Decomposing the Parameter Space of Biological Networks via a Numerical Discriminant Approach

  • Heather A. Harrington
  • Dhagash Mehta
  • Helen M. Byrne
  • Jonathan D. HauensteinEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1125)


Many systems in biology (as well as other physical and engineering systems) can be described by systems of ordinary differential equation containing large numbers of parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and characterize the steady-state solutions as the model parameters vary, a technically challenging problem in a high-dimensional parameter landscape. Rather than simply determining the number and stability of steady-states at distinct points in parameter space, we decompose the parameter space into finitely many regions, the number and structure of the steady-state solutions being consistent within each distinct region. From a computational algebraic viewpoint, the boundary of these regions is contained in the discriminant locus. We develop global and local numerical algorithms for constructing the discriminant locus and classifying the parameter landscape. We showcase our numerical approaches by applying them to molecular and cell-network models.


Parameter landscape Numerical algebraic geometry Discriminant locus Cellular networks 



We thank J. Byrne and G. Moroz for helpful discussions. JDH was supported in part by NSF ACI 1460032 and CCF 1812746, Sloan Research Fellowship, and Army Young Investigator Program (YIP). HAH acknowledges funding from EPSRC Fellowship EP/K041096/1, Royal Society University Research Fellowship, and AMS Simons Travel Grant.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Heather A. Harrington
    • 1
  • Dhagash Mehta
    • 2
  • Helen M. Byrne
    • 1
  • Jonathan D. Hauenstein
    • 2
    Email author
  1. 1.Mathematical InstituteThe University of OxfordOxfordUK
  2. 2.Department of Applied and Computational Mathematics and StatisticsUniversity of Notre DameNotre DameUSA

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