Improving Prediction Capabilities of Complex Dynamic Models via Parameter Selection and Estimation

Many mathematical models describing complex (bio-)chemical reaction networks with a high level of detail are available in the literature. While such detailed models are desirable for investigating the dynamics of a particular component, it is often questionable if it is possible to verify these models due to the limited amount of quantitative data that can be generated. Even if it is not possible to estimate all parameters of these models then one would still be interested in determining which parameters should be estimated.

This paper addresses this point and introduces a technique for determining the parameters of a model that should be estimated from experimental data. The focus of this work is on ensuring that the model has good prediction capability as over-fitting the model to noisy experimental data is avoided. Towards this goal, a forward selection approach for selecting a subset of parameters for estimation while taking uncertainty into account is developed to minimize the mean squared prediction error of the model. It is shown that the developed technique is closely related to the often-used orthogonalization method. The technique is applied to a model of the NF-kB signal transduction pathway. The presented method is able to generate a smaller mean squared error than estimation of all parameters and also outperforms the orthogonalization method.