Introduction
Comprehending biological pathways stands as a pivotal endeavor in the
realm of life sciences. However, merely possessing visual
representations such as PNG or SVG files is insufficient for
comprehensive analysis. The WayFindR package is a robust tool
meticulously crafted for both biologists and bioinformaticians. Its
primary objective is streamlining the intricate task of dissecting
cellular pathways. Through seamless integration of WikiPathways (a
well-known repository for biological pathways) and R’s igraph package,
WayFindR bestows users with the capability to transform complex pathway
architectures into actionable insights.
From a mathematical perspective, control theory asserts that negative
feedback is essential for effective regulation and control of dynamic
systems. Negative feedback mechanisms serve as stabilizing forces,
ensuring that deviations from desired states are minimized and the
system returns to equilibrium. In the context of biological pathways,
where intricate networks of molecular interactions govern cellular
processes, the concept of negative feedback is paramount.
Biologists rely on understanding the dynamics of biological pathways
to elucidate mechanisms underlying disease, identify potential drug
targets, and uncover regulatory networks. Negative feedback loops within
these pathways play crucial roles in maintaining cellular homeostasis,
modulating responses to external stimuli, and preventing excessive or
aberrant signaling.
By enabling the conversion of pathway structures into computationally
tractable formats and providing tools for analysis, WayFindR facilitates
the identification and characterization of negative feedback loops
within pathways. This capability is invaluable for deciphering the
regulatory logic governing cellular processes and designing
interventions to modulate pathway activity.
In essence, by bridging the gap between biological knowledge and
mathematical principles, WayFindR empowers researchers to navigate the
intricate landscapes of cellular pathways with precision and insight,
ultimately advancing our understanding of complex biological systems and
paving the way for innovative therapeutic strategies.
Retrieving data structure from GPML file
We will explore the functionality of WayFindR using one example file.
You can obtain a GPML file by visiting https://www.wikipathways.org/ and selecting a pathway
that piques your interest. We previously downloaded the pathway named
“Factors and pathways influencing insulin-like growth factor (IGF1)-Akt
signaling (WP3850),” which can be accessed directly at https://www.wikipathways.org/pathways/WP3850.html. We
included this GPML file in the package, and you can find it as a system
file.
gpmlFile <- system.file("pathways/WP3850.gpml", package = "WayFindR")
Functions in WayFindR rely on the XML R
package to parse GPML files. (GPML is a “dialect” of the extensible
markup language, XML.) You can simly supply the file name to the
functions, but they also work is you explicitly parse them yourself:
xmlfile <- XML::xmlParseDoc(gpmlFile)
We are going to illustrate the use of functions that allow users to
explore the various types of entities that are present in GPML files.
These are useful for understanding both how GPML files are defined and
how WayFindR works. You do not need to use them separately
on every file; if you just want to get to the resulting
igraph, you can skip ahead to the section on “Converting
pathways into igraph objects”.
Edges
A user can generate a matrix with information about edges from the
provided GPML file:
edges <- collectEdges(xmlfile)
class(edges)
## [1] "matrix" "array"
## [1] 46 3
The matrix comprises 46 rows (representing edges) and 3 columns:
Source, Target, and MIM (Molecular Interaction Maps). Each edge is
identified by a unique ID, such as id2257fd8. These edges are
directional, indicating they originate from one node and terminate at
another. The Source and Target columns contain labels corresponding to
these nodes. The MIM column illustrates the type of interaction
occurring between the nodes.
## Source Target MIM
## id2257fd8 "c0520" "b2305" "mim-inhibition"
## id25882942 "a531f" "b3910" "Arrow"
## id25c739ca "f5259" "ceb96" "Arrow"
## id2848101a "cc7e6" "fea9d" "Arrow"
## id295ae5fe "a8bb6" "b687e" "Arrow"
## id2e105012 "fea9d" "cd260" "Arrow"
## Source Target MIM
## idf7bb43f7 "f2f0d" "a2d31" "mim-inhibition"
## idfc5a5200 "f58ce" "d3cde" "Arrow"
## idfea9f3db "ceb96" "a2d31" "Arrow"
## idfed646d2 "ba0fb" "fca28" "Arrow"
## id2d5bc3d8 "b0088" "b2d78" "mim-inhibition"
## id70c7e487 "b62b2" "b3356" "mim-inhibition"
Nodes
Likewise, users can acquire a matrix of nodes in a similar
manner.
nodes <- collectNodes(xmlfile)
class(nodes)
## [1] "matrix" "array"
## [1] 52 3
In the selected pathway, there are a total of 52 nodes. The resulting
matrix consists of three columns: GraphId, label, and Type. GraphId
correlates to a distinct node ID extracted from the GPML file, while
label corresponds to the name of a gene, protein, group, complex or
biological process. The Type column contains information regarding the
type of node.
