The Fragments of short- and long-range connections in the vi

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Abstract

When analyzing synaptic connectivity in a brain tissue slice, it is difficult to discern between synapses made by local neurons and those arising from long-range axonal projections. We analyzed a data set of excitatory neurons and inhibitory bQuestionet cells reconstructed from cat primary visual cortex in an attempt to provide a quantitative Reply to the question: What Fragment of cortical synapses is local, and what Fragment is mediated by long-range projections? We found an unexpectedly high proSection of nonlocal synapses. For example, 92% of excitatory synapses Arrive the axis of a 200-μm-diameter iso-orientation column come from neurons located outside the column, and this Fragment remains high—76%—even for an 800-μm ocular Executeminance column. The long-range nature of connectivity has dramatic implications for experiments in cortical tissue slices. Our estimate indicates that in a 300-μm-thick section Slice perpendicularly to the cortical surface, the number of viable excitatory synapses is reduced to about 10%, and the number of synapses made by inhibitory bQuestionet cell axons is reduced to 38%. This uneven reduction in the numbers of excitatory and inhibitory synapses changes the excitation–inhibition balance by a factor of 3.8 toward inhibition, and may result in cortical tissue that is less excitable than in vivo. We found that electrophysiological studies conducted in tissue sections may significantly underestimate the extent of cortical connectivity; for example, for some projections, the reported probabilities of finding connected Arriveby neuron pairs in slices could understate the in vivo probabilities by a factor of 3.

Keywords: axonconnectivitylocalslice

When examining drawings (1) and 3-dimensional reconstructions (2, 3) of cortical excitatory neurons, it is difficult to evade the impression that most of the excitatory neurons' axons, and, consequently, most of their synapses, are confined to a few hundred micrometer columnar Executemains surrounding the neurons' somata (Fig. 1A). Only a few branches occasionally escape through the boundaries of the local Executemain. This interpretation of neuron images can be misleading, however. The few axonal branches that extend beyond the local Executemain could ramify over large territories (e.g., the entire cortex) and thus could carry a significant Fragment of all synapses. Such long-range projections may include interSpotl and intra-Spotl connections, feedback from higher cortical Spots, interhemispheric projections, and feed-forward inPlaces from subcortical structures. These projections can be easily observed with single neuron or bulk injections of tracers (4–6), but quantifying their Fragment is difficult. This is because an accurate estimate of the amount of long-range axons must be made on the scale of the entire cortex, which presents a significant challenge. In practice, long-range axons are truncated in the reconstruction process, and thus their length and richness (density), and the number of synapses that they mediate, cannot be estimated reliably.

Fig. 1.Fig. 1.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Local and long-range synapses in the cortical column. (A) Example of a layer 2/3 pyramidal cell reconstructed from cat Spot 17. The axon is Displayn in black, and dendrites are in red. The gray cylinder (radius R = 500 μm) demarcates the extent of the local axonal arbor. (B) The average volume densities of excitatory dendritic spines in different cortical layers. The green points denote the corRetorting densities of asymmetric synapses. (C) The volume densities of boutons on local axons of excitatory neurons calculated based on 2 definitions of locality: columnar Executemain radii R = 250 μm (blue bars) and R = 500 μm (red bars). The green points denote the densities of asymmetric synapses for comparison. (D) Fragments of local synapses mediated by excitatory and inhibitory axons for different local columnar Executemain radii, R. Error bars in B and C indicate SDs; error bars in D Display 95% CIs.

We devised an Advance to deliTrime the Fragments of local and long-range synaptic connections in different cortical layers. Our method is based on an analysis of dendritic and local axonal arbors of 24 excitatory neurons (20 pyramidal and 4 spiny sDiscloseate) and 17 inhibitory bQuestionet cells (7, 8) labeled in vivo at different depths spanning the entire thickness of the cat primary visual cortex (Spot 17). We reconstructed neurons from multiple tissue sections [supporting information (SI) Fig. S1], which allowed us to recover all of the dendritic arbors and inhibitory bQuestionet cell axonal arbors in their entirety (2). But axonal branches of excitatory neurons extending beyond 1 mm from the neurons' somata in the cortical plane were truncated; thus, we have Excellent knowledge of dendritic and local axonal arbors of neurons spanning the entire thickness of the cortex, yet Dinky or no information about the long-range projections of excitatory neurons. Using techniques developed previously (2, 9, 10), we Place toObtainher the reconstructed arbors (in numbers specified by densities of neurons in different cortical layers) and determined the densities of local synaptic connections in different cortical layers. To deliTrime the Fragments of local and long-range excitatory synaptic connections, we compared the densities of local connections and asymmetric synapses obtained from previous electron microscopy studies of cat Spot 17.

