Modeling and simulation of complex networks in systems biology

The central question of systems biology is to understand how individual components of a biological system engage in novel behavior and produce unique phenomena with the system itself constraining the components. The evolution of disease-related phenotypes in biological cells is driven by emerging patterns arising from the mutual interactions of thousands of molecular entities of a similar type, such as genes or proteins. Each network of entities interact with the respective networks of other entities, where the nature of the detailed interaction across these multiple levels of molecular functionalities is not known. Nevertheless, network biology reveals generic organizational structures within the interaction networks of similar entities across the functional level. Moreover, in terms of systems theory, living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment. Hence, it has been hypothesized that the translation of computational techniques that have been successfully applied in statistical thermodynamics in order to describe the evolution of emerging patterns as phase transitions in non-living systems may provide new insights to emerging behavior of biological systems. However, in contrast to complex interaction networks in physics, the topology of biological interaction networks is characterized by almost scale-free network topologies. Therefore, computational techniques in solid state physics requiring invariance groups in the interaction network topology, e.g. translational invariance, periodicities or symmetries, are not directly applicable to biological systems. Moreover, the size of the biological networks