Symbolic Methods for Biological Networks

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Modeling the dynamics of networks is a key challenge in systems medicine and, more generally, in systems biology. Currently applied numeric methods face obstacles like parameter indeterminacy, instability, and curse of dimensionality. We propose new methods for a symbolic analysis, which overcome those obstacles and even impose an entirely new paradigm replacing thinking about single instances with thinking about orders of magnitude. Corresponding computational algebra problems are NP-hard, but experiments point at their feasibility for biological networks. We have already shown that complexity parameters such as tree-width or number of distinct metastable regimes grow only slowly with size for models available in existing biological databases. We will exploit this observation to solve challenging problems in network analysis including determination of parameter regions for the existence and stability of attractors, model reduction, and hybrid modeling of networks.