BowTieBuilder: modeling signal transduction pathways
© Supper et al; licensee BioMed Central Ltd. 2009
Received: 28 November 2008
Accepted: 30 June 2009
Published: 30 June 2009
Sensory proteins react to changing environmental conditions by transducing signals into the cell. These signals are integrated into core proteins that activate downstream target proteins such as transcription factors (TFs). This structure is referred to as a bow tie, and allows cells to respond appropriately to complex environmental conditions. Understanding this cellular processing of information, from sensory proteins (e.g., cell-surface proteins) to target proteins (e.g., TFs) is important, yet for many processes the signaling pathways remain unknown.
Here, we present BowTieBuilder for inferring signal transduction pathways from multiple source and target proteins. Given protein-protein interaction (PPI) data signaling pathways are assembled without knowledge of the intermediate signaling proteins while maximizing the overall probability of the pathway. To assess the inference quality, BowTieBuilder and three alternative heuristics are applied to several pathways, and the resulting pathways are compared to reference pathways taken from KEGG. In addition, BowTieBuilder is used to infer a signaling pathway of the innate immune response in humans and a signaling pathway that potentially regulates an underlying gene regulatory network.
We show that BowTieBuilder, given multiple source and/or target proteins, infers pathways with satisfactory recall and precision rates and detects the core proteins of each pathway.
Most signal transduction events are initialized by cell-surface proteins that respond to specific environmental stimuli. When activated these proteins emanate a signaling cascade which involves a series of (de)-phosphorylation events. In many cases such signaling events transduce the signal to transcription factors (TFs), which in turn regulate the expression level of downstream genes. Understanding this cellular processing of information, from the source proteins (e.g., cell-surface proteins) to the target proteins (e.g., TFs), is important when generating comprehensive models of regulatory networks. For several biological processes the signaling pathway has been derived experimentally [1, 2]. However, a large number of complex signaling pathways are yet to be discovered. To unravel these, computational inference methods are a valuable tool.
The basis for the computational inference of novel signaling pathways are protein-protein interaction (PPI) datasets. These datasets are derived from biological studies on individual PPIs, but recently also by large-scale genomic, proteomic, and bioinformatic analyses. The yeast-two hybrid method, for instance, was a major driving force in this development [3–5]. These technological advances in measuring and predicting PPIs have fueled numerous databases [6–9].
Based on such PPI datasets several methods have been developed for inferring signal transduction pathways [10–13]. Some of these methods combine PPI with gene expression datasets [10, 13], improving the overall performance. Here, the dataset provided by the STRING database is utilized . STRING already integrates PPI information from various sources (e.g., coexpression, the literature, and genomic context) and provides confidence scores for each reported PPI.
In this work we present BowTieBuilder, which aims at integrating multiple source proteins (e.g., membrane proteins) and target proteins (e.g., TFs) into one signaling pathway. As input, BowTieBuilder requires a set of source and/or target proteins. Given this input, BowTieBuilder searches for the most probable pathway that connects the input and output proteins. Thereby, core proteins are favored implicitly through the objective function. For every inferred signaling pathway, the core proteins are determined and their bow tie score is calculated, this value indicates whether the pathway is bow tie structured. These core proteins constitute gateways that integrate all information and are, therefore, often the key regulators in these signaling pathways. In contrast to metabolic networks where the core often forms a large cluster with interconnected nodes, bow ties in signaling networks are reported to have fewer nodes with sparse interconnections  – if they exist at all. Accordingly, The BowTieBuilder does not require a bow tie structure, so that pathways without a bow tie structure can also be inferred and analyzed.
To validate this method various sets of source and target proteins from yeast (Saccharomyces cerevisiae) and human (Homo sapiens) are inferred and compared against signaling pathways from KEGG (Kyoto Encyclopedia of Genes and Genomes) . To compare BowTieBuilder to other heuristics, three additional inference methods are described and applied to the same pathways. After validating the results against KEGG signaling pathways, two signaling pathways with no related KEGG pathway are inferred. One pathway involved in the innate immune system of human and another pathway that connected signal transduction and gene regulatory networks, which was inferred in a separate study .
Protein-protein interaction (PPI) data
The PPI dataset is represented as a weighted directed graph G = (V, E, w), where nodes (V) represent proteins, edges (E) PPIs, and the scores (w) the confidence in each interaction. The scores (edge weight w) range from 0, indicating no interaction, to 1, indicating an interaction with high confidence.
The PPI dataset used in this work is obtained from the STRING database (version 7.1) [9, 22–24]. This dataset contains computationally and experimentally derived PPIs, including interactions from other databases (e.g., MINT , BioGRID , DIP , and Reactome ), microarray experiments, high-throughput experiments, and a mined literature corpus. Furthermore, PPIs are transferred between orthologous pairs of proteins over different organisms. All of these datasets are combined and for each PPI a confidence score is calculated. This way the information from multiple sources is combined into a single score that expresses the overall confidence in each PPI. This score is derived by calculating the joint membership of proteins with PPI in KEGG pathways .
