Highly Selective Receptive Fields in Mouse Visual Cortex

Laminar and cell-type identity

We recorded 235 isolated single units from 27 adult mice. Individual recording sessions consisted of simultaneous recordings of ∼4–12 isolated single units across the 16 sites of the multielectrode array. Of these units, 87% (204 of 235) were responsive to at least one episodic visual stimulus. Nonresponsive units were not included in analysis of tuning properties. We generally performed only one electrode insertion per animal to avoid damage to cortex from multiple penetrations and to maintain a stable anesthetic state without needing to redose.

To verify the laminar location of each recording site of the multielectrode array, we measured in addition to electrode depth the LFP response to square-wave contrast reversal of a checkerboard. As shown in Figure 1 B, the averaged responses show a large deflection starting ∼40 ms after the contrast reversal, which varies in both amplitude and waveform across the recording sites. CSD analysis provides a method to transform the set of LFP recordings into the locations of current sources and sinks, with current sinks generally corresponding to sites of synaptic conductances (Mitzdorf, 1985; Swadlow et al., 2002). This transformation revealed a laminar distribution of activation in response to checkerboard reversal (Fig. 1 C), with a current sink beginning in layer 4, in which sensory input first arrives, spreading up to layer 2/3, and finally a weak sustained sink in layer 5. Retrospective histology (supplemental Fig. S1, available at www.jneurosci.org as supplemental material) confirmed the correspondence between CSD and laminar identity. Furthermore, layer 4 corresponded to the maximum negativity of initial dip in the LFP (Fig. 1 B,C) (supplemental Fig. S1, available at www.jneurosci.org as supplemental material), which allowed us to deduce the laminar location even for recordings that did not span the entire depth of cortex and therefore could not generate a full CSD map of the layers. As shown below, this assignment of layers correlates with different properties of the visual response. Furthermore, during recording, it was generally possible to recognize these laminar positions qualitatively by the nature of ongoing activity: layer 2/3 has very sparse background activity; in layer 4, the spontaneous rate increases and more units are present on each recording site; layer 5 has dramatically higher spontaneous rates and much larger spike amplitudes; and, in layer 6, spontaneous rates and spike amplitudes decrease and evoked responses are more sparse.

Interestingly, we often saw a fast oscillation, at ∼50–55 Hz, superimposed on the LFP and CSD (Fig. 1 B, arrows). This oscillation was stimulus evoked, with coherent activity commencing with the onset of the evoked LFP. Furthermore, its frequency spectrum was distinct from typical 60 Hz noise and did not change as we varied the refresh rate of the display. We thus presume that this corresponds to gamma oscillations that have been described in many species (Buzsáki and Draguhn, 2004), including mice (Nase et al., 2003). However, we did not investigate this oscillation further.

As an additional means of correlating visual responses with cortical circuit elements, we classified units based on their spike waveform. Figure 1 D shows the average waveforms from all the units recorded, except for four units that had unusual waveforms and were excluded from classification. The waveforms can be seen to fall into two general classes, narrow spiking (blue) and broad spiking (green), with averages across the two classes shown in Figure 1 E. Previous results have suggested that narrow-spiking cells correspond to inhibitory, predominantly fast-spiking, interneurons (McCormick et al., 1985; Connors and Kriegstein, 1986; Barthó et al., 2004), and recent studies have used this extracellular signature as a means of distinguishing excitatory and inhibitory neurons (Swadlow, 2003; Andermann et al., 2004; Lee et al., 2007; Mitchell et al., 2007; Atencio and Schreiner, 2008). A variety of waveform parameters have been used to separate these two classes, including trough-to-peak time (Barthó et al., 2004; Mitchell et al., 2007), the ratio of trough-to-peak amplitude (Andermann et al., 2004; Hasenstaub et al., 2005), and the duration of the longer, positive peak (Bruno and Simons, 2002; Atencio and Schreiner, 2008). Because our acquisition did not record the entire duration of the positive peak, we used the slope 0.5 ms after the initial trough (i.e., how quickly the voltage is returning to baseline) as a proxy for this parameter. These three parameters provided good separability and distinguished the same two groups of waveforms, as shown in Figure 1, F and G. Nineteen percent of the total population of recorded cells (45 units) fell into the narrow-spiking category, and there was not a significantly greater fraction of narrow-spiking units in any particular layer (p > 0.1, χ² test). This proportion matches the fraction of GAD-positive neurons previously identified histochemically (Tamamaki et al., 2003). For simplicity, we refer to these two groups as “putative inhibitory” and “putative excitatory,” but this should not imply that there is a perfect correspondence between the spike waveform and cell type assignment (see Discussion).

