Methods for logic modeling of signaling networks
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 different approaches, and we are particularly focused on logic models. Logic models, due to their simplicity, 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, models are built by training a generic network to perturbation dataset (Fig. 1). This generic prior knowledge network (PKN), is built based on literature and interaction databases, for which we use our resource Omnipath (Türei, Korcsmáros, and Saez-Rodriguez 2016). 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 type of models from the PKN, ranging from Boolean networks to differential equations. The model is then trained to the measured data using optimisation methods. We also have tools to expand the PKN as our knowledge is generally incomplete (Eduati et al. 2012).
This optimization problem can be solved sometimes using formal methods (specially when the models are binary, i.e. Boolean), such as Integer Linear Programming (Melas et al. 2015; Mitsos et al. 2009) or Answer Set Programming (Guziolowski et al. 2013). For continuous formalisms, we rely on heuristics implemented in the tool MEIGO (Egea et al. 2014) developed jointly with the group of Julio Banga. For large-scale systems, we can use parallel optimization methods such as SaceSS (Penas et al. 2017).
The aforementioned workflow is performed with our open source tool CellNOpt (CellNetOptimizer) (Saez-Rodriguez et al. 2009; MacNamara et al. 2012; Morris et al. 2011; Morris, Melas, and Saez-Rodriguez 2012). CellNOpt uses different logic formalisms. These formalisms include Boolean, Fuzzy, Probabilistic, and Ordinary Differential Equation models (C. Terfve et al. 2012) which are trained against (phosphoproteomic) data. Applications range from cancer (Eduati et al. 2017) to multiple sclerosis (Bernardo-Faura et al. 2019).
We have also developed PHONEMeS (Terfve et al. 2015), a related tool to build logic models from discovery mass-spectrometry based Phosphoproteomic data. We apply PHONEMeS to various contexts, in particular in cancer. We are currently exploring the application of logic modelling to single-cell signaling data and the integration of signaling and metabolic data.
In addition, we have developed CARNIVAL (Liu, Trairatphisan, Gjerga et al. 2019), a method to train signaling networks from gene expression data. Here, we use the causal-reasoning paradigm to infer the topology of signaling pathway from downstream transcripts’ levels, using Integer Linear Programming (Melas et al. 2015). An application was shown for the case of IgA nephropathy: a chronic kidney disease (Liu, Trairatphisan, Gjerga et al. 2019)
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.
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