title: Algebraic Systems Biology: A Case Study for the Wnt Pathway.
abstract: 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.affiliation: San José State University, San José, CA, USA. elizabeth.gross@sjsu.edu.
authors.forename: Elizabeth
authors.initials: E
authors.lastname: Gross
authors.affiliation: University of Oxford, Oxford, England. harrington@maths.ox.ac.uk.
authors.forename: Heather A
authors.initials: HA
authors.lastname: Harrington
authors.affiliation: Pennsylvania State University, State College, PA, USA. zur10@psu.edu.
authors.forename: Zvi
authors.initials: Z
authors.lastname: Rosen
authors.affiliation: University of California at Berkeley, Berkeley, CA, USA. bernd@berkeley.edu.
authors.forename: Bernd
authors.initials: B
authors.lastname: Sturmfels
mesh_terms: D000818:Animals; D006801:Humans; D055641:Mathematical Concepts; D053858:Metabolic Networks and Pathways; D008954:Models, Biological; D049490:Systems Biology / Q000706:statistics & numerical data*; D060449:Wnt Signaling Pathway
keywords: -catenin/Wnt signaling; Algebraic matroids; Biochemical reaction networks; Nonlinear algebra; Polyhedra; Steady-state variety