Selective and nonselective responses

A characteristic of visual cortex responses is the transformation from primarily center-surround, nonoriented receptive fields observed in retina and lateral geniculate nucleus of thalamus (LGN), to responses in V1 that are optimal for bars and edges of a particular orientation. To measure the degree of orientation and other response selectivity in mouse visual cortex, we presented full-length 5° wide bars of varying orientations drifting at 30°/s and drifting sinusoidal gratings moving at 2 Hz of varying orientation and spatial frequency. We found a range of response types, including many units that were highly selective for stimulus orientation, other units that responded to a wide range of stimuli, and a small fraction of units that did not significantly change their firing in response to visual stimuli. Examples of a highly selective and a poorly selective response are shown in Figures 2 and 3, respectively.

The unit shown in Figure 2 was a broad-spiking, putative excitatory neuron located in layer 4. Figure 2 A shows spike rasters for repeated presentations of a bar drifting in 16 different directions. It gives a strong response to bars over a narrow range of orientations and has a short duration of peak response, corresponding to <10° of visual space, as the bar crosses its receptive field. The tuning curve shown in Figure 2 B, measuring peak response for each orientation, demonstrates that the orientation tuning width is less than ±30° and that it has ∼2:1 preference for one direction of motion. Figure 2 C shows spike rasters from the same unit in response to full-field sinusoidal drifting gratings, which demonstrate a similar orientation tuning and selectivity (Fig. 2 D). Furthermore, it responds to gratings only over a particular range of spatial frequencies (Fig. 2 E), with maximal response ∼0.08 cpd, corresponding to grating bars spaced 12° apart. Finally, the unit responds to the drifting grating with a periodically modulated response. This is characteristic of a linear, or simple cell, response, such that the unit responds maximally when an oriented stimulus is in phase, i.e., aligned, with ON and OFF subregions of its receptive field, and responds minimally or reduces its response when the stimulus is out of phase with the receptive field. The amplitude of this modulation relative to the average firing rate, the F ₁/F ₀ ratio, has become a standard quantitative metric for the qualitatively defined simple and complex cell distinction (Skottun et al., 1991).

Figure 3 shows a much less selective response, from a narrow-spiking putative inhibitory unit also in layer 4. This unit responds to bars of all orientation (Fig. 3 A), with only a slightly elevated response to certain orientations (Fig. 3 B). It also responds over a much larger region of visual space, up to 40° across. The response to drifting gratings (Fig. 3 C) is similarly untuned for orientation (Fig. 3 D), and it extends over a wider range of spatial frequencies (Fig. 3 E), even giving a small response to 0 cpd, i.e., a full-field flicker. This unit also shows a relatively constant rate of firing as the grating drifts rather than the periodically modulated response seen in Figure 2 C. This would thus be classified as a nonlinear, or phase-invariant, response, because its response does not depend on the precise alignment of the grating within the receptive field.

Response properties across the population

The responses of these two units are representative of the two ends of the selectivity spectrum. We used two measures to describe the selectivity of the orientation tuning curves in response to drifting gratings. First, the OSI measures the relative response at the preferred orientation versus the orthogonal orientation, in other words, the tuned versus untuned response. Figure 4 A shows the OSI across the entire population of units that responded to drifting gratings (n = 182). The OSI was defined as (R _pref − R _ortho)/(R _pref + R _ortho), where R _pref is the peak response in the preferred orientation, and R _ortho is the response in the orthogonal direction. By this criterion, perfect orientation selectivity would give OSI of 1, an equal response to all directions would have OSI = 0, and 3:1 selectivity corresponds to OSI = 0.5. A large fraction of units thus show orientation selectivity, with 74% (135 of 182) having OSI > 0.5, and many showing nearly complete selectivity, such as the unit in Figure 2. Figure 4 B shows the preferred angle for units that were orientation selective and responded strongly to both gratings and bars (n = 87), demonstrating that this tuning was consistent between stimuli (r ² = 0.85), and showed little systematic preference for certain orientations. For orientation-selective units (OSI > 0.5), we measured the width of the tuned response, as the half-width at half-maximum above the baseline. Figure 4 C shows that most of the oriented units show relatively narrow tuning, similar to that seen in the unit of Figure 2, with median tuning width ±28.0°. It should be noted that some studies have measured tuning width as half-width at half-maximum including the untuned response rather than above the untuned baseline. Because this predominantly affects the poorly selective units, including the untuned baseline only shifted the median width of units with OSI > 0.5 to 28.9°.

