Data-based identifiability analysis of non-linear dynamical models.
BACKGROUND
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.
Hengl
S
S
Physics Institute, University of Freiburg, Hermann Herder Strasse 3, 79104 Freiburg i.Br., Germany. hengl@fdm.uni-freiburg.de
Kreutz
C
C
Timmer
J
J
Maiwald
T
T
D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D016208:Databases, Factual; D016247:Information Storage and Retrieval / Q000379:methods*; D008954:Models, Biological; D017711:Nonlinear Dynamics; D010363:Pattern Recognition, Automated / Q000379:methods*; D020543:Proteome / Q000378:metabolism; D015398:Signal Transduction / Q000502:physiology
D020543:Proteome