A null model of the mouse whole-neocortex micro-connectome

Abstract

In connectomics, the study of the network structure of connected neurons, great advances are being made on two different scales: that of macro- and meso-scale connectomics, studying the connectivity between populations of neurons, and that of micro-scale connectomics, studying connectivity between individual neurons. We combine these two complementary views of connectomics to build a first draft statistical model of the micro-connectome of a whole mouse neocortex based on available data on region-to-region connectivity and individual whole-brain axon reconstructions. This process reveals a targeting principle that allows us to predict the innervation logic of individual axons from meso-scale data. The resulting connectome recreates biological trends of targeting on all scales and predicts that an established principle of scale invariant topological organization of connectivity can be extended down to the level of individual neurons. It can serve as a powerful null model and as a substrate for whole-brain simulations.

Fig. 1

Predicted synapse densities in target regions. Modules are labeled: PF: prefrontal, AL: anterolateral, SoM: somatomotor, Vis: visual, Med: medial, Temp: temporal. Exact order of brain regions and assignment to modules by Harris et al. are also listed in Supplementary Table 1. White regions indicate no projections placed for that combination of source and target region

Fig. 2

Predicted layer profiles. a Predictions for all projection classes. Exact order of brain regions and assignment to modules by Harris et al. are also listed in Supplementary Table 1. b–f Relative error of the predicted synapse densities in all layers. That is, the difference between prediction and the mean of the raw biological data, divided by the standard deviation of the biological data. b For projections from L2/3. c From L4. d From L5IT. e From L5PT. f From L6. Dashed black lines indicate the biological variability of density under the assumption that it is Gaussian distributed. We used only projections where more than five raw data points to establish the biological variability were available. g Fraction of projections where with the relative error under two standard deviations for each source layer

Fig. 3

Projection mapping in the visual system. a The primary visual area (VISp) and its defined source coordinate system. The three points defining the barycentric system are indicated as colored triangles. Each coordinate is associated with the indicated red, green, or blue color channel to decide the color of each pixel in the region. b The spatial structure of projections from VISp is indicated by coloring pixels in the surrounding regions according to the color in a of the area they are innervated from. c Center: as in b, but the color of each pixel is normalized such that the sum of the red, green, and blue channels is constant. Periphery: target coordinate systems for the surrounding regions were fit to recreate the color scheme of the center, when colored as in a

Fig. 4

Validation of predicted mapping. Relative error of the mapping defined by the barycentric coordinate systems in the target area, compared with the data. Values along the main diagonal: for contralateral mapping; all others: ipsilateral mapping. The data shown where the sum of densities from all projection classes is above 0.025 μm⁻³

Fig. 5

Innervation of brain regions by individual axons. a Projection density according to Harris et al. (top row), ranging from no projection (white) to strong projections (black), and brain regions innervated by 61 reconstructed axons (rows) indicated by gray squares. b Probability to innervate individual brain regions, predicted from the normalized projection strength from MOs, against the observed innervation probability (L2/3: calculated from n = 25 axons, L5: n = 61 axons, L6a: n = 35 axons). c Normalized projection strength against the mean total length of axon branches in individual brain regions (n as in b). d Observed interactions between the innervation of individual brain regions, i.e., increase in innervation probability of one region when the other is known to be innervated. e Increase in innervation probability as in d against the innervation probability of a pair of regions under the assumption of independence. Gray dotted line indicates the point where the product of independent probability and increase is one that can logically not be exceeded. All innervations and projection strengths in this figure are for projections from MOs

Fig. 6

A model to generate p-types. a Toy example of a p-type generating model with four regions (A–D). The regions are associated with the leaves of a directed tree (black), edges of the tree are associated with a probability to cross it. Two exemplary axons (orange, blue) spread from region D either crossing an edge (dashed lines) or not (dashed X-marks). Inset: resulting p-types; black regions are innervated; s indicates the source region. b Examples of innervation of brain regions predicted by the full model for L5IT (left column) and of reconstructed axons (right column). Sampled axons along the y-axis, brain regions along the x-axis. A black pixel indicates that an axon is innervating a region. Top row: axons originating from L5 of MOs; bottom row: from MOp. c Pairwise distances (hamming distance) between the profiles of brain region innervation. Blue: the data from reconstructed axons (see a); orange: from 10,000 profiles sampled from the tree-based model; green: from 1000 profiles sampled from a naive model taking only the first-order innervation probabilities into account. Left: for axons originating from MOp; right: from MOs. d Increase in innervation probability against the basic innervation probability as in Fig. 5e

Fig. 7

Validation of the tree-model. Validation against the results of Han et al.. a Top, results of in terms of the number of visual areas innervated by single axons originating in layer 2/3 of VISp. Bottom, corresponding results of the tree-model for axons originating in layers 2/3, 4, 5, and 6 (top left to bottom right; n = 10,000 innervation profiles each). b Top, results of Han et al. in terms of common innervation of pairs of visual brain areas by axons originating in layer 2/3 of VISp. Bottom, corresponding results of the tree-model, based on n = 10,000 innervation profiles

Fig. 8

Bidirectional micro-connectivity and modularity. a Connectivity between individual neurons in VISa and VISam was sampled by defining a subvolume with various radii in VISam (sampling radius), then by finding the center of the projection from the subvolume to VISa according to the mapping (dashed arrow), moving it (sampling offset) and defining a subvolume with the same radius around it. b Unidirectional (red) and reciprocal connection probabilities for various sampling radii with zero-sampling offset. Gray: expected from unidirectional connectivity; black: model. c Ratio of reciprocal connectivity measured in the model over the expected value. Gray: three instances; black: mean of n = 3 instances. d As b, but for a sampling radius of 150 μm with various sampling offsets. e As c, but for sampling offsets. f Bottom: edge density, i.e., the number of connections over the number of pairs, of the microconnectivity between within-region modules that were defined by clustering the connectivity within the two brain regions (see the Methods section). Top: neuron-to-neuron connectivity between 7 × 7 within-region modules outlined in green. Gray lines indicate boundaries between within-region modules. g Distribution of edge densities in f (top right quadrant) compared with a random control. h Width of the distribution of edge densities (as in g) at half height, model against control, for projections with a density over 0.02 μm⁻¹. Circles: projection originating in the prefrontal module; stars: anterolateral module; left-pointing triangles: medial; downward-pointing triangles: somatomotor; right pointing: temporal; upward pointing: visual; dark blue: intramodule projection; light blue: intermodule