Macroscopic Modeling of Metabolic Reaction Networks and Dynamic Identification of Elementary Flux Modes by Column Generation

Sammanfattning: In this work an intersection between optimization methods and animal cell culture modeling is considered. We present optimization based methods for analyzing and building models of cell culture; models that could be used when designing the environment cells are cultivated in, i.e., medium. Since both the medium and cell line considered are complex, designing a good medium is not straightforward. Developing a model of cell metabolism is a step in facilitating medium design.In order to develop a model of the metabolism the methods presented in this work make use of an underlying metabolic reaction network and extracellular measurements. External substrates and products are connected via the relevant elementary flux modes (EFMs). Modeling from EFMs is generally limited to small networks, because the number of EFMs explodes when the underlying network size increases. The aim of this work is to enable modeling with more complex networks by presenting methods that dynamically identify a subset of the EFMs.In papers A and B we consider a model consisting of the EFMs along with the flux over each mode. In paper A we present how such a model can be decided by an optimization technique named column generation. In paper B the robustness of such a model with respect to measurement errors is considered. We show that a robust version of the underlying optimization problem in paper A can be formed and column generation applied to identify EFMs dynamically.In papers C and D a kinetic macroscopic model is considered. In paper C we show how a kinetic macroscopic model can be constructed from the EFMs. This macroscopic model is created by assuming that the flux along each EFM behaves according to Michaelis-Menten type kinetics. This modeling method has the ability to capture cell behavior in varied types of media, however the size of the underlying network is a limitation. In paper D this limitation is countered by developing an approximation algorithm, that can dynamically identify EFMs for a kinetic model.