Abstract
The understanding of the growth and production behaviour of microorganisms requires a detailed knowledge in microbiology and genetics. To use the high potential of biological systems, e.g. in biotechnology, the knowledge has to be structured and collected in an apparent form. This will be a basis for setting up mathematical models. The thesis starts with a presentation of the research field, followed by an introduction in the modeling concept. In the thesis, a systematic approach to develop a detailed metabolic model is introduced. The approach is based on the definition of modeling objects (submodels) with defined in- and outputs. To guarantee a high biological transparency the modeling objects can be assigned directly to cellular units, e.g. a single enzymatic reaction step or e.g. complete pathways for transport and degradation of carbohydrates. Elementary modeling objects represent modeling objects with the highest resolution, i.e. substance storages, substance transformers and signal transformers. Substance storages represent metabolites, substance transformers stand for enzymatic reaction steps or polymerization steps while signal transformers describe processes of signal transduction and processing. A mathematical description is realized by assigning equations to the modeling objects. The following chapter describes the aggregation of elementary modeling objects to ’functional units’,i.e. units with higher complexity. Three criteria are given to demarcate functional units. The most important one describes the organization according signal transduction and processing. Special characteristics of functional units are (i) a hierarchical structure and (ii) signal processing in local as well as global signal transduction elements. An important point discussed in the chapter is signal processing in hierarchical structured units. For the initiation of transcription, in general, activators or inhibitors interact with the RNA polymerase to modify the initiation frequency. However, the influence of these effectors is limited to a small number of binding sites, e.g. the lactose repressor LacI has only one binding site on the whole E. coli genome. Hence, the repressor will clearly influence the initiation frequency of the lac-operon, but it will not influence the overall distribution of the RNA polymerase inside the cell. This fact is used in a new method to describe signal processing. Every protein involved in transcription of a gene is assigned to one level in hierarchy. Signals are transduced from top level to the lower level, but not vice versa. A computer tool is necessary to set up models with a large number of equations. The software package CellMod is based on C++ and supports the modeler by generating the required equations automatically. A number of elementary and aggregated modeling objects are implemented. Central in this tool is a model library for enzyme catalysed reactions, including about 42 entrys, starting from a simple Michaels-Menten equation up to complex models for 4 reaction partners. The modeling concept is applied to carbohydrate uptake in Escherichiacoli. The phenomenon of “glucose catabolite repression” means the repression of uptake of carbon sources if glucose is present in the medium. Only if glucose has run out, transport systems of other available carbohydrates are synthesised. This is due to a complex signal transduction pathway starting from the main glucose uptake system. The mathematical model developed in this thesis describes the main glucose uptake system and further elements in the signal transduction pathway. They represent the highest level of control in a functional unit called crp-modulon, named after the final target of the signal transduction pathway, the protein Crp. Besides the description of the signal transduction pathway, the metabolic pathways for lactose uptake and degradation and for the glycolysis are also included in the model. Finally the simulation results are compared to data published in the literature. The comparision of simulation results and experimental data of a wild type strain and of strains which are genetically modified are in good agreement.
