The dominator tree model
Consider a digraph D with a distinguished start node, called the root, in which every node is connected to the root by a path if arc orientation is ignored. We call a node u a dominator of another node v if every directed path from the root to v contains u. In the signalling pathway context, this implies that any signal flowing to the protein component v from the entry point must be relayed through the protein u. The dominator relation is a transitive binary relation on the vertices of D. It can be represented by a tree, called the dominator tree of D, in which there is an edge from x to y if x is the least dominator of y for every pair of nodes x and y of D [5]. The dominator tree is unique (Fig. 1, Additional file 1: Fig. S1) and computable in near-linear time [4].
The ZDOG program
The ZDOG has two key functions (Fig. 2). First, it allows the user to examine gene mutations of different types in a cancer signalling pathway. After uploading a KEGG pathway from a local file or retrieving a pathway using KEGGscape [8], the user can examine genes that bear mutations in the datasets of the COSMIC and TCGA. Presently, the user can choose mutations of up to 16 types in up to 47 datasets available in the COSMIC and 18 types in up to 32 datasets in TCGA (Fig. 2a, left; Additional file 2: Table S1; Additional file 3: Table S2). Based on the selected mutation types and datasets, the mutation frequencies of the genes encoding protein components of the pathway are calculated and displayed in the right panel. Mutated genes are then coloured red, blue or grey according to whether they are oncogenes, tumour suppressors or neither, respectively, whereas unmutated genes are not coloured (Additional file 4). Additionally, the user can further examine mutations occurring in a particular gene by right-clicking the gene tag and then following “ZDOG – view mutation details” in the popped up context menu.
Second, the user can further zoom in on key mutated genes by viewing them in the dominator tree model of the signalling pathway (Fig. 2b). Here, we model a signalling pathway as a rooted connected digraph by selecting an entry point of the pathway signal, where each edge is oriented in the direction the signal flows in the pathway. Unfortunately, we are unable to distinguish inhibitory from stimulatory modification in the current implementation. The dominator tree is uniquely computed once the entry point of the signal is designated.
Re-examining mutated genes in the dominator tree of the signalling pathway allows the user to identify conveniently dominating mutated genes and to find out how they may affect the activation of downstream components that control important biological processes - cell proliferation, growth, apoptosis, etc. To this end, the user first selects a stimulus or a receptor protein as the entry point of the signal in the pathway displayed and then clicks the “calculate dominator tree” button. The gene mutations are redisplayed in the dominator tree of the pathway (Fig. 2b).
Installation of ZDOG
As a Cytoscape app, ZDOG must be installed and run in Cytoscape 3.6.0 or later. Cytoscape is downloadable from http://www.cytoscape.org. ZDOG requires the yFiles Tree Layout procedure and the KEGGscape tool for support. After these programs are installed, ZDOG can be easily installed via the App Manager in Cytoscape. Simple search for ZDOG in the App Manager and click Install. Alternatively, the ZDOG-1.0.jar file can be downloaded from https://github.com/rudi2013/ZDOG and installed using the App Manager – install from local file. Presently, only pathways in KEGG format are supported. Detailed installation instructions can be found in the user manual (Additional file 5).