Identifying parameter regions for multistationarity

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Mathematical modeling has become an established tool for studying biological dynamics. Current applications range from building models that reproduce quantitative data to identifying models with predefined qualitative features, such as switching behavior, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce an algorithm to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria. The algorithm is based on a simple idea, the computation of the Brouwer degree, and creates a multivariate polynomial with parameter depending coefficients. Using algebraic techniques, the signs of the coefficients reveal parameter regions with and without multistationarity. We demonstrate the algorithm on models of gene transcription and cell signaling, and argue that the parameter constraints defining each region have biological meaningful interpretations.
TidsskriftP L o S Computational Biology (Online)
Udgave nummer10
Antal sider25
StatusUdgivet - 13 aug. 2017


  • q-bio.MN, math.AG, math.DS

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