Mice (C57BL/6) of either sex between P15–P25 were deeply anesthetized with isofluorane (Halocarbon). A block of brain containing A1 and the medial geniculate nucleus (MGN) was removed and tangential slices (400 μm thick) were cut on a vibrating microtome (Leica) in ice-cold ACSF containing (in mM): 130 NaCl, 3 KCl, 1.25 KH₂PO₄, 20 NaHCO₃, 10 glucose, 1.3 MgSO₄, 2.5 CaCl₂ (pH 7.35–7.4, in 95% O₂–5% CO₂). Slices were cut by blocking the brain in a direction perpendicular to the thalamocortical cutting angle of 15° (Zhao et al., 2009) and then removing approximately 150 μm from the tangential surface. Before slicing, a cut was made in medial-lateral (ML) direction of the intact brain, at the rostral end of the approximate slice location. This straight cut was used so the slice could be oriented in the recording chamber with respect to the ML and rostral-caudal (RC) directions. The recording location in A1 was confirmed by comparing with the location of intact vasculature on the tangential slice (Figure 1A) and inserting DiI into the remaining hemisphere and confirming retrograde labeling of MBGv (Figure 1B). Tangential visual slices were created by blocking orthogonal to the thalamocortical visual slice angle (MacLean et al., 2006) for a horizontal cutting angle 35° from rostral and a coronal angle 65° relative to the hemispheric midline. Slices were incubated for 1 hour in ACSF at 30°C and then kept at room temperature. For recording, slices were held in a chamber on a fixed stage microscope (Olympus BX51) and superfused (2–4 ml/min) with ACSF at room temperature to reduce spontaneous activity in the slice. 50 μM (2R)-amino-5-phosphonovaleric acid (AP5, NMDA antagonist) was added to reduce excitability for photostimulation experiments performed at 40x magnification.

Whole-cell recordings were performed with a patch clamp amplifier (Multiclamp 700B, Axon Instruments, CA, USA) using pipettes with input resistance of 4–8 MΩ. Data acquisition was performed by National Instruments AD boards and custom software (Ephus; Suter et al., 2010). Ephus (http://www.ephus.org) is written in MATLAB (Mathworks, MA, USA) and was adapted to our setup. Voltages were corrected for an estimated junction potential of 10 mV. Electrodes were filled with (in mM) 115 cesium methanesulfonate (CsCH₃SO₃), 5 NaF, 10 EGTA, 10 HEPES, 15 CsCl, 3.5 MgATP, 3 QX-314 (pH 7.25, 300 mOsm). Biocytin or Neurobiotin (0.5%) was added to the electrode solution as needed. Series resistances were typically 20–25 MΩ.

In order to investigate connectivity of layer 2/3 neurons in A1 relative to the tonotopic axis, we perform LSPS on auditory tangential slices at low magnification (10× objective, allowing a mapped area of approximately 700 × 700 μm). The high spatial mapping resolution of 30 μm relative to the functional resolution of ~100 μm (Viswanathan et al., 2012; see Figure 2) causes activation of a neuron from neighboring spatial locations, and thus represents spatial oversampling. At these distances both EPSCs (Figure 3A, top) as well as IPSCs (Figure 3B, top) could be mapped. Maps of single neurons at this magnification often show more connectivity near the soma, and spatially non-uniform regions of distant input (Figures 3A,B, bottom).

To identify an eventual underlying spatial pattern of connectivity, we first calculate the probability to observe a connection from a particular relative location in space. For the population of recorded neurons we align neurons at their soma with respect to the cardinal axes (ML and RC, see Methods). After alignment, we plot the probability of obtaining an EPSC or IPSC (>8 ms latency) at each stimulus location, which we refer to as the connection probability. The connection probability simply represents the average percent of responses at a particular location relative to the soma divided by the total number of times this position is photostimulated (typically once per recorded neuron). Both mean excitatory (N = 26 cells and N = 7 slices) and inhibitory (N = 24 cells and N = 7 slices) connection probability maps show that inputs can be evoked from a large area (Figures 4A,B). The marginal profiles along the cardinal orientations (ML vs. RC; Figure 4C) show peaks near the soma with connection probability decreasing with increasing radial distance from cell-center. The extent of the excitatory and inhibitory RC marginal is somewhat broader than that of the ML marginals (Figure 4C, arrow). The shape resembles that of a 2D Gaussian, as expected from paired patch recordings (Oswald et al., 2009; Levy and Reyes, 2012). Areas near to the soma show a decrease in connection probability, which is due to the masking of both response types by direct photo-stimulation currents (“doughnut-hole” in the center of maps in Figures 4A,B). Moreover the marginal profiles in the RC and ML directions demonstrate patchiness with some local peaks, particularly in the ML direction. To characterize the decrease in connection probability with distance we plot the connection probability in polar coordinates. The mean radial profile shows that there is significantly greater connection probability within 240 μm from cell-center for both excitatory and inhibitory connections (Figure 4D, left). The angular profiles showed undulations suggesting spatial periodicities (Figure 4D, right). A comparison on the marginal profiles of excitation and inhibition revealed a similar spatial extent with a bias for inhibitory connections to be broader in the RC direction (Figure 4E, arrow).