## GraphId label Type
## a169c "a169c" "GSK3B" "GeneProduct"
## a2d31 "a2d31" "PI3K" "GeneProduct"
## a4cc9 "a4cc9" "SMAD3" "GeneProduct"
## a531f "a531f" "4EPB" "GeneProduct"
## a5550 "a5550" "EIF2B2" "GeneProduct"
## a8bb6 "a8bb6" "N-WASP" "GeneProduct"
## GraphId label Type
## b3910 "b3910" "Protein synthesis" "Pathway"
## c2a5c "c2a5c" "MTOR" "GeneProduct"
## f5051 "f5051" "MLST8" "GeneProduct"
## e1ccf "e1ccf" "MAPKAP1" "GeneProduct"
## c6e5f "c6e5f" "RICTOR" "GeneProduct"
## a3b41 "a3b41" "MTOR" "GeneProduct"
Groups
We’ve already extracted all edges (Interactions) and vertices
(DataNodes) from a GPML file. Another significant element within a GPML
file is referred to as a “Group.” In some instances, Groups denote a
complex, often associated to a separate DataNode labeled
with the attribute Type="Complex". In other cases, Groups
seem to represent genes with interchangeable roles within the pathway.
For instance, within the IGF1-AKT pathway, there is an anonymous group
featuring SMAD2 and SMAD3.
groups <- collectGroups(xmlfile)
class(groups)
## [1] "list"
## [1] "nodes" "edges"
## GraphId label Type
## b5c6b b5c6b mTORC2 complex Complex
## b3356 b3356 mTORC1 complex Complex
## d51fd d51fd Group1 Complex
## dae36 dae36 Group2 Group
## Source Target MIM
## ec1 a4cc9 d51fd contained
## ec2 b3463 d51fd contained
## ec3 bb118 b3356 contained
## ec4 bd3fb dae36 contained
## ec5 ca5fb b3356 contained
## ec6 efb74 dae36 contained
## ec7 f8fb6 b3356 contained
## ec8 fad48 b3356 contained
## ec9 c2a5c b3356 contained
## ec10 f5051 b5c6b contained
## ec11 e1ccf b5c6b contained
## ec12 c6e5f b5c6b contained
## ec13 a3b41 b5c6b contained
The entry “contained” in the MIM column does not come from the MIM
standard, the WayFindR package has invented this edge type
to be able to relate a group to its constituent parts.
Anchors
The Anchor, which is the fourth and final “semantic” structure
outlined in the GPML specification, serves a specific purpose. It is
used to designate edges (or interactions, or arrows) that act as targets
for other edges, instead of the typical nodes (or DataNodes, or
vertices). To handle this scenario, WayFindR modifies the
target arrow, originally represented as A -> B, into a two-step
arrow, A -> EDGE -> B. Subsequently, we transform the
unconventional arrow into a simpler, more standardized representation
that now points to the newly introduced EDGE node.
links <- collectAnchors(xmlfile)
class(links)
## [1] "list"
## GraphId label Type
## 1 b2d78 Anchor1 EDGE
## Source Target MIM
## 1 b2305 b2d78 Source
## 2 b2d78 cd260 Arrow
Converting Pathways into igraph objects
The core feature of WayFindR is its ability to convert pathways from
WikiPathways GPML format into igraph objects. In the preocess, we also
define “standard” colors, line types, and shapes to display edges and
nodes.
data(edgeColors)
data(edgeTypes)
data(nodeColors)
data(nodeShapes)
if (requireNamespace("Polychrome")) {
opar <- par(mfrow = c(2,1))
Polychrome::swatch(edgeColors, main = "Edge Types")
Polychrome::swatch(nodeColors, main = "Node Types")
} else {
opar <- par(mfrow = c(1,2))
plot(0,0, type = "n", xlab="", ylab = "", main = "Edges")
legend("center", legend = names(edgeColors), lwd = 3,
col = edgeColors, lty = edgeTypes)
num <- c(rectangle = 15, circle = 16)
plot(0,0, type = "n", xlab="", ylab = "", main = "Nodes")
legend("center", legend = names(nodeColors), cex = 1.5,
col = nodeColors, pch = num[nodeShapes])
}
## Loading required namespace: Polychrome
Bundling the Process
The main function collects all the entities from the GPML file, adds
colors and styles, and produces an igraph.
