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Open Access Highly Accessed Methodology article

Simultaneous model discrimination and parameter estimation in dynamic models of cellular systems

Maria Rodriguez-Fernandez14, Markus Rehberg2, Andreas Kremling3 and Julio R Banga4*

Author Affiliations

1 Institute for Collaborative Biotechnologies, University of California, Santa Barbara, CA 93106-5080, USA

2 Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany

3 Faculty of Mechanical Engineering Specialty Division for Systems Biotechnology, Technische Universitat München, Boltzmannstr. 15, 85748 Garching, Germany

4 (Bio) Process Engineering Group, IIM-CSIC, C/Eduardo Cabello 6, 36208 Vigo, Spain

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BMC Systems Biology 2013, 7:76  doi:10.1186/1752-0509-7-76

Published: 12 August 2013



Model development is a key task in systems biology, which typically starts from an initial model candidate and, involving an iterative cycle of hypotheses-driven model modifications, leads to new experimentation and subsequent model identification steps. The final product of this cycle is a satisfactory refined model of the biological phenomena under study. During such iterative model development, researchers frequently propose a set of model candidates from which the best alternative must be selected. Here we consider this problem of model selection and formulate it as a simultaneous model selection and parameter identification problem. More precisely, we consider a general mixed-integer nonlinear programming (MINLP) formulation for model selection and identification, with emphasis on dynamic models consisting of sets of either ODEs (ordinary differential equations) or DAEs (differential algebraic equations).


We solved the MINLP formulation for model selection and identification using an algorithm based on Scatter Search (SS). We illustrate the capabilities and efficiency of the proposed strategy with a case study considering the KdpD/KdpE system regulating potassium homeostasis in Escherichia coli. The proposed approach resulted in a final model that presents a better fit to the in silico generated experimental data.


The presented MINLP-based optimization approach for nested-model selection and identification is a powerful methodology for model development in systems biology. This strategy can be used to perform model selection and parameter estimation in one single step, thus greatly reducing the number of experiments and computations of traditional modeling approaches.

Dynamic modelling; Parameter estimation; Model discrimination; Global optimization