Theoretical biology

Mathematical modeling and simulation techniques have turned out to be valuable tools for the understanding of complex systems in different areas of research and engineering. In recent years this approach came to application frequently also in biology resulting in the establishment of the research area systems biology. Systems biology tries to understand the behavior of complex biological systems by means of mathematical approaches. This requires the integration of qualitative and quantitative experimental data into coherent models. Currently, systems biology usually investigates biochemical reaction networks of cellular systems. A challenging task is the construction of large models that requires computer-assisted data integration, simulation and evaluation. In this work I have elaborated technical bases for the computer- assisted modeling of biological systems and experimental techniques. For this I have developed the program PyBioS that provides a user-friendly Web application and brings in automation for several important tasks required for the development, implementation, and simulation of cellular models. For the description of cellular reaction systems PyBioS makes use of object-oriented programming, well established methods for the mathematical description of biochemical reaction systems based on ordinary differential equation systems, and novel interfaces to biochemical pathway databases (e.g., Reactome, KEGG). In addition PyBioS provides several different functions for the analysis and visualization. The benefit obtained by mathematical modeling of biological systems using PyBioS is illustrated for segmentation of the body (somitogenesis) as, e.g., taking place during embryogenesis. The parameterized somitogenesis model I have developed comprises three signaling pathways, namely Notch, Wnt, and FGF that are known to be relevant for somitogenesis. The model shows a regular oscillation controlled by extracellular Wnt3a. Below a critical threshold concentration of Wnt3a the oscillation that is controlled by Wnt signaling arrests and approaches a steady state. These findings are conform to experimental observations found during determination of somite boundaries. Besides the analysis of biological systems, modeling strategies can also be used for the evaluation of biotechnological experimental techniques. To study this I have perfomed simulations of DNA array hybridization experiments for the evaluation of critical parameters during subsequent image and data analysis. Therefore I have carried out simulation studies on several error parameters arising in complex hybridization experiments, such as spot shape, spot position and background noise. My results show how measurement errors can be balanced by the analysis tools.