Observability Based Parameter Identifiability for Biochemical Reaction Networks

Dara Geffen, Rolf Findeisen, Monica Schliemann, Frank Allgöwer, Martin Guay

Abstract: In systems biology, models often contain a large number of unknown or only roughly known parameters that must be identified. This work examines the question of whether or not these parameters can in fact be estimated from available measurements. We consider identiflability of unknown parameters in biochemical reaction networks obtained from first-principles-modeling of metabolic and signal transduction networks. Such systems consist of continuous time, nonlinear differential equations. Several methods exist for answering the question of identiflability for such systems; many of which restate the question of identiflability as one of observability. We consider the application of such methods to a representative biological system: the NF- <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</sub> B signal transduction pathway. It is shown that existing observability based strategies, which rely on finding an analytical solution, require significant simplifications to be applicable to systems biology problems which are often not feasible. For this reason, a new method based on the use of an 'empirical observability Gramian' for checking identifiability is proposed. This method is demonstrated through the use of a simple biological example.