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 basket cells reconstructed from cat primary visual cortex in an attempt to provide a quantitative answer to the question: What fraction of cortical synapses is local, and what fraction is mediated by long-range projections? We found an unexpectedly high proportion of nonlocal synapses. For example, 92% of excitatory synapses near the axis of a 200-m-diameter iso-orientation column come from neurons located outside the column, and this fraction remains high-76%-even for an 800-m ocular dominance column. The long-range nature of connectivity has dramatic implications for experiments in cortical tissue slices. Our estimate indicates that in a 300-m-thick section cut perpendicularly to the cortical surface, the number of viable excitatory synapses is reduced to about 10%, and the number of synapses made by inhibitory basket cell axons is reduced to 38%. This uneven reduction in the numbers of excitatory and inhibitory synapses changes the excitationinhibition 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 nearby neuron pairs in slices could understate the in vivo probabilities by a factor of 3.axon ͉ connectivity ͉ local ͉ slice W hen 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 domains surrounding the neurons' somata (Fig. 1A). Only a few branches occasionally escape through the boundaries of the local domain. This interpretation of neuron images can be misleading, however. The few axonal branches that extend beyond the local domain could ramify over large territories (e.g., the entire cortex) and thus could carry a significant fraction of all synapses. Such long-range projections may include interareal and intraareal connections, feedback from higher cortical areas, interhemispheric projections, and feed-forward inputs from subcortical structures. These projections can be easily observed with single neuron or bulk injections of tracers (4-6), but quantifying their fraction 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.We devised an approach to deli...

Excitatory lateral connections within the primary visual cortex are thought to link neurons with similar receptive field properties. Here we studied whether this rule can predict the distribution of excitatory connections in relation to cortical location and orientation preference in the cat visual cortex. To this end, we obtained orientation maps of areas 17 or 18 using optical imaging and injected anatomical tracers into these regions. The distribution of labeled axonal boutons originating from large populations of excitatory neurons was then analyzed and compared with that of individual pyramidal or spiny stellate cells. We demonstrate that the connection patterns of populations of nearby neurons can be reasonably predicted by Gaussian and von Mises distributions as a function of cortical location and orientation, respectively. The connections were best described by superposition of two components: a spatially extended, orientation-specific and a local, orientation-invariant component. We then fitted the same model to the connections of single cells. The composite pattern of nine excitatory neurons (obtained from seven different animals) was consistent with the assumptions of the model. However, model fits to single cell axonal connections were often poorer and their estimated spatial and orientation tuning functions were highly variable. We conclude that the intrinsic excitatory network is biased to similar cortical locations and orientations but it is composed of neurons showing significant deviations from the population connectivity rule.

Time invariant description of synaptic connectivity in cortical circuits may be precluded by the ongoing growth and retraction of dendritic spines accompanied by the formation and elimination of synapses. On the other hand, the spatial arrangement of axonal and dendritic branches appears stable. This suggests that an invariant description of connectivity can be cast in terms of potential synapses, which are locations in the neuropil where an axon branch of one neuron is proximal to a dendritic branch of another neuron. In this paper, we attempt to reconstruct the potential connectivity in local cortical circuits of the cat primary visual cortex (V1). Based on multiple single-neuron reconstructions of axonal and dendritic arbors in 3 dimensions, we evaluate the expected number of potential synapses and the probability of potential connectivity among excitatory (pyramidal and spiny stellate) neurons and inhibitory basket cells. The results provide a quantitative description of structural organization of local cortical circuits. For excitatory neurons from different cortical layers, we compute local domains, which contain their potentially pre- and postsynaptic excitatory partners. These domains have columnar shapes with laminar specific radii and are roughly of the size of the ocular dominance column. Therefore, connections between most excitatory neurons in the ocular dominance column can be implemented by local synaptogenesis. Structural connectivity involving inhibitory basket cells is generally weaker than excitatory connectivity. Here, only nearby neurons are capable of establishing more than one potential synapse, implying that within the ocular dominance column these connections have more limited potential for circuit remodeling.

The brain contains a complex network of axons rapidly communicating information between billions of synaptically connected neurons. The morphology of individual axons, therefore, defines the course of information flow within the brain. More than a century ago, Ramón y Cajal proposed that conservation laws to save material (wire) length and limit conduction delay regulate the design of individual axon arbors in cerebral cortex. Yet the spatial and temporal communication costs of single neocortical axons remain undefined. Here, using reconstructions of in vivo labelled excitatory spiny cell and inhibitory basket cell intracortical axons combined with a variety of graph optimization algorithms, we empirically investigated Cajal's conservation laws in cerebral cortex for whole three-dimensional (3D) axon arbors, to our knowledge the first study of its kind. We found intracortical axons were significantly longer than optimal. The temporal cost of cortical axons was also suboptimal though far superior to wire-minimized arbors. We discovered that cortical axon branching appears to promote a low temporal dispersion of axonal latencies and a tight relationship between cortical distance and axonal latency. In addition, inhibitory basket cell axonal latencies may occur within a much narrower temporal window than excitatory spiny cell axons, which may help boost signal detection. Thus, to optimize neuronal network communication we find that a modest excess of axonal wire is traded-off to enhance arbor temporal economy and precision. Our results offer insight into the principles of brain organization and communication in and development of grey matter, where temporal precision is a crucial prerequisite for coincidence detection, synchronization and rapid network oscillations.