Problem complexity and formalization
The problem posed here is similar to the problem of finding Steiner trees in graphs , or more specifically, vertex-weighted Steiner trees. In this problem formalization, a weighted graph G = (V, E, w) and a non-emtpy set of terminals T ⊆ V is given, with w ∈ ℝ+. The optimal Steiner tree is defined as the connected subgraph G' = (V', E', w') with G' ⊆ G, for which the summed weight wsum(E') = ∑e∈E'w e is minimal, and T ⊆ V' holds. The Steiner tree problem on graphs was shown to be -complete  and, thus, is in most cases solved with heuristics. One of these heuristics is Prim's algorithm , which iteratively extends the subgraph G' by adding the vertex with the smallest distance until all nodes in T are connected in G'. A more recent heuristic presented by Melhorn et al.  proceeds by first calculating the minimal distance between all nodes in T, and then assembling the minimal Steiner tree by iteratively connecting the nodes with the smallest distance to each other.
Here, the aim is to select a subgraph of G' ⊆ G that connects a set of source proteins S to a set of target proteins T. Given a graph G = (V, E, w) with w ∈ [0, 1] and a disjoint source S ⊆ V and target set T ⊆ V (S ∩ T = ∅), the aim is to find the optimal subgraph G' ⊆ G such that for every s ∈ S and for every t ∈ T at least one path P(s, t) exists in G', whenever such a path exists in G. If either the source or the target set is empty, the problem formalization of Steiner trees is applied. Then the aim is to connect all nodes that are given either in S or in T (S ∩ T) to each other.
Objective function for the pathways
This objective is based on the assumption that the edge scores reflect independent confidence values, and implies that the resulting score gives the overall confidence in the pathway – that all contained edges are true biological interactions.
Inferring signal transduction pathways
Finding optimal paths between two proteins
Although the problem of finding the optimal pathway is -complete, some special instances exist that are solvable in polynomial time. If, for instance, the source set S and target set T both contain one node, the problem reduces to finding the highest scoring path between them. This problem can be solved by applying Dijkstra's algorithm . Given two nodes, this algorithm finds the highest scoring path with a runtime complexity of ((|E| + |V|) log |V|), where |V| gives the number of proteins and |E| the number of PPIs. For PPI networks, it can be assumed that most proteins are not connected to each other |E| ≪ |V|2; therefore, Dijkstra's algorithm is implemented using adjacency lists, and thus the runtime is reduced to (|V| log |V| + E). The scores between all nodes, obtained by Dijkstra's algorithm, will be stored in a distance matrix D|S|×|T|with |S| rows and |T| columns and the respective paths will be referred to by P D (s, t).
Initialize the pathway P with all nodes S ∩ T, and flag all nodes in S ∩ T as 'not visited'.
Calculate the distance matrix D|S|×|T|between the nodes in S and T with Dijkstra's algorithm.
Select the shortest path in D that connects a 'not visited' and a 'visited' node in P, or, if no such path exists, a 'not visited' node in S to a 'not visited' node in T.
Add the nodes and edges of the selected path to P and flag all nodes in the pathway as 'visited'.
Update D to include all distances to the nodes in P D (s, t).
Repeat the steps 2–5 until every node in S is connected to some node in T, and vice versa if such a path exists in G.
Export final pathway P.
As an optional parameter, the maximum path length l is introduced, since very long paths can increase the introduction of false positive PPIs. This is accomplished by setting the length of a path with more than l edges to ∞.
Additional inference methods
When applying heuristics, it is advisable to compare different approaches to each other to analyze their properties. For this purpose, we implemented three alternative inference methods: all interactions, shortest paths, and all shortest paths.
all interactions: In this modification, the standard BowTieBuilder is applied and the resulting pathway P is obtained. Then, all PPIs (edges) between any two nodes in P are added whenever they are contained in G.
shortest paths: In this inference method, every node in the source set S is connected to the target set T through the maximal scoring path, and vice versa. In this case the pathway P can be directly derived from paths corresponding to the maximal scores in matrix D. More specifically, for each row and column, the path corresponding to the maximal entry in D is added to P.
all shortest paths: In this inference method, for every pair of source (S) and target (T) proteins the highest scoring path P D (s, t) is added to P. Thus, every source and target node is directly connected if a corresponding path exists in G.
The topological validation is only performed for pathways that are provided by KEGG. Another possibility for testing the plausibility of inferred pathways – without the need for validation pathways – is to test if the inferred pathway can be associated with a certain biological process. To perform such an analysis, we map the proteins contained in each pathway to their 'biological process', defined by the Gene Ontology (GO) . The tool Term Finder  is used for this purpose, which calculates a p-value for each biological process using the hypergeometric distribution.
A direct validation against other methods for automatically inferring signal transduction pathways is omitted, because most of these algorithms are validated through pathways with one source and one target protein [10, 11, 13]. The recall and precision rates obtained by the different methods can, however, give a rough estimate of the relative performance.
Source and target proteins
BowTieBuilder is applied to several sets of source and target proteins. In principle, any type of source or target protein can be processed by BowTieBuilder; in this work, however, if not stated otherwise, the source proteins are membrane-bound proteins and the target proteins are TFs.
