The oxidative phosphorylation is the most important step of the aerobic respiration. Here, electrons are transferred along several membrane-embedded enzyme complexes to finally reduce molecular oxygen to water in Cytochrome c Oxidase. The energy released by the electron flow and the oxygen reduction is used to translocate protons across the membrane. Thereby, an electro-chemical gradient is established which subsequently drives the synthesis of the biological energy carrier Adenosine Triphosphate. Numerous diseases, e.g. Alzheimer or Parkinson, are partially assigned to malfunctions of the oxidative phosphorylation, rendering a detailed understanding of this step indispensable. Common computational investigations, employing Molecular Dynamics simulations, enhanced sampling techniques, or transition pathway finding algorithms, are limited in their description of quantum effects and often only provide a limited, or biased, description of complex reactions. The alternative Transition Network approach, divides a complex reaction of interest into numerous simpler transitions, connecting various local potential energy minima of the potential energy surface by minimum energy pathways, yielding a Transition Network, or simple graph, which can be analyzed in terms of optimal transition pathways by standard graph theoretical algorithms. A major drawback of the Transition Network approach is the exponential increase of stationary points of the potential energy surface with increasing numbers of degrees of freedom to sample, rendering the Transition Network approach infeasible for most complex reactions. Within the framework of this thesis two methods optimizing the Transition Network approach are developed and extensively tested in small proton transfer model systems. These are: 1) the TN-MD method coupling the discrete sampling of states separated by substantial energy barriers with Molecular Dynamics simulations for the sampling of states separated by minor energy barriers, e.g. amino acid side chain dihedral angle rotations or water molecule translations, respectively, and 2) the TN prediction method using a known, initial Transition Network and an excessive two-step coarse-graining procedure for the determination of an unknown Transition Network in a perturbed environment, e.g. different protonation states. Both methods provide significant cost reductions, while important properties of the proton transfer reactions, e.g. rate-determining, maximal transition barriers and the variability of transition pathways or mechanisms, are maintained. Furthermore, the TN-MD method is used to investigate the proton transfer through the D-channel of Cytochrome c Oxidase in a minimal model system, providing various proton transfer pathways with rate-determining, maximal transition barriers which are in agreement to computational results from Liang et al using a much more involved model and simulation setup. Other decisive aspects of previous proton transfer investigations along the D-channel, e.g. the identity of the rate-determining, maximal transition state and the behavior of the proposed asparagine gate, are reproduced and extended. Overall, this thesis provides a methodical leap forward in terms of the Transition Network approach as well as another piece of analysis required for the understanding of the proton translocation along the oxidative phosphorylation.
