Journal of Mathematical Biology

, Volume 67, Issue 6, pp 1795–1832

On the identifiability of metabolic network models

  • Sara Berthoumieux
  • Matteo Brilli
  • Daniel Kahn
  • Hidde de Jong
  • Eugenio Cinquemani
Article

DOI: 10.1007/s00285-012-0614-x

Cite this article as:
Berthoumieux, S., Brilli, M., Kahn, D. et al. J. Math. Biol. (2013) 67: 1795. doi:10.1007/s00285-012-0614-x

Abstract

A major problem for the identification of metabolic network models is parameter identifiability, that is, the possibility to unambiguously infer the parameter values from the data. Identifiability problems may be due to the structure of the model, in particular implicit dependencies between the parameters, or to limitations in the quantity and quality of the available data. We address the detection and resolution of identifiability problems for a class of pseudo-linear models of metabolism, so-called linlog models. Linlog models have the advantage that parameter estimation reduces to linear or orthogonal regression, which facilitates the analysis of identifiability. We develop precise definitions of structural and practical identifiability, and clarify the fundamental relations between these concepts. In addition, we use singular value decomposition to detect identifiability problems and reduce the model to an identifiable approximation by a principal component analysis approach. The criterion is adapted to real data, which are frequently scarce, incomplete, and noisy. The test of the criterion on a model with simulated data shows that it is capable of correctly identifying the principal components of the data vector. The application to a state-of-the-art dataset on central carbon metabolism in Escherichia coli yields the surprising result that only \(4\) out of \(31\) reactions, and \(37\) out of \(100\) parameters, are identifiable. This underlines the practical importance of identifiability analysis and model reduction in the modeling of large-scale metabolic networks. Although our approach has been developed in the context of linlog models, it carries over to other pseudo-linear models, such as generalized mass-action (power-law) models. Moreover, it provides useful hints for the identifiability analysis of more general classes of nonlinear models of metabolism.

Keywords

Systems biology Metabolic network modeling Parameter estimation Structural and practical identifiability  Principal component analysis  Singular value decomposition  Escherichia coli carbon metabolism 

Mathematics Subject Classification (2000)

92 Biology and other natural sciences 93 System theory Control 

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sara Berthoumieux
    • 1
  • Matteo Brilli
    • 2
  • Daniel Kahn
    • 2
  • Hidde de Jong
    • 1
  • Eugenio Cinquemani
    • 1
  1. 1.INRIA Grenoble-Rhône-AlpesMontbonnotFrance
  2. 2.Laboratoire de Biométrie et Biologie Evolutive, CNRS UMR 5558Université Lyon 1, INRAVilleurbanneFrance

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