Introduction

Network propagation has become a critical analysis technique in computational systems biology. Most commonly, the basic network propagation process starts with some query nodes, and a network. The query nodes are given some initial value, then a smoothing process is applied to the initial values on those query nodes, passing some of the value to neighboring nodes. By examining the final distribution of values, we can, for instance, find a subnetwork where the nodes are closely related by the network to the original query. More abstractly, network propagation supplies a robust estimate of network closeness, which can be used for many different applications. In computational biology, the most common meaning for the nodes is genes, and the edges usually represent various types of functional relationships between genes, for instance protein binding interaction, transcriptional regulation or signaling by phosphorylation.

Of the many applications of network propagation in systems biology, one of the most critical has been disease gene prioritization in genome-wide association studies. Genetic variants or mutations that otherwise would not pass a test for statistical significance, due to low power of association with the disease phenotype, can be prioritized due to their close association with each other in molecular networks. Koehler et al. [1] were some of the first to use network propagation in this fashion, which has since been extended to prioritizing protein complexes [2] and applied in a variety of other disease settings [3,4].

Vandin et al. [5] applied network propagation to discover significantly mutated subnetworks in cancer. Since then, the method has become a cornerstone of cancer genome analysis. Hofree et al. [6] used a network propagation method (Network-Based Stratification, or NBS) to cluster cancer patient data, Paull et al. [7] identified causal paths linking mutations to expression regulators, and Liu et al. and Zhong et al. [8,9] applied the NBS method across a wide variety of cancer types.

Given the success of this wide variety of applications, it is essential for network propagation to be readily available to any biologist, including those without dedicated bioinformatics support. Cytoscape is a well-established platform for many network applications [10], so it is a natural choice to host a network propagation algorithm. There have been a few Cytoscape Apps (GeneMania [11], propagate, and TieDIE) that have previously implemented network propagation algorithms; however, in these cases the basic network propagation operation is embedded within a more complex and extensive workflow or does not scale well to large biological networks. Nonetheless, the presence of these Apps demonstrate the community’s need for a stand-alone, robust network propagation algorithm.

Here we introduce Diffusion, a network propagation algorithm delivered as both a new Cytoscape feature and as an internet service available to a broad array of web, desktop and server-based applications such as Jupyter notebooks. The service is callable via a REST-based Application Programming Interface [12,13] (API, documented at https://github.com/idekerlab/heat-diffusion).

Results

To demonstrate the Diffusion service with a simple example, we created a 10-by-10 grid network and diffused a query from the upper left corner of the grid. The resultant output (Fig 1A) is a good proxy for distance to the upper left corner.

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Fig 1. Example uses of diffusion.

a. Diffusion of heat from a single query gene in the upper left, denoted with a green diamond, demonstrates that heat diffusion recapitulates network distance to the query set. b. A local network hypothesis for Vemurafenib resistance in cell line LOX-IMVI, correcting for a responsive cell line, A375. LOX-IMVI mutated genes appear outlined in red. The original Vemurafenib query genes appear as green diamonds. Three interaction types are present in this network: Grey dotted lines are protein-protein binding interactions, green arrows indicate control of localization, and blue arrows indicate phosphorylation.

https://doi.org/10.1371/journal.pcbi.1005598.g001

As a biological example, we chose to investigate a Vemurafenib resistant melanoma cell line, LOX-IMVI, as compared to a sensitive cell line A375 [16,17] with the goal of implicating mutations that may be affecting LOX-IMVI’s response to the drug. As an input query, we chose six genes (BRAF, PDGFRB, NRAS, HGF, MAP2K1, MAPK1) with known relationships to the drug [18–20]. The goal of this analysis is to find a subnetwork that is near the mutations of LOX-IMVI (which may be conferring resistance) and the known drug associated genes, but not near mutations that occur in the sensitive A375 line. For the underlying network, we used the NCI Pathway Interaction Database [21], an amalgamation of expert-curated cancer pathways. The version of this database that we used is provided in the supporting information as S1 File. As described in the following protocol, using a cutoff of the top 10 percent of nodes relevant to both Vemurafenib and LOX-IMVI mutations, but not A375 mutations according to diffusion, we produced a subnetwork of 53 nodes and 448 edges (Fig 1B). We demonstrate how this network-based hypothesis was reached using our Cytoscape application in the following example:

First, we performed a simple query to create a subnetwork relevant to Vemurafenib, based on the literature-implicated genes above:

1. Download and install Cytoscape from http://www.cytoscape.org/

2. Start Cytoscape, and instantiate a new session.

3. Install the “diffusion” app. Apps>App Manager> Select “diffusion” > Click install (Cytoscape versions earlier than 3.6).

4. Import the example network. File>Import>Network>File. In this case, S1 File.

Select a set of nodes using the mouse or by entering the node names separated by spaces into the Search Bar. We used BRAF, PDGFRB, NRAS, HGF, MAP2K1, and MAPK1. This will select the nodes with these gene names.

