Computational modeling of signal transduction networks without kinetic parameters: Petri net approaches

More and more computational techniques have been applied to model biological systems, especially signaling pathways in medical systems. Due to the large number of experimental data driven by high-throughput technologies, new computational concepts have been developed. Nevertheless, often the necessary kinetic data cannot be determined in sufficient number and quality because of experimental complexity or ethical reasons. At the same time, the number of qualitative data drastically increased, for example, gene expression data, protein-protein interaction data, and imaging data. Especially for large-scale models, the application of kinetic modeling techniques can fail. On the other hand, many large-scale models have been constructed applying qualitative and semiquantitative techniques, for example, logical models or Petri net models. These techniques make it possible to explore system's dynamics without knowing kinetic parameters. Here, we summarize the work of the last 10 years for modeling signal transduction pathways in medical applications applying Petri net formalism. We focus on analysis techniques based on system's invariants without any kinetic parameters and show predictions of all signaling pathways of the system. We start with an intuitive introduction into Petri nets and system's invariants. We illustrate the main concepts using the tumor necrosis factor receptor 1 (TNFR1)-induced nuclear factor κ-light-chain-enhancer of activated B cells (NF-κB) pathway as a case study. Summarizing recent models, we discuss the advantages and challenges of Petri net applications to medical signaling systems. In addition, we provide exemplarily interesting Petri net applications to model signaling in medical systems of the last years that use the well-known stochastic and kinetic concepts developed about 50 years ago.