2.5. Random walk with restart network analysis

We used Random Walk with Restart (RWR) on multiplex networks to explore the network-topology based associations among LysM-RLKs in Populus. The RandomWalkRestartMH (RWR-MH, version 1.14.0) package in R was used to create multiplex networks and run the RWR process [102]. RWR-MH takes as input a multiplex network and set of genes that will be used as seeds that are the origin nodes for the random walk. We used the following network layers to create a multiplex network using default parameters (delta=0.5): a coexpression network derived from [103], knockout phenotype network derived from [104], predictive expression networks (PEN) from leaf and xylem [105], metabolic pathway network derived from PoplarCyc [106], and protein-protein interactions from STRING-DB [107].

The initial gene set comprised twelve LysM-RLK genes (Table 1). These genes were used as seeds in our RWR-Filter method using default parameters (restart=0.7). Briefly, RWR-Filter begins by using RWR to assign a random-walk score to all genes in the network using network-topology based associations. RWR-Filter then uses the scores to calculate a ‘mutual rank’ among all the genes in the initial gene set; this mutual rank is a measure of how related each gene is to all other genes in the initial gene set. Next, RWR-Filter iteratively rejects each gene from the gene set, starting with the poorest ranking gene, separating the initial gene set into ‘active’ and ‘reject’ sets. At each iteration, RWR-Filter tests the connectivity of the genes in the active set and the reject set by comparing the distribution of ranks to a uniform distribution using the Kolmogorov-Smirnov test. The active set genes were then used as seed genes in the RWR-Lines of Evidence (LOE) method with default parameters (restart=0.7). RWR-LOE also begins with RWR but differs from RWR-Filter in that it attempts to find genes in the network that were functionally related to, but not included in, the given gene set.

Initial hypothesized function of Populus lysin motif receptor-like kinases (LysM-RLKs) based on phylogenetic relatedness with functionally characterized LysM-RLKs from other plant species.

From the 40,815 genes in the multiplex networks, we selected the top 200 (0.5 %) for further analysis. We explored potential common biological processes among these genes by annotating them with both gene ontology (GO) and MapMan ontology and visualizing them in their network-context in Cytoscape [109]. First, we identified the most frequent MapMan terms among the top 200. Then, for the genes annotated with these terms, we selected nodes (genes) with high a degree of connectivity both with the seed genes and with each other. In addition, we performed gene ontology enrichment analysis on these 200 genes using the GO Term Enrichment tool from PlantRegMap (http://plantregmap.gao-lab.org/go.php) [110]. This allowed us to identify GO terms that were significantly represented among the top 200 genes. Furthermore, it helped us identify key genes within significant GO term categories that we could further evaluate for their potential role in signaling events downstream of LysM-RLKs based on functional characterization of gene homologs in other plant species (e.g., Arabidopsis).