Representing dynamic biological networks with multi-scale probabilistic models.

Dynamic models analyzing gene regulation and metabolism face challenges when adapted to modeling signal transduction networks. During signal transduction, molecular reactions and mechanisms occur in different spatial and temporal frames and involve feedbacks. This impedes the straight-forward use of methods based on Boolean networks, Bayesian approaches, and differential equations. We propose a new approach, ProbRules, that combines probabilities and logical rules to represent the dynamics of a system across multiple scales. We demonstrate that ProbRules models can represent various network motifs of biological systems. As an example of a comprehensive model of signal transduction, we provide a Wnt network that shows remarkable robustness under a range of phenotypical and pathological conditions. Its simulation allows the clarification of controversially discussed molecular mechanisms of Wnt signaling by predicting wet-lab measurements. ProbRules provides an avenue in current computational modeling by enabling systems biologists to integrate vast amounts of available data on different scales.