Fig 1.
Visualization of an immunoreceptor signaling model [9].
(A) Contact map showing the types of molecules in the model (Lig, Rec, Lyn, Syk), their components, and the internal states (Y,pY) and bonds available to those components. (B) The 24 rules in the model visualized as reactant-to-product transformations, showing what structures need to be matched for each rule to be triggered. (C) Rule influence diagram showing interactions between pairs of rules, computed by explicitly comparing each pair of rules from panel B. (D) Extended Contact Map drawn by manually interpreting the model according to a defined set of conventions [23]. Each diagram in panels B-D raises specific complexity and usability issues (see main text).
Fig 2.
Visualizing rules of an enzyme-substrate system.
(A) Structured molecule types Enz and Sub, their respective components (enclosed in ‘()’) and their available internal states (prefixed by ~), shown in BioNetGen syntax and graphic. (B) Reaction rules specifying the adding and removing of an enzyme-substrate bond (binding partners tagged by !1) and phosphorylation of components p1 and p2, shown in BioNetGen syntax. The reactants and products of a reaction rule are called patterns. (C) Conventional rule visualization by drawing reactant and product patterns separately. (D) Compact rule visualization displays operations (purple nodes) that transform the reactant patterns in each rule. On operation nodes, outward edges indicate that a new structure is produced (bond in R1, state pY in R2 and R3) and inward edges indicate that a structure is consumed (bond in _reverse_R1, state Y in R2 and R3). To see operation nodes with their labels, see S1 Fig.
Fig 3.
(A) Atoms, which are elementary structural features, shown in BioNetGen syntax and graphic. (B) Atom-rule graphs derived from the individual rules in Fig 2B. (C) The full atom-rule graph of the model, merged from individual graphs in panel B. AR graphs have three edge types: reactant (dark color, pointed towards rule), product (dark color, pointed away from rule), and context (light color, pointed towards rule), which indicate whether an instance of an atom is present in the rule’s reaction center (reactant/product) or reaction context.
Fig 4.
(A) The full model AR graph from Fig 3C. (B) Removing atoms and rules with low priority, such as free binding sites, unphosphorylated states and the unbinding rule. (C) Grouping structurally similar atoms, e.g., Sub_pY = phosphorylated states of p1 and p2, Enz|Sub = bond linking Enz and Sub. (D) Grouping rules with similar edge signatures, e.g., rules R2 and R3 both have a context edge from Enz|Sub and a product edge into Sub_pY. (E) Each group is merged into a single node that combines all incident edges. Panels B-C are semi-automated, whereas panels D-E are fully automated.
Fig 5.
Visualizing Lyn-FcεRI interactions.
(A) Lyn binds β domain of receptor that is unphosphorylated (constitutive binding–rule R3) or phosphorylated (activated binding–rule R6) via U or SH2 domains respectively. Recruited Lyn trans-phosphorylates β domain on the ligand-crosslinked receptor dimer (constitutively recruited Lyn–rule R4, actively recruited Lyn–rule R7). (B) The compressed atom-rule graph reveals a positive feedback loop between activated Lyn recruitment and receptor phosphorylation (highlighted with bold lines).
Fig 6.
Atom-rule graphs of the immunoreceptor signaling model of Fig 1 at various levels of compression.
(A) Full AR graph. (B) AR graph with low priority nodes removed. (C,D) Compressed AR graph following grouping and merging of nodes with a strict edge signature (C) or a permissive edge signature (D). For uncompressed versions of panels C-D, see S2B–S2C Fig.
Fig 7.
Compressed AR graph (63 nodes, 112 edges) generated from the FcεRI model of Chylek et al. [10] with 178 rules. The uncompressed graph has 305 nodes and 1076 edges. The model elements can be roughly classified into six subsystems shown above. The files needed to reproduce this diagram are provided in S1 Dataset.
Fig 8.
Compressed AR graph (79 nodes, 144 edges) generated from the ErbB model of Creamer et al. [14]) with 625 rules. The uncompressed graph has 930 nodes and 5269 edges. The model elements can be roughly classified into eight subsystems shown above. The files needed to reproduce this diagram are provided in S1 Dataset.
Fig 9.
Signaling motifs in the FcεRI library recovered from the compressed AR graph.
(A) Positive feedback loops enhance binding of Src family kinases Lyn and Fyn (denoted SFK) to receptor and Pag1 scaffold as well as Syk auto-phosphorylation. (B) Pag1 phosphorylated by SFKs recruits Csk, which negatively regulates SFKs by phosphorylation. (C) A coherent feed-forward loop activates Plcg1 from phosphorylated Lat. (D) An incoherent feed-forward loop involving enzymes PI3K and Inpp5d (a.k.a. SHP2) regulates levels of phosphoinositide PIP3, which is phosphorylated at both 3’ and 5’ hydroxyl positions (denoted PI_3P and PI_5P respectively).
Fig 10.
Comparison of readability metrics across visualization methods.
Graph size and edge density averaged over 27 models (geometric mean) for 9 automated visualizations: contact map (cmap), conventional rule visualization (rv), compact rule visualization(crv), Simmune Network Viewer diagram (sim), rule influence diagram (rinf), full model atom-rule graph (ar), AR graph with background removed (ar1), AR graph compressed with strict edge signature (ar2) or permissive edge signature (ar3). The compression pipeline (ar1-3) is semi-automated, but here it was applied automatically with default settings. The full dataset is shown in S3 Fig.
Fig 11.
Other visualization approaches applied to the enzyme-substrate phosphorylation model of Fig 2.
(A) The binding rule drawn using SBGN Process Description conventions, which require visual graph comparison. (B) Kappa story, showing the causal order of rules that produces sub_pp, which refers to doubly phosphorylated substrate. (C) Simmune Network Viewer diagram, which merges patterns across rules and hides certain causal dependencies (details in S4 Fig). Here, the Enz.Sub node merges all enzyme-substrate patterns shown in Fig 2. (D) SBGN Entity Relationship. (E) Molecular Interaction Map. Panels D-E require manual interpretation of the model, like the extended contact map. (F) rxncon regulatory graph visualization of the rxncon model format, which can only depict a limited subset of reaction rules (details in S5 Fig).