Discrete logic modelling as a means to link protein signalling networks with functional analysis of mammalian signal transduction

Large-scale protein signalling networks are useful for exploring complex biochemical pathways but do not reveal how pathways respond to specific stimuli. Such specificity is critical for understanding disease and designing drugs. Here we describe a computational approach—implemented in the free CNO software—for turning signalling networks into logical models and calibrating the models against experimental data. When a literature-derived network of 82 proteins covering the immediate-early responses of human cells to seven cytokines was modelled, we found that training against experimental data dramatically increased predictive power, despite the crudeness of Boolean approximations, while significantly reducing the number of interactions. Thus, many interactions in literature-derived networks do not appear to be functional in the liver cells from which we collected our data. At the same time, CNO identified several new interactions that improved the match of model to data. Although missing from the starting network, these interactions have literature support. Our approach, therefore, represents a means to generate predictive, cell-type-specific models of mammalian signalling from generic protein signalling networks

Modeling approaches for qualitative and semi-quantitative analysis of cellular signaling networks

A central goal of systems biology is the construction of predictive models of bio-molecular networks. Cellular networks of moderate size have been modeled successfully in a quantitative way based on differential equations. However, in large-scale networks, knowledge of mechanistic details and kinetic parameters is often too limited to allow for the set-up of predictive quantitative models. Here, we review methodologies for qualitative and semi-quantitative modeling of cellular signal transduction networks. In particular, we focus on three different but related formalisms facilitating modeling of signaling processes with different levels of detail: interaction graphs, logical/Boolean networks, and logic-based ordinary differential equations (ODEs). Albeit the simplest models possible, interaction graphs allow the identification of important network properties such as signaling paths, feedback loops, or global interdependencies. Logical or Boolean models can be derived from interaction graphs by constraining the logical combination of edges. Logical models can be used to study the basic input–output behavior of the system under investigation and to analyze its qualitative dynamic properties by discrete simulations. They also provide a suitable framework to identify proper intervention strategies enforcing or repressing certain behaviors. Finally, as a third formalism, Boolean networks can be transformed into logic-based ODEs enabling studies on essential quantitative and dynamic features of a signaling network, where time and states are continuous. We describe and illustrate key methods and applications of the different modeling formalisms and discuss their relationships. In particular, as one important aspect for model reuse, we will show how these three modeling approaches can be combined to a modeling pipeline (or model hierarchy) allowing one to start with the simplest representation of a signaling network (interaction graph), which can later be refined to logical and eventually to logic-based ODE models. Importantly, systems and network properties determined in the rougher representation are conserved during these transformations. © 2013 Samaga and Klamt; licensee BioMed Central Ltd. [accessed July 18th

Detecting and Removing Inconsistencies between Experimental Data and Signaling Network Topologies Using Integer Linear Programming on Interaction Graphs

<div><p>Cross-referencing experimental data with our current knowledge of signaling network topologies is one central goal of mathematical modeling of cellular signal transduction networks. We present a new methodology for data-driven interrogation and training of signaling networks. While most published methods for signaling network inference operate on Bayesian, Boolean, or ODE models, our approach uses integer linear programming (ILP) on interaction graphs to encode constraints on the qualitative behavior of the nodes. These constraints are posed by the network topology and their formulation as ILP allows us to predict the possible qualitative changes (up, down, no effect) of the activation levels of the nodes for a given stimulus. We provide four basic operations to detect and remove inconsistencies between measurements and predicted behavior: (i) find a topology-consistent explanation for responses of signaling nodes measured in a stimulus-response experiment (if none exists, find the closest explanation); (ii) determine a minimal set of nodes that need to be corrected to make an inconsistent scenario consistent; (iii) determine the optimal subgraph of the given network topology which can best reflect measurements from a set of experimental scenarios; (iv) find possibly missing edges that would improve the consistency of the graph with respect to a set of experimental scenarios the most. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGFR/ErbB signaling against a library of high-throughput phosphoproteomic data measured in primary hepatocytes. Our methods detect interactions that are likely to be inactive in hepatocytes and provide suggestions for new interactions that, if included, would significantly improve the goodness of fit. Our framework is highly flexible and the underlying model requires only easily accessible biological knowledge. All related algorithms were implemented in a freely available toolbox <i>SigNetTrainer</i> making it an appealing approach for various applications.</p></div

MCoS for scenario 14 in Figure 3.

<p>Five MCoS are identified for the EGFR network model (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003204#pcbi-1003204-g004" target="_blank">Figure 4</a>) with respect to scenario 14 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003204#pcbi-1003204-g003" target="_blank">Figure 3</a>. Each MCoS would lead to a perfect fit for this scenario and all five MCoS contain three nodes to be enforced to a certain value. Nodes p90rsk and erk12 are common in all MCoS. Nodes rac_cdc42, sos1_eps8_e3b1, vav2, pi34p2 and pip3 are perturbed respectively in MCoS 1–5. In columns MCoS 1–5, three sub-columns are shown: sub-column “Val” shows the corrected state of the node (the actual MCoS), the entry 1 in sub-column “” indicates that a positive input edge is added to the node in order to alter its state, and the entry 1 in sub-column “” indicates that a negative input edge is added to the node (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003204#s3" target="_blank">Methods</a> section).</p

Basic network compression rules.

<p>(A) Parallel edges. (B) Nodes with single input. (C) Nodes with single output. (D) Shown is the compressed version of the network in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003204#pcbi-1003204-g001" target="_blank">Figure 1A</a> after applying the compression rules. For further explanations see main text.</p

Comparison of the fitting errors of the initial model structure (see Figures 3 and 4) and of the optimal interaction graph shown in Figure 7.

<p>Green fields indicate an error that has been present in the original model structure, but could be removed by optimizing the model structure. Yellow fields refer to errors that could not be resolved, and red fields indicate errors that have not been present in the original model structure, but were introduced by the optimization.</p

Interaction graph model of the EGFR/ErbB signaling network.

<p>(A) The full network adopted from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003204#pcbi.1003204-Samaga1" target="_blank">[18]</a> after removal of non-observable and non-controllable nodes. All edges are activating edges (having positive signs). (B) The compressed model obtained after applying the compression rules to (A).</p

Combined view of the three optimal subgraphs resulting when adding TGF<i>α</i> to CREB to the initial model structure.

<p>In all three solutions, the edges erk12→p70s6_1, tgfa→stat3, p90rsk→creb and p38→creb are removed. Edges tgfa→mek12 and rac_cdc42→mek12 represent alternative pathways; at least one of both must be contained.</p