The individual maps (Figure 3) and marginal distributions (Figures 4C,D) show peaks, suggesting spatial periodicities. We thus investigate whether, on average, neurons demonstrate significant spatial periodicity of inputs and also if significant periodicities show any spatial bias with respect to RC or ML direction. To reveal spatial periodicities, we perform a two-dimensional (2D) Fourier Analysis (FFT) of connection probability maps. The 2D FFT converts an image into spatial frequency components that essentially represent how the original image can be reconstructed as the linear combination of gratings at different periodicities and in different directions (Figure 5). Spatial periodicities will be evident in the FFT maps as significant components in a particular direction (see Methods). If these periodicities are anisotropic, e.g., present in only one direction, then significant FFT components will only be present in one direction. One can convert from significant components at a particular frequency back to the spacing of the peaks in the original map in the same manner as the conversion between time and frequency (for one-dimensional signals). This operation in effect reduces noise in the connection probability map by removing frequency components that are not significant. The significant components in the 2D FFT define the spatial spacing of peaks in the original maps. For example, a significant component in the 2D FFT at 10 mm^-1 represents peaks in the original image at a spacing of 100 μm while a significant component at 5 mm^-1 represents spatial peaks at 200 μm. The spatial periodicity of a grating in a particular direction is simply a single point (two points because of Fourier component symmetry) in the direction of the grating relative to the origin (Figures 5A–C). Thus a grating occurring in one dimension (e.g., along the x-axis) will be represented by two distinct spatial frequency components long the x-axis (Figures 5A,B). A diagonal grating in space would have spatial frequency components in both the x- and y-axes (Figure 5C). A spatial sinusoid in all directions becomes a circle in spatial periodicity with the radius of the circle being larger for higher spatial periodicities (Figure 5D, compare upper and lower). A 2D Gaussian spatial profile transforms into spatial periodicity components that also appear as a 2D Gaussian in spatial frequency space (Figure 5E). Importantly, a Gaussian that is wider in the spatial domain is narrower in spatial frequency domain and vice versa. Thus, an anisotropic 2D Gaussian in space is also anisotropic in frequency but with the wider direction in space being narrower in frequency and vice versa (Figure 5F compare upper and lower).

2D Fast Fourier Transform analysis of excitatory and inhibitory inputs reveals significant components at multiple spatial frequencies (Figure 6A). The central significant components (with the lowest spatial frequency) form a ring, reflecting the central 2D Gaussian distribution of the connection profile (see Figure 4D). 2D FFT analysis of excitatory inputs reveals multiple significant components at higher spatial frequencies (~300 μm), with more components and “hot spots” in the ML directions (Figure 6A). Thus, on average excitatory inputs have anisotropic spatial frequency components, with periodic hot spots of connectivity biased to the ML direction. However, the spatial periodicity of inhibition does not show this same number of high spatial frequency components and only a weak anisotropy of spatial periodicity (Figure 6A). Significant spatial frequency components for inhibition were clustered at low frequencies, indicative of a wide 2D Gaussian, as apparent from the mean connection probability map (Figure 4B). However, the significant components of inhibitory inputs are somewhat more spread in the ML direction consistent with a somewhat wider profile in the RC direction (see Figure 4C).

