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Geometric and functional organization of cortical circuits

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Abstract

Can neuronal morphology predict functional synaptic circuits? In the rat barrel cortex, 'barrels' and 'septa' delineate an orderly matrix of cortical columns. Using quantitative laser scanning photostimulation we measured the strength of excitatory projections from layer 4 (L4) and L5A to L2/3 pyramidal cells in barrel- and septum-related columns. From morphological reconstructions of excitatory neurons we computed the geometric circuit predicted by axodendritic overlap. Within most individual projections, functional inputs were predicted by geometry and a single scale factor, the synaptic strength per potential synapse. This factor, however, varied between projections and, in one case, even within a projection, up to 20-fold. Relationships between geometric overlap and synaptic strength thus depend on the laminar and columnar locations of both the pre- and postsynaptic neurons, even for neurons of the same type. A large plasticity potential appears to be incorporated into these circuits, allowing for functional 'tuning' with fixed axonal and dendritic arbor geometry.

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Figure 1: LSPS maps of functional excitatory synaptic input (Qxy) to L2/3 neurons in different columnar positions.
Figure 2: Axonal and dendritic structure.
Figure 3: Potential connectivity.
Figure 4: Average maps of geometric input (Gxy) for L2/3 pyramidal cells grouped by columnar and laminar location.
Figure 5: Comparison of geometric and functional projections.
Figure 6: Ratios of functional and geometric projections in barrel- and septum-related columns.

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  • 15 May 2005

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Notes

  1. Note:In the version of this article initially published online, the legend for Figure 6 contained an error. The first line of the description of Figure 6a should read, “Average ratio of functional/geometric connectivity (< Qxy/ Gxy>) for projections to L2 septum and L3septumcells.” This error has been corrected for the HTML and print versions of the article.

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Acknowledgements

We thank K. Zito and V. Scheuss for a critical reading of the manuscript, members of the Svoboda laboratory for useful discussions, J. Huang and C. Wu for access to their Neurolucida system and B.J. Burbach and C. Zhang for technical assistance. Funded by the Howard Hughes Medical Institute (G.S. and K.S.), US National Institutes of Health (D.C., A.S. and K.S.), Klingenstein Foundation (D.C.) and Human Frontier Science Program (I.B.).

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Correspondence to Karel Svoboda.

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Supplementary information

Supplementary Fig. 1

Geometric input calculation and optimal barrel cortex template. (a) Schematic depicting method used to calculated geometric input from a particular location. See Supplementary Methods for description. (b) Optimal template of the barrel cortex and the respective positions of all recorded and reconstructed neurons. In L2/3, positions of pyramidal cells for which LSPS maps where obtained are marked by green dots (32 cells). Positions of reconstructed cells used to produce potential connectivity maps are marked with red dots in L2/3 (13 pyramidal cells), and blue dots in L4 and L5A (49 spiny stellate and pyramidal cells). Bottom and left axes provide the scale in micrometers. Right axis indicates distance from pia. Numbers to left of right axis indicate widths of laminae. (GIF 8 kb)

Supplementary Fig. 2

Comparisons of functional and geometric input. (a) Inputs to L2barrel neurons: i, horizontal profile of functional input; ii, horizontal profile of geometric input; iii, plot of functional versus geometric horizontal profiles. (b) Inputs to L3barrel neurons. (c) Inputs to L2septum neurons. (d) Inputs to L3septumneurons. (e) Plot of the ratios of functional to geometric input. Projections from L4 are indicated by green lines (see inset); those from L5A indicated by blue lines. Home-column projections are indicated by black lines and bars; those from left and right side columns indicated by red lines and bars. Values were calculated using different home-column widths (from 100 to 400 m) and for the side columns separately or combined, as indicated in the boxed annotated example for the L4 L2barrel projection. (GIF 33 kb)

Supplementary Methods (PDF 186 kb)

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Shepherd, G., Stepanyants, A., Bureau, I. et al. Geometric and functional organization of cortical circuits. Nat Neurosci 8, 782–790 (2005). https://doi.org/10.1038/nn1447

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