In the medium resolution volume, we identified neuronal somata in order to locate the cortical layer boundaries ( Figure 3 A) and reconstructed the shapes of a subset of cells running in a cortical mini-column ( Figure 3 A; Movie S6 ). Most (∼70%, 21/30) of these cells were pyramidal and the rest fell into several different categories, including putative interneurons, atypical excitatory cells, and glial cells. We then fully annotated a sub-volume of somatosensory cortex within this same volume ( Movie S9 http://openconnecto.me/Kasthurietal2014/data/segments ). Building on work done previously in the hippocampus (), we itemized all the neuronal and non-neuronal cells in three cylindrical volumes that encompass apical dendrite segments of two cortical pyramidal cells, including their spines ( Movie S10 ). We selected these particular apical dendrites because they ran very close to each other (see pink arrow in Figures 3 A and 3D) and originated from nearby neuronal somata (in upper layer 6; red and green arrows in Figures 3 A and 3D). Thus, they appeared to be in the same mini-column and perhaps participated in the same neural processing unit (). The three cylinder site was in layer 5, 100 μm and 135 μm superficial to the pseudo-colored “red” and “green” neuronal somata, respectively. Cross-sections of the annotations of two cylinders are shown in Figures 3 B and 3D; reconstruction of the three cylinders is shown in Figure 3 E; and the location of all three cylinders in the full volume is shown with pink arrows in Figures 3 A, 3D, and 3O. These three slightly overlapping ∼600 μmcylinders, two of which (cylinders 1 and 3) are centered on the “red” neuron’s apical dendrite and one (cylinder 2) on the “green” apical dendrite, provided a total reconstructed volume of 1,500 μm. In cylinder 3, rather than tracing the objects manually, we edited the computer-segmented data ( Figure 3 C). All of the 193 dendrites in this volume were traced out into the surrounding high-resolution cube, and some were traced onto the medium resolution data to locate somata (n = 30; Figure 3 O).

Shown are skeletonizations of all 660 excitatory axons ordered from longest (top left) to shortest lengths (bottom right). Total length of each axon within the cylinder in μms is indicated below each axon. Only 3 axons (boxes) have non-terminal branches.

The ∼7-fold disparity between the number of axons and dendrites (1,407 versus 193) likely reflects a real difference in the numbers of pre- and postsynaptic cells that send processes into the volume. We analyzed the shape of the 660 excitatory axons that entered cylinder 1 and found that only three of them (0.5%) established branches that were non-terminal within the volume ( Figure S3 ). To estimate the number of axons that branched outside the cylinders and sent more than one branch in, we analyzed axonal arbors from light microscopy reconstructions of mouse neocortical pyramidal neurons ( NeuroMorpho.org ; see the Methods) by superimposing them on the cylindrical volumes at random locations. The result of this analysis argues that only ∼8 of the 1,308 excitatory axons (< 1%) in the volume are likely to be branches originating from the same parent neuron. Also, the dendrites in the cylinder only rarely originated from the same neuron: we found two dendritic shafts in cylinder 1 that were from the same neuron (out of 100). Presumably, therefore, axons extend into a 7-fold greater volume than dendrites, on average. The ∼1,600 different neurons within this small region of mammalian brain (several billionths of the volume of a whole brain) is more than five times as many neurons as are contained within the entire nervous system of a Caenorhabditis elegans ().

We did not find evidence of electrical connections in the three cylinder volume. Gap junction proteins are seen in inhibitory neurons in layers 4 and 6, but not so much in layer 5, where this study was carried out ().

(A) Ten axonal varicosities, which were presynaptic to multiple dendritic spines, are shown. In most cases a single large cluster of vesicles served the multiple synapses. In some cases two spines from the same dendrite were postsynaptic to the same varicosity (e.g., the two purple spines in #5).