The degree of orientation selectivity varied dramatically across layers and between putative excitatory and inhibitory units, as shown in Figure 4 D, a scatter plot of orientation selectivity for all units that responded to drifting gratings, and Figure 4 E, which shows the mean orientation selectivity for each of these groups. In layers 2/3, 4, and 6, there is a sharp distinction between cell types, because almost all putative excitatory units were highly orientation selective, whereas most putative inhibitory units were untuned. Although there was not a great difference in the orientation selectivity index (tuned vs untuned response) between excitatory units across these layers, we did observe a slight sharpening in the width of orientation tuning in upper layer 2/3, as shown in Figure 4 F. In layer 5, putative excitatory units showed a range of orientation selectivity, but, overall, the selectivity was much less (p < 0.001) and very few showed the high orientation selectivity that was typical of the more superficial layers. Furthermore, even among orientation-selective units, the width of tuning in layer 5 was much broader (p < 0.001), demonstrating that both the width of the tuned response and the magnitude of the untuned response are increased. A second measure of orientation selectivity, based on the circular variance of response across orientations, gave similar results for both individual units and population comparisons (supplemental Fig. S2, available at www.jneurosci.org as supplemental material).

Although many cells showed preferential responses for a particular orientation, it was less common for them to be selective for the direction of motion at that orientation. Figure 5 A shows the response to drifting bars for one such direction-selective unit, which responded strongly to bars moving at 202° but negligibly to bars moving in the opposite direction, 22.5° (which corresponds to the same bar orientation). Figure 5 B shows the prevalence of direction selectivity in response to drifting gratings across the population, demonstrating that, although a small fraction show quite strong selectivity, most (77%, 140 of 182) are substantially less selective, with indices <0.5, which corresponds to a 3:1 bias for preferred versus opposite direction. As Figure 5 C shows, almost all direction-selective units were putative excitatory units in layers 2/3 and 4.

As shown in Figures 2 and 3, units in mouse V1 responded preferentially to particular spatial frequencies of sinusoidal grating. Figure 6 A presents a histogram of the spatial frequency that elicited the maximum response at the optimal orientation, which generally ranged from 0.02 to 0.08 cpd (median of 0.036 cpd), although several units responded optimally at spatial frequencies up to 0.32 cpd, the highest tested. A small fraction responded best to 0 cpd, full-field contrast reversal. The preferred spatial frequency did not show any systematic variation across layers (Fig. 6 B), except for layer 6, which responded to significantly lower spatial frequencies, as did putative inhibitory units. The preferred spatial frequency did not show any significant variation with receptive field eccentricity, which ranged from 20 to 90° in azimuth (r ² = 0.009; p < 0.37), consistent with the lack of a fovea/area centralis, the relatively constant photoreceptor and retinal ganglion cell spacing across the mouse retina (Jeon et al., 1998), and the uniform magnification of the cortical representation (Kalatsky and Stryker, 2003). Most neurons showed bandpass spatial frequency tuning (Fig. 6 C). The median bandwidth of spatial frequency tuning for bandpass units was 2.46 octaves, although some neurons responded to only one of the spatial frequencies presented, and a small fraction showed low-pass tuning (Fig. 6 C). The width of spatial frequency tuning was greater for both putative inhibitory and layer 5 putative excitatory units (Fig. 6 D).

A common classification of visual responses is into simple cells, whose response to stimuli can be predicted by the linear sum of responses to spots at individual locations, and complex cells, which demonstrate nonlinear spatial summation. Correspondingly, simple cells are phase dependent, in that they generally respond to an edge of particular orientation at a specific location, whereas complex cells are phase invariant, in that they respond to the edge at any location within the receptive field. This distinction may be measured using the modulation of response to drifting gratings (Skottun et al., 1991). A high F ₁/F ₀ ratio indicates that the firing of the unit is modulated at the temporal frequency of the grating, whereas a low F ₁/F ₀ indicates that the unit fires relatively constantly throughout the presentation of the grating. The units in Figures 2 and 3 had F ₁/F ₀ of 1.43 and 0.36, respectively. Figure 7 A shows the bimodal distribution of the F ₁/F ₀ ratio for all units that responded to gratings (n = 182), emphasizing the distinction of linear and nonlinear units by this metric. Most putative inhibitory units showed nonlinear responses, as did layer 5 broad-spiking units (Fig. 7 B,C). In layers 2/3, 4, and 6, the majority of putative excitatory units were linear, although a sizeable fraction were nonlinear.

