title: Driving the Model to Its Limit: Profile Likelihood Based Model Reduction.
abstract: In systems biology, one of the major tasks is to tailor model complexity to information content of the data. A useful model should describe the data and produce well-determined parameter estimates and predictions. Too small of a model will not be able to describe the data whereas a model which is too large tends to overfit measurement errors and does not provide precise predictions. Typically, the model is modified and tuned to fit the data, which often results in an oversized model. To restore the balance between model complexity and available measurements, either new data has to be gathered or the model has to be reduced. In this manuscript, we present a data-based method for reducing non-linear models. The profile likelihood is utilised to assess parameter identifiability and designate likely candidates for reduction. Parameter dependencies are analysed along profiles, providing context-dependent suggestions for the type of reduction. We discriminate four distinct scenarios, each associated with a specific model reduction strategy. Iterating the presented procedure eventually results in an identifiable model, which is capable of generating precise and testable predictions. Source code for all toy examples is provided within the freely available, open-source modelling environment Data2Dynamics based on MATLAB available at http://www.data2dynamics.org/, as well as the R packages dMod/cOde available at https://github.com/dkaschek/. Moreover, the concept is generally applicable and can readily be used with any software capable of calculating the profile likelihood.
authors: Institute of Physics, University of Freiburg, Freiburg im Breisgau, Germany.
authors: Tim
authors: http://orcid.org/0000-0002-4525-9556
authors: T
authors: Maiwald
authors: Institute of Physics, University of Freiburg, Freiburg im Breisgau, Germany.
authors: Helge
authors: H
authors: Hass
authors: Institute of Physics, University of Freiburg, Freiburg im Breisgau, Germany.
authors: Bernhard
authors: B
authors: Steiert
authors: Institute of Physics, University of Freiburg, Freiburg im Breisgau, Germany.
authors: Joep
authors: J
authors: Vanlier
authors: Institute of Physics, University of Freiburg, Freiburg im Breisgau, Germany.
authors: Raphael
authors: R
authors: Engesser
authors: Merrimack Pharmaceuticals, Boston, MA, United States of America.
authors: Andreas
authors: A
authors: Raue
authors: Department of Gastroenterology, Hepatology and Infectiology, University Hospital Duesseldorf, Duesseldorf, Germany.
authors: Friederike
authors: F
authors: Kipkeew
authors: Department of Gastroenterology, Hepatology and Infectiology, University Hospital Duesseldorf, Duesseldorf, Germany.
authors: Hans H
authors: HH
authors: Bock
authors: Institute of Physics, University of Freiburg, Freiburg im Breisgau, Germany.
authors: Daniel
authors: D
authors: Kaschek
authors: Institute of Physics, University of Freiburg, Freiburg im Breisgau, Germany.|Center for Biosystems Analysis (ZBSA), University of Freiburg, Freiburg im Breisgau, Germany.
authors: Clemens
authors: C
authors: Kreutz
authors: Institute of Physics, University of Freiburg, Freiburg im Breisgau, Germany.|Center for Biosystems Analysis (ZBSA), University of Freiburg, Freiburg im Breisgau, Germany.|BIOSS Centre for Biological Signalling Studies, University of Freiburg, Freiburg im Breisgau, Germany.
authors: Jens
authors: J
authors: Timmer
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008954:Models, Biological; D017711:Nonlinear Dynamics; D012984:Software; D049490:Systems Biology / Q000379:methods*