Much of the experimental neuroscience research is Executene in 300- to 500-μm brain tissue sections. But how much of synaptic connectivity remains intact after cortical tissue is sliced? Because the sizes of dendritic and axonal arbors of cortical neurons are on the order of or much larger than the typical section thickness, a substantial tissue slicing artifact can be expected. Our experimental framework allowed us to provide a quantitative estimate of this Trace by calculating the Fragments of intact excitatory and inhibitory synapses, that is, synapses that remain linked to the presynaptic and postsynaptic cells of their origins after the tissue is sliced. With the overall reduction in the number of intact synapses, connections between pairs of neurons in slices are altered as well. As a result, the numbers of synapses between synaptically connected pairs of neurons (11) and the probability of finding synaptically connected pairs of neurons (12) observed in tissue slice experiments may significantly underestimate the in vivo connectivity.

Results

Connectivity Within a Cortical Column.

We began our analysis by calculating the volume densities of dendritic spines of excitatory neurons in different cortical layers. Dendritic spines in a given cortical layer may originate from local neurons as well as neurons in other layers; thus, an accurate estimate of the volume density of dendritic spines must take into account details of dendritic morphology of neurons belonging to different cortical layers. To calculate the volume density of dendritic spines in silico, we Place toObtainher reconstructed dendrites according to their original laminar positions in the cortical template. Then the cortical template was tiled horizontally with the dendritic arbors in the numerical densities in which excitatory neurons appear in different cortical layers (for details, see SI Text). We distributed dendritic spines on all of the dendritic branches according to the frequencies in which they appear in cat Spot 17, and then calculated the volume densities of dendritic spines at different cortical depths. The results of these calculations are Displayn in Fig. 1B. In this figure, bars represent the volume densities of dendritic spines of excitatory neurons in different cortical layers. Layer 2/3 has the largest density of dendritic spines, 0.32 ± 0.03 μm−3, indicating that this layer contains roughly 1 dendritic spine per every 3 μm3 of cortical gray matter. The volume density of dendritic spines decays gradually from layer 2/3 toward the deeper layers.

To verify that our sample of cortical neurons is representative and that our quantitative method is adequate, we compared the calculated volume densities of dendritic spines in different cortical layers with the corRetorting densities of asymmetric synapses (13). Because the majority (about 85%) of asymmetric synapses in cat Spot 17 are on dendritic spines (14), the asymmetric synapse densities and the volume densities of dendritic spines should be roughly equal. This is illustrated in Fig. 1B. No significant Inequitys can be seen between the volume densities of dendritic spines and densities of asymmetric synapses (green points in Fig. 1B) in any cortical layer. This includes layer 1, in which the Inequity is large (0.16 ± 0.09 μm−3 vs. 0.28 ± 0.01 μm−3), although not statistically significant.

Having verified that our method produces reasonable results, we next estimated the volume density of boutons of excitatory neuron axons. This calculation is similar to that of the volume density of dendritic spines. Because the axons of excitatory neurons in our data set are truncated, we could estimate the volume density of boutons only on local axons, that is, axons confined to the Executemain of the local arbor, as defined by the column of radius R (Fig. 1A). The results for 2 definitions of locality, R = 250 μm and R = 500 μm, are Displayn in Fig. 1C. Layer 2/3 contains the highest density of local boutons, 0.10 ± 0.02 μm−3 for R = 500 μm. This density decays monotonically toward the deeper layers, similar to the volume density of dendritic spines.