5. Right click on one of the selected nodes and select Diffusion>Diffuse Selected Nodes. This creates three table columns:

a. diffusion_input is a column representing the selected nodes. This is the h vector in Eq 1

b. diffusion_output_heat is a column representing the output vector d in the Eq 1

c. diffusion_output_rank is the rank of diffusion_output_heat from largest to smallest.

6. Construct a filter to select the most relevant subnetwork. First click on Select on the Control Panel on the left. Click the plus sign to create a new selection criterion. Choose Column Filter to specify that the information for the filter is in a Node Column. From the Choose column selector menu, select Node:diffusion_output_rank. Then select the most relevant nodes by sliding upper rank threshold slide to the left to select the desired number of nodes. In our case, we selected the top 10 percent most relevant genes, i.e. where the rank of the heat is less than 262 (Fig 2A).

7. Click the File>New>Network>From selected nodes, all edges to create a new network from the most relevant subnetwork.

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Fig 2. Cytoscape example screenshots.

a. Cytoscape after a simple diffusion query. The selection filter is set to pick the top 10 percent most relevant genes by rank to the input query. b. The filter settings for the selection of the subnetwork that is closely related to the Vemurafenib genes and the mutations in the LOX-IMVI cell line, but not the A375 genes. c. The filter settings for the original the query’s first neighbors that were not in the result network from step 15.

https://doi.org/10.1371/journal.pcbi.1005598.g002

Subsequent queries after the first diffusion will create new input and output columns, with each new entry denoted with an incremented counter. One can also use an imported table of data to drive a query. We have provided the mutations of the two cell lines in question (LOX-IMVI and A375) in a table that can be imported, downloaded from the Cancer Cell Line Encyclopedia [22]. Steps 9–12 provide an example of performing diffusion based on an imported set of features from a table:

9. Return to the original network by clicking on the Network tab from the Control Panel and selecting the original network.

10. Import the data table by choosing File>Import>Table>File and selecting the data table, S1 Dataset.txt. Click OK to import the data table as node features.

11. Create a new selection filter based on the imported data by clicking the Select tab on the control panel, then clicking the down arrow next to the filter name. Select Create new filter and name the filter. Click the plus sign to create a new selection criterion. Choose Column Filter to specify that the information for the filter is in a Node Column. From the Choose column selector menu, select one of the node columns corresponding to the data that you imported from the table, in this case LOXIMVI_SKIN. Slide the selector so that only nodes with a 1 in the relevant node column are selected.

12. Right click on one of the selected nodes, and select Diffusion>Diffuse Selected Nodes. Since this is the second query on this network, two new diffusion result columns are added to the network, named diffusion_output_rank_1 and diffusion_output_heat_1. Subsequent diffusion queries after the first are denoted with incremented integers in the output column names.

Diffusion results can be combined in informative ways. In steps 13–15 we combine our previous two query results with a third query from the A375 mutations to create a final network. The goal of this third criteria is to select against mutations that are similar to observed mutations in the Vemurafenib sensitive A375 cell line, which may be unlikely to be conferring resistance in LOX-IMVI.

13. Repeat steps 11 and 12 with the A375_SKIN column to create a new diffusion result.

14. Create a new filter, selecting nodes that are in the top 10 percent of each of the original Vemurafinib query and LOX-IMVI query, but not in the top 10 percent of the A375 query (Fig 2B).

15. Invoke File>New>Network>From selected nodes, all edges to create a new network.

Although not strictly necessary, it can be useful to add in the original query to better understand why nodes were selected. In the following sequence, we add in the original Vemurafenib nodes.

16. With the original complete NCI-PID network selected, run the original query again to select BRAF, PDGFRB, NRAS, HGF, MAP2K1, and MAPK1. Right click one of the selected nodes and click Select First Neighbors.

17. Create a new network by using File>New>From Selected Nodes, All edges.

18. Merge the networks created in step 15 and 17, by clicking Tools > Merge Networks and selecting those two networks to create a new Merged Network.

19. Filter out the first neighbors of the Vemurafenib query that did not make the LOX-IMVI filter cut by making a filter to select nodes where diffusion_input is 0 (i.e. not in the query) and diffusion_output_rank_1 is not less that 262 (Fig 2C).

20. Delete the selected nodes by clicking Edit> Delete selected nodes.

This technique is similar to Paull et al. [7] and Drake et. al [23], in that it uses multiple diffusion queries to select a specific subnetwork from multiple sources of evidence. TSC2 and BLNK were both mutated in the LOX-IMVI cell line and interacted with both BRAF and MAPK1, but similar mutations did not occur in A375, suggesting that these mutations may have a role in the cell line’s resistance to Vemurafenib. TSC2 is especially well supported, since it is a member of the PI3K/AKT/mTOR pathway, which has been shown to harbor resistance-conferring alterations [24].

Supporting information