Building pathway graphs from BioPAX data in R

Biological pathways are increasingly available in the BioPAX format which uses an RDF model for data storage. One can retrieve the information in this data model in the scripting language R using the package rBiopaxParser, which converts the BioPAX format to one readable in R. It also has a function to build a regulatory network from the pathway information. Here we describe an extension of this function. The new function allows the user to build graphs of entire pathways, including regulated as well as non-regulated elements, and therefore provides a maximum of information. This function is available as part of the rBiopaxParser distribution from Bioconductor.

Biological pathways represent signalling and/or metabolic events involving protein and non-protein molecules. They are increasingly used in gene and protein expression studies to provide an aggregate score for gene sets encoding for defined biological events 1 . Several pathway databases, either curated or not, have adopted the BioPAX [RRID:SCR_009881] (Biological Pathway Exchange) language as a standard for pathway representation using the RDF (Resource Description Framework) data model 2 .
The structure of BioPAX is founded upon groupings, called classes, for physical entities and interactions with hierarchical networks of their sub-classes. Interactions between physical entities are represented such that conjoint interactions may form a specific pathway with defined, but different types of interactions between the involved physical entities. The BioPAX format is being actively developed, with BioPAX level 2 format focusing on metabolic pathways and BioPAX level 3 introducing full support for signalling pathways.
SPARQL (Simple Protocol And RDF Query Language) is a query language able to retrieve and manipulate data stored in RDF. Pathway information is often combined with statistical data analysis using tools such as R 3 . The rBiopaxParser [RRID:SCR_002744] 4 is an R package to retrieve data stored in a BioPAX RDF format. It comes with several options that are useful to probe the data and extract specific information from it, for example participants of a pathway, stoichiometric conditions to be fulfilled for an interaction, etc.
One such option is the pathway2RegulatoryGraph (P2RG) function that converts a pathway into a graphical structure. This is extremely useful for visual representation and subsequent graph-based network analysis. The P2RG function returns the parts of a pathway that are regulated (activated or inhibited) by proteins or protein complexes; this is important to understand the role of regulated proteins in pathways. Here we present an adaptation of P2RG, denoted pathway2Graph (P2G) which can be used to build a graph of the entire pathway, including the regulated as well as the non-regulated elements. This new function expands P2RG and can be used to investigate all different types of processes and connections of pathways instead of only studying the regulated elements of pathways. P2RG retrieves regulatory interactions, such as inhibitions and activations (shown in Figure 1 as continuous

Amendments from Version 1
The new version of the manuscript describes in more detail the differences between the existing function and the new function now added to the package. The information gained with the new function is illustrated with biologically relevant material. edges). The new P2G additionally, retrieves protein modifications, such as translocations or complex formation, which are shown as discontinuous edges in Figure 1.

REVISED
P2G is specifically aimed at retrieving results from Reactome BioPAX level 3. In this paper we describe detailed information on this function which, we believe, will help rBiopaxParser users to better understand the graphs generated from pathway information. We have verified P2G results by directly querying the original BioPAX data using SPARQL.

Methods and results
The classes of PhysicalEntity and Interaction that are used in Reactome v51 to represent information on pathways are shown in Figure 2. This graph was generated using the tool RDF2Graph 5 on the Reactome Level 3 RDF file. The nodes in Figure 2 represent classes and the edges show the possible relationships, called predicates, these classes could have in the database. As depicted in Figure 2, the node Pathway could have one or more Pathway-Steps that consist of different types of Interaction sub-classes.
All the Interaction nodes shown in Figure 2 describe interactions between PhysicalEntities, hence are connected to them by particular types of predicates as indicated in the edge labels.
The Interaction classes are interconnected because they can be dependent on each other. The Control interaction and its subclasses (Catalysis and Modulation) represent signalling events. They regulate BiochemicalReaction and Degradation interactions which mostly represent metabolic reactions.
To create a regulatory graph, the P2RG function starts with the Control, Catalysis and Modulation interactions that are either activating or inhibiting other interactions. This method provides a graph with plenty of information on the regulatory components of the pathway. The nodes of this graph are physical entities like Proteins or SmallMolecules and the directed edges are either activation or inhibition events. An example of such a reconstruction is shown in Figure 1, where P2RG is able to retrieve the black nodes and the continuous edges. However, interactions can be missed if they are not regulated by the Control interactions and could result in the loss of valuable information in the graphical representation of the pathway.
The new function P2G can start with any type of interaction in order to obtain a graph with all possible physical entities involved in the pathway. Similar to the result of the P2RG function, the P2G function gives a graph with nodes that are physical entities, but the edges are not strictly activation or inhibition events. The directed edges could represent several types of events like translocation of a protein or cleavage of DNA, these are shown as dis-continuous edges in the cartoon in Figure 1. The P2G function recognizes the continuous and the dis-continuous edges and thus retrieves the black as well as the red nodes shown in Figure 1.
In some cases there is more than one documented connection between the same physical entities. In this case only the first connection is used as an edge in the final pathway graph.

