Algebraic systems biology: a case study for the Wnt pathway

Journal article

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.

Authors: Gross, E; Harrington, H; Rosen, Z; Sturmfels, B

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer US
• Journal: Bulletin of Mathematical Biology
• Volume: 78
• Issue: 1
• Pages: 21–51
• Publication date: 2015-12-08
• Acceptance date: 2015-11-12
• DOI: 10.1007/s11538-015-0125-1
• EISSN: 1522-9602
• ISSN: 0092-8240
• Language: English
• Keywords: nonlinear algebra; biochemical reaction networks; algebraic matroids; polyhedra; steady-state variety; β-catenin/Wnt signaling