Bioinformatics Advance Access originally published online on July 28, 2007
Bioinformatics 2007 23(19):2612-2618; doi:10.1093/bioinformatics/btm382
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Data-based identifiability analysis of non-linear dynamical models
Physics Institute, University of Freiburg, Hermann Herder Strasse 3, 79104 Freiburg i.Br., Germany
*To whom correspondence should be addressed.
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Abstract |
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Motivation: Mathematical modelling of biological systems is becoming a standard approach to investigate complex dynamic, non-linear interaction mechanisms in cellular processes. However, models may comprise non-identifiable parameters which cannot be unambiguously determined. Non-identifiability manifests itself in functionally related parameters, which are difficult to detect.
Results: We present the method of mean optimal transformations, a non-parametric bootstrap-based algorithm for identifiability testing, capable of identifying linear and non-linear relations of arbitrarily many parameters, regardless of model size or complexity. This is performed with use of optimal transformations, estimated using the alternating conditional expectation algorithm (ACE). An initial guess or prior knowledge concerning the underlying relation of the parameters is not required. Independent, and hence identifiable parameters are determined as well. The quality of data at disposal is included in our approach, i.e. the non-linear model is fitted to data and estimated parameter values are investigated with respect to functional relations. We exemplify our approach on a realistic dynamical model and demonstrate that the variability of estimated parameter values decreases from 81 to 1% after detection and fixation of structural non-identifiabilities.
Availability: Our algorithm is written in Matlab and R. It is available from the authors on request. An implementation of ACE, written in Matlab as well as in C, is available online at www.stefanhengl.de
Contact: hengl{at}fdm.uni-freiburg.de
Supplementary information: Supplementary data are available at Bioinformatics online.
Associate Editor: Limsoon Wong
Received on April 4, 2007; revised on July 10, 2007; accepted on July 10, 2007
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