In this talk I will focus on a specific signaling pathway of gene regulation and present a new method for analysing models from systems biology. The focus of these techniques will be a set of models of the Wnt signaling pathway, which is involved in development, adult tissue cells and cancer.
We propose a new mechanistic model that includes spatial localization, compare this model and existing models from the literature to data. We develop and employ statistical and algebraic approaches-- focusing on both parameter-dependent and parameter-independent methods to compare and reject models. Specifically we use ideas from chemical reaction network theory, computational algebraic geometry, algebraic combinatorics and statistics to study the Wnt signaling system, enabling us to inform design of experiments and reject a competing Wnt model. The techniques are applicable to other problems in systems biology.