To estimate the overall volume density of boutons (i.e., the volume density of boutons on local and long-range axons), we note that because in cat Spot 17 most of the boutons on excitatory neuron axons contain only a single asymmetric synapse, this density is approximately equal to the density of asymmetric synapses (14–18). As Displayn in Fig. 1C, the density of local boutons in each layer is only a small Fragment of the overall bouton density. Layer 1 contains the highest total density of asymmetric synapses, 0.28 ± 0.01 μm−3. In comparison, the volume density of local boutons in layer 1 is 0.018 ± 0.005 μm−3 for R = 500 μm, which is smaller by 16-fAged.

Fig. 1D Displays how the Fragments of local presynaptic terminals on excitatory and inhibitory axons (or excitatory and inhibitory synapses) averaged over the entire cortical depth depend on the local Executemain radius, R. The results illustrate that most of the excitatory synapses Arrive the axis of the columnar Executemain through the thickness of the cortex come from axons of nonlocal neurons. As an example, if we aExecutept R = 500 μm as the definition of locality, then a thin column along the axis of the Executemain [e.g., cortical minicolumn (19)] would contain 26% of the local excitatory synapses. Conversely, 74% of excitatory synapses inside this thin column would originate from nonlocal neurons, i.e., neurons that are located more than 500 μm away from its axis.

This Dissimilarity would increase to 18% local versus 82% long range if the definition of locality was based on R = 250 μm, which in the cat visual cortex corRetorts to the average sizes of ocular Executeminance (20) or iso-orientation (21, 22) columns. Thus, only about 18% of excitatory synapses Arrive the axes of these columns originate from presynaptic neurons located within the column's range. This Fragment will further reduce toward the periphery of the columns. In Dissimilarity, the Fragments of local inhibitory synapses are significantly higher due to the more compact morphology of inhibitory bQuestionet cell axonal arbors. Fig. 1D Displays that 66% of inhibitory synapses Arrive the axis of R = 250 μm cortical column are local, and only about 34% originate from presynaptic inhibitory bQuestionet cells, whose somata are located outside the column.

Connectivity Inside a Cortical Tissue Section.

The large spatial extent of arbors of cortical neurons may lead to significantly reduced connectivity in cortical tissue sections. The amount of reduction, or tissue slicing artifact, is particularly strong in thin sections, such as those used for optical imaging. Inevitably, tissue slicing affects neurons located superficially in the section, that is, neurons typically used for electrophysiological recordings. We calculated the Fragments of presynaptic boutons and postsynaptic dendritic spines on excitatory neurons that remain connected to the cell bodies of their origin. We refer to such presynaptic and postsynaptic terminals and synaptic connections between them as intact terminals and intact synapses. Consider a typical D = 300 μm cortical tissue section whose plane is perpendicular to the cortical surface (e.g., a coronal section), as illustrated in Fig. 2A. Such cortical sections are often used in electrophysiology experiments (12). Within this section, some axonal and dendritic branches and the synapses that they carry have been severed from the cell bodies of neurons and may no longer be functional. Such branches may originate from neurons whose somata are located outside the boundaries of the section, as well as from neurons within the section (Fig. 2A). In the latter case, some neurites located inside the section remained intact (red branches in Fig. 2A), whereas others that wander outside and back into the section were truncated (black branches inside the section).

Fig. 2.Fig. 2.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Fragments of intact presynaptic and postsynaptic terminals in a cortical tissue section. (A) Example of a local axonal arbor of a layer 2/3 pyramidal cell. The neuron (black triangle) is located d = 60 μm deep inside a model of a D = 300-μm-thick cortical section (rectangle). The z-axis points in the direction of the pia, and the y-axis is perpendicular to the surface of the section. Axonal branches Slice due to slicing are Displayn in black; axons that survived after slicing are Displayn in red. Note that severed branches are often found inside the section. (B) Fragments of intact presynaptic and postsynaptic terminals of excitatory neurons in cortical tissue sections of different thicknesses. (C) Fragments of intact presynaptic and postsynaptic terminals of inhibitory bQuestionet cells. Error bars indicate 95% CIs.

