Fig 1.
Workflow of our MultiCens measures.
(A) Each layer in the network represents a tissue, and connections represent gene-gene interactions (e.g., inferred from transcriptomic data). (Created with BioRender.com) (B) Supra-adjacency matrix (M) contains within-tissue connections on the diagonal blocks (intra-layer matrix A), and across-tissue connections on the off-diagonal blocks (inter-layer matrix C). The A, C matrices are used to compute different hierarchically-organized centralities as shown (note: the “collectively exhaustive node-sets” mentioned actually partition all the nodes in a layer or the network; see text). The centrality vectors (x, l, and g) have an entry for each gene in every tissue. (C) The centrality scores are used to obtain gene rankings which are further validated using different methods, and interpreted to predict novel mediators of inter-tissue signaling.
Fig 2.
Synthetic multilayer network construction.
(A) Synthetic network construction starts with a base random multilayer network with edge probability 0.05; (B) On the base synthetic multilayer network, more edges are added, according to the connection strength desired, both within the selected communities (indicated by circles) and between certain pairs of communities (indicated by thick dark edges connecting the pair; e.g. between source set 1 and source set 2). In the second layer, when only one community, query-set, is used, we call this model as the Synthetic Multilayer Network Model 1. When another community (marked in dotted circle) is connected to the query-set, we call this configuration Synthetic Multilayer Network Model 2.
Fig 3.
Synthetic multilayer network evaluation.
In both the panels, plots on the left and right are respectively obtained using Synthetic Multilayer Network Model 1 and 2. (A) As more nodes from source set 2 become part of the ground truth (shown as increasing fraction x), our MultiCens query-set centrality (QC) outperforms the existing methods and other MultiCens measures (local and global centrality, denoted LC and GC respectively) to a larger extent, especially in the presence of extra communities in the query-set layer (right). We calculated inter-layer degree and versatility using inter-layer connections to the query-set only; and let RWR-H’s seed nodes be same as the query-set. Each plot shows the connection strength (x-axis) against the number of ground truth nodes in the top 100 ranked nodes (y-axis). (B) Analysis of ranks based on MultiCens QC and our closely related method RWR-H. MultiCens QC (y-axis) distinguishes nodes coming from different sets somewhat better than RWR-H (x-axis), with this trend more clear in Synthetic Multilayer Network Model 2 than 1. Both these plots correspond to connection strength 1 as shown in (A).
Fig 4.
MultiCens on human multilayer networks: Ground-truth validation.
(A) Recall (# of ground truth genes recovered; y-axis) in the top k ranked genes (x-axis) are plotted using MultiCens query-set centrality based ranking vis-à-vis a random ranking (random curve). Only primary hormones shown here; see Fig B in S1 Text for comparison with other methods, and Fig C in S1 Text for plots for the other tested hormones. (B) For hormones with 10 or more genes in either producing or responding set, the smaller set is used as the query-set, and the plot reports AUC score for predicting the bigger set (marked in bold-face font in x-axis). For the four primary hormones having at least 10 genes on both producing and responding sets, plot reports AUC for predicting both sets. See also Table A in S1 Text.
Fig 5.
MultiCens on human multilayer networks: Prior support and novel predictions.
(A) Shown are all disease gene sets based on OMIM (Online Mendelian Inheritance in Man) that are enriched for top MultiCens centrality scores at FDR 5%, as reported by WebGestalt (see Methods; when predicting somatotropin-responding genes in liver, no disease enrichments pass this FDR cutoff; see also Fig D in S1 Text for the other two primary hormones’ disease enrichments). (B) Literature support for our top 10 predicted genes (ranked only among genes involved in peptide secretion) for the two peptide hormones, along with their co-occurrence scores and similarity in embedding space with hormone-related terms. Genes with a yellow background are present in the ground truth (HGv1 database); from the remaining genes, the green background represents genes supported by scores (co-occurrence score ≥ 1) for either or both hormone-related terms, and white background represents the other genes not supported by scores for both hormone-related terms. See also Table B in S1 Text for gene names corresponding to the gene symbols shown.
Table 1.
Top five ranked lncRNAs by MultiCens in source and target tissues of the four considered hormones.
Fig 6.
MultiCens on multi-brain-region networks in disease.
Study of changes in MultiCens Query-set centrality based gene rankings of four-layer networks of control and Alzheimer affected population. We rank genes of frontal pole (FP), superior temporal gyrus (STG) and inferior frontal gyrus (IFG) using MultiCens centralities calculated using a query-set of synaptic signaling genes in parahippocampal gyrus (PHG). (A) Bar-plot showing region-wise shift of centrality scores of the three regions. (B) Reactome pathways and Gene Ontology-based process (GO-BP) enrichment analysis of each region in control and AD state. Color map represents the normalized enrichment score from WebGestalt. The highlighted boxes pass the 0.01 FDR cut-off. If centrality-based gene rankings of a region do not pass the 0.05 FDR cut off for an enrichment, we set the corresponding normalized enrichment score to 0.