Parameter identification, experimental design and model falsification for biological network models using semidefinite programming

One of the most challenging tasks in systems biology is parameter identification from experimental data. In particular, if the available data are noisy, the resulting parameter uncertainty can be huge and should be quantified. In this work, a set-based approach for parameter identification in discrete time models of biochemical reaction networks from time series data is developed. The basic idea is to determine an outer approximation to the set of parameters for which trajectories are consistent with the available data. In order to approximate the set of consistent parameters (SCP) a feasibility problem is derived. This feasibility problem is used to verify that complete parameter sets cannot contain consistent parameters. This method is very appealing because instead of checking a finite number of distinct points, complete sets are analysed. With this approach, model falsification simply corresponds to showing that the SCP is empty. Besides parameter identification, a novel set-based method for experimental design is presented. This method yields reliable predictions on the information content of future measurements also for the case of very limited a priori knowledge and uncertain inputs. The properties of the method are presented using a discrete time model of the MAP kinase cascade.