Cytochrome c oxidase couples the reduction of dioxygen to proton pumping against an electrochemical gradient. The D-channel provides the principal uptake pathway for protons. A water chain is thought to mediate the relay of protons through the D-channel, but it is interrupted at N139 in all crystallographic structures. Here, free energy simulations are used to examine the proton uptake pathway in the wild type and in single-point mutants N139V and N139A, where reduction and pumping is compromised. A general approach for the calculation of water occupancy in protein cavities is presented and demonstrates that combining efficient sampling algorithms with long simulation times is required to achieve statistical convergence of equilibrium properties in the protein interior. The relative population of conformational and hydration states of the D-channel is characterized. Results shed light onto the role of N139 in the mechanism of proton uptake and clarify the physical basis for inactive phenotypes.

Cytochrome c oxidase couples the reduction of dioxygen to proton pumping against an electrochemical gradient. The D-channel provides the principal uptake pathway for protons. A water chain is thought to mediate the relay of protons through the D-channel, but it is interrupted at N139 in all crystallographic structures. Here, free energy simulations are used to examine the proton uptake pathway in the wild type and in single-point mutants N139V and N139A, where reduction and pumping is compromised. A general approach for the calculation of water occupancy in protein cavities is presented and demonstrates that combining efficient sampling algorithms with long simulation times is required to achieve statistical convergence of equilibrium properties in the protein interior. The relative population of conformational and hydration states of the D-channel is characterized. Results shed light onto the role of N139 in the mechanism of proton uptake and clarify the physical basis for inactive phenotypes.

<p>Bridging the accuracy of ab initio (AI) QM/MM with the efficiency of semi-empirical<br> (SE) QM/MM methods has long been a goal in computational chemistry. This dissertation<br> presents four ∆-Machine learning schemes aimed at achieving this objective. Firstly, the in-<br> corporation of negative force observations into the Gaussian process regression (GPR) model,<br> resulting in GPR with derivative observations, demonstrates the remarkable capability to<br> attain high-quality potential energy surfaces, accurate Cartesian force descriptions, and reli-<br> able free energy profiles using a training set of just 80 points. Secondly, the adaptation of the<br> sparse streaming GPR algorithm showcases the potential of memory retention from previous<br> phasespace, enabling energy-only models to converge using simple descriptors while faith-<br> fully reproducing high-quality potential energy surfaces and accurate free energy profiles.<br> Thirdly, the utilization of GPR with atomic environmental vectors as input features proves<br> effective in enhancing both potential energy surface and free energy description. Further-<br> more, incorporating derivative information on solute atoms further improves the accuracy<br> of force predictions on molecular mechanical (MM) atoms, addressing discrepancies arising<br> from QM/MM interaction energies between the target and base levels of theory. Finally, a<br> comprehensive comparison of three distinct GPR schemes, namely GAP, GPR with an aver-<br> