Local Diversity and Fine-Scale Organization of Receptive Fields in Mouse Visual Cortex

Wide-field video-rate imaging of neural populations

To study the activity of populations of neurons in the cortex of mice, we built a video-rate two-photon microscope for calcium imaging (Fig. 1). The microscope, based on a resonant scanner (Fig. 1A), could image >300 μm fields of view (Fig. 1B) at a rate of 31 images per second (see Materials and Methods). The microscope yielded high signal-to-noise images using relatively low average laser power (Fig. 1C) (∼10–20 mW at 150–250 μm depth) and allowed the measurement of somatic calcium fluorescence of >100 neurons simultaneously (Fig. 1D). At these low laser power levels, we could image for up to 90 min with limited changes in absolute fluorescence or in the magnitude of evoked responses (1 − F_min/F_max < 15%, ΔF/F₀ ∼ 0.9–1.3%s⁻¹, eight planes).

We devised a simple procedure to correct for the effects of brain motion and neuropil contamination on the somatic calcium time courses (Fig. 2) (see Materials and Methods). Small cell movements are common during in vivo imaging due to heartbeat, respiration, and, in awake animals, voluntary movements (Göbel and Helmchen, 2007). These movements cause cell bodies to move in and out of the regions of interest, causing fluorescence changes that can be as large as those caused by neural activity (Fig. 2B1, first row). To correct for brain motion, we aligned each image frame (Fig. 2A), and applied principal component analysis (Mitra and Pesaran, 1999; Mukamel et al., 2009) to the somatic regions to estimate the components due to z-motion (Fig. 2B1, second row) as well as to neuropil regions to obtain a measure of contamination (Fig. 2B1, third row). We then computed somatic time courses by averaging fluorescence over cell bodies and subtracting the estimated motion and neuropil components (Fig. 2B1, fourth row, black). We used these corrected time courses to estimate firing activity (Fig. 2B1, fourth row, red).

This procedure effectively corrected for the effects of brain motion and neuropil contamination (Fig. 2B–E). The correction worked for poorly sectioned cells (Fig. 2B1, left column), which could be strongly affected by motion, and for well sectioned cells (Fig. 2B1, right column), which were generally less affected. The procedure removed the common signals that are shared between time courses (Fig. 2C), thereby allowing a more precise characterization of coactive ensembles (Fig. 2E). Because images were acquired at video rate, we could remove non-spike-related signals at various time scales (Fig. 2D1), including breathing (<2 Hz) and heart beat (9 Hz). The corrected time courses have a near perfect exponential amplitude spectrum (Fig. 2D2, thick black curve) as expected from the time course of spike-related calcium fluorescence (Smetters et al., 1999; Kerr et al., 2005; Kerlin et al., 2010). Importantly, the correction procedures made no assumption about the frequency spectrum of the components.

To reconstruct firing rates from the calcium signals, we used the model-based deconvolution method of Vogelstein et al. (2010) (see Materials and Methods). We selected this method because it is fast and allows reconstruction of firing rates while the experiment is taking place. Based on a generative model of calcium responses, the method outputs a time series of positive real numbers that are proportional to the neurons' firing rates (Fig. 2B1, red ticks). We expressed these deconvolved time courses as calcium transient rate (percentage ΔF/F s⁻¹). The method explained the time course of responses (Fig. 2B1, red curves), capturing their amplitude spectrum (Fig. 2D2, red curve), as evidenced by the flat spectrum of the residuals (Fig. 2D2, gray curve). When tested on simultaneous calcium imaging and cell-attached recordings in a similar in vivo preparation (Kerlin et al., 2010), the firing rate estimates were highly consistent with the measured spiking (Fig. 2B2). The correlation coefficient between the measured and estimated firing rates was 0.81 ± 0.05 (n = 3 cells) for regular spiking neurons, and 0.37 ± 0.15 (n = 5) for fast-spiking neurons (eight frames or 240 ms bins). The lower performance of the method for fast-spiking neurons was largely attributable to the small field of view in these calibration experiments, typically a single cell, which made it difficult to compensate for slow baseline drifts. This problem generally did not arise when imaging large fields (Fig. 2C).