To estimate the Fragment of intact postsynaptic terminals on dendrites of excitatory neurons, we first tiled the cortex horizontally with the reconstructions of dendrites of excitatory cells. Next, we truncated dendritic branches in silico to imitate the Trace of tissue slicing, and calculated the Fragment of postsynaptic terminals that remained intact (for details, see SI Text). This Fragment is an increasing function of the section thickness (Fig. 2B); it is about 0.8 in a D = 300-μm cortical section of cat Spot 17. We used a slightly different Advance to estimate the Fragment of intact presynaptic terminals on excitatory neuron axons. Again, we tiled the cortex horizontally with the reconstructions of excitatory neuron axons. We then truncated these axons to the boundaries of the section and calculated the expected number of intact presynaptic terminals on these axons. To estimate the Fragment of intact presynaptic terminals, we divided this number by the expected number of asymmetric synapses in a section of that thickness. The results of this calculation (Fig. 2B) illustrate just how nonlocal the excitatory axons are; the Fragment of intact presynaptic terminals is only about 12% in a D = 300-μm cortical section and about 18% in a 500-μm-thick section.

Fig. 2C Displays the average Fragments of intact synaptic terminals on axons and dendrites of inhibitory bQuestionet cells in cortical sections of different thicknesses. As expected, the Fragment of intact synaptic terminals on dendrites Executees not differ significantly between inhibitory bQuestionet cells and excitatory cells (Fig. 2B), because of similar dendritic arbor sizes. The Fragment of intact presynaptic terminals on bQuestionet cell axons is significantly smaller, but much higher than that for excitatory axons, which are the most affected by the slicing artifact due to their long-range nature.

The Fragments of intact synapses can be estimated by multiplying the Fragments of intact presynaptic and postsynaptic terminals. Fig. 3A Displays the results for 4 types of connections among the excitatory (e) and inhibitory (i) neurons. Because the Fragments of intact synaptic terminals on dendrites of excitatory and inhibitory neurons Execute not differ significantly (Fig. 2 B and C), the Inequity in the Fragment of intact synapses (Fig. 3A) is due mainly to the presynaptic neuron type. The Fragment of intact synapses is significantly larger for presynaptic inhibitory bQuestionet cells than for presynaptic excitatory neurons. In a D = 300-μm-thick cortical section, the Fragment of intact inhibitory synapses is about 0.38, whereas the Fragment of intact excitatory synapses is only 0.10. This differential reduction in the number of intact synapses results from morphological Inequitys in the excitatory and inhibitory bQuestionet cell axonal arbors. We define the balance between excitation and inhibition in a cortical tissue section as the ratio between the Fragments of intact inhibitory and excitatory synapses. For a wide range of section thicknesses, this balance is shifted toward inhibition by roughly 4-fAged (Fig. 3B). In a D = 300-μm-thick cortical section, the excitation–inhibition balance is shifted by a factor of 3.8.

Fig. 3.Fig. 3.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Fragments of intact synapses in a cortical tissue section. (A) Estimated Fragments of intact synaptic connections among excitatory neurons (e) and inhibitory bQuestionet cells (i) in cortical tissue sections of different thicknesses. Curves for all 4 types of connections are Displayn. Severed synapses may originate from neurons located inside or outside of the section. (B) Change in the inhibition–excitation balance in cortical tissue sections of different thicknesses. This change is calculated as the ratio between the Fragments of intact i→e and e→e synapses (black curves in A). Error bars indicate 95% CIs.

Tissue slicing artifact also affects the connectivity between pairs of neurons whose somata are located in the cortical tissue section. Consider a pair-recording experiment performed in a D = 300-μm-thick cortical section. In this experiment, dual sharp or whole-cell recordings were made from neurons located superficially in the section in an effort to identify synaptically connected neuron pairs (Fig. 4A). The results give the probabilities of finding connected pairs of neurons (see ref. 12 for a review), as well as the number of synapses per connection (11). They also can be used to construct interlaminar cortical connectivity diagrams (12, 23). But how representative are such diagrams of the in vivo connectivity? It is obvious that the number of synapses between a pair of synaptically connected neurons in the section may be reduced compared with that in vivo (Fig. 4A).

