Algebraic Systems Biology: A Case Study for the Wnt Pathway

TL;DR

This paper applies algebraic geometry and combinatorics to analyze the steady state of a complex biological network model, specifically the Wnt signaling pathway, revealing insights into its algebraic structure.

Contribution

It introduces a novel algebraic approach to analyze the steady states of the Wnt pathway model using computational algebraic geometry.

Findings

Polynomial system in 19 unknowns and 36 parameters characterized

Algebraic varieties associated with the model analyzed

Method demonstrates potential for biological network analysis

Abstract

Steady state analysis of dynamical systems for biological networks give 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. Current methods from computational algebraic geometry and combinatorics are applied to analyze this model.