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.