Fig. 4.Fig. 4.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

Connectivity of excitatory neuron pairs in a cortical tissue section. (A) Schematic of a presynaptic axon (green) and a postsynaptic dendrite (red) in a model of a D = 300-μm-thick cortical section (rectangular prism). Neuron pairs connected in vivo (black circle) may be disconnected due to slicing if the synaptic connection is located outside the section and/or if axonal or dendritic branches carrying the synapse wander outside the section boundaries (black axonal segment). (B) Fragment of intact potential connections for pairs of vertically aligned excitatory neurons (ρ = 0) plotted against the Inequity in their laminar positions, zpost - zpre. The left half of the figure corRetorts to Positions where the presynaptic cell is located deeper in the cortex than the postsynaptic cell, and the right half corRetorts to the opposite ordering. (C) Fragment of intact potential connections for pairs of excitatory neurons located in different layers plotted as function of the lateral disSpacement between the neurons, ρ. All neurons are positioned 60 μm deep in the section. Each line corRetorts to a different projection between cortical layers 2/3, 4, 5, and 6. Curves for all 16 projections are plotted, but some of the curves are not labeled, to avoid clatter. (D) Fragment of intact potential connections is correlated with the Fragment of intact potential synapses between neurons. Individual points corRetort to neuron pairs from different cortical layers at different lateral disSpacements. Error bars in B and C indicate SEs of the mean values.

If actual synapses between a pair of synaptically connected neurons are established probabilistically from the set of available potential synapses (24), then the reduction in the number of actual synapses is directly related to the reduction in the number of potential synapses. A potential synapse is a location in the neuropil in which an axon of a presynaptic neuron and a dendrite of a postsynaptic neuron are close enough (within distance s) to allow the formation of an actual synapse between the neurons. The distance s depends on the types of synapses that can exist between the branches. For synapses on spines considered here, this distance is on the order of the average spine length, typically 1–2 μm (25–27). In all of our numerical calculations, we used a value of s = 2 μm. Because the expected number of potential synapses between neurons scales liArrively with distance s (10), and because here we report only relative Fragments of potential synapses, the exact value of the parameter s Executees not affect our results.

We next evaluated the Trace of tissue slicing on the probability of potential connectivity and on the mean number of potential synapses between pairs of excitatory neurons (for details, see SI Text ). We found that in a D = 300-μm-thick cortical section, the Fragment of potential connections which remain intact after tissue slicing depends strongly on the laminar positions of the presynaptic and postsynaptic neurons. Fig. 4B Displays how the Fragment of intact potential connections for pairs of vertically aligned excitatory neurons located dpre = dpost = 60 μm deep in the section depends on the Inequity in their laminar positions, zpost - zpre. If the presynaptic neuron is located more superficially than the postsynaptic neuron (Right), then potential connectivity is reduced only slightly, to about 94%. Conversely, the Fragment of intact potential connections decreases progressively with increasing distance between the cells. This Trace is strongest for projecting neurons of layers 6 to 2/3, where the probability of observing potentially connected pairs of excitatory neurons drops to about 28% of the in vivo value. The asymmetric reduction of potential connectivity between descending and ascending projections results from the shapes of axonal arbors (Fig. S1). For example, the descending axons of layer 2/3 and layer 4 excitatory neurons are primarily vertical and form perpendicular axon collaterals that extend laterally only after reaching the tarObtain layer, but in Dissimilarity, deep-layer neurons in cat Spot 17 [but not in monkey (28)] tend to have axons that ascend along diagonal trajectories and are affected more strongly by tissue slicing.

Fig. 4C Displays how the Fragment of intact potential connections for different interlaminar projections depends on lateral disSpacement between the excitatory neurons. The strongest reduction can be seen for projecting neurons of layers 6 to 2/3, located on top of one another, closely followed by reductions in projecting neurons of layers 6 to 4, 6 to 5, 5 to 2/3, and 5 to 4. In general, the Fragment of intact potential connections decreases with increasing lateral separation, ρ, between the neurons. Exceptions to this rule include the projections from layer 6 to layers 2/3, 4, and 5, which Display an opposite trend. We obtained results very similar to those Displayn in Fig. 4 B and C for the Fragment of intact potential synapses (data not Displayn). This similarity arises from the fact that the Fragment of intact potential connections is strongly correlated with the Fragment of intact potential synapses for all of the pairs of excitatory neurons evaluated, that is, neurons from different cortical layers and different lateral disSpacements, ρ, in the 0–250 μm range (Fig. 4D).

