In systems biology, one of the major tasks is to tailor model complexity to information content of the data. A useful model should describe the data and produce well-determined parameter estimates and predictions. Too small of a model will not be able to describe the data whereas a model which is too large tends to overfit measurement errors and does not provide precise predictions. Typically, the model is modified and tuned to fit the data, which often results in an oversized model. To restore the balance between model complexity and available measurements, either new data has to be gathered or the model has to be reduced. In this manuscript, we present a data-based method for reducing non-linear models. The profile likelihood is utilised to assess parameter identifiability and designate likely candidates for reduction. Parameter dependencies are analysed along profiles, providing context-dependent suggestions for the type of reduction. We discriminate four distinct scenarios, each associated with a specific model reduction strategy. Iterating the presented procedure eventually results in an identifiable model, which is capable of generating precise and testable predictions. Source code for all toy examples is provided within the freely available, open-source modelling environment Data2Dynamics based on MATLAB available at http://www.data2dynamics.org/, as well as the R packages dMod/cOde available at https://github.com/dkaschek/. Moreover, the concept is generally applicable and can readily be used with any software capable of calculating the profile likelihood.

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Reelin is a large glycoprotein with a dual role in the mammalian brain. It regulates the positioning and differentiation of postmitotic neurons during brain development and modulates neurotransmission and memory formation in the adult brain. Alterations in the Reelin signaling pathway have been described in different psychiatric disorders. Reelin mainly signals by binding to the lipoprotein receptors Vldlr and ApoER2, which induces tyrosine phosphorylation of the adaptor protein Dab1 mediated by Src family kinases (SFKs). In turn, phosphorylated Dab1 activates downstream signaling cascades, including PI3-kinase-dependent signaling. In this work, a mechanistic model based on ordinary differential equations was built to model early dynamics of the Reelin-mediated signaling cascade. Mechanistic models are frequently used to disentangle the highly complex mechanisms underlying cellular processes and obtain new biological insights. The model was calibrated on time-resolved data and a dose-response measurement of protein concentrations measured in cortical neurons treated with Reelin. It focusses on the interplay between Dab1 and SFKs with a special emphasis on the tyrosine phosphorylation of Dab1, and their role for the regulation of Reelin-induced signaling. Model selection was performed on different model structures and a comprehensive mechanistic model of the early Reelin signaling cascade is provided in this work. It emphasizes the importance of Reelin-induced lipoprotein receptor clustering for SFK-mediated Dab1 trans-phosphorylation and does not require co-receptors to describe the measured data. The model is freely available within the open-source framework Data2Dynamics (www.data2dynamics.org). It can be used to generate predictions that can be validated experimentally, and provides a platform for model extensions both to downstream targets such as transcription factors and interactions with other transmembrane proteins and neuronal signaling pathways.