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Finding identifiable parameter combinations in nonlinear ODE models and the rational reparameterization of their
Nicolette Meshkat1, Chris Anderson, Joseph J Distefano
1UCLA, Department of Mathematics, USA. nmeshkat@math.ucla.edu
Mathematical Biosciences
|July 19, 2011
Summary
This study introduces an algorithm using Gröbner Bases to identify parameter combinations in dynamic systems, enabling unique model reparameterization for accurate analysis. This method addresses parameter unidentifiability in complex models.
Area of Science:
- Systems Biology
- Mathematical Modeling
- Computational Science
Background:
- Dynamic systems often suffer from structural non-identifiability, where parameters yield identical input-output data.
- Unidentifiable parameters hinder quantitative analysis and accurate computation of model solutions.
- Reparameterization using identifiable parameter combinations is crucial for model analysis.
Purpose of the Study:
- To explore and prove theoretical properties of an algorithm for finding identifiable parameter combinations.
- To demonstrate a unique rational reparameterization of dynamic system models.
- To apply the developed procedure to a nonlinear biological model.
Main Methods:
- Utilizing Gröbner Bases to identify algebraically independent parameter combinations.
- Developing a novel algorithm for parameter combination identification.
- Applying the algorithm to a nonlinear biomodel for validation.
Main Results:
- Proving that a set of M algebraically independent identifiable parameter combinations can be found.
- Demonstrating the existence of a unique rational reparameterization over these combinations.
- Successfully applying the procedure to a nonlinear biomodel, showcasing its practical utility.
Conclusions:
- The Gröbner Bases algorithm effectively identifies parameter combinations for unique model reparameterization.
- This approach enhances the quantitative analysis and computational feasibility of dynamic systems.
- The method holds significant potential for applications in systems biology and other complex modeling fields.
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