Data-driven reverse engineering of signaling pathways using ensembles of dynamic models

Despite significant efforts and remarkable progress, the inference of signaling networks from experimental data remains very challenging. The problem is particularly difficult when the objective is to obtain a dynamic model capable of predicting the effect of novel perturbations not considered during model training. The problem is ill-posed due to the nonlinear nature of these systems, the fact that only a fraction of the involved proteins and their post-translational modifications can be measured, and limitations on the technologies used for growing cells in vitro, perturbing them, and measuring their variations. As a consequence, there is a pervasive lack of identifiability. To overcome these issues, we present a methodology called SELDOM (enSEmbLe of Dynamic lOgic-based Models), which builds an ensemble of logic-based dynamic models, trains them to experimental data, and combines their individual simulations into an ensemble prediction. It also includes a model reduction step to prune spurious interactions and mitigate overfitting. SELDOM is a data-driven method, in the sense that it does not require any prior knowledge of the system: the interaction networks that act as scaffolds for the dynamic models are inferred from data using mutual information. We have tested SELDOM on a number of experimental and in silico signal transduction case-studies, including the recent HPN-DREAM breast cancer challenge. We found that its performance is highly competitive compared to state-of-the-art methods for the purpose of recovering network topology. More importantly, the utility of SELDOM goes beyond basic network inference (i.e. uncovering static interaction networks): it builds dynamic (based on ordinary differential equation) models, which can be used for mechanistic interpretations and reliable dynamic predictions in new experimental conditions (i.e. not used in the training). For this task, SELDOM’s ensemble prediction is not only consistently better than predictions from individual models, but also often outperforms the state of the art represented by the methods used in the HPN-DREAM challenge.Author summary: Signaling pathways play a key role in complex diseases such as cancer, for which the development of novel therapies is a difficult, expensive and laborious task. Computational models that can predict the effect of a new combination of drugs without having to test it experimentally can help in accelerating this process. In particular, network-based dynamic models of these pathways hold promise to both understand and predict the effect of therapeutics. However, their use is currently hampered by limitations in our knowledge of the underlying biochemistry, as well as in the experimental and computational technologies used for calibrating the models. Thus, the results from such models need to be carefully interpreted and used in order to avoid biased predictions. Here we present a procedure that deals with this uncertainty by using experimental data to build an ensemble of dynamic models. The method incorporates steps to reduce overfitting and maximize predictive capability. We find that by combining the outputs of individual models in an ensemble it is possible to obtain a more robust prediction. We report results obtained with this method, which we call SELDOM (enSEmbLe of Dynamic lOgic-based Models), showing that it improves the predictions previously reported for several challenging problems.