Spatial summation in excitatory and inhibitory neurons

We first studied the spatial summation properties of excitatory and inhibitory neurons. The two major functional cell types in visual cortex are simple and complex cells, which differ in the spatial properties of their receptive fields as originally described in the cat (Hubel and Wiesel, 1962). Simple cells have receptive fields with segregated ON and OFF subregions that are elongated along the axis of the preferred orientation. Complex cells are also tuned for orientation but have receptive fields with spatially overlapping ON and OFF response fields (ON/OFF receptive fields). Spike recordings in mouse visual cortex also identified a third physiological type, with ON/OFF receptive fields and broad tuning for orientation (Dräger, 1975; Niell and Stryker, 2008). Recent electrophysiological and imaging studies in transgenic animals suggest that these nonselective complex-like cells may correspond to GABAergic interneurons (Sohya et al., 2007; Liu et al., 2009; Kerlin et al., 2010).

To determine whether excitatory and GABAergic neurons indeed show distinct modes of spatial summation, we studied the timing of their calcium responses. In the cat, simple and complex cells can be distinguished from the timing of their firing responses to sine-wave grating stimuli (Movshon et al., 1978a,b). These stimuli elicit periodic responses in simple cells but not in complex cells, which show more tonic responses. We studied calcium responses in visual cortex of GAD67-GFP knock-in mice whose GABAergic interneurons are labeled with GFP (Tamamaki et al., 2003). We stimulated with sinusoidal gratings moving at 1 Hz in different directions and used the method of Vogelstein et al. (2010) to infer neural firing. We then compared the tuning and the periodicity of responses between GFP-positive and GFP-negative neurons. Our ability to resolve the time course of calcium responses at a resolution of tens of milliseconds (Fig. 1), free of the artifacts that tend to be concentrated at low temporal frequencies (Fig. 2), made these experiments possible.

Neurons responded strongly to the grating stimuli (Fig. 3). Over a third of the imaged cells showed large stimulus-driven calcium transients (ΔF/F > 10%, N = 103/262 cells from two planes in two animals). Of these cells, ∼15% were GAD67 positive. Consistent with past studies (Sohya et al., 2007; Niell and Stryker, 2008; Kerlin et al., 2010; Zariwala et al., 2011), responses of excitatory neurons were highly selective for a narrow range of stimulus orientations (Fig. 3A1), while responses of inhibitory neurons were nonselective or weakly selective (Fig. 3A2) (but see Ma et al., 2010; Runyan et al., 2010). We quantified response selectivity with a tuning index whose value ranges from 0, for not tuned, to 1, for highly tuned (see Materials and Methods). The tuning index for inhibitory responses was significantly lower than for excitatory responses (0.22 ± 0.05 vs 0.59 ± 0.02, mean ± SE).

Responses of excitatory and inhibitory neurons differed strikingly in their time courses. Because somatic time courses were sampled at video rate (31 Hz), we could resolve periodic modulations of responses at a range of frequencies. We found that excitatory neurons often showed a strong periodic response at the temporal frequency of the grating (Fig. 3A1), indicative of simple receptive fields with segregated ON and OFF subregions (Movshon et al., 1978a; Niell and Stryker, 2008). This modulation was visible in both the calcium time courses (Fig. 3A1, black traces) and the inferred firing activity (Fig. 3A1, red histograms). GABAergic interneurons, in contrast, showed an increase in fluorescence with little periodic response (Fig. 3A2), suggestive of complex-like receptive fields with ON/OFF responses (Movshon et al., 1978b; Niell and Stryker, 2008).

