Fig 1.
The multi-scale cortical wiring model.
(A) Wiring features, i.e., GD, MPC, and diffusion-based TS were estimated between all pairs of nodes. (B) Normalised matrices were concatenated and transformed into an affinity matrix. Manifold learning identified a lower-dimensional space determined by cortical wiring. (C) Left: node positions in this newly discovered space, coloured according to proximity to axis limits. Closeness to the maximum of the first eigenvector is redness, towards the minimum of the second eigenvector is greenness, and towards the maximum of the second eigenvector is blueness. The first 2 eigenvectors are shown on the respective axes. Right: equivalent cortical surface representation. (D) Calculation of interregional distances in the wiring space from specific seeds to other regions of cortex. Overall distance to all other nodes can also be quantified to index centrality of different regions, with more distinctive areas having longer distances to nodes. Replication with the Freesurfer-style preprocessing pipeline in S1 Fig. Essential data are available on https://git.io/JTg1l. a.u., arbitrary units; E, eigenvector; GD, geodesic distance; MPC, microstructure profile covariance; TS, tractography strength.
Fig 2.
Cytoarchitectural substrates of the wiring space.
(A) A 3D postmortem histological reconstruction of a human brain [35] was used to estimate cytoarchitectural similarity and externopyramidisation. Here, we present a coronal slice, a drawing of cytoarchitecture [135], magnified view of cortical layers in BigBrain and a staining intensity profile with example of calculation of externopyramidisation [44]. (B) Matrix and density plot depict the correlation between BigBrain-derived cytoarchitectural similarity and wiring distance between pairs of regions. (C) Externopyramidisation, projected onto the cortical surface and into the wiring space, is highest at the bottom of the structural manifold. Replication with the Freesurfer-style preprocessing pipeline in S5 Fig. Essential data are available on https://git.io/JTg1l.
Fig 3.
Transcriptomic substrates of the wiring space.
(A) mRNA-seq probes, assigned to 11 representative nodes (coloured as in Fig 1C, i.e., their position in the wiring space), provided good coverage of the space and enabled characterisation of cell type–specific gene expression patterns. Average cell type–specific gene expression patterns projected in the wiring space, with brighter colours signifying higher expression. (B) Equally spaced intercardinal axes superimposed on the wiring space, and below, line plots showing correlation of gene expression patterns with each of the axes. Colours correspond to the cell types shown in part A. (C) Strongest axis of variation (i.e., maximum |r|) in expression of each cell type overlaid on the structural manifold. Replication with the Freesurfer-style preprocessing pipeline in S6 Fig. Essential data are available on https://git.io/JTg1l. E, eigenvector; mRNA-seq, mRNA sequencing; OPC, oligodendrocyte progenitor cell; RNA-seq, RNA sequencing.
Fig 4.
From cortical wiring to functional connectivity.
(A) Nodes in the wiring-derived coordinate system coloured by functional community [47], with the distribution of networks shown by density plots along the axes. (B) Wiring distance between nodes, ordered by functional community, revealed a modular architecture. (C) Violin plots show the average wiring distance for nodes in each functional community, with higher values being more specialised in their cortical wiring. (D) Using the boosting regression models from the “Discovery” dataset, we used features of the wiring space to predict z-standardised functional connectivity in a “Hold-out” sample. The model was enacted for each node separately. (E) MSE across nodes are shown in the wiring space and on the cortical surface (Table C in S1 Text). (F) Predictive accuracy of various cortical wiring models, involving the use of different features, multifeature fusion, eigenvectors from diffusion map embedding, and a linear or ML learner. (G) MSE of the wiring space model stratified by functional community. Replication with the Freesurfer-style preprocessing pipeline in S8 Fig. Essential data are available on https://git.io/JTg1l. ΔE1, difference on eigenvector 1; ΔE2, difference on eigenvector 2; a.u., arbitrary units; FC, functional connectivity; ML, machine learning; MSE, mean squared error; WD, wiring distance.
Fig 5.
Large-scale organisation of coherence in the structural manifold.
(A) Intracerebral implantations of 10 epileptic patients were mapped to the cortical surface and intracortical EEG contacts selected. We studied 5 minutes of wakeful rest. (B) Mean and standard deviation in the variance explained in undirected coherence by wiring space features using adaboost machine learning across all nodes. (C) Clusters of the wiring space. (D) Phase slope index (Ψ) was calculated for each pair of intra-subject electrodes, then cluster-to-cluster estimates were derived from a linear mixed-effect model. Pearson correlation across Ψ estimates was used to measure the similarity of clusters, and the major axis of regional variation was identified via principle component analysis. (i) Average Ψ spectra for each region coloured by loading on the first principle component (accounting for 39% of variance). (ii) Component loadings presented in the wiring space and on the cortical surface illustrate a gradient from upper left regions, corresponding to central areas, towards lower right areas, corresponding to temporal and limbic areas. (iii) Lasso regularisation demonstrates the contribution of cell type–specific gene expression (colours matching Fig 3) and externopyramidisation (red) to explain variance in the component loadings. Shaded areas show the standard deviation in fitted least-squares regression coefficients across leave-one-observation-out iterations. For example, inhibitory neurons expression levels (green) are closely related to the component loading, as shown in the scatterplot. Replication with the Freesurfer-style preprocessing pipeline in S11 Fig. Essential data are available on https://git.io/JTg1l. a.u., arbitrary units; EEG, electroencephalography.
Fig 6.
Hierarchical information processing is organised within the structural manifold.
“Top”: The most influential frequencies on the component loading were identified through a correlation of average Ψ spectra (Fig 5Di) with the component loading. For the global maxima (24 Hz, left) and minima (86 Hz, right), we present cluster-to-cluster Ψ estimates, thresholded at p < 0.05. “Bottom”: Suprathreshold edges are plotted as a hierarchical schema, where the directed coherence estimates indicate flow of oscillations from the top to the bottom of the hierarchy. The hierarchical level of each cluster is also presented on the cortical surface and in the wiring space, illustrating unique spatial patterns of the frequency-specific hierarchies. Replication with the Freesurfer-style preprocessing pipeline in S13 Fig. Essential data are available on https://git.io/JTg1l.