The size of the receptive fields was measured by sweeping short bars (4° wide × 8° long) of different orientations across the visual field. Figure 8 A show the radius of the receptive field (half-width at half-maximum) for 108 units that gave sufficiently strong response to this stimulus. The radius of the receptive field was smallest among layer 2/3 and 4 broad-spiking units and was generally ∼5–7° (Fig. 8 B). Putative inhibitory and layer 6 units tended to be somewhat larger, and layer 5 units were nearly twice as large (p < 0.001), with some receptive fields up to 15° radius by this measure.

The spontaneous firing rate also varied dramatically across layers and cell type (Fig. 8 C,D). Putative excitatory units in the superficial layers had extremely low spontaneous rates, often firing less than once every 10 s, whereas layer 4 broad-spiking units were almost twice as active (p < 0.05). Putative inhibitory units had a wide range of spontaneous rates but tended to fire at rates almost an order of magnitude higher. Nearly all units in layer 5 had high spontaneous rates: the dramatic increase in firing rate generally provided a clear indication of the layer 5 boundary. It is interesting to note that cell types with high spontaneous rate (layer 5 and putative inhibitory) have the lowest stimulus selectivity.

The magnitude of the evoked firing rate did not vary as dramatically across layers as the spontaneous rate. Figure 8 E shows the average firing rate over 1.5 s in response to the optimal grating stimulus (with spontaneous rate subtracted), for all units (n = 204) that responded to at least one of the episodic stimuli, even if they were not considered responsive to the gratings. Figure 8 F demonstrates that the evoked rate is relatively constant across layers, although greater in putative inhibitory neurons. The median evoked firing rate across the population was 6.7 spikes/s, which is lower than studies in V1 of other species (Girman et al., 1999; Heimel et al., 2005) but higher or consistent with that seen in other regions of rodent cortex (Brecht et al., 2003; DeWeese et al., 2003; Sato et al., 2007). It is possible that anesthesia level contributed to these lower rates or that our method of isolating units without regard to responsiveness may allow us to detect units with lower firing rates. It should also be noted that these firing rates are averages over 1.5 s. The peak instantaneous firing rate can be significantly higher (supplemental Fig. S3, available at www.jneurosci.org as supplemental material), particularly for simple cells, which modulate their firing rate periodically in response to gratings. Additional details of response magnitude, spontaneous rate, and variability are presented in supplemental Figure S4 (available at www.jneurosci.org as supplemental material).

We measured temporal frequency response by presenting contrast-reversing sinusoidal gratings at a fixed spatial frequency (0.04 cpd) and varying temporal frequency (Fig. 8 G). Most units responded optimally at ∼2 Hz (median of 1.68 Hz) although we saw a significant increase in peak temporal frequency in layer 4. This is shown in Figure 8 H, which presents the average temporal frequency tuning curves for layers 2/3 and 4, demonstrating an increased response by layer 4 units to stimuli at 4 and 8 Hz (p < 0.05).

The relative proportion of different functional response categories across the layers and cell types is illustrated in Figure 9, using OSI = 0.5 and F ₁/F ₀ = 1 as thresholds for orientation selectivity and linearity. A binary classification, which depends on an arbitrary threshold, is difficult when the parameter is not bimodally distributed. Even when a parameter does show a bimodal distribution, such as the F ₁/F ₀ ratio, this may not represent a true distinction in either taxonomy or mechanism (Mechler and Ringach, 2002). Our categorization is thus meant only to provide a summary overview of response types for comparison with other studies.

Across the population, 13% of units were not responsive to any of the stimuli we used, and 9% were left unclassified because they failed to give sufficient response to drifting gratings to estimate orientation selectivity and linearity. In layers 2/3 and 4, broad-spiking putative excitatory units were nearly always simple and orientation selective, with a fraction of nonlinear oriented units and a small number of simple nonoriented units in layer 4. Layer 5, in contrast, showed mostly nonlinear responses, with a large fraction of classic complex oriented units and a smaller number of nonlinear nonoriented units. Layer 6 was similar to layers 2/3 and 4, although with a greater number of nonlinear oriented units and the highest proportion of nonresponsive units. Finally, three-quarters of putative inhibitory units were nonlinear, of which the vast majority were nonoriented.