These functional differences in orientation tuning and response modulation were highly correlated with cell types. To quantify the periodicity of responses, we calculated the harmonic component of the inferred firing at the temporal frequency of the stimulus (Fig. 3C, gray) and compared it to the average response (Fig. 3C, black). These response components closely followed each other in excitatory neurons (Fig. 3C, left) but less so in GABAergic neurons (Fig. 3C, right). The modulation ratio—the ratio of the periodic response to the mean response—is significantly lower in interneurons than in excitatory neurons (Fig. 3D) (0.60 ± 0.09 vs 1.32 ± 0.04, mean ± SE; N = 15 and 84 cells). The depth of modulation was highly correlated with the selectivity of responses for orientation (r = 0.60, p < 1e-10, t test). Excitatory and inhibitory neurons were readily distinguished by these properties (Fig. 3D, red and blue symbols). These differences were robust. Stimulus-locked transients were visible in single trials in excitatory neurons (Fig. 3B, top) but not in interneurons (Fig. 3B, bottom).

While excitatory neurons and interneurons differ in the size and decay constant of their spike-related calcium fluorescence (Kerlin et al., 2010), these functional differences are not likely to reflect differences in the calcium-buffering properties of the neurons. At the stimulus frequency (1 Hz), our ability to resolve firing rate modulations is not limited by the decay time in fluorescence, but its rise time, which is similar in both cell types (Kerlin et al., 2010, less than one imaging frame or 63 ms). We confirmed the validity of this assertion using simulations (data not shown).

Thus, excitatory neurons in visual cortex often have simple receptive fields, and GABAergic neurons have receptive fields that are complex-like but, unlike classical complex cells seen in species such as cats and primates, are broadly tuned for stimulus orientation (Dräger, 1975; Niell and Stryker, 2008; Liu et al., 2009; Kerlin et al., 2010; Liu et al., 2010).

Characterizing receptive fields with wavelet stimuli

We next devised a method to measure the spatial receptive fields of excitatory neurons. Receptive fields have been effectively studied with random stimuli (Jones and Palmer, 1987a; Reid and Shapley, 1992; Reid and Alonso, 1995; Reid et al., 1997; DeAngelis et al., 1999; Hetherington and Swindale, 1999). However, stimulation with white, uncorrelated stimuli such as random single spots (sparse stimuli) or multiple spots (dense stimuli) produces small responses (Ringach et al., 1997; Liu et al., 2009; Ma et al., 2010) and can drive only a fraction of the neurons simultaneously. To obtain a dense sampling of receptive fields with calcium imaging, we needed a dense, structured stimulus that produces robust firing responses (Niell and Stryker, 2008).

We designed a wavelet stimulus to produce responses that are easily detectable using calcium imaging. The stimulus consists of localized oriented stimuli, or wavelets (Selesnick et al., 2005), whose positions, sizes, and directions were chosen randomly (Fig. 4A). The wavelets resemble Gabor functions, which have been used in the past to model the receptive fields of visual cortical simple cells (Jones and Palmer, 1987b; Ringach et al., 2002). We chose their sizes to match the properties of mouse visual cortical neurons (Niell and Stryker, 2008) and their density so that only a few wavelets were on the display at any given time (see Materials and Methods).

