Symbolic Methods for Biological Networks

网络动态建模是系统医学和系统生物学中的一个关键挑战。目前应用的数值方法面临的障碍，如参数的不确定性，不稳定性和维数灾难。我们提出了新的符号分析方法，克服了这些障碍，甚至施加了一个全新的范式，取代了对单个实例的思考与思考的数量级。相应的计算代数问题是NP难的，但实验表明它们对生物网络的可行性。我们已经表明，复杂性参数，如树的宽度或数量不同的亚稳态制度增长缓慢的大小模型在现有的生物数据库。我们将利用这一观察来解决网络分析中的挑战性问题，包括确定吸引子存在和稳定性的参数区域、模型降阶以及网络的混合建模。

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.