Modeling Non-Linear Dynamic Phenomena in Biochemical Networks

Facilitated by the development of high-throughput techniques, the focus of biological research has changed in the last decades from the investigation of single cell components to a system-level approach, which aims at an understanding of interactions between these cell components. This objective requires modeling and analysis methods for these regulatory networks. In this thesis, we investigate mechanisms causing qualitative dynamic behaviors of regulatory subsystems. For this purpose, we introduce a differential equation model based on underlying molecular binding reactions, whose parameters are estimated using time series concentration data. In the first part, the model is applied to subsystems with qualitatively different dynamic behaviors: The response of the Mycobacterium tuberculosis to DNA damages is described as the relaxation of a system to its steady state after external perturbation. Specific repression of genes in Escherichia coli by the global regulator protein H-NS is explained by the interrelation of feedback mechanisms. In order to prevent overfitting, a typical problem in network inference from experimental data, we introduce an approach based on Bayesian statistics, which includes prior knowledge about the system in terms of prior probability distributions. This approach is applied to simulated data and to the regulatory network of the Saccharomyces cerevisiae cell cycle. Motivated by results on the yeast cell cycle, the second part of this thesis investigates the robustness of periodic behavior in regulatory networks. The model presented belongs to a class of differential equations whose solutions tend to converge to a steady state. Accordingly, periodic behavior is not robust with respect to parameter variations. We explain this phenomenon by applying a bifurcation analysis and investigating the stability of steady states. It is shown that large time scale differences and an inclusion of time-delays can stabilize sustained oscillations, and we postulate that they are important to maintain oscillations in biological systems