Responses to noise movies

To measure responses to more complete, yet still well parameterized, stimuli, we generated movies of stochastic noise with defined spatial and temporal frequency spectra (Fig. 10 A) (supplemental movie, available at www.jneurosci.org as supplemental material). We used these movies to probe the overall visual responsiveness of units by periodically modulating the contrast so that each movie transitioned sinusoidally from a gray background to full contrast movie and back to gray again, with a 10 s period. This generally resulted in a periodic modulation of firing, as demonstrated in Figure 10 B. Modulating the contrast also served to maintain high firing rates throughout the presentation, because units often habituated and firing rates decreased during long movies without varying contrast.

By measuring the ratio of the response amplitude at the frequency of the movie modulation to the average firing rate throughout the movie (Fig. 10 C), we obtained a measure of overall visual drive. This value is 0 if the firing rate is constant during the movie (no response) and 1 for a perfect sinusoidal modulation with no baseline firing. It should be noted that, because this is measuring the net firing in response to a rich stimulus, it thereby combines both peak responsiveness and broadness of tuning in a single metric. Figure 10 D demonstrates that most units were responsive to this visual stimulus, including many of the units (55%, 17 of 31) for which we could not elicit a response and measure receptive field properties using the episodic stimuli described previously. The phase of the Fourier component at the contrast-modulation frequency describes the time of optimal response, which was generally slightly before the contrast maximum at 180°. Interestingly, a few units showed the opposite response and actually decreased their firing rate in response to the movies, as indicated by a phase near 0°, opposite to the rest of the population. Figure 10 E shows the responsiveness by layer and cell type, demonstrating that layer 5 and 6 units tended to modulate their firing rate less in response to the white noise movies (p > 0.001), whereas upper layer 2/3 was the most responsive (p < 0.01). Modulating the contrast in this manner and plotting the averaged response over all cycles also permitted a form of contrast–response curve, as well as a rough measure of contrast adaptation over periods <10 s (supplemental Fig. S5, available at www.jneurosci.org as supplemental material).

Noise movies have been used extensively to measure linear spatiotemporal receptive field structure directly by calculating the spike-triggered average (Jones and Palmer, 1987a; Chichilnisky, 2001). For each spike that a neuron fires, we collected the frame that preceded the spike by a time τ. The average of all these frames is known as the STA and, for a Gaussian white noise stimulus, represents the linear kernel of the spatiotemporal response of a neuron. In this case, we corrected the STA to account for the non-white Gaussian spectrum of the stimuli, via normalization by the power spectrum of the stimulus set (Theunissen et al., 2001; Sharpee et al., 2004).

For units that responded linearly to drifting gratings, we were generally able to recover a STA receptive field from responses to the contrast-modulated noise movies. Approximately two-thirds (64%, 63 of 98) of simple cells produced a receptive field by STA for a 10–15 min movie presentation. In general, the primary limitation in generating an STA receptive field for linear units was the number of spikes observed; for simple cells that generated at least 400 spikes, >90% produced an STA with sufficient signal-to-noise, suggesting that longer movie presentations could reveal an STA for more units. Note that, because the stimulus set was spatially frequency limited, the noise in the STA receptive fields is also frequency limited, leading to the beaded or rippled appearance of the residual noise in the estimated RFs. Monte Carlo simulations of Gabor receptive fields with our movie stimuli show similar rippled appearance at low numbers of spikes, which average out for longer movie presentations or higher spike count. For nonlinear units, with a low F ₁/F ₀ ratio, the STA generally showed no structure, corresponding to the lack of a linear kernel. Because of the relatively small number of spikes collected during these movie presentations, we did not attempt to use spike-triggered covariance or other methods to extract nonlinear receptive fields.

Figure 11 A–C shows examples of STA receptive fields, including the unit (Fig. 11 B1) whose response to gratings and bars was illustrated in Figure 2. Many RFs had both an ON and OFF subregion (55%), or often three subregions (27%), whereas 18% of units only had one subregion (Fig. 11 A–C, respectively). The orientation of the STA receptive fields generally agreed quite well with the preferred orientation determined from drifting gratings (Fig. 11 D) (r ² = 0.91). The correspondence between the spatial frequency of the STA and the peak response to gratings was also significant (Fig. 11 E) (r ² = 0.63) but only for units that had a peak spatial frequency > 160 cpd as measured by drifting gratings (blue circles). It is not surprising that the units with the lowest spatial frequencies (< 160 cpd; gray circles) gave STAs with inaccurate spatial frequencies, because the total size of the movie was 60° (corresponding to 160 cpd), preventing us from matching lower spatial frequencies than this. Interestingly, the more subunits found in the STA, the narrower the orientation tuning width as determined from gratings (Fig. 11 F), consistent with linear models of orientation selectivity. Similarly, spatial frequency bandwidth narrowed with increasing number of subunits (Fig. 11 G).

