Mechanistic and predictive models of signaling networks are powerful tools to understand signal transduction, its deregulation in disease, and drugs’ mode of action. We use logic models, because they can handle large networks and phospho-proteomic and transcriptomic datasets with coverage of up to thousands of proteins and genes. We develop methods and tools based on this formalism and apply them in different contexts.
Regardless of the data and formalism, we translate a generic network to logic model, which is then trained to perturbation dataset (see Fig.). The generic prior knowledge network (PKN), is built based on literature and interaction databases, for which we use our resource Omnipath . The PKN describes the possible interactions among the signaling molecules and connects the perturbations to the measured molecular markers. Different formalisms, as described below, build different types of models from the PKN, ranging from Boolean networks to differential equations. Then we train the models to the measured data using optimisation methods. We also have tools to expand the PKN as our knowledge is generally incomplete [2,3].
This optimization problem can be solved sometimes using formal methods (specially when the models are binary, i.e. Boolean), such as Integer Linear Programming  or Answer Set Programming . For continuous formalisms, we rely on heuristics implemented in the tool MEIGO  developed jointly with the group of Julio Banga. For large-scale systems, we can use parallel optimization methods such as SaceSS .
The aforementioned workflow is performed with our open source tool CellNOpt (CellNetOptimizer) . CellNOpt uses different logic formalisms. These formalisms include Boolean, Fuzzy, Probabilistic, and Ordinary Differential Equation models which are trained against (phosphoproteomic) data. Applications range from cancer [8,9] to multiple sclerosis . We are also exploring the application of logic modelling to single-cell signaling data.
We have also developed PHONEMeS , a related tool to build logic models from discovery mass-spectrometry based Phosphoproteomic data. We apply PHONEMeS to various contexts, in particular in cancer.
In addition, we use similar approaches to extract mechanistic insights from multi-omics data: we developed CARNIVAL  to train signaling networks from gene expression data using ILP to infer causal paths linking signaling drives with downstream transcripts’ levels. We have scaled CARNIVAL up to multiple types of omic data with COSMOS .
Figure 1. General pipeline for training mechanistic models. Perturbation data is used to train a model that is generated from the interaction network (Prior Knowledge Network). Depending on the selected formalism, the appropriate parameterised model is built and the model parameters are tuned using optimisation algorithm until a reasonable fit between the model predictions and measured data is obtained. This way we can obtain mechanistic models tailored to the experimental data.