Multi-scale account of the network structure of macaque visual cortex

Abstract

Cortical network structure has been extensively characterized at the level of local circuits and in terms of long-range connectivity, but seldom in a manner that integrates both of these scales. Furthermore, while the connectivity of cortex is known to be related to its architecture, this knowledge has not been used to derive a comprehensive cortical connectivity map. In this study, we integrate data on cortical architecture and axonal tracing data into a consistent multi-scale framework of the structure of one hemisphere of macaque vision-related cortex. The connectivity model predicts the connection probability between any two neurons based on their types and locations within areas and layers. Our analysis reveals regularities of cortical structure. We confirm that cortical thickness decays with cell density. A gradual reduction in neuron density together with the relative constancy of the volume density of synapses across cortical areas yields denser connectivity in visual areas more remote from sensory inputs and of lower structural differentiation. Further, we find a systematic relation between laminar patterns on source and target sides of cortical projections, extending previous findings from combined anterograde and retrograde tracing experiments. Going beyond the classical schemes, we statistically assign synapses to target neurons based on anatomical reconstructions, which suggests that layer 4 neurons receive substantial feedback input. Our derived connectivity exhibits a community structure that corresponds more closely with known functional groupings than previous connectivity maps and identifies layer-specific directional differences in cortico-cortical pathways. The resulting network can form the basis for studies relating structure to neural dynamics in mammalian cortex at multiple scales.

Keywords: Cellular architecture; Cortical layers; Macaque visual cortex; Multi-scale connectivity; Predictive connectomics.

Fig. 1

Overview of the model. Each area is modeled as the volume under $1{\mathrm{mm}}^2$ of cortical surface with area- and layer-specific population sizes. The local connectivity inside each area is based on the microcircuit model of Potjans and Diesmann (2014). Cortico-cortical connectivity is area- and layer-specific. It is derived from tracing data stored in the CoCoMac database (Stephan et al. ; Bakker et al. 2012), quantitative retrograde tracing data from Markov et al. (2014a, b) and reconstructed morphologies from Binzegger et al. (2004). Microcircuit diagrams adapted from Potjans and Diesmann (2014) (with permission). Large-scale network diagram adapted from Kunkel et al. (2009). The dendritic morphologies in the cortico-cortical connectivity illustration are extracted from Stepanyants et al. (2008) (inhibitory L4 cell) and Mainen and Sejnowski (1996) (L5 pyramidal cell), respectively (source: http://NeuroMorpho.org; Ascoli et al. 2007)

Fig. 2

Aspects of cortical architecture determining population sizes. a Laminar neuron densities for the architectural types in the model. Type 2, here corresponding only to area TH, lacks L4. We treat L1 as containing synapses but no neurons. Data provided by H. Barbas (personal communication). b Total thickness versus logarithmized overall neuron density and linear least-squares fit ($r=-0.7,p=0.005$). c Relative laminar thickness (see Supplementary Table S3) versus logarithmized overall neuron density and linear least-squares fits (L1: $r=-0.51,p=0.08$, L2/3: $r=-0.20,p=0.52$, L4: $r=0.89,p=0.0001$; L5: $r=-0.31,p=0.36$, L6: $r=-0.26,p=0.43$). Total cortical thicknesses D(A) and overall neuron densities for 14 areas from Hilgetag et al. (2016), Table 4. The overall densities are based on Nissl staining for 11 areas and for 3 areas on NeuN staining. Laminar neuron densities are based on NeuN staining for all 14 areas. Values based on NeuN staining are linearly scaled to account for a systematic undersampling as determined by repeat measurements in the 11 aforementioned areas

Fig. 3

Construction principles of the network connectivity. a Each neuron receives four different types of connections. I: Intra-area synapses from within the $1{\mathrm{mm}}^2$ patch, II: Intra-area synapses from outside the $1{\mathrm{mm}}^2$ patch, III: Cortico-cortical synapses from vision-related areas, IV: Synapses from subcortical and non-visual cortical areas. b Average number of synapses per neuron across the 32 areas of the network versus overall neuron density. The dashed line shows the average indegree across all neurons of the network

