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Analyses of antigen dependency networks unveil immune system reorganization between birth and adulthood
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Figures

Image of FIG. 1.

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FIG. 1.

(Color) The hybrid presentation of the informative subgraphs of the correlationvs dependency network. (a) Maternal dependency network, and (b) maternal correlations. (c) and (d), the same as (a) and (b) for the newborns. To simplify the presentation, we show the subgraphs for a selected subset of only 20 antigens that are the top separators between the two groups of subjects using t-test ranking between the two datasets. Arrows indicate the directionality of the influence. The antigen (nodes) influence scores (SLI) is color coded from dark blue for the least influential antigens to dark red for the most influential ones.

Image of FIG. 2.

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FIG. 2.

(Color) The hybrid presentation of the informative subgraphs of the dependency network. The selected layout, Fruchterman–Reingold three-dimensional (3D), visualizes the differences between the maternal (a, c) and the newborns (b, d) networks. In (a, b), the nodes were colored according to the isotypes, IgG: green and IgM: red. In (c, d), the colors indicate the strength of the SLI of each antigen on the correlations between all other antigen pairs, from most affecting antigen (dark red) to least affecting antigen (dark blue), The arrows indicate the directionality of the influence. Note the wide dispersal of highly affecting antigens in the networks.

Image of FIG. 3.

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FIG. 3.

(Color online) Top 20 most influential antigens in the dependency networks of the (a) mothers and (b) newborns. The bars indicate the SLI of each antigen on the correlations between all other antigen pairs in the network. For visualization proposes, influence score (SLI) values were rescaled between 0 and 1.

Image of FIG. 4.

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FIG. 4.

(Color) The hybrid presentation of the informative subgraphs of the dependency isotypic network presented with the Fruchterman–Reingold 3D layout. (a) Mothers’ IgG, (b) mothers’ IgM, (c) newborns’ IgG, and (d) newborns’ IgM. The colors indicate the strength of the SLI of each antigen on the correlations between all other antigen pairs, from most affecting antigens (dark red) to least affecting antigens (dark blue). The arrows indicate the directionality of the influence.

Image of FIG. 5.

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FIG. 5.

(Color) The hybrid presentation of the informative subgraphs of the dependency network for the separate isotypes. The selected layout, Kamada–Kawai, was partitioned by Newman’s algorithm, and each cluster was assigned a different color. (a) Mothers’ IgG, (b) mothers’ IgM, (c) newborns’ IgG, and (d) newborns’ IgM networks. Arrows indicate the directionality of the influence. Note that the same colors between two networks do not indicate similar members.

Image of FIG. 6.

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FIG. 6.

(Color) The hybrid presentation of the largest conserved element between the (a) IgG informative subgraphs of mothers and newborns. (b) The same for IgM isotype. Arrows indicate the directionality of the influence.

Image of FIG. 7.

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FIG. 7.

(Color) Top 100 most influential antigens in the dependency networks of the (a) mothers, (b) newborns, (c) mothers IgG, (d) newborns IgG, (e) mothers IgM, and (f) newborns IgM. The antigens were ranked according to their SLI scores and divided by the maximum score to get a relative SLI score. Note the change in SLI scores around 20 antigens mainly in the integrated diabetic and healthy IgM networks.

Image of FIG. 8.

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FIG. 8.

(Color) The hybrid presentation of the informative subgraphs of the correlation vs dependency network. (a) Maternal IgG correlation, (b) maternal IgG dependency network, (c) maternal IgM correlations, and (d) maternal IgM dependency network. (a, c) The selected layout, Kamada–Kawai, for the correlation based PMFG was partitioned by Newman’s algorithm, and each cluster was assigned a different color. (b, d) Superimposing the cluster coloring on the dependency networks. Arrows indicate the directionality of the influence. Note that the same colors between two networks do not indicate necessarily similar nodes but members of the same cluster.

Image of FIG. 9.

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FIG. 9.

(Color) Conserved subnetworks. (a) The IgG conserved subnetworks between the maternal and newborns networks. (b) The same for IgM. (c) The maternal IgG dependency network with all conserved elements marked in red. (d) The same for the IgM network.

Tables

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Table I.

Top 20 most influential antigens in the isotype networks.

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/content/aip/journal/chaos/21/1/10.1063/1.3543800
2011-03-29
2014-04-16

Abstract

Much effort has been devoted to assess the importance of nodes in complex biological networks (such as gene transcriptional regulatory networks,protein interaction networks, and neural networks). Examples of commonly used measures of node importance include node degree, node centrality, and node vulnerability score (the effect of the node deletion on the network efficiency). Here, we present a new approach to compute and investigate the mutual dependencies between network nodes from the matrices of node-node correlations. To this end, we first define the dependency of node i on node j (or the influence of node j on node i), D(i, j) as the average over all nodes k of the difference between the i − k correlation and the partial correlations between these nodes with respect to node j. Note that the dependencies, D(i, j) define a directed weighted matrix, since, in general, D(i, j) differs from D( j, i). For this reason, many of the commonly used measures of node importance, such as node centrality, cannot be used. Hence, to assess the node importance of the dependency networks, we define the system level influence (SLI) of antigen j, SLI( j) as the sum of the influence of j on all other antigens i. Next, we define the system level influence or the influence score of antigen j, SLI( j) as the sum of D(i, j) over all nodes i. We introduce the new approach and demonstrate that it can unveil important biological information in the context of the immune system. More specifically, we investigated antigen dependency networks computed from antigen microarray data of autoantibody reactivity of IgM and IgG isotypes present in the sera of ten mothers and their newborns. We found that the analysis was able to unveil that there is only a subset of antigens that have high influence scores (SLI) common both to the mothers and newborns. Networks comparison in terms of modularity (using the Newman’s algorithm) and of topology (measured by the divergence rate) revealed that, at birth, the IgG networks exhibit a more profound global reorganization while the IgM networks exhibit a more profound local reorganization. During immune system development, the modularity of the IgG network increases and becomes comparable to that of the IgM networks at adulthood. We also found the existence of several conserved IgG and IgM network motifs between the maternal and newborns networks, which might retain networkinformation as our immune system develops. If correct, these findings provide a convincing demonstration of the effectiveness of the new approach to unveil most significant biological information. Whereas we have introduced the new approach within the context of the immune system, it is expected to be effective in the studies of other complex biological social, financial, and manmade networks.

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Scitation: Analyses of antigen dependency networks unveil immune system reorganization between birth and adulthood
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/1/10.1063/1.3543800
10.1063/1.3543800
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