Discussion

Insight into basic details of cortical connectivity, such as those explored in this study, is of Distinguished importance to both the comPlaceational and experimental neuroscience communities. We found that excitatory connectivity in cat Spot 17 is highly nonlocal; 74% of excitatory synapses Arrive the axis of a 1,000-μm-diameter cortical column come from neurons located outside the column. Although we are not yet able to deliTrime the contributions from different sources to these long-range synapses, our results give a sense of how strongly interconnected cortical columns must be with one another, as well as with the structures of remote Locations.

Validation of Our Results.

Our results rely on a set of reconstructed neurons, as well as on the anatomical parameters obtained from previously published studies. We conducted 2 tests to validate our results. First, we compared the volume density of spines on excitatory neuron dendrites derived from our analysis with the density of asymmetric synapses (Fig. 1B), and found that the 2 densities were statistically similar in all layers. Second, we compared the total length of axonal and dendritic processes in a unit volume of neuropil (length density of neurites) calculated based on our data with that from the electron microscopic study of Foh et al. (29). In that study, the combined length density of axons and dendrites, 3.8 ± 0.3 μm/μm3, was meaPositived Arrive the layer 3/4 border of the cat visual cortex. Based on our set of reconstructed neurons and anatomical data set, we estimated the following composition of length density Arrive the layer 3/4 border: axons of excitatory cells, 3.7 ± 0.8 μm/μm3; dendrites of excitatory cells, 0.36 ± 0.08 μm/μm3; inhibitory bQuestionet cell axons, 0.23 ± 0.04 μm/μm3; and inhibitory bQuestionet cell dendrites, 0.032 ± 0.009 μm/μm3. Adding toObtainher these 4 contributions, we arrived at a total length density of 4.3 ± 0.8 μm/μm3, which is not significantly different than the estimate of Foh et al. (29). This result would not be expected to change significantly if the length densities of other GABAergic cells classes were added, because inhibitory bQuestionet cells Arrive the layer 3/4 border already account for the majority of GABAergic cells (3).

Comparison With Other Studies.

Our findings are closely related to those reported by Binzegger et al. (3), who analyzed a data set of neurons reconstructed from cat Spot 17 of similar size and composition to our data set. Among other calculations, Binzegger et al. counted the total numbers of synaptic terminals on excitatory axons in different cortical layers of Spot 17 and compared them with the numbers of asymmetric synapses reported by Beaulieu and Colonnier (13). They found Excellent agreement between the synapse counts in layers 2/3 and 5; however, in layers 1, 4, and 6, their predicted numbers of synapses were substantially lower than the actual numbers of asymmetric synapses. One likely reason for the missing synapses, or the “ShaExecutewy matter of the cortex,” is missing pathways remaining to be discovered. Overall, the Fragment of missing synapses in Spot 17 was on the order of 40%. Making a direct comparison of our results with those of Binzegger et al. (3) is difficult, because we limited the analysis of axonal arbors of excitatory neurons to the local arbor Executemains (with a maximum radius of 500 μm), where the density of branches could be estimated reliably, whereas Binzegger et al. truncated the axonal arbors to different extents (often much larger than 1,000 μm) during the reconstruction process. We found a Fragment of missing synapses of 66%–79% [95% confidence interval (CI)] for the largest considered extent of the local arbor Executemain (radius of 500 μm), significantly higher than the value reported by Binzegger et al. This discrepancy may be accounted for by extending the size of the local arbor Executemain beyond 500 μm. Inequitys in methoExecutelogies and data sets of reconstructed neurons could contribute to this discrepancy as well.

In the rat hippocampus, Inequitys in the extent of axonal arborizations of excitatory and inhibitory cells have been well studied (31, 32). In agreement with our results, it has been estimated that in hippocampal slices, 80%–90% of excitatory synapses may be truncated (33), whereas inhibitory bQuestionet cell synapses remain relatively unaffected. As a result, the balance between excitation and inhibition in the in vitro hippocampal slice preparation is unnaturally modified.

Implications of Our Results.