Most (71%; n = 1,207/1,700) of the synapses in the volume derive from varicosities along axons (en passant synapses), and the rest are at the end of short branches (terminal synapses). 18% of excitatory, and 43% of the inhibitory, axonal varicosities are presynaptic to multiple partners ( Figure 4 A). Multi-synaptic excitatory varicosities were previously described in the hippocampus (). The most extreme example in this dataset is a large excitatory en passant bouton innervating five different postsynaptic targets ( Figure 4 B). Tracing ten randomly chosen axons (with 78 varicosities) into the larger surrounding volume showed all but one axon had at least one multi-synaptic varicosity, suggesting that axons in general establish both mono- and multi-synaptic varicosities. Excitatory axons establish synapses mostly on spines (94%; n = 1,406/1,700), and inhibitory axons establish mostly on shafts (81%, n = 70/86). A few (1%; n = 7) of the unmyelinated axons, despite having vesicle-filled varicosities, do not make traditional close synaptic contacts with any target cell within the volume (listed as “2” in column 12 in Table S1 ). Some of these axons have relatively large vesicles that match the description of cortical aminergic axons (see, for example, http://openconnecto.me/Kasthurietal2014/view/bigVesicles ) (). We also notice that glial processes associate with synapses in an uneven way ( Figure 3 J; Movies S9 and S10 ): ∼50% of synapses were not adjacent to any glial process.

The spreadsheet shows that the connectivity is highly skewed toward excitatory elements: 92% (177/193) of the dendrites are spiny and purportedly excitatory ( Figure 3 K;), and 93% (1,308/1,407) of the axons are excitatory. Looking at each presynaptic varicosity, we found that 95% (1,610/1,700) of them also meet the criteria for being excitatory. Each excitatory axon establishes slightly more synapses in the volume than each inhibitory axon (∼1.2 synapses/excitatory axon versus ∼0.9 synapses/inhibitory). The excitatory-to-inhibitory-synapse ratio () is 20.2 for the dendrites of excitatory neurons (1,494 excitatory synapses versus 74 inhibitory synapses), whereas the ratio is only 9.7 (116 excitatory synapses and 12 inhibitory synapses) for the input to inhibitory dendrites. These ratios are in line with what has been described in hippocampal studies ().

(B) The horizontal axis is the distance from the vesicle’s center at which the two sections (green and violet rectangles) split the vesicle. The vertical axis is the ratio of the brightness at the center to the maximum brightness in the vesicle’s image. The figure shows two brightness profiles. The green one is for the light-green section on the left-hand-side of the figure, the blue one for the adjacent section (violet rectangle at the right). The figure shows also an example of how to read the graph for the case when the vesicle is split at 4 nm above its center. Following a vertical line from the 4 nm mark we read from the green profile the relative brightness at vesicle center in the green section (0.40) and from the blue profile the relative gray level in the violet section (0.64). The two profiles cross at a relative brightness of 0.5. That is, when the brightness at the center is 50% of the brightest portion of the vesicle image. Consequently, it is not possible for both sections to show, for the same vesicle, a core brighter than 50% its membrane intensity. Thus counting the number of vesicles with bright centers in a serial stack of images provides the number of synaptic vesicles.

(A) A Matlab script goes over a grid of lateral distances away from the vesicle center in one axis (r-axis) and distance from the vesicle center at which the portion of the vesicle within the section begins (z c ). At each radius r (e.g., r 1 and r 2 in the figure) we calculate the thickness for each depth z c from a vertical line through the section (shown for section 1). The thickness is the length of the red portions of the vertical lines at r 1 and r 2 . A similar calculation is done for the adjacent serial section (2).

(C) All of the mitochondria (n = 635) contained in cylinder 1 from side view of the cylinder (left) and end-on view (right). Three tables show mitochondrial metrics for cell and process types. Colors of mitochondria in the rendering refer to the classes listed. Scale bars, 1 μm for (A), 7 μm for (B), and 3 μm for (C).

In cylinder 1, we identified the location of each synaptic vesicle at 774 synapses ( Figures 4 A, 4B, 5 A, and 5 B; Table S1 http://openconnecto.me/Kasthurietal2014/data/vesicles ). The counts were similar (±4.6%) when two expert tracers independently counted the same synapses, and they likely reflect the actual number per synapses ( Figure S4 ). The number of vesicles per synaptic varicosity range from 2 to 1,366 for varicosities with one postsynaptic target (mean = 153 ± 127), with significantly greater numbers of vesicles at multi-synaptic varicosities (mean = 200 ± 173; Wilcoxon rank-sum test; p = 0.0005). The number of vesicles is not significantly different in excitatory and inhibitory synapses.

