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 .
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 .
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modeling
modelling
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biological dynamics
the dynamics of biological systems
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models
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behavior
behaviour
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an algorithm
a procedure
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algorithm
procedure
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a simple idea,
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it
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Using algebraic techniques, the
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We demonstrate the algorithm on
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
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signaling, and argue that the parameter constraints defining each region have biological meaningful interpretations
signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity