Modeling and Simulation of Complex Networks in Systems Biology

Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2019; Aachen 1 Online-Ressource (212 Seiten) : Illustrationen (2019). = Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2019
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(𝑁 ≈ 10^5 to 10^6) is very small compared to structures in solid state physics. On the one hand, such that size-related effects may not be neglected, but are far too large for a brute force calculation of the sum over the states as well. In the first part of the thesis, we will systematically evaluate the translation of computational techniques from solid-state physics to biological interaction networks and develop specific translational rules to tackle the finite size problem, the topology problem and the challenge of the necessary reduction of complexity for the scale-free network topologies. We will focus our computational analysis on biological networks in a quasi-steady state with a focus on disease propagation in chronic diseases as well as dynamical networks arising from neurological challenges. Because of the high degree of uncertainty of the detailed biological mechanisms driving the respective networks in cells, we will focus our analysis on the established generic features in network biology which provide a reasonable approximation of the reality in single cells, namely systems where any entity can exhibit only two states. In addition, we present an approximation of the Ising model on scale-free networks by an Ising model on the lattice by approximating the adjacency matrix with an effective coupling constant. The latter part of the thesis focusses on modeling and analysis of neuronal networks. Neurons emit spikes when they reach a specific threshold voltage owing to input from external sources, usually neighboring neurons. Traditional schemes adopted to propagate neuron dynamics may miss spikes arriving from upstream neurons. We present a general method to catch these spikes using the geometric idea of back propagation of the threshold plane. Also, we present an analysis of calcium oscillations in dopaminergic neurons that distinguishes firing patterns of neural cells at early from advanced stages of differentiation based on their periodicity, the structure of correlation matrixes and spiking frequency. The methods outlined in this thesis offer a framework for investigating complexity in biologically relevant networks of large sizes and hence have applicability outside of the specific network types considered herein.
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