We also identified 607 mitochondria in cylinder 1 with a density of ∼1/μm Figure 5 C; mitochondrial dataset available http://openconnecto.me/Kasthurietal2014/view/highResAnnotated and http://openconnecto.me/Kasthurietal2014/data/mitochondria ). Mitochondria occupy twice as much volume in inhibitory dendrites than in excitatory dendrites, perhaps related to the metabolic demands associated with greater levels of activity (). In addition, mitochondria are present in axonal varicosities, most typically varicosities that had large numbers of vesicles ( Table S1 ). Only very rarely (n = 3/1,425) do mitochondria reside in dendritic spines, a surprising result given the fact that mitochondria are transported to spines with intense stimulation (). Among the three mitochondria that enter spines, two were continuations of mitochondria in the parent dendrite ( http://openconnecto.me/Kasthurietal2014/view/spineMito1 http://openconnecto.me/Kasthurietal2014/view/spineMito3 ).

Approximately 5% (39/780) of spines belonging to the central dendrite were not innervated by an axon. They appeared longer and thinner than spines that were innervated and often did not terminate in “heads” ( Figure S5 ). These are termed filopodia (). Individual filopodia occupied less volume (0.03 ± 0.02 μm) than innervated spines (0.10 ± 0.08 μm) and only ∼30% of them have spine apparati versus 60% of innervated spines.

In general, spines appear more densely packed (∼51 spines per 10 μm dendritic length for the red dendrite in cylinder 1) and often of greater length (mean ∼1.8 ± 0.6 μm and longest ∼3.8 μm; n = 77) than expected in mouse cortex based on previous reports (). Perhaps this is a consequence of the saturated method of reconstruction, where no spine could be overlooked. The long neck lengths could mean that some of these spines are electrically invisible to the soma (). Larger spine volumes were positively correlated with spine apparati (r = 0.36; p < 0.000001), larger postsynaptic densities (r = 0.77; p < 0.000001), larger numbers of presynaptic vesicles (r = 0.58; p < 0.000001), and presynaptic mitochondria (r = 0.141; p = 0.007).

We itemized 1,425 dendritic spines in the 3 cylinder volume. They occupy ∼9% percent of the intracellular space. Although each of the three cylinders was constructed around a single apical dendrite to capture nearly all of its spines, there were many more spines from other dendrites that invaded this territory, i.e., the central “red” dendrite contributes only 12%; n = 77/628 of the spines in cylinder 1. Furthermore, the central dendrite’s spines were completely intermingled with the spines of other dendrites (see Figure 7 A; Movie S12 ).

Connectivity Patterns of Excitatory Axons

Markram et al., 1998 Markram H.

Wang Y.

Tsodyks M. Differential signaling via the same axon of neocortical pyramidal neurons. Song et al., 2005 Song S.

Sjöström P.J.

Reigl M.

Nelson S.

Chklovskii D.B. Highly nonrandom features of synaptic connectivity in local cortical circuits. Chicurel and Harris, 1992 Chicurel M.E.

Harris K.M. Three-dimensional analysis of the structure and composition of CA3 branched dendritic spines and their synaptic relationships with mossy fiber boutons in the rat hippocampus. Markram et al., 1997 Markram H.

Lubke J.

Frotscher M.