To further analyze the structure of STA receptive fields, we fit the measured RFs to Gabor functions, which are sinusoids multiplied by a Gaussian envelope. Figure 11 H shows the fraction of signal variance that was accounted for by the fit (n = 63), demonstrating that, for many units, the Gabor provided a good description of the data. Because our measured RFs had relatively large noise (up to 20% of the STA variance) as a result of the small number of spikes, we expect that longer movie presentations, or further optimization of movie parameters based on the tuning properties determined in this study, would produce STAs with lower noise and better fits.

The shape of a Gabor can be characterized by two numbers, n_x = σ _xf and n_y = σ _yf, which correspond to width along the sinusoid and perpendicular to the sinusoid, in terms of number of cycles of the sinusoid (Ringach, 2002). The ratio of n_x to n_y can be thought of as the aspect ratio, whereas the value of n_x is related to the number of subunits that can fit in the Gaussian. Figure 11 I shows the values of n_x and n_y for units that were best fit by the Gabor (fit error <0 0.33; n = 50) compared with similar data from macaque (Ringach, 2002). The mouse STA receptive fields overlap with most of the macaque data, indicating that they have similar shapes. However, the mouse does not have units with very large n_x , consistent with the fact that we did not observe STAs with more than three strong subunits. A histogram of the phase of the sinusoid (Fig. 11 J), mapped onto the range 0–90° to remove symmetries (Field and Tolhurst, 1986), shows an over-representation of odd-symmetric receptive fields. Estimates of the spatial phase distribution show a wide range in other studies, including uniform, peaked at 90°, or bimodal at 0 and 90° (Field and Tolhurst, 1986; Jones and Palmer, 1987b; DeAngelis et al., 1993; Ringach, 2002).

Contrast-invariant tuning

An important aspect of cortical visual responses is that orientation selectivity does not vary with increasing stimulus contrast, a phenomenon known as contrast-invariant tuning (Ferster and Miller, 2000; Priebe and Ferster, 2008). This constancy constrains models of cortical processing, because simple feedforward models such as the original Hubel and Wiesel proposal (Hubel and Wiesel, 1962) generally predict an increase in tuning width as the visual drive (e.g., contrast) is increased (Fig. 12 A, right). However, it is generally observed that, as contrast increases, the visual response increases but units do not lose selectivity, resulting in a multiplicative scaling of the tuning curve (Fig. 12 A, left). Numerous factors have been identified that could explain this property, including recurrent connectivity, inhibition, membrane potential fluctuations attributable to background activity, and the spike threshold, among others (Sompolinsky and Shapley, 1997; Ferster and Miller, 2000; Shapley et al., 2003; Finn et al., 2007; Priebe and Ferster, 2008).

We sought to determine whether this constancy is present in the mouse as well, to both assess the similarity in cortical processing to other species and ascertain whether genetic manipulations in mice could provide causal tests of proposed mechanisms of invariant tuning. For a subset of recordings (n = 6 animals), we presented drifting gratings of varying contrast and orientation, at fixed spatial frequency (0.04 cpd). A typical response from an oriented unit shown is shown in Figure 12 B, demonstrating contrast-invariant tuning, as the tuning curve only changes in amplitude, not shape, as contrast increases. Aligning and averaging the tuning curves of all orientation-selective units that responded to this spatial frequency (n = 22 units) resulted in the mean tuning curve observed in Figure 12 C, which shows no increase in width with increased contrast. Furthermore, a comparison of all individual orientation tuning curves at two different contrasts shows no systematic change in either orientation selectivity (Fig. 12 D) or tuning width (Fig. 12 E).

In addition to testing contrast-invariant tuning, this stimulus set allowed us to measure the response as a function of contrast for those units that were responsive to this spatial frequency. Figure 12 F shows the value of contrast that resulted in half-maximal response, which showed a wide range, with a median value of 19.8%. The slope of response over contrast at the half-maximal response is shown in Figure 12 G; for normalized contrast–response curves, a slope of 1 indicates a relatively linear increase in response with contrast, whereas a greater slope indicates a sharp transition from low to high response at the midsaturation contrast. Although many units had slope near 1, again there was a wide range, with a median value of 2.4.