The stimulus evoked strong calcium responses from the neurons (Fig. 4B). We stimulated with periods of wavelets interleaved with epochs of gray screen. Responses consisted of large calcium fluorescence transients followed by a slow decay to baseline (Fig. 4B, traces) from which we estimated the timing and the magnitude of firing events (Fig. 4B, red). We calculated the average percentage of calcium activity (percentage ΔF/F) for the periods of gray and for the periods of wavelet stimuli. Many neurons showed increased calcium activity upon stimulation (290 of 536 cells, N = 7 planes in two animals, z-score >3.0, range 30–85% of identified somas of each plane), with an average deconvolved fluorescence signal of 0.75 ± 0.06% ΔF/F s⁻¹ during the epochs of gray screen and 1.32 ± 0.18% ΔF/F s⁻¹ upon stimulation (mean ± SE, 290 cells, N = 7 planes). The calcium transient frequency (ΔF/F > 3%, 30 ms bins) and magnitudes increased upon stimulation (0.03 ± 0.01 Hz and 0.76 ± 0.06% ΔF/F during gray screen, and 0.11 ± 0.02 Hz and 1.32 ± 0.18% during stimulation, mean ± SE, 290 cells, N = 7 planes). The peak transient magnitude also increased upon stimulation (5.20 ± 0.52% to 7.74 ± 0.98%, 99th percentile, mean ± SE). Responses were very sparse with only a small fraction of all neurons simultaneously active (Fig. 4C, top). Yet the stimulus was very effective, yielding time-locked responses in most cells (Fig. 4C, bottom).

From these responses, we calculated event-triggered averages as initial, approximate measures of the receptive fields (Fig. 4D). We computed the cross-correlation between the stimulus and the response, and compared results across repetitions to express them as z-scores (mean/SE). The triggered averages had segregated and elongated ON (Fig. 4D, red) and OFF subregions (Fig. 4D, blue), characteristic of visual cortical simple cells (Fig. 4E). Receptive fields were obtained in as little as 20 min of imaging (three repetitions of the stimulus) (Fig. 4F), comparable to the time required for measuring receptive fields with electrode recordings of responses to structured stimuli (Niell and Stryker, 2008).

The measured receptive fields were consistent with the tuning of responses to oriented stimuli. In some experiments, we also measured responses to moving sinusoidal gratings and compared these responses to the predictions obtained from the estimated receptive fields (Fig. 4G). There was agreement between the measured and predicted orientation tuning curves (Fig. 4G, black and red lines). The mean (±SE) difference in preferred orientation was 4.1 ± 5.1° (n = 61), and the mean absolute difference was 31.5 ± 3.1° (n = 61). The predicted tuning was generally broader than the measured responses, likely because the analysis did not include a spiking mechanism, which acts to sharpen the tuning of responses (Priebe and Ferster, 2008). The triggered averages of dozens of neurons could be measured simultaneously. Overall, the experiments yielded triggered averages for approximately half the imaged neurons (peak z-score >5.0, N = 263 of 533 imaged cells, N = 7 planes in 2 animals), and for up to 80% of cells in some imaged planes.

Thus, high-speed calcium imaging of responses to random stimuli can reveal the receptive fields of dense populations. Critical to these experiments was our ability to estimate firing rates free of motion artifacts and the use of a stimulus that evoked large responses from many neurons (Fig. 4B,C).

Receptive-field model and parameters

To study receptive-field diversity and organization, we needed to quantify receptive-field parameters. The event-triggered averages are blurred by the spatial structure and the slow time course of the stimulus, and therefore cannot be used to estimate receptive-field parameters without bias (Theunissen et al., 2001). Receptive fields can be quantified by fitting a model to the responses (Carandini et al., 1997). This provides receptive-field parameters and quantifies the degree to which the receptive fields explain the neural responses.

We fitted a linear rectification model to explain responses and to extract receptive-field parameters. The model consists of a linear filter whose output is a time-varying signal, analogous to an intracellular potential, followed by a rectifying nonlinearity to obtain firing rates (Carandini et al., 1997). The linear filter consisted of a spatial receptive field, which filters the visual stimulus through a Gaussian window-oriented sinusoidal function (a Gabor function), (Jones and Palmer, 1987b; Ringach, 2002; Niell and Stryker, 2008), and a temporal filter (a gamma function) (Cai et al., 1997), which delays and smooths the responses (Fig. 5A). We fitted the model to the trial average of deconvolved responses smoothed with a Gaussian filter (σ = 30 ms). Using fits of the event-triggered averages as initial parameters, we estimated the model parameters that minimized the squared error between measured and model responses.