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Sakmann B. Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. We examined excitatory axonal input to dendritic spines that account for three-quarters of the synapses (n = 1,286/1,700) in the 3 cylinder volume and quickly found by mining the data in the synapse spread sheet ( Table S1 ) a potential anatomical correlate of the physiological finding that different excitatory axons can have strikingly different strength connections with the same dendrite (). There were many instances in which the same axon innervated the same dendrite at multiple different spines. Such multiple contacts have been described in the hippocampus () and inferred from light microscopy of cortex (). In cylinder 1, the 77 excitatory spine synapses onto its central (red) apical dendrite came from only 63 different axons because eight axons innervated two spines each and three axons innervated three spines ( Movie S13 ). In cylinder 2, 12 of a total of 84 axons innervated two spines of the green dendrite, accounting for 22% of that dendrite’s spines. Such multiple contacts were not restricted to apical dendrites because the most extreme example was an axon that innervated five different spines of a basal pyramidal dendrite ( Figure 6 ). The spines innervated by the same axon were not by rule adjacent either in terms of the location of the spine heads or their origins from the dendritic shaft ( Figure 6 ). In cylinder 1 there were 34 instances in which an axon established synapses on two spines of the same dendrite, 4 instances in which an axon innervated three spines on the same dendrite, and the 1 instance of five just mentioned. Therefore, 46 synapses were “redundant” in the sense that these synapses replicated synaptic connections that were already established by a different synapse of the same axon on the same target cell. For all spines in cylinders 1–3, we counted 97 redundant synapses. However, given the shape of the volume, only the red and green dendrites had all their spines assayed, and thus the measured redundancy almost certainly underestimates the actual amount.

Figure 6 Multiple Synapses of the Same Axon Innervate Multiple Spines of the Same Postsynaptic Cell Show full caption An extreme example in which one axon (blue) innervates five dendritic spines (orange, labeled 1–5) of a basal dendrite (green) is shown. Arrows point to other varicosities of this axon that are innervating dendritic spines of other neurons (data not shown). Scale bar, 2 μm.

Stepanyants et al., 2004 Stepanyants A.

Tamás G.

Chklovskii D.B. Class-specific features of neuronal wiring. Next, we consider potential reasons for why multiple spine synapses between an axon and a dendrite exist. One idea is that, by virtue of having substantially more branches or a more convoluted path through the volume, some axons have a greater opportunity to establish multiple synapses with the same dendrite than simpler axons. However, there was only a weak correlation between the total length of excitatory axons that crossed through cylinder 1 and the number of synapses they established with its central dendrite (n = 63 axons, 77 synapses; correlation = 0.16; Figure S6 A). Alternatively, some axons may have a strong affinity to run near the spines of particular dendrites. We therefore looked at the trajectory of each excitatory axon in greater detail to see if we could discover any differences between the axons that innervated the central (“red”) dendrite in cylinder 1 and a cohort of excitatory axons that did not innervate the central dendrite in the cylinder but at least passed immediately adjacent to at least one of its spines (contacts we call “touches,” see the Methods for details). Many axons touched each spine (8.9 ± 4.3 excitatory axons touched each spine), but in almost all cases (∼99%) only one excitatory axon innervated each ( Figure 7 B; Movie S14 http://openconnecto.me/Kasthurietal2014/data/touchSynapse ). The analysis of axons making touches and those that innervated the central dendrite argues against the idea that the trajectory axons predict their synaptic connectivity. First, for the 77 dendritic spines of the central dendrite in cylinder 1, we found little correlation (correlation coefficient = 0.0001) between the number of these spines that an excitatory axon touches versus the number of synapses it establishes on these spines, as would be expected if synapse probability is just related to the number of opportunities based on proximity to spines ( Figure S6 B). Second, we found no evidence to support the idea that axons that established the synapses with the central dendrite grew in closer proximity to that dendrite than the axons that touched but did not establish synapses. We compared the length of axons that entered the cylinder and touched a spine of the central dendrite without establishing any synapses with it to the lengths of axons that established synapses with the central dendrite. The axons that touched, but did not establish synapses with the central dendrite, were on average slightly longer in the volume than the axons that established synapses (mean 9.9 ± 6.6 μm synapsing versus mean 10.8 ± 5.18 μm touching), providing no support for the idea that innervating axons had a greater affinity to grow along the central dendrite than axons that passed by but did not innervate it ().

