Integrated mechanistic and data-driven modelling for multivariate analysis of signalling pathways

Mathematical models of highly interconnected and multivariate signalling networks provide useful tools to understand these complex systems. However, effective approaches to extracting multivariate regulation information from these models are still lacking. In this study, we propose a data-driven modelling framework to analyse large-scale multivariate datasets generated from mathematical models. We used an ordinary differential equation based model for the Fas apoptotic pathway as an example. The first step in our approach was to cluster simulation outputs generated from models with varied protein initial concentrations. Subsequently, decision tree analysis was applied, in which we used protein concentrations to predict the simulation outcomes. Our results suggest that no single subset of proteins can determine the pathway behaviour. Instead, different subsets of proteins with different concentrations ranges can be important. We also used the resulting decision tree to identify the minimal number of perturbations needed to change pathway behaviours. In conclusion, our framework provides a novel approach to understand the multivariate dependencies among molecules in complex networks, and can potentially be used to identify combinatorial targets for therapeutic interventions.