The model fits provided a simple description of the neurons' receptive fields. The estimated spatial filters captured the main features of the event-triggered averages (Fig. 5B,D), providing a method to measure receptive-field parameters. The estimated temporal filters showed less blur than the corresponding triggered averages (Fig. 5B), indicating that the least-square fits account for the correlations contained in the stimulus. As a result, the model output is more temporally precise and can explain some of the calcium responses locked to the stimulus (Fig. 5C). To assess the quality of fits, we calculated the percentage of stimulus-locked variance in the responses that is explained by the model output. Model performance varied across neurons, explaining up to 75% of the variance in the stimulus-locked responses of the neurons (Fig. 5D). We considered fits that had predictive power (explained variance >10%, N = 222 of 463 imaged cell bodies, six planes in two animals). The average size of the spatial filters was ∼12° (12.1 ± 6.3°, mean ± SD, half-width at half-maximum), and the average delay of the temporal filters was generally <250 ms (140 ± 78 ms, median ± interquartile range; N = 181). These results are commensurate with similar measurements using electrode recordings (Niell and Stryker, 2008; Gao et al., 2010).

Local receptive-field populations: diversity and organization

We used model fits to study the receptive fields' diversity and organization. Are spatial receptive fields unique within their surrounding populations or do they show redundancy? How is this diversity distributed over the visual space and over the imaged plane? Receptive fields of nearby neurons could be arranged randomly or could show clustering, with nearby cells having similar receptive fields. By addressing these questions, we constrain how local populations of excitatory neurons sample the visual scene.

Receptive fields of different orientations and positions were scattered over the imaged field (Fig. 6A). Nearby neurons could have similar receptive fields (Fig. 6A, cells 14 and 19), receptive fields with overlapping position but different orientations (Fig. 6A, cells 58 and 60), or receptive fields with different positions and orientations (Fig. 6A, cells 17 and 20). In addition, distant neurons could have similar receptive fields (Fig. 6A, cells 33 and 58). This random arrangement of receptive-field orientation and position is consistent with the arrangement of orientation preference measured with grating stimuli (Ohki et al., 2005; Wang et al., 2006; Sohya et al., 2007; Kerlin et al., 2010), and with the scatter of ON and OFF receptive-field subregions of nearby neurons measured with sparse noise (Smith and Häusser, 2010).

The receptive fields, however, were not entirely random. First, as reported by Smith and Häusser (2010), ON and OFF subregions fell on average onto spatially offset regions of the visual field (Fig. 6B). This segregation was not strict; overlapping subregions of opposite signs were also frequently observed (Fig. 6A), and, as a result, the overall bias was small compared with the local diversity (Fig. 6B, note the small magnitude of the average receptive field, peak ∼0.25). Second, despite local scatter, a global retinotopic shift in receptive-field position was often discernible across the cortical surface (Fig. 6A, left to right). These measurements, to our knowledge, are the first to unambiguously demonstrate the mapping of receptive field position in a small patch of cortex. We study retinotopy further in the next section (Fig. 7).

To quantify receptive-field diversity, we calculated for each neuron pair in the imaged plane an index of similarity and studied its distribution. We defined similarity as the dot product between the normalized spatial filters (DeAngelis et al., 1999; Usrey et al., 1999; Alonso et al., 2001), which mirrors the spatial filtering of the visual scene performed by the neurons. This measure equals 1 for identical receptive fields, 0 for dissimilar receptive fields (orthogonal or nonoverlapping), and −1 for receptive fields of opposite signs. We considered for each plane the neurons for which we obtained significant event-triggered averages (mean/SE >5.0) and for which the model explains >5% stimulus-evoked variance (50/82 cells for the plane in Fig. 6 and 192/455 cells, six planes in two animals).