Figure S6 Axonal Proximity to Either a Dendrite or Its Spines Is Not a Strong Predictor of Synaptic Connectivity, Related to Figure 7 Show full caption (A) Graph that shows that the average length of axons (represented by discrete red lines) was weakly correlated with the number of synapses established by those axons on the central dendrite in cylinder 1 (Red line; R = 0.162, assuming normally-distributed, homoschedastic residuals). Shown are the lengths of all the axons that intersected the cylinder arranged by the number of synapses they established on the central dendrite (which received the largest share of synapses of any dendrite in the cylinder). This data does not provide strong support for the idea that it is simply the amount of axonal overlap with the cylindrical spinous territory surrounding an apical dendrite that explains the degree of synaptic coupling (the green line is a least-squares fit of a line that would indicate that the number of synapses is proportional to the axon’s length in the neighborhood of the dendrite. If two quantities in a plot are proportional to each other, the line passes through the origin). (B) Graph compares the number of synapses axons established with the number of times an axon came within the immediate proximity of a spine without forming a synapse. If the probability of synapse formation between an axon and a dendrite was proportional to the number of times that axon was immediately adjacent to the spines of that dendrite, then the axons that innervated the central dendrite the most times should have had more opportunities as evidenced by more close encounters (touches). The data do not support this idea and instead show a weak correlation r = 0.000086 between the number of synapse formed and the number of spines touched (dotted line is the horizontal least-squares regression line).

Figure 7 Specificity of Spine Innervation by Excitatory Axons Show full caption (A) A rendering demonstrating the high density and intermixing of spines from the red dendrite (red) and many other dendrites (gray) in the cylinder surrounding the “red” apical dendrite. See also Movie S13 (B) A reconstruction showing 12 additional excitatory axons in the immediate vicinity of a dendritic spine (arrow) and its innervating axon (arrow). See also Movie S14 (C) A reconstruction showing the nine spines (blue) that “touch” one excitatory axon (green) and the three spines (orange) that are innervated by it. (D) A histogram showing the number of redundant synapses (see text) in 80,000 randomizations of the synapses among the touches of each axon. In none of these trials was the number of redundant synapses equal to, or greater than, the actual number (red line). (E) Sites in which the axons that form synapses with the “red” dendrite’s spines inside the cylinder establish 11 additional synapses with this dendrite outside the cylinder (yellow spheres). Axons that only touched the “red” dendrite spines in the cylinder form only one synapse with it outside of the cylinder (blue sphere). (F) A graph showing the result described in (E) (p = 0.003). Scale bars, 2 μm for (A) and 15 μm for (E). See also Figures S5 and S6 and Movies S12 S13 , and S14

We tested whether the axon-spine connectivity observed could be based on purely stochastic mechanisms. Specifically, did redundant excitatory synapses originate by synapse formation among a random subset of the close encounters (i.e., touches) between excitatory axons and dendritic spines? This analysis tests a high-resolution version of the so called Peters’ rule (see discussion). We analyzed the 7,505 spine touches and 1,037 synapses between all the excitatory axons (n = 916) with dendritic spines (n = 1,036) in cylinders 1 and 2. For each axon we itemized all the spines that it touched and the subset of these that were actual synapses ( Figure 7 C). If synaptic connections occurred randomly among the close encounters of axons and spines then a randomization of the synapses among the spine touches should not significantly change the number of times the same axon innervates a dendrite more than once. To assure that each axon in the randomization still established the identical number of synapses as it did in the actual data and that each spine was still innervated by only one excitatory axon (or in 10 cases, two excitatory axons), we developed an algorithm that essentially solved a Sudoku matrix of axons and spines in that it kept the numbers of synapses in the rows and columns unchanged from the actual data ( http://openconnecto.me/Kasthurietal2014/Code/touchSynapse ; see also the Methods). In this randomization, both the quantitative aspects of the synaptic connectivity of each axon and each dendrite and the spatial overlap of all axons and dendrites are identical to the actual data. The only change made is the particular identity of which of the close axon-spine touches are synaptic. We calculated for each randomization the number of redundant synapses. In a run of 80,000 randomization trials, none of the randomized connectivity patterns had as many redundant synapses as the 78 found in the actual dataset of cylinder 1+2 (simulation median = 52 redundant synapses; p < 0.00001; Figure 7 D). Thus axon-dendrite adjacency, while of course necessary for synapses to form, is insufficient to explain why some axons establish multiple synapses on some dendrites and not others. This is an explicit refutation of Peters’ rule. Rather this result argues that there are different probabilities for synapses between particular dendrites and particular excitatory axons.