doi:10.1016/j.pneurobio.2010.05.001 | How to Cite or Link Using DOI
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Most current computational models of neocortical networks assume a homogeneous and isotropic arrangement of local synaptic couplings between neurons. Sparse, recurrent connectivity is typically implemented with simple statistical wiring rules. For spatially extended networks, however, such random graph models are inadequate because they ignore the traits of neuron geometry, most notably various distance dependent features of horizontal connectivity. It is to be expected that such non-random structural attributes have a great impact, both on the spatio-temporal activity dynamics and on the biological function of neocortical networks. Here we review the neuroanatomical literature describing long-range horizontal connectivity in the neocortex over distances of up to eight millimeters, in various cortical areas and mammalian species. We extract the main common features from these data to allow for improved models of large-scale cortical networks. Such models include, next to short-range neighborhood coupling, also long-range patchy connections.
We show that despite the large variability in published neuroanatomical data it is reasonable to design a generic model which generalizes over different cortical areas and mammalian species. Later on, we critically discuss this generalization, and we describe some examples of how to specify the model in order to adapt it to specific properties of particular cortical areas or species.
Keywords: Cortical network; Distant synapses; Patchy projections
- A model of horizontal cortical connectivity
- 2.1. Working assumptions
- 2.2. The generalized computational network model
- Neuroanatomical basis of the model
- 3.1. Local connections
- 3.2. Intrinsic horizontal distant connections
- 3.2.4. Quantitative data on patches
- 22.214.171.124. Size of the patches
- 126.96.36.199. Lateral distance from a patch to the cell body
- 188.8.131.52. Number of patches
- Validity and specifications of the generalized model
- 4.1. Cortical hierarchy and patches
- 4.2. Model validity with respect to different species
- 5.1. Basic spatial settings and local connections
- 5.2. Patches and single-cell data
- 5.3. Patches and group data
- 5.4. What we did not include
Fig. 1. Network model comprising spatially embedded pyramidal neurons (black dots) with both local (red) and long-range (blue) connectivity. Surface view of a 2D sheet of neocortex. Neurons connected to the center neuron are represented by open blue circles. Left: Uniformly distributed distant projections. Right: Clustered long-range connectivity. Cyan disks represent patches.
Fig. 2. Scheme illustrating the types of projections made by pyramidal cells (PC). Local connections are shown in red, horizontal distant projections within the gray matter (GM) in blue. Left: Lateral view including the white matter (WM) projections shown in black. Right: Top view onto a sheet of cortex with embedded PCs (black dots) and their patchy axonal ramifications. The gray disks represent patchy projection sites.
Fig. 3. Parameters of patchy projections. Left: Detail from Fig. 1 describing the size of a patch rp, and its position relative to the cell body, described by dp and Φ. Top view on the flattened cortex. Right: Lateral view of the cortex with a single schematic pyramidal cell forming two patches.
Fig. 4. Scheme illustrating the patchy projection pattern (disks) of a group of adjacent neurons (represented by dots in a quadratic box), matched to data from extracellular tracer injections. Left: Example of two cells located in a box that form local (red, magenta) and patchy distant projections (blue, cyan), sharing two of their terminal fields. Right: Simplified scheme of the joint projection pattern: two sets of 3 single cells (filled colored dots) located within two neighboring boxes (squares), each of them projecting to 3 out of 6 common patches (disks). The color of each synapse (small open circle) indicates the cell by which it is established.
List of publications on patchy projections resulting from extracellular tracer injections (‘group data’, focused on anterogradely labeled fibers), ordered according to the species brain size and cortical areas.
Listed are the injection size σ (diameter), the average number of patches per injection Np, the average patch diameter Øp (or stripe width), the average and maximum lateral distance between the injection site and its patches dp, dpmax, the maximum lateral axonal spread Σ, and the average distance between the patches dcc. All length measurements are given in millimeters.
List of publications on patchy projections resulting from extracellular injections focusing on retrogradely labeled cells, same order and nomenclature as for Table 1.
List of publications on 2D or 3D reconstructions of single patchy PC projections, ordered according to the species brain size and the cortical area they refer to. Listed are the layers, the average number of patches per cell/axon Np, the average patch diameter Øp, the average and maximum lateral distance between the cell body and its patches dp, dpmax, the maximum lateral axonal spread Σ, and the average distance between the patches dcc. All measurements are given in millimeters. Part one: intracellular injections.
List of publications on 2D or 3D reconstructions of single patchy PC projections, continuation of Table 3. Part two: extracellular injections with single axon reconstructions.
Corresponding author at: INSERM U751 – Université Aix-Marseille, Faculté de Médecine La Timone, 27 Bd Jean Moulin, 13385 Marseille Cedex 05, France. Tel.: +33 491 29 98 13; fax: +33 491 78 99 14.