To visualize the spatial patterns reflected in the significant components we perform an inverse 2D FFT (I2DFFT) on the significant components. This reconstruction thus highlights portions of the spatial structure that are significant based on the bootstrap test (p < 0.05). The reconstructed excitatory connection probability map shows a “doughnut” shape with two areas of high connection probability ~200 μm from the soma in the ML direction (Figure 6B, left, red arrows). The reconstructed inhibitory probability map shows a 2D Gaussian profile (Figure 6B, right). To compare more closely the spatial shape of the reconstructed maps we plot the marginal profiles along the RC and ML direction (Figure 6C). We find that both excitatory and inhibitory profiles are wider (full width at half max excitation: ML 326 μm vs. RC 505 μm; inhibition: ML 288 μm vs. RC 500 μm) in the RC direction than the ML direction indicating an anisotropy in the spatial pattern. This spatial anisotropy is consistent with the anisotropy of the significant spatial frequency components (see Figures 6A and 5D). While the inhibitory marginal shows a Gaussian shape, the excitatory marginal shows a widening in the caudal direction. To investigate this further we separate the central spatial components (<3 mm^-1 spatial frequency), which have large amplitudes and thus dominate the profile. Plotting the connection probability map for the central components shows the spatial profile of the central (<3 mm^-1) 2D Gaussian (Figure 6D). Both the excitatory and inhibitory profiles are elongated in the RC direction (red circles), which is also evident from the broader marginal profiles in the RC direction than the ML direction (Figure 6E; full width at half max excitation: ML 282 μm vs. RC 516 μm; inhibition: ML 288 μm vs. RC 510 μm). We then re-plot the connection probability maps for the higher spatial frequency components. The excitatory map shows the large peaks in the ML direction visible before, but also additional smaller amplitude peaks ~350 μm in RC from the soma (Figure 6F, arrows). In contrast after removal of the central components, the inhibitory connection probability map does not show any additional peaks. The marginal profiles also show the spatial periodicity with a period of ~350 μm in RC and ~300 μm in ML (Figure 6G). Together these analyses show that the intralaminar connection probability in layer 2/3 of A1 is spatially anisotropic and also shows spatially anisotropic connectivity peaks visible as periodicities in the 2DFFT. These periodicities have a spatial frequency of ~300–350 μm.

The above analysis focuses on connection probability. However, inputs originating from certain spatial locations might have different synaptic strengths. We investigate this hypothesis by calculating the spatial distribution of event amplitudes, measured as average normalized total charge (normalized per single map), which we refer to as mean strength maps. Connection probability is the total number of times an event occurred at a photostimulation location divided by the total number of times that location was photostimulated over all recorded neurons, whereas mean strength is the mean transferred charge for events that occurred at a photostimulation location. These maps (Figures 7A,B) are sparser (since average amplitudes can only be computed where significant connection probability exists) but also patchy, indicating that connections from certain relative positions are particularly strong (for example ~100 μm in RC direction). The marginal distributions are largely overlapping, indicating little spatial anisotropy in connection strength (Figure 7C). Excitatory and inhibitory connection strength decrease as a function of radial distance (Figures 7C,D). The angular maps show peaks, consistent with the hot spots in the connection maps (Figures 7A,B). The inhibitory and excitatory peaks are present at different angles. Together this suggests that excitatory input strength decreases uniformly with distance but hot spots occur at some angular orientations. When compared, inhibition shows more asymmetry in the RC and ML directions than excitation (Figure 7E).

Spatial periodicity analysis of mean strength maps shows significant high spatial frequency components for excitatory inputs offset in the ML and RC direction, indicating anisotropy (Figure 8A), consistent with the connection probability maps (Figure 6A). The reconstructed map of excitatory mean strength (Figure 8B) and marginal distributions (Figure 8C) shows the overall isotropic low spatial frequency decrease in strength (Figures 8D,E, red circles). This is in contrast to the anisotropy observed in spatial connection probability (Figure 6C). Moreover, the reconstructed map of excitatory mean strength (Figure 8B) and marginal distributions (Figure 8C) also shows that the areas of high mean strength form diagonal lobes. This feature becomes even more evident when the central components are removed (Figure 8F, red arrows, 8G). Thus excitatory inputs originating from a band angled ~30 degrees in the ML directions are of higher strength. Inhibitory spatial periodicities show high frequency components, but without spatial bias (Figures 8A,B,D). While the lack of spatial bias was consistent with the dominant 2D Gaussian pattern also seen in the connection probability (Figure 6A), the largest components were not closest to the soma but where of higher frequency. This is likely due to the fact that inhibitory inputs close to the soma are reduced because of shunting due to direct activation of the neuron. When the central components are subtracted ~150 μm wide bands of high mean strength become visible in the RC and ML orientations.

Our results show periodic regions of higher connection probability along the isofrequency and tonotopic direction. To investigate if this anisotropy of spatial periodicity is reflected by the underlying dendritic architecture, we investigate if proximal dendritic trees showed significant spatial or spatial periodicity patterning. We use the spatial pattern of the direct response recorded while photostimulating at 40× magnification in order to characterize the shape of the proximal dendritic tree. Evoked excitatory responses close to the soma or proximal dendrites are masked by the direct response (see Figure 2) allowing us to measure the spatial extent of the proximal dendritic tree. We create average maps analogous to connection probability, but instead of connection probability these maps indicate the probability of a direct response at each location relative to the soma. The resulting maps (Figures 9A,B) and marginal profiles (Figure 9C) reveal a roughly symmetric pattern, thus indicating that the basal dendrites of layer 2/3 neurons in A1 (N = 33) show no spatial anisotropy. The radial profile demonstrates decreased probability as a function of distance, consistent with decreased dendritic density and attenuation of the direct dendritic response (Figure 9D). The angular profile is consistent with the rostral-lateral bias from the RC and ML profiles (Figure 9D). We also perform the spatial periodicity analysis with the direct probability maps. We find that the significant components of the 2D FFT are also spatially symmetric (Figure 9E). The spatial periodicity shows significant components (p < 0.05, red pixels) in all directions, also visible in the angular profile (Figure 9D). Together our data indicate that on average there is no spatial or spatial periodicity anisotropies of dendritic orientation in A1.

