A multiscale cerebral neurochemical connectome of the rat brain

<div><p>Understanding the rat neurochemical connectome is fundamental for exploring neuronal information processing. By using advanced data mining, supervised machine learning, and network analysis, this study integrates over 5 decades of neuroanatomical investigations into a multiscale, multilayer neurochemical connectome of the rat brain. This neurochemical connectivity database (ChemNetDB) is supported by comprehensive systematically-determined receptor distribution maps. The rat connectome has an onion-type structural organization and shares a number of structural features with mesoscale connectomes of mouse and macaque. Furthermore, we demonstrate that extremal values of graph theoretical measures (e.g., degree and betweenness) are associated with evolutionary-conserved deep brain structures such as amygdala, bed nucleus of the stria terminalis, dorsal raphe, and lateral hypothalamus, which regulate primitive, yet fundamental functions, such as circadian rhythms, reward, aggression, anxiety, and fear. The ChemNetDB is a freely available resource for systems analysis of motor, sensory, emotional, and cognitive information processing.</p></div

Schematic representation of the neurochemical connectome.

<p>(a) Connectogram of the 125-node cerebral connectome partitioned in 19 large-scale brain regions. With 18.36%, the gamma-aminobutyric acid-ergic (GABAergic) neuronal connections constitute the dominant chemical components (b) followed by dopaminergic subnetwork 15.37% (c), serotoninergic connections 13.47% (d), glutamate system 10.75% (e), and enkephalinergic connections 7.76% (f).</p

Driver nodes and maximum matching in the <i>G</i>_125×125 network.

<p>(a) Purple edges show the links, which belong to the maximum matching and the driver nodes are highlighted as rectangles. The nodes are colored according to the brain regions they belong to. (b) The number of driver nodes as function of graph density, while sequentially removing the longest links from the <i>G</i>_125×125 network (red curve), starting from the intact network. Degree-preserving randomizations/rewirings were done on the intact network, generating 500 randomized graphs. The edge removal process and driver node measurements were repeated on each of the randomized versions (average: black curve, SD: gray area). The inset shows the same figure but on a log-scale for the <i>y</i> axis.</p

Core-periphery structure at the two resolution levels, <i>G</i>_19×19 and <i>G</i>_125×125.

<p>(a,c) Results found by the stochastic block model, where <i>γ</i>_<i>c</i> is the probability for a node to belong to the core. Core nodes, with <i>γ</i>_<i>c</i> > 0.5, are labeled with red dots. (b,d) Dendrograms showing the hierarchical decomposition of the networks based on the Girvan-Newman algorithm. The core nodes (labeled with red dots) are located towards the inside of the onion structure, while the periphery nodes (labeled with blue dots) are in the outer layers. (e) Graphical representation of the <i>G</i>_125×125 network using a force directed layout. Core nodes are concentrated towards the center. For the lists of core areas at the two resolution levels, see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2002612#pbio.2002612.s013" target="_blank">S13 Fig</a>.</p

Modeling the <i>G</i>_125×125 with an exponential distance rule (EDR) network.

<p>(a-e) Matching graph properties between model and data as function of the <i>λ</i> parameter. There is no narrow common band for <i>λ</i>, where all properties would match closely with the data. Averages were taken over 1,000 model-generated networks for each value of <i>λ</i>. (a) The number of uni- and bidirectional links: <i>M</i>₁ and <i>M</i>₂. (b) Root-mean-square (RMS) of deviations for the ratio of the 3-motif counts between model and data. (c) RMS of deviations between the clique counts for the model and data. (d) RMS of deviations between the eigenvalues of <i>AA</i>^<i>T</i> in the model and data. (e) The average local clustering coefficient in the undirected version of the graph. Dashed lines in (a) and (e) indicate values measured on the dataset. (f,g) Comparison of 3-motif counts between the dataset, EDR model with <i>λ</i> = 0.6, and CDR model (<i>λ</i> = 0). (g) Log-ratios between motif-counts. (h) Number of cliques with different sizes in the data and then the EDR and CDR network models. (i) The eigenspectrum of the co-occurrence matrix <i>AA</i>^<i>T</i>.</p

Modeling the <i>G</i>_19×19 with an exponential distance rule (EDR) network.

<p>(a-e) Matching graph properties between model and data as function of the <i>λ</i> parameter. The vertical grey band indicates the range of optimal fit for: 0.60 − 0.65<i>mm</i>⁻¹. Averages were taken over 1,000 model-generated networks for each value of <i>λ</i>. (a) The number of uni- and bidirectional links <i>M</i>₁ and <i>M</i>₂, respectively. (b) Root-mean-square (RMS) of deviations between the 3-motif counts of model and data. (c) RMS of deviations between the clique-counts of model and data. d) RMS of deviations between the eigenvalues of <i>AA</i>^<i>T</i> in the model and data, where <i>A</i> is the adjacency matrix. (e) The average local clustering coefficient in the undirected version of the graph. Dashed lines in (a) and (e) indicate values measured on the dataset. (f,g) Comparison of 3-motif counts between the dataset, EDR model with optimal <i>λ</i> = 0.6, and constant distant rule (CDR) model (<i>λ</i> = 0). (g) Log-ratios between motif counts. (h) Number of cliques with different sizes in data, EDR, and CDR models. (i) The eigenspectrum of the co-occurrence matrix <i>AA</i>^<i>T</i>.</p

Graph properties at the two resolution levels, <i>G</i>_19×19 and <i>G</i>_125×125.

<p>(a,b) In- and out-degree distributions and the fit obtained through the exponential distance rule (EDR) model (being a random model provides the same distribution for in- and out-degree). (c,d) Degree ranking and its EDR fit. Nodes are listed as function of their in- (top, red) and out-degree ranking (bottom, blue). In (d) only the first 20 nodes are listed, the inset shows the whole ranking plot for all 125 nodes. (e,f) Histogram of node-betweenness values. (g,h) Histogram of edge-betweenness values. Insets in (f,h) show the histograms on log-linear scale.</p