Parameter Identification in Systems Biology: Solving Ill-posed Inverse Problems using Regularization

Biochemical reaction networks are commonly described by non-linear ODE systems. Model parameters such as rate and equilibrium constants may be unknown or inaccessible and have to be identified from time-series measurements of chemical species. However, parameter identification is an ill-posed inverse problem in the sense that its solution lacks certain stability properties. In particular, modeling errors and measurement noise can be amplified considerably. These problems can be overcome by the use of so-called regularization methods. More specifically, parameter identification can be formulated in a stable way as a minimization problem with a data mismatch and a regularization term. On a benchmark problem, we demonstrate the stabilizing effect of Tikhonov regularization, i.e. we are able to identify the parameters from noisy measurements in a stable and accurate manner. In the algorithmic realization, we use the adjoint technique to efficiently compute the gradient of the data mismatch. Furthermore, we have developed a software package which allows the identification of parameters in valid SBML models of biochemical reaction networks. ∗ [email protected] Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Straße 69, 4040 Linz, Austria Industrial Mathematics Institute, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, Austria Rector’s Office, University of Vienna, Dr.-Karl-Lueger-Ring 1, 1010 Wien, Austria