Steady-state analysis of dynamical systems for biological networks gives rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here, the variety is described by a polynomial system in 19 unknowns and 36 parameters. It has degree 9 over the parameter space. This case study explores multistationarity, model comparison, dynamics within regions of the state space, identifiability, and parameter estimation, from a geometric point of view. We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics.
CITATION STYLE
Gross, E., Harrington, H. A., Rosen, Z., & Sturmfels, B. (2016). Algebraic Systems Biology: A Case Study for the Wnt Pathway. Bulletin of Mathematical Biology, 78(1), 21–51. https://doi.org/10.1007/s11538-015-0125-1
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