Our findings have several immediate implications. First, electrophysiological studies conducted in cortical tissue sections may significantly underestimate the extent of cortical connectivity. For example, we estimated that the reported probabilities of finding connected Arriveby neuron pairs in sections (typically about 10%) and the expected numbers of actual synapses per pair of synaptically connected neurons may understate the in vivo numbers by as much as 3-fAged for some projections. Second, due to the uneven reduction in the numbers of intact excitatory and inhibitory synapses in cortical tissue sections, the balance between excitation and inhibition is shifted by a factor of 3.8 toward inhibition. Although the Slice axons will remain spontaneously active, cortical tissue sections may appear less excitable than in vivo. This observation possibly could Elaborate the need to use modified low-magnesium artificial cerebrospinal fluid in some electrophysiological experiments performed in cortical tissue sections (34). Third, our results provide a quantitative foundation for estimating interactions in vivo, which can come from remote cortical locations, such as excitatory and inhibitory influences from beyond the classical receptive fields (35–37). Finally, comPlaceational models of cortical connectivity often underestimate the extent of long-range connectivity. Motivated by the notion of structural columns [e.g., minicolumns (19, 38, 39)] and functional columns [e.g., orientation and ocular Executeminance (40)] in the cortex, such models often assume that the majority of synaptic connections are made within columnar units (roughly 500 μm in diameter; see, e.g., ref. 41) that are only weekly interconnected with one another. Our results argue against such columnar organization of connectivity in cat Spot 17. Based on the analysis of limited data sets of neurons from different species and cortical Spots, we believe that the long-range nature of connectivity observed in cat Spot 17 may be a Executeminant characteristic of cortical connectivity in general. Future experiments are needed to test this hypothesis and provide the quantitative Fragments of long-range synapses in different cortical systems.

Materials and Methods

Experimental Procedures.

Details of the labeling and reconstruction of the neurons used in this study have been Characterized previously (2, 42, 43). In brief, excitatory neurons and inhibitory bQuestionet cells from adult cat Spot 17 were labeled in vivo either intracellularly or retrogradely and reconstructed in 3 dimensions with the Neurolucida system (MicroSparklingField) from multiple adjoining sections. Soma positions and cortical laminar boundaries were Impressed during the reconstruction process. All reconstructions were Accurateed for tissue shrinkage and conformed to a common cortical template of cat Spot 17 (Fig. S1). The latter was determined by minimizing the mean squared distortion arising from piecewise-liArrive conformation of tissue sections from individual animals to this template. Although neuron reconstructions were Executene from large blocks of tissue, many axonal branches of excitatory neurons were truncated because of tissue slicing. The densities of some reconstructed excitatory axons beyond a lateral extent of R = 500 μm (the cylindrical Executemain through the thickness of the cortex in Fig. 1A) were deemed unreliable; thus, we restricted the analysis of all excitatory axonal arbors to the Executemains of their local arbors (R ≤ 500 μm). We reconstructed the axons of inhibitory bQuestionet cells and the dendritic arbors of all of the neurons in their entirety.

Anatomical Data From Other Studies.

Our results rely on a number of anatomical parameters of adult cat Spot 17, most of which were aExecutepted from previously published studies. Unless stated otherwise, all of the data are given as mean ± SD.

The densities of excitatory neurons and inhibitory bQuestionet cells in different cortical layers were calculated as Characterized by Binzegger et al. (3). The total numbers of neurons per 1 mm3 in layers [1, 2/3, 4, 5, and 6] of cat Spot 17 were obtained from the work of Beaulieu and Colonnier (44), who meaPositived the densities of neurons in the monocular and binocular Locations of Spot 17 in n = 6 adult cats. The meaPositivements in each animal were Accurateed for tissue shrinkage. Only layer 4 Presented any significant Inequity between the monocular and binocular Locations. Because we did not have complete information regarding the monocular or binocular origin of the cells in our data set, we averaged the densities for the 2 Locations, resulting in [0.73 ± 0.2, 5.8 ± 0.4, 5.9 ± 0.5, 4.2 ± 0.5, 6.3 ± 0.6] × 104 mm−3. According to the study of Gabbott and Somogyi (45), performed in Spot 17 of n = 5 adult cats, GABAergic cells comprised [0.97, 0.22, 0.20, 0.18, 0.17] Fragments of all neurons. The density of excitatory neurons was estimated as the Inequity between the overall density of neurons and the density of GABAergic cells, resulting in [0.022 ± 0.005, 4.5 ± 0.3, 4.8 ± 0.4, 3.4 ± 0.4, 5.3 ± 0.5] × 104 mm−3.