According to this measure, nearby neurons generally had quite dissimilar spatial receptive fields (Fig. 6C). The similarity distribution showed a peak at zero and few counts near 1 and −1 where highly similar and oppositely signed receptive fields should fall (Fig. 6D). This degree of diversity is more pronounced than in the cat visual cortex where highly similar receptive fields were more frequently observed (DeAngelis et al., 1999), probably reflecting the difference in functional organization between the visual cortices of the two species. In cat visual cortex, nearby simple cells have similar orientation preference (Hubel and Wiesel, 1959), so spatial receptive fields can only differ in their position or phase.

We then investigated whether there was any clustering across the cortex of functionally similar neurons. We related receptive-field similarity to the distance between cell bodies, as inferred from the hand segmentation mask (Fig. 6A). If there were clustering over short cortical distances, then similarity should depend on cortical distance. Overall, there was only a weak dependence of similarity on cortical distance (Fig. 6C). Neurons <100 μm apart had more similar receptive fields (Fig. 6D, solid line) than neurons between 100 and 200 μm apart (Fig. 6D, gray line), reflecting a slow fall off in receptive-field overlap with cortical distance (Fig. 7E). Thus, aside from retinotopy, receptive fields are disorganized over cortex.

We next studied the clustering of receptive fields in visual space. Are receptive fields more similar than would be expected from random sampling of visual features? To test this hypothesis, we recalculated the similarity indices assigning receptive fields random orientations or phases while maintaining their positions. The similarity distribution in these surrogate data differed slightly from the measured (Fig. 6E). As expected from the clustering of ON and OFF subregions, randomization increased the frequency of oppositely signed receptive fields (Fig. 6E, left of ordinate). However, randomization only mildly affected the frequency of highly similar receptive fields (Fig. 6E, right of ordinate), suggesting that the receptive fields show about the same level of clustering as expected from random sampling.

Local receptive-field populations: retinotopy and scatter

Thus far, the principal source of organization we observed was retinotopy, the map of receptive-field position across the cortical surface. Retinotopy has been studied with electrode recordings (Hubel and Wiesel, 1974; Dräger, 1975; Van Essen et al., 1984) and optical imaging (Grinvald et al., 1994; Schuett et al., 2002; Kalatsky and Stryker, 2003). Electrode recordings of nearby neurons in primate (Hubel and Wiesel, 1974; Dow et al., 1981), cat (Das and Gilbert, 1997; DeAngelis et al., 1999; Hetherington and Swindale, 1999), and mouse (Dräger, 1975; Wagor et al., 1980) have shown deviations from smooth retinotopy. This scatter may reflect true deviations or it may reflect the sampling of cell bodies (and other cell processes) at a distance of the electrode tip (Hetherington and Swindale, 1999). Our imaging data can resolve this question.

We estimated global retinotopy from the model fits (Fig. 7). When we plotted receptive-field centers against the position of cell bodies (Fig. 7A), a progression of receptive-field azimuth and elevation could be seen along two orthogonal directions across the cortical surface (Fig. 7B). This retinotopic map was well described by a simple 2D rigid transformation of cortical space (Fig. 7C). From this transformation, we could estimate cortical magnification, the distance in cortex that corresponds to an average 1° displacement of receptive-field centers. The magnification factor along azimuth and elevation was 8.2 ± 2.3 μm/° (mean ± SD, N = 6 planes in 2 animals). This is slightly lower than measurements made at the millimeter scale at a range of eccentricities (Dräger, 1975; Wagor et al., 1980; Schuett et al., 2002; Kalatsky and Stryker, 2003) (range 12–24 μm/°).

We then estimated receptive-field scatter (Fig. 7D). The receptive-field centers (Fig. 7D, symbols) showed clear deviations from the estimated smooth retinotopy (Fig. 7D, lines). This scatter likely does not reflect uncertainty in receptive-field measurements; the magnitude of deviations and the degree to which receptive fields capture the responses were unrelated (Fig. 7D, gray shades). Similar results were obtained by considering ON and OFF subregions separately (data not shown). We quantified scatter as the SD of receptive-field center position minus the estimated global retinotopy. Across experiments, scatter was 7.0 ± 2.2° (mean ± SD, N = 6 planes), amounting to about one-half the size of a typical receptive field (∼12°, see previous section).

