 8 Hz. We fit each response curve with the Naka-Rushton function R(c) = Rmc/(b + c), where Rm is proportional to the maximum firing rate and b is the contrast that evokes one-half the maximum firing (Naka and Rushton 1966). Response curves in our study were generally fairly linear, but some were slightly saturating or slightly hyperbolic. We found that the Naka-Rushton function fit every curve in our study reasonably well with a minimal number of free parameters. We compared contrast gain measurements using the Naka-Rushton fit (gain = Rm/b) to manual estimation of contrast gain in the linear portion of several response curves, and the two measures were in agreement to within approximately 10% (data not shown).
Naka-Rushton fits to contrast response curves at 1, 4, and 8 Hz from one X-like cell, Y-like cell, and W-like cell are plotted in Fig. 12A. The mean response curves from each cell group at each temporal frequency are shown in Fig. 12B. Although the mean responses from each cell group are slightly saturating and slightly hyperbolic, the responses are remarkably linear compared with contrast curves observed in other animals (see DISCUSSION).
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Mean contrast gain, defined as Rm/b from the Naka-Rushton fit, for each temporal frequency and each cell group is plotted in Fig. 12C. The mean contrast gains at 4 Hz for X-like cells and Y-like cells were similar (0.76 Hz/%contrast and 0.77 Hz/%contrast, respectively), and slightly larger than the mean gains for W-like cells (0.47 Hz/%contrast). The differences in contrast gain across the three groups were slightly significant for 4-Hz gratings (K-W, P = 0.0148), but not for 1- or 8-Hz gratings (K-W, P = 0.0828, P = 0.3012). The contrast gains observed in the squirrel were notably lower than those observed in cat X and Y cells and macaque magnocellular cells, for which gains in the 2-10 Hz/%contrast range have been reported (Benardete et al. 1992; Croner and Kaplan 1995; Kaplan and Shapley 1986). Only five of 67 cells tested this way had gains >2 Hz/%contrast, and the maximum was 3.5 Hz/%contrast.
We defined C50 as the contrast that elicited half of the maximum measured firing, and the mean C50 values for all cells at each temporal frequency are plotted in Fig. 12D. The X-like and Y-like had similar mean C50 values at a temporal frequency of 4 Hz (37 and 32%, respectively), whereas W-like cells showed a slightly higher mean C50 (48%). These values are significantly different across all classes (ANOVA, P = 0.0018), although the difference between the X-like and Y-like cells was not significant (mod t-test, P = 0.1260). There were no significant differences in C50 values across the groups for 1- or 8-Hz gratings (ANOVA, P = 0.5343, P = 0.4185). The C50 values in squirrel are much closer to 50% compared with measurements in some other animals (see DISCUSSION). It is also evident from examining the mean response curves, contrast gain, and C50 contrast across different temporal frequencies that the response curves at 4 and 8 Hz show more saturation than curves at 1 Hz for all three cell groups.
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DISCUSSION |
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TOPABSTRACT |
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) and also to determine sign of the cell (ON or OFF). B: in the center of each cell's receptive field, we measured the response of sign-appropriate spots of varying diameter to determine the size of the center region, indicated by the diameter with largest response. C: after determining the extent of the center region, we ran additional trials with spots of optimal diameter to construct a peristimulus time histogram (PSTH) of the center response (1-ms bins). From these histograms, we computed time of initial latency, peak latency, peak response, maintained response, and 