G <- GPMLtoIgraph(xmlfile)
To visualize and analyze our graph, we can apply the graphopt (or any
of the many other) layout algorithm(s) from the igraph package:
set.seed(13579)
L <- igraph::layout_with_graphopt
plot(G, layout=L)
nodeLegend("topleft", G)
edgeLegend("bottomright", G)
Finding cycles
Once the pathway is converted, WayFindR provides a suite of tools for
in-depth analysis. Let’s explore how to find cycles within the pathway
graph (if they exist).
cyc <- findCycles(G)
length(cyc)
## [1] 5
## [[1]]
## dbe54 c0520 b2305 c7b3c b3356 ef7f5 ceb96 a2d31
## 2 27 15 8 18 52 30 23 2
##
## [[2]]
## dbe54 c0520 b2305 b3356 ef7f5 ceb96 a2d31
## 2 27 15 8 52 30 23 2
##
## [[3]]
## c7b3c b2305
## 8 18 8
##
## [[4]]
## c7b3c b3356 d51fd c0520 b2305
## 8 18 52 53 15 8
##
## [[5]]
## b3356 d51fd c0520 b2305
## 8 52 53 15 8
The output consists of a list of cycles extracted from a directed
graph. Each cycle is represented as a sequence of vertices, where each
vertex is indicated by its numerical position within the graph’s vertex
list. These cycles denote closed loops of vertices in the graph,
signifying paths that both start and end at the same vertex. The WP3850
pathway has 5 cycles.
Furthermore, within WayFindR, there exists a function named
“interpretCycle” designed to interpret a cycle within the
context of the associated graph. This function takes a cycle and the
graph it belongs to as inputs. Its purpose is to extract pertinent
details from the cycle, including edge ids, arrow types (indicating the
edge direction), and labels associated with genes.
lapply(cyc, interpretCycle, graph = G)
## [[1]]
## genes arrows
## 1 PI3K mim-stimulation
## 2 PDK1 mim-stimulation
## 3 AKT1 mim-inhibition
## 4 FoxO mim-stimulation
## 5 MAFbx mim-inhibition
## 6 mTORC1 complex mim-stimulation
## 7 S6K mim-inhibition
## 8 IRS1 mim-stimulation
##
## [[2]]
## genes arrows
## 1 PI3K mim-stimulation
## 2 PDK1 mim-stimulation
## 3 AKT1 mim-inhibition
## 4 FoxO mim-inhibition
## 5 mTORC1 complex mim-stimulation
## 6 S6K mim-inhibition
## 7 IRS1 mim-stimulation
##
## [[3]]
## genes arrows
## 1 FoxO mim-stimulation
## 2 MAFbx mim-stimulation
##
## [[4]]
## genes arrows
## 1 FoxO mim-stimulation
## 2 MAFbx mim-inhibition
## 3 mTORC1 complex mim-inhibition
## 4 Group1 mim-inhibition
## 5 AKT1 mim-inhibition
##
## [[5]]
## genes arrows
## 1 FoxO mim-inhibition
## 2 mTORC1 complex mim-inhibition
## 3 Group1 mim-inhibition
## 4 AKT1 mim-inhibition
Notice that the cycles in the chosen pathway include only inhibition
and stimulation processes.
Finally, we can generate a subgraph from the original graph,
containing only the vertices that participate in the specified
cycles.
S <- cycleSubgraph(G, cyc)
We depict the section of the graph that impacts cycles within the
IGF1-AKT wikiPathway.
set.seed(93217)
plot(S)
nodeLegend("topleft", S)
edgeLegend("bottomright", S)
Here, Group1 corresponds to the the pair SMAD2, SMAD3.