title: Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks.
abstract: Parametric uncertainty is a particularly challenging and relevant aspect of systems analysis in domains such as systems biology where, both for inference and for assessing prediction uncertainties, it is essential to characterize the system behavior globally in the parameter space. However, current methods based on local approximations or on Monte-Carlo sampling cope only insufficiently with high-dimensional parameter spaces associated with complex network models. Here, we propose an alternative deterministic methodology that relies on sparse polynomial approximations. We propose a deterministic computational interpolation scheme which identifies most significant expansion coefficients adaptively. We present its performance in kinetic model equations from computational systems biology with several hundred parameters and state variables, leading to numerical approximations of the parametric solution on the entire parameter space. The scheme is based on adaptive Smolyak interpolation of the parametric solution at judiciously and adaptively chosen points in parameter space. As Monte-Carlo sampling, it is "non-intrusive" and well-suited for massively parallel implementation, but affords higher convergence rates. This opens up new avenues for large-scale dynamic network analysis by enabling scaling for many applications, including parameter estimation, uncertainty quantification, and systems design.
authors: Seminar for Applied Mathematics, ETH Zürich, Zürich, Switzerland.
authors: Claudia
authors: C
authors: Schillings
authors: Department of Biosystems Science and Engineering and SIB Swiss Institute of Bioinformatics, ETH Zürich, Zürich, Switzerland.
authors: Mikael
authors: M
authors: Sunnåker
authors: Department of Biosystems Science and Engineering and SIB Swiss Institute of Bioinformatics, ETH Zürich, Zürich, Switzerland.
authors: Jörg
authors: J
authors: Stelling
authors: Seminar for Applied Mathematics, ETH Zürich, Zürich, Switzerland.
authors: Christoph
authors: C
authors: Schwab
mesh_terms: D000465:Algorithms; D066246:ErbB Receptors; D005947:Glucose / Q000378:metabolism; D008954:Models, Biological; D009010:Monte Carlo Method; D012441:Saccharomyces cerevisiae / Q000378:metabolism; D015398:Signal Transduction; D049490:Systems Biology / Q000379:methods*
chemical_list: D066246:ErbB Receptors; D005947:Glucose