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Algebraic Systems Biology: A Case Study for the Wnt Pathway.

Elizabeth Gross1, Heather A Harrington2, Zvi Rosen3

  • 1San José State University, San José, CA, USA. elizabeth.gross@sjsu.edu.

Bulletin of Mathematical Biology
|December 10, 2015
PubMed
Summary

This study uses algebraic geometry to analyze the Wnt signaling pathway model, revealing complex dynamics and enabling better parameter estimation for biological networks.

Keywords:
-catenin/Wnt signalingAlgebraic matroidsBiochemical reaction networksNonlinear algebraPolyhedraSteady-state variety

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Area of Science:

  • Systems Biology
  • Computational Algebraic Geometry
  • Biophysics

Background:

  • Analyzing biological networks often involves studying complex dynamical systems.
  • Steady-state analysis yields algebraic varieties, which are mathematical objects of interest.
  • The Wnt signaling pathway is a crucial biological network with complex dynamics.

Purpose of the Study:

  • To apply geometric and algebraic methods to understand the Wnt signaling pathway model.
  • To explore concepts like multistationarity, model comparison, and parameter identifiability.
  • To demonstrate the utility of algebraic varieties in biological network analysis.

Main Methods:

  • Formulating the Wnt shuttle model as a polynomial system.
  • Utilizing computational algebraic geometry to study the resulting variety.
  • Employing polyhedral geometry and combinatorics for analysis.

Main Results:

  • The Wnt signaling pathway model corresponds to an algebraic variety of degree 9.
  • The study explores multistationarity, model comparison, and parameter estimation from a geometric perspective.
  • Demonstrated the application of advanced mathematical techniques to a specific biological model.

Conclusions:

  • Geometric analysis provides powerful insights into biological network dynamics.
  • The methods employed offer a novel approach to understanding complex biological systems.
  • This work highlights the interplay between mathematics and systems biology.