Identifying parameter regions for multistationarity
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Identifying parameter regions for multistationarity. / Conradi, Carsten; Feliu, Elisenda; Mincheva, Maya; Wiuf, Carsten.
I: P L o S Computational Biology (Online), Bind 13, Nr. 10, e1005751., 13.08.2017.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Identifying parameter regions for multistationarity
AU - Conradi, Carsten
AU - Feliu, Elisenda
AU - Mincheva, Maya
AU - Wiuf, Carsten
PY - 2017/8/13
Y1 - 2017/8/13
N2 - Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure 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 procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity.
AB - Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure 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 procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity.
KW - q-bio.MN
KW - math.AG
KW - math.DS
U2 - 10.1371/journal.pcbi.1005751
DO - 10.1371/journal.pcbi.1005751
M3 - Journal article
C2 - 28972969
VL - 13
JO - P L o S Computational Biology (Online)
JF - P L o S Computational Biology (Online)
SN - 1553-734X
IS - 10
M1 - e1005751.
ER -
ID: 167881007