Comparison of two methods: P2G vs P2RG
The Reactome database (v51) categorizes pathways into 27 branches. Here we worked with pathways that have more than one interaction, which resulted in 1,666 pathways. Using P2RG, graphs for 1,548 pathways were retrieved. By using the new P2G function, we were able to retrieve information on all 1,666 pathways. The highest number of pathways were obtained, using either method, in the "Disease" category (P2RG: 3,396 pathways, P2G: 4,888 pathways). In 85% of the cases, pathways retrieved using P2G consisted of more physical entities (nodes) than those retrieved using P2RG. 19% of the P2G retrieved pathways have at least twice the number of nodes, and 60% have at least twice the number of interactions between nodes (edges) as compared to the P2RG version, Figure 3 is an example of this difference. Total numbers of nodes and edges in major Reactome categories are given in Table 1. Missing information causes the appearance of disconnected graphs when reconstructing pathways. By using the new P2G function, the percentage of disconnected pathways is reduced by 9%. Additionally, P2G also has the option of only retrieving the largest connected component, for example with this option, in Figure 3. A only the top left part of the graph will be retrieved and the two other disconnected parts discarded. The   3. Graphs of the pathway 'Apoptosis induced DNA fragmentation'. Both graphs were extracted from the same BioPAX file. A) Graph recovered using the new P2G function; B) Graph recovered using P2RG function. In both panels blue nodes are proteins or protein complexes, white nodes are non-protein entities. Black encircled nodes are found in both graphs and red encircled nodes are only detected with the new P2G function. Names of the nodes are in Table 2. pathways have directed edges because most of the interactions have direction. Edges without a direction are represented as bidirectional edges in the output of P2G.
As an example, we discuss here the 'Apoptosis induced DNA fragmentation' pathway, which is in the "Programmed Cell Death' category ( Figure 3). When the information in the BioPAX file is reconstructed with the P2RG function, the pathway has seven nodes (Figure 3.B); with the P2G function the same pathway has 16 more nodes (Figure 3.A). Detailed information on these nodes, as retrieved with P2G and P2RG, is given in Table 2 and demonstrates the additional information retrieved by P2G. The node 'Complex4169', which is found in the cytosol, translocates to the nucleus where it is called 'Complex4238'. However, this information is only available from the P2G function because the node 'Complex4169' does not regulate any other interaction or node. The presence of extra nodes in the P2G retrieved graph (Figure 3) also visualizes that 'Complex4240' breaks up into its' individual components after being cleaved by Caspase-3 ('Complex4238'). This extra information is very useful for researchers analysing the phenomena represented by the pathway. In case P2G retrieved pathways graphs are used for analysis (e.g, differential gene expression analysis) the presence of these extra nodes may improve biological interpretation of experimental data.

Conclusion
P2G is a useful addition to the rBiopaxParser package because it retrieves all the components of a pathway from the database and provides complete graphical information for both signalling as well as metabolic pathways. The P2G function (pathway2Graph) is currently available in the rBiopaxParser package in the Bioconductor 3.4 release.

Data availability
The input data for this package is the BioPAX format of any pathway database. We used the Reactome database which is freely available for download in different formats from the website www. reactome.org. A subset of this database is given as Supplementary file 1.

Software availability
Software available from: The function pathway2Graph is available in the latest version of the R package rBiopaxParser and can be installed from Bioconductor. Table 2. Node names and locations of the "Apoptosis induced DNA fragmentation" pathway. The first column has the names of the nodes in the pathwayas depicted in Figure 3. The second column has the actual name of the node and the third column the cellular location of the node. All this information is represented as given in Reactome version 51. The nodes shown with a black outline in Figure 3 are shown here in bold font.