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Identifying parameter regions for multistationarity.

Carsten Conradi1, Elisenda Feliu2, Maya Mincheva3

  • 1Life Science Engineering, HTW Berlin, Berlin, Germany.

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Summary
This summary is machine-generated.

This study introduces a novel mathematical procedure to identify parameter regions in biological models exhibiting multiple steady states (multistationarity). The method uses Brouwer degree computation, avoiding numerical analysis for robust parameter space partitioning.

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Area of Science:

  • Mathematical Biology
  • Systems Biology
  • Computational Biology

Background:

  • Mathematical modeling is crucial for understanding biological system dynamics.
  • Identifying parameter values linked to qualitative features like multistationarity is a key challenge.

Purpose of the Study:

  • To develop a procedure for partitioning the parameter space of ordinary differential equations based on the number of equilibria.
  • To identify parameter regions associated with unique or multiple equilibria (multistationarity).

Main Methods:

  • The procedure is based on computing the Brouwer degree.
  • It generates a multivariate polynomial with parameter-dependent coefficients.
  • Signs of coefficients determine parameter regions with and without multistationarity.

Main Results:

  • The method partitions the parameter space regarding multistationarity.
  • It successfully avoids numerical analysis and parameter sampling.
  • Demonstrated on gene transcription and cell signaling models.

Conclusions:

  • The Brouwer degree-based procedure offers a robust method for analyzing multistationarity in biological models.
  • This approach provides a complete partitioning of parameter space in tested models.
  • It offers a powerful, non-numerical alternative for qualitative systems analysis.