Fig. 4

Combination of binary and quantitative tracing data into an area-level connectivity map. a Binary connectivity from CoCoMac. Black, existing connections; white, absent connections. b Fractions of labeled neurons (FLN) from Markov et al. (2014a) mapped from their parcellation scheme (M132) to that of Felleman and Van Essen (1991). c Connection densities decay exponentially with inter-area distance. Black line, linear regression with $log(\text{FLN})={\left(ln10\right)}^{-1}·\left(lnc-\mathit{\lambda }d\right)$ ($c=0.045,\mathit{\lambda }=0.11{\mathrm{mm}}^{-1},p={10}^{-19}$; cf. Eq. (10)). d Area-level connectivity of the model, based on data in a–c, expressed as relative indegrees for each target area

Fig. 5

Layer- and population-specific cortico-cortical connection patterns. a Fraction of source neurons in supragranular layers (SLN) versus logarithmized ratio of the overall neuron densities of the two areas. SLN from Markov et al. (2014b), neuron densities from Hilgetag et al. (2016). Black curve, fit using a beta-binomial model (Eq. (1); $a_0=-0.152,a_1=-1.534,\mathit{\varphi }=0.214$). b Laminar target patterns of synapse locations in relation to the SLN value of the source pattern. Target patterns are taken from the CoCoMac database (Felleman and Van Essen ; Barnes and Pandya ; Suzuki and Amaral ; Morel and Bullier ; Perkel et al. ; Seltzer and Pandya 1994) and SLN data from Markov et al. (2014b) mapped to the FV91 scheme. c Illustration of the procedure (Supplementary Eq. 3) for distributing synapses across layers and populations. A source neuron from population j in area B sends an axon to layer v of area A where a cortico-cortical synapse $s_{\mathrm{CC}}$ is formed at the dendrite of a neuron from population i. The dendritic morphology is from Mainen and Sejnowski (1996) (source: http://NeuroMorpho.org; Ascoli et al. 2007). d Laminar patterns of cortico-cortical connections in the feedback, lateral, and feedforward direction, measured as the indegree of the population pairs divided by the sum of indegrees over all pairs, and then averaged across area pairs with the respective connection type ($K_{ij}={⟨K_{iA,jB}/{\sum }_{i^{\prime },j^{\prime }}{K}_{i^{\prime }A,j^{\prime }B}⟩}_{A,B}$). The categorization into feedback, lateral, and feedforward types follows the SLN value as in b

Fig. 6

Population sizes matter for connectivity. Connectivity within and between areas V1 and V2 computed as pairwise indegrees (left) and connection probabilities (right). The latter are defined as the probability of $\ge 1$ synapse between any pair of source and target neurons, and can be obtained in linear approximation from the former by dividing by the size of the source population. The histograms show the occurrence of values in the bins defined by the color scales

Fig. 7

Community structure of the network. Clusters in the connectivity graph, indicated by the color of the nodes: lower visual areas (green), dorsal stream areas (red), superior temporal polysensory areas (light red), mixed cluster containing areas VP, VOT, PITd and MSTd (light blue), ventral stream (dark blue), and frontal areas (purple). Black, connections within clusters; gray, connections between clusters. Line thickness encodes logarithmized outdegrees. Only edges with relative outdegree $>{10}^{-3}$ are shown. For visual clarity, clusters are spatially segregated and inside clusters, areas are positioned using a force-directed algorithm (Kamada and Kawai 1989)

Fig. 8

Population specificity organizes paths hierarchically and structurally. a Population-specific patterns of shortest paths between directly connected pairs of areas categorized according to their hierarchical relation as defined by fractions of supragranular labeled neurons (SLN). Arrow thickness indicates the relative occurrence of the particular pattern. The symbols mark excitatory (blue triangles) and inhibitory (red circles) populations stacked from L2/3 (top) to L6 (bottom). b Population-specific patterns of shortest paths between all pairs of areas categorized according to the difference between their architectural types. Arrow thickness indicates the occurrence of the particular pattern. c Occurrence of population patterns in areas that appear in the intermediate stage in the shortest path between two areas