In order to test whether the absence of a spatial arrangement of basal dendritic arbors was specific to auditory cortex or was a general cortical feature, we also record from layer 2/3 neurons in tangential slices of primary visual cortex (V1). These slices are created by cutting perpendicularly to the thalamocortical V1 slice preparation (MacLean et al., 2006). Average direct response probability maps (N = 20 neurons) demonstrate a similar result as those in A1, with a roughly spatially symmetric pattern (Figures 9B–D). Similar to A1, V1 marginal profiles show a symmetric periodic structure (Figure 9F). The spatial frequency components in V1 are smaller than those in A1 with significant components being 200 μm in V1 and 100–200 μm in A1, implying a wider spatial extent of the basal dendritic tree in V1 vs. A1.

We next investigate whether inhibitory maps in A1 and V1 have similar or different spatial anisotropies. While inhibitory maps recorded near the soma of individual neurons are patchy (Figures 2B,C), inhibitory connection probability maps (at 40× magnification, 200 × 200 μm) from A1 (N = 31 cells, N = 14 slices) and V1 (N = 20 cells, N = 14 slices) are roughly spatially symmetric (Figures 10A,B). Marginal profiles of A1 mean inhibitory connection probability maps demonstrate a slight bias toward the lateral direction (Figure 10C). This bias is not present in the RC direction. Outside of the area of direct activation where inhibitory currents are potentially masked by direct currents, the radial profile demonstrates a decrease in connection probability with distance (Figure 10D), consistent with previous studies (Oswald et al., 2009). Marginal profiles of V1 inhibitory maps also demonstrate symmetry in the RC and ML directions (Figure 10C). We fit the radial profiles (Figure 10D) with a single exponential decay function after the peak and the decay constant for A1 (λ = 207 μm) is about twice as long as that for V1 (λ = 112 μm). Thus the radial falloff of connection probability is much wider for A1 compared to V1, indicating a wider extent of inhibitory inputs in A1.

We next perform the spatial periodicity analysis to test if, on average, local inhibitory inputs demonstrated significant repeating areas of high input probability. The 2D FFT of the A1 mean inhibitory map shows significant components (p < 0.05) along the ML (isofrequency) direction (Figure 10E). This suggests that locally A1 layer 2/3 neurons receive functional inhibitory synaptic inputs from locations that are spatially non-uniform, with a periodic structure of high inhibitory connection probability in the isofrequency direction. In contrast to A1 mean maps, V1 mean maps do not show anisotropy of significant spatial periodicity (Figure 10F). Together these results show a distinct difference in the spatial distribution of inhibitory connections in A1 and V1 (Figures 10G,H).

Similar to our analysis of maps obtained under 10× magnification, we also calculate inhibitory mean strength maps recorded at 40×. A1 and V1 maps are relatively symmetric in space (Figures 11A,B). V1 maps of connection strength show the same degree of symmetry as for connection probability in the RC and ML marginal profiles (Figure 11C). Radial marginal profiles indicate a significant peak at 104 μm from cell-center for A1 but not for V1 (Figure 11D). Although the peak of inhibitory mean strength in the radial profile is further out than for connection probability, the spatial decay from this point out is still steeper for V1 (λ = 43 μm) than for A1 (λ = 148 μm), consistent with the radial profiles of connection probability (Figure 10D). We also calculate 2D FFT of the mean connection strength maps. Increased patchiness of the mean strength relative to connection probabilities for A1 is reflected in significant components in the RC direction (Figure 11E). Mean strength maps for V1 are symmetric in spatial frequency (Figure 11F). Thus overall A1 is patchier than V1 in connection probability and in connection strength (Figures 10G,H and 11G,H). Yet the anisotropy of connectivity in A1 is more ML for mean connection probability and more RC for mean strength. Part of this may have been due to a larger masking effect on inhibitory inputs by direct responses (compare sizes of “doughnut hole” in Figures 10A and 11A), making the connection probability a more reliable metric of overall anisotropy than mean strength.