To infer signaling pathways for different biological processes, we collect several sets of membrane-bound proteins and TFs. To infer signaling pathways that control the yeast cell cycle, we collect membrane-TF sets for the yeast cell cycle phases G1 and S from the respective KEGG pathway (KEGG identifier: sce04111). For the analysis of the yeast MAPK pathway, the membrane and TF sets are obtained from the KEGG MAPK pathway (KEGG identifier: hsa04010). In addition, the human membrane and TF sets of the Erb pathway are collected from KEGG (KEGG identifier: hsa04012), and the human membrane and TF sets related to the TLR-mediated innate immune pathway are collected from a publication of Kitano et al. .
To combine signal transduction pathways with gene regulatory networks, all TFs that were inferred as regulators in a previous study  are used here as the target list. In this study, TFs were inferred to have a regulatory effect from two gene expression datasets [40, 41] and known cis-regulatory elements. In addition to these TFs a list of membrane proteins was collected from the Yeast Membrane Protein Library (YMPL). Based on these TFs and membrane proteins, a signaling pathway is inferred that potentially explains the higher-level regulation of these TFs in the respective gene regulatory network. All source and target proteins are provided in Additional File 1.
Bow tie score
As mentioned earlier, BowTieBuilder favors signaling pathways that are structured like a bow tie, but it does not demand such a structure. Thus, it is of interest to quantify to what extent signaling pathways follow the bow tie structure and, in addition, to determine the core proteins. For this purpose, we provide a bow tie score (b(p) ∈ [0, 1]) that determines how 'central' a protein p is. This score is also used to determine the bow tie score of the complete pathway. This score is related to the 'betweenness' measure, in which the number of shortest paths that include the core protein determines the centrality.
To determine the core elements of any signaling pathway, b(p) is calculated for every intermediate protein p. Given these scores, the core component is defined by the set of proteins with the maximal b(p) score. This also gives the overall score of the signaling pathway. In some cases it is helpful to distill the subnetwork that constitutes the bow tie structure by removing all paths that do not pass through the core component. We refer to such signaling pathways as 'core bow tie'.
Validation with KEGG signal transduction pathways
Comparison of different heuristics.
all shortest paths
Depending on the type of validation (protein or PPI), the performance of some heuristics varies strongly. The all interactions heuristic, for instance, has high precision when inferring proteins, although the precision for inferring edges is significantly lower in comparison to BowTieBuilder.
In summary, BowTieBuilder has the highest average precision but the lowest average recall. The all interactions heuristic, on the other hand, has the lowest precision and highest recall rate. Thus, the average precision decreases and the average recall increases in the following order: BowTieBuilder, shortest paths, all shortest paths, and all interactions. Several of the inferred pathways are provided in Additional File 2.
Yeast cell cycle pathways
Yeast MAPK pathway
Human Erb pathway
TLR-mediated innate immune pathway
Integrating signal transduction pathways and gene regulatory networks
In this work, we have presented several heuristics that allow inferring signal transduction pathways when several source and/or target proteins are given. The resulting pathways provide the researcher with a interconnected signaling pathway, which unravels the core proteins that integrate and transduce signals from multiple source to multiple target proteins.
Most current methods for the automated reconstruction of signal transduction pathways infer linear pathways and incorporate gene expression data into their scoring function [10–14]. BowTieBuilder allows inferring signal transduction pathways from an arbitrary number of source and target proteins.
Furthermore, the scoring function of BowTieBuilder is based solely on the PPI dataset from STRING and the associated confidence values. Hence, we build upon the integration of PPI information by STRING. The inferred signaling pathways had satisfactory recall and precision rates for most signaling pathways; for some, however, there is room for improvement. Two main sources of error could be observed. The first source of error was that some PPIs allow a 'shortcut' from the source to the target protein, in comparison to the reference pathway. This was, for instance, the case for several MAPK pathways, where these 'shortcuts' were even interactions with a high confidence level. Another source of error arises from the cyclic patterns that are neglected by inference methods when maximizing the pathway score.
In conclusion, when keeping the potential pitfalls of such inference methods in mind, the signaling pathways obtained can be of great help in understanding and constructing regulatory networks. BowTieBuider is capable of uncovering core proteins that integrate multiple source proteins and transduce these signals to TFs. This could be observed for the TLR-mediated innate immune pathway, where MyD88 and Fadd constitute the core proteins that function as a hub for all possible signaling pathways. Furthermore, Cdc28 was inferred as a core protein in both cell cycle related pathways, which is confirmed in the literature .
In other cases, such as the Erb pathway, no clear bow tie structure could be uncovered. Furthermore, proteins that were core proteins in certain pathways (e.g., Cdc28 in both cell cycle pathways) had very low bow tie scores in other pathways. Thus, which proteins constitute the core of a signal transduction pathway seems to be dynamic and depends on the context of target and source proteins.
This work was funded by the German Federal Ministry of Education and Research (BMBF) in the project 'National Genome Research Network' (NGFNplus) under grant number 01GS08134 and 'HepatoSys' under grant number 0313080 L.
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