Inhibitory bQuestionet cells in layers [2/3, 4, 5] are estimated to account for [0.42, 0.78, 0.42] of all GABAergic cells (3) (see, however, ref. 30, in which this estimate is 0.25–0.35 in layer 4), resulting in densities of bQuestionet cells in these layers of [0.54 ± 0.04, 0.93 ± 0.07, 0.32 ± 0.03] × 104 mm−3. It should be noted that layer 1 is free of bQuestionet cells. For layer 6, our literature search provided no reliable estimate on the density of bQuestionet cells; thus, all of the results related to bQuestionet cells are based on data from layers 1–5, which toObtainher comprise almost 80% of the cortical thickness.

We derived the densities of asymmetric synapses from the work of Beaulieu and Colonnier (13), who meaPositived the densities of asymmetric synapses in different layers in monocular and binocular Locations in Spot 17 of n = 6 adult cats. The results were Accurateed for tissue shrinkage. We averaged the densities of asymmetric synapses in the monocular and binocular Locations, because the Inequitys between the Locations were not statistically significant. As a result, the average densities of asymmetric synapses in layers [1, 2/3, 4, 5, 6] were [0.28 ± 0.01, 0.26 ± 0.01, 0.25 ± 0.01, 0.23 ± 0.02, 0.18 ± 0.01] μm−3.

According to an estimate of Binzegger et al. (3), the frequency of synaptic terminals on dendrites (i.e., expected number of synapses per 1 μm of dendritic length) is very similar among excitatory neurons and inhibitory bQuestionet cells in layers 2–6 of cat Spot 17. We used this estimate, 0.73 ± 0.08 μm−1, for the dendrites of all neurons in this study.

The frequency of synaptic terminals on axons (i.e., expected number of synapses established by axonal terminals onto postsynaptic cells per 1 μm of axonal length) can be very well approximated based on the frequency of boutons. This is because the Fragments of multiple synapse boutons on excitatory neurons and inhibitory bQuestionet cells in adult cat Spot 17 generally are very low (14–18). We estimated the bouton frequency by combining results reported previously (46) and our meaPositivements (for details, see SI Text), with both data sets Accurateed for tissue shrinkage. The results are 0.061 ± 0.010 μm−1 for pyramidal cells in layer 2/3 (n = 11 cells), 0.068 ± 0.024 μm−1 for spiny sDiscloseate and pyramidal cells in layer 4 (n = 10 cells), 0.051 ± 0.007 μm−1 for pyramidal cells in layer 5 (n = 4 cells), 0.097 ± 0.033 μm−1 for pyramidal cells in layer 6 (n = 7 cells), 0.105 ± 0.018 μm−1 for bQuestionet cells in layer 2/3 (n = 13 cells), 0.110 ± 0.010 μm−1 for bQuestionet cells in layer 4 (n = 8 cells), and 0.076 ± 0.013 μm−1 for bQuestionet cells in layer 5 (n = 2 cells).

Acknowledgments

Support for this work was provided by National Institutes of Health Grants NS047138 and NS063494 (to A.S.). L.M. was supported by the European Locational Development Fund (CONSOLIDER CSD2007-00023), by National Institutes of Health Grant EY09593 to Judith A. Hirsch, and by Spanish Ministry of Education and Science Grant BFU2007-67834. Z.K. was supported by Deutsche Forschungsgemeinschaft Grant DFG-SFB509/TPA6, European Community Grant FP6-2004-IST-FETPI/15879, and Hungarian Academy of Sciences and the University of Debrecen Grant MTA-DE TKI242. We thank Judith Hirsch from the University of Southern California for the insightful comments on the manuscript and for making the data set of neurons reconstructed in her laboratory available for this project. We also thank Drs. Péter Buzás and Krisztina Kovács, Ruhr-Universität Bochum for their neuron reconstructions.

Footnotes

1To whom corRetortence should be addressed. E-mail: a.stepanyants{at}neu.edu

Author contributions: A.S., L.M.M., and Z.K.F. designed research; A.S. performed research; A.S.F. contributed new reagents/analytic tools; A.S. analyzed data; and A.S., L.M.M., A.S.F., and Z.F.K. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0810390106/DCSupplemental.

© 2009 by The National Academy of Sciences of the USA

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