Thus, cellular imaging can resolve the global progression of receptive-field position across cortex as well as deviations in nearby neurons. The deviations likely reflect true receptive-field scatter, not measurement noise. The receptive-field scatter we observed in mouse V1 is approximately one-half the size of a typical receptive field.

Functional diversity of local visual cortical populations

We observed pronounced functional differences between the responses of excitatory and inhibitory populations in mouse visual cortex. When studied with grating stimuli, inhibitory neurons had less diverse responses than excitatory neurons (Figs. 3​3​–6), showing a weak tuning for orientation and complex-like responses. These results are consistent with studies of the responses of fast-spiking cells (Niell and Stryker, 2008) and parvalbumin-positive neurons (Sohya et al., 2007; Kerlin et al., 2010; Liu et al., 2010; Ma et al., 2010; Zariwala et al., 2011) in mouse visual cortex but do not exclude the possibility that distinct subpopulations of GABAergic neurons may have more diverse properties (Ma et al., 2010; Runyan et al., 2010).

Together, these functional differences suggest that inhibitory neurons may inherit their visual properties by promiscuously summing signals from surrounding excitatory neurons (Kerlin et al., 2010; Bock et al., 2011; Fino and Yuste, 2011). Weak tuning of GABAergic responses in mouse visual cortex could be explained by summing the responses of a range of highly tuned cells. Likewise, complex-like properties could reflect the summing of responses of neurons with overlapping ON and OFF receptive-field subregions. In cat visual cortex, fast-spiking neurons have more diverse response properties. Some of these neurons have been shown to have weak tuning and complex-like receptive fields (Hirsch et al., 2003; Nowak et al., 2008), but orientation-tuned and simple cell responses have also been observed. This difference may reflect the difference in functional architecture between cats and rodents.

In contrast to inhibitory neurons, excitatory neurons in mouse visual cortex showed high diversity. The responses of pairs of neurons to the wavelet stimulus were on average only weakly correlated. Some but not all of this diversity could be attributed to the spatial receptive fields (Figs. 5​5–7). The remainder likely reflects differences in spatiotemporal summation (Fig. 5), additional nonlinear mechanisms (Vinje and Gallant, 2000; Haider et al., 2010), or noise in the measurements. This diversity is reminiscent of that observed in mouse barrel (Sato et al., 2007) and auditory cortices (Bandyopadhyay et al., 2010; Rothschild et al., 2010) where neurons with distinct properties are found next to each other.

The high diversity in local population responses has important implications for coding and decoding by downstream neurons. Theoretical studies suggest that receptive-field diversity may serve to establish a sparse and/or efficient visual code (Barlow, 1961; Simoncelli, 2003). The low correlations we observed are consistent with this hypothesis, though they are not a direct test of it. Studies of decoding also indicate that summing responses of several neurons with similar receptive fields can compensate for response variability (Paradiso, 1988; Vogels and Orban, 1990; Zohary, 1992; Mazurek and Shadlen, 2002; Seriès et al., 2004). We have shown that very few such neurons are likely to exist, let alone project to the same target area. A plausible decoding scheme should therefore consider how to pool responses from diverse populations with little overlap in their tuning properties. Data like those presented here could yield more realistic models of visual processing and allow prediction of psychophysical performance in tasks involving complex visual stimuli.

Local organization of visual cortical populations

We have found little evidence for organization of visual cortical responses at small scales (i.e., the scale of a few tens of micrometers). Spatial receptive fields were locally disorganized (Fig. 6A), and responses of nearby neurons at times differed strongly (Fig. 8). While there was a weak tendency for ON and OFF subregions to fall over distinct regions of the visual field (Fig. 6B) (Smith and Häusser, 2010), receptive fields were otherwise arranged as if they sampled orientation and phase randomly (Fig. 6E).

Receptive fields of nearby cells were scattered over a region of visual space of about half a receptive-field size (Fig. 7). This scatter is about half that inferred by the hand-mapped receptive fields of consecutive units encountered in vertical electrode penetrations (Dräger, 1975) but is on par with the scatter of ON or OFF receptive-field subregions measured with calcium imaging (Smith and Häusser, 2010). This scatter is also consistent with the scatter observed in visual cortex of cats (Das and Gilbert, 1997; DeAngelis et al., 1999; Hetherington and Swindale, 1999) and monkeys (Hubel and Wiesel, 1974; Dow et al., 1981) (ranging from one-quarter to one-half a receptive-field size).

The random organization of orientation preferences remains an unexplained difference between rodents and carnivores or primates, which have well organized orientation maps (Ohki et al., 2005; Van Hooser et al., 2005; Ohki and Reid, 2007). By contrast, retinotopic organization is a common feature of all species studies, and local retinotopic scatter has been well described in cats (DeAngelis et al., 1999). Because local diversity is so prevalent, and cortical maps are so variable, it has been proposed that functional architecture might not be an essential feature of cortical organization (Horton and Adams, 2005).

Despite the random local arrangement, some organization was visible at the scale of <100 μm. Receptive-field similarity and overlap decreased with cortical distance (Figs. 6, ​,77E). As distance over cortex increased, receptive-field azimuth and elevation shifted along two approximately perpendicular axes (Fig. 7B,C), consistent with measurements at coarser scales in the mouse (Dräger, 1975; Schuett et al., 2002; Kalatsky and Stryker, 2003). To our knowledge, these measurements are the first to unambiguously demonstrate the mapping of receptive-field position in a small patch of cortex.

In fact, our results suggest that retinotopy may represent the sole source of tangential organization in mouse visual cortex. Signal correlations fell with cortical distance (Fig. 8F) but were approximately constant across distance once the spatial receptive fields were taken into account (Fig. 8G). While our experiments cannot exclude organization of other stimulus features that are in register with the map of spatial receptive fields, it is likely that we would have been able to detect clustering at other scales. There was little indication for such clustering. Our results only hold for pairwise relationships between neurons. Higher-order patterns of activity have been observed locally in cortex (Ohiorhenuan et al., 2010). In the future, it would be interesting to study these patterns using calcium imaging.

Random stimuli for population imaging

Critical to our experiments was our ability to measure the receptive fields of dense populations of neurons (Fig. 4). Random stimuli are useful to quantify receptive fields (Jones and Palmer, 1987a; Reid and Shapley, 1992; Reid and Alonso, 1995; Reid et al., 1997; Ringach et al., 1997; DeAngelis et al., 1999). These stimuli, however, generally evoke weak responses (Liu et al., 2009; Ma et al., 2010), which may not be reliably detected with in vivo calcium imaging whether due to limitations in signal-to-noise ratio (Göbel and Helmchen, 2007) or to limitations of the calcium indicator (Kerr et al., 2005; Tian et al., 2009). Sparse random stimuli have been successfully applied to measure receptive fields from calcium signals (Smith and Häusser, 2010), but these stimuli can only drive a fraction of the neurons simultaneously. Structured dense stimuli such as natural scenes (Vinje and Gallant, 2000; David et al., 2004) or filtered Gaussian noise (Niell and Stryker, 2008) drive populations more effectively because they stimulate multiple receptive-field subregions from multiple neurons simultaneously. Rather than isotropic noise, our stimuli were made of wavelets, which, like visual cortical receptive fields, are oriented in space and slanted in space-time. This match contributes to the strong calcium responses we have observed (Fig. 4C) and to our ability to measure receptive fields for over half the labeled neurons (Fig. 6B). In contrast to uncorrelated noise, the wavelets are localized in space and in frequency so they can be tailored to stimulate populations with specific tuning properties.