Core-box Modelling - Theoretical Contributions and Applications to Glucose Homeostasis Related Systems

Doctoral thesis, 2006

The study of biological systems through a combination of in vitro characterisations, quantitative in vivo experiments, and mathematical modelling, is receiving an increasingly growing interest through the field system biology. Systems biology uses methods from many different research fields, but the existing methods need to be extended and adapted to fit the new situations. This dissertation presents new methods for various modelling situations, and the developments have been driven by examples related to glucose homeostasis. The modelling methods are contained in a new modelling framework denoted core-box modelling. Core-box modelling attempts to combine the strengths of mechanistic grey-box models (e.g., to describe detailed processes) with the strengths of minimal models (e.g., identifiability and hypothesis testing). The main new steps in the modelling process are: identifiability analysis, model reduction, system identification and a translation between different versions of the same model. In all these sub-disciplines, a review is given and new methods are developed; these contributions are of course valid in any framework. Methods are given for detection and handling of both structural and practical unidentifiability in individual rate expressions. This also yields in vivo expressions for the reactions. Special methods are derived for systems with oscillations. First, two methods for identification of the interactions generating the oscillations in a model are given. Then, two methods are! presented for parameter estimation of a system close to a Hopf bifurcation. The first method reduces the dimension of the parameters appearing in the differential equations, and the second method eliminates the parameters describing the initial state at time zero. Finally, it is shown how the results can be back-translated to a core-box model; a model with all the details of the original grey-box model, but with quality tags from the core model to its possible predictions. The new methodologies are applied to the development of three models. The first is a core-box model for insulin signalling in fat cells. The core model is obtained using hypothesis testing, which shows that the internalisation is necessary to generate the observed dynamics, and that the internalisation is of the same time-scale as an observed overshoot in the data. These predictions are validated experimentally, and the advantages of the core-box model with respect to the both the core and grey-box model are illustrated. The second model describes oscillations in yeast glycolysis. Many of the developed methods are applied, and their performances are demonstrated. This leads, e.g., to a refined prediction of the biochemical mechanisms generating the oscillations. The third model describes muscle metabolism under anaerobic exercise. The developed model is used to resolve a 25 year old contradiction between data and current biochemical understandings regarding the control of g! lycolysis following anaerobic contraction. Finally, an existing model of neutrophil metabolism is analysed. The main conclusion is that the model's apparent lack of robustness lies on the structural level and not on the parametric level. All these contributions show, in various ways, how the combined usage of models, biochemical characterisations, and quantitative in vivo data can work together in a fruitful way; a way which surpasses the abilities of either of these research fields working in isolation.