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Biological systems such as cells or whole organisms are governed by complex regulatory networks of transcription factors, hormones and other regulators which determine the behavior of the system depending on internal and external stimuli. In mathematical models of these networks, genes are represented by interacting “nodes” whose “value” represents the activity of the gene.
Control processes in these regulatory networks are challenging to elucidate and quantify. Previous control centrality metrics, which aim to mathematically capture the ability of individual nodes to control biological systems, have been found to suffer from problems regarding biological plausibility.
This thesis presents a new approach to control centrality in biological networks. Three types of network control are distinguished: Total control centrality quantifies the impact of gene mutations and identifies potential pharmacological targets such as genes involved in oncogenesis (e.g. zinc finger protein GLI2 or bone morphogenetic proteins in chondrocytes). Dynamic control centrality describes relaying functions as observed in signaling cascades (e.g control in mouse colon stem cells). Value control centrality measures the direct influence of the value of the node on the network (e.g. Indian hedgehog as an essential regulator of proliferation in chondrocytes). Well-defined network manipulations define all three centralities not only for nodes, but also for the interactions between them, enabling detailed insights into network pathways.
The calculation of the new metrics is made possible by substantial computational improvements in the simulation algorithms for several widely used mathematical modeling paradigms for genetic regulatory networks, which are implemented in the regulatory network simulation framework Jimena created for this thesis.
Applying the new metrics to biological networks and artificial random networks shows how these mathematical concepts correspond to experimentally verified gene functions and signaling pathways in immunity and cell differentiation. In contrast to controversial previous results even from the Barabási group, all results indicate that the ability to control biological networks resides in only few driver nodes characterized by a high number of connections to the rest of the network. Autoregulatory loops strongly increase the controllability of the network, i.e. its ability to control itself, and biological networks are characterized by high controllability in conjunction with high robustness against mutations, a combination that can be achieved best in sparsely connected networks with densities (i.e. connections to nodes ratios) around 2.0 - 3.0.
The new concepts are thus considerably narrowing the gap between network science and biology and can be used in various areas such as system modeling, plausibility trials and system analyses.
Medical applications discussed in this thesis include the search for oncogenes and pharmacological targets, as well their functional characterization.

Background: Boolean networks capture switching behavior of many naturally occurring regulatory networks. For semi-quantitative modeling, interpolation between ON and OFF states is necessary. The high degree polynomial interpolation of Boolean genetic regulatory networks (GRNs) in cellular processes such as apoptosis or proliferation allows for the modeling of a wider range of node interactions than continuous activator-inhibitor models, but suffers from scaling problems for networks which contain nodes with more than ~10 inputs. Many GRNs from literature or new gene expression experiments exceed those limitations and a new approach was developed.
Results: (i) As a part of our new GRN simulation framework Jimena we introduce and setup Boolean-tree-based data structures; (ii) corresponding algorithms greatly expedite the calculation of the polynomial interpolation in almost all cases, thereby expanding the range of networks which can be simulated by this model in reasonable time. (iii) Stable states for discrete models are efficiently counted and identified using binary decision diagrams. As application example, we show how system states can now be sampled efficiently in small up to large scale hormone disease networks (Arabidopsis thaliana development and immunity, pathogen Pseudomonas syringae and modulation by cytokinins and plant hormones).
Conclusions: Jimena simulates currently available GRNs about 10-100 times faster than the previous implementation of the polynomial interpolation model and even greater gains are achieved for large scale-free networks. This speed-up also facilitates a much more thorough sampling of continuous state spaces which may lead to the identification of new stable states. Mutants of large networks can be constructed and analyzed very quickly enabling new insights into network robustness and behavior.

Control of genetic regulatory networks is challenging to define and quantify. Previous control centrality metrics, which aim to capture the ability of individual nodes to control the system, have been found to suffer from plausibility and applicability problems. Here we present a new approach to control centrality based on network convergence behaviour, implemented as an extension of our genetic regulatory network simulation framework Jimena (http://stefan-karl.de/jimena). We distinguish three types of network control, and show how these mathematical concepts correspond to experimentally verified node functions and signalling pathways in immunity and cell differentiation: Total control centrality quantifies the impact of node mutations and identifies potential pharmacological targets such as genes involved in oncogenesis (e.g. zinc finger protein GLI2 or bone morphogenetic proteins in chondrocytes). Dynamic control centrality describes relaying functions as observed in signalling cascades (e.g. src kinase or Jak/Stat pathways). Value control centrality measures the direct influence of the value of the node on the network (e.g. Indian hedgehog as an essential regulator of proliferation in chondrocytes). Surveying random scale-free networks and biological networks, we find that control of the network resides in few high degree driver nodes and networks can be controlled best if they are sparsely connected.