Cellular function is powered by mitochondria through an energy conversion process known as oxidative phosphorylation. Central to this process is respiratory complex I, an enzyme that couples NADH oxidation with ubiquinone reduction and the pumping of protons across the inner mitochondrial membrane. In this thesis, the mechanistic principles of complex I were investigated using multi-scale simulations, including atomistic molecular dynamics simulations and hybrid quantum/classical mechanics (QM/MM) calculations. We found that complex I drives quinone reduction and proton pumping through a network of buried charged residues. These residues couple protonation changes to conformational shifts, electrostatic interactions, and modulations of the hydration dynamics. Additionally, we expanded the applicability of QM/MM to long-range protonation dynamics by developing a novel sampling scheme. This scheme combines advanced sampling methods with a general reaction coordinate to provide a quantitative description of hydration dynamics and conformational changes during proton transfer reactions, which are indispensable for understanding the function of the respiratory enzymes. We further investigated the molecular details of how and why respiratory complexes cluster together to form supercomplexes. Our findings indicate that membrane proteins alter the membrane properties and introduce strain, which could drive the formation of these assemblies. The combined mechanistic findings of this thesis enhance our understanding of respiratory complex I and supercomplexes and their underlying proton transfer reactions, conformational changes, and enzymatic activity.

All life fundamentally relies on the efficient capture and conversion of energy into forms that support vital biochemical processes. Central to this process is the respiratory chain, a set of membrane-bound protein complexes that harness energy-rich molecules to drive ion translocation across biological membranes. This process generates an electrochemical gradient, known as the proton motive force (pmf) or sodium motive force (smf), that in turn powers the synthesis of ATP, the universal energy currency of the cell. In this thesis, the mechanistic principles underlying the function of respiratory enzymes are explored using a combination of classical molecular dynamics simulations, quantum mechanical methods, and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations.

The respiratory Complex I couples the oxidation of NADH and the reduction of quinone to the translocation of four protons across biological membranes. Our results indicate that this coupling is mediated by a network of charged residues. Switching within this network triggers a conformational change of a key gating residue, thereby linking the redox reaction to ion translocation. Additionally, we identify proton translocation pathways through the membrane domain of Complex I, whose dynamics are governed by the conformation of conserved ion pairs. We investigate the mechanism of oxygen reduction and quinol oxidation by the alternative oxidase (AOX), and find that the diiron center forms a ferryl/ferric intermediate, which is reduced by the quinol in a highly exothermic reaction. To understand what drives supercomplex (SC) formation, we analyze their membrane interactions and observe that the association of Complex I and III₂ into SCs reduces membrane strain. Finally, we examine the redox-coupled Na⁺ translocation mechanism of the Rnf complex and identify conformation dependent Na⁺ binding sites, based on which we propose a mechanism for ion transport. Together, the results presented in this thesis provide new insights into the mechanistic principles that govern membrane-bound respiratory enzymes.