Wiring cost and topological participation of the mouse brain connectome

Abstract

Brain connectomes are topologically complex systems, anatomically embedded in 3D space. Anatomical conservation of "wiring cost" explains many but not all aspects of these networks. Here, we examined the relationship between topology and wiring cost in the mouse connectome by using data from 461 systematically acquired anterograde-tracer injections into the right cortical and subcortical regions of the mouse brain. We estimated brain-wide weights, distances, and wiring costs of axonal projections and performed a multiscale topological and spatial analysis of the resulting weighted and directed mouse brain connectome. Our analysis showed that the mouse connectome has small-world properties, a hierarchical modular structure, and greater-than-minimal wiring costs. High-participation hubs of this connectome mediated communication between functionally specialized and anatomically localized modules, had especially high wiring costs, and closely corresponded to regions of the default mode network. Analyses of independently acquired histological and gene-expression data showed that nodal participation colocalized with low neuronal density and high expression of genes enriched for cognition, learning and memory, and behavior. The mouse connectome contains high-participation hubs, which are not explained by wiring-cost minimization but instead reflect competitive selection pressures for integrated network topology as a basis for higher cognitive and behavioral functions.

Keywords: conservation law; cytoarchitectonics; graph theory; transcriptomics; viral tracing.

Fig. 1.

Connectivity and costs of the mouse connectome. (A–C) Illustration of projection of tracer signal in one experiment (Allen Institute ID 157062358), coronal view. (A) Tracer injected into a source region (temporal association areas, TEa) was axonally transported to a target region (dorsal auditory area, AUDd). Connection weight was estimated with the normalized connection density (NCD), defined as the signal density in the target region (AUDd, red voxels) divided by the density of tracer injected in the source region (TEa, red voxels). (B) Image of tracer signal intensity on logarithmic scale. (C) Axonal distance was defined as the shortest estimated distance of the directed axonal projection from source to target (solid black line); normalized axonal bandwidth was defined as the proportion of the target’s boundary that shows signal (solid navy line); wiring cost was defined as the product of axonal distance and bandwidth. (D–F) Matrices of interregional NCD, wiring cost, and axonal distance ordered by block diagonalization of the NCD matrix. (G) Scatter plot of the NCD weight–distance relationship in the connectome, and locally smoothed weight–distance relationships in the connectome, lattice, and random graphs (solid lines). (H and I) Cumulative probability distributions of wiring cost of edges and nodes in the connectome, lattice, and random graphs. Confidence intervals for random graphs are interquartile ranges estimated from 100 random networks.

Fig. 2.

Community structure of the mouse connectome. Representations of hierarchical modules, core and high-participation, or hi-par, hubs. (A) Anatomical representation in sagittal sections with regions color-coded according to modular affiliation. Hi-par regions are in red. Sections are numbered as in the Allen Reference Atlas, mouse.brain-map.org/static/atlas; Inset shows section locations in coronal plane. (B) Connectivity matrix representation with blocks of hierarchical modules, the core embedded in the auditory-visual module (cyan), and intermodular connections mediated by hi-par hubs (red). (C–E) Graph representations with nodes arranged either in anatomical space (C), in topological space (force-directed graph layout) (D), or with nodes vertically arranged according to values of participation (E). Nodes are color-coded by modular affiliation; core nodes are squares with cyan borders; hi-par hubs are red squares. ACA, anterior cingulate area; AI, agranular insular area; GU, gustatory areas; m1, midbrain (mesomere 1); MOp, primary motor area; MOs, secondary motor area; ORB, orbital area; p1, pretectum (prosomere 1); p2, thalamus (prosomere 2); p3, prethalamus (prosomere 3); PTLp, posterior parietal association areas; SSp, primary somatosensory area; SSs, supplemental somatosensory area; Stri, intermediate stratum of striatum; Strp, caudate nucleus (periventricular stratum of striatum); VISC, visceral area.

Fig. 3.

High-participation hubs are expensive. (A–C) Scatterplots of participation coefficient versus degree, wiring cost, power-law exponent α for lo-par (gray), core (cyan), and hi-par (red) nodes (diamonds show posterior parietal association cortex, which is simultaneously a core and a hi-par node). ***P < 0.001 (D and E) Weight–distance scaling fits for the whole network (D), and for lo-par, core and hi-par nodes (E), estimated from weight–distance scatter plots of individual nodes. Graph representations in anatomical space of the high-cost subnetwork (brown) and low-cost subnetwork (gray) (F), the connectome (G), the cost-minimized lattice (H), and the topologically adaptive model of weight/distance scaling (I). See Fig. 2 for regional abbreviations.

Fig. 4.

Histological and gene-expression profiles of hi-par hubs. Scatterplots of participation versus neuronal volume density (A) and partial least squares gene-expression predictor (B). ***P < 0.001. (C) The total number of genes annotated for cognition, learning or memory, and single organism behavior (total length of bars), the number of annotated genes predictive of participation (dark portion of bars), and the expected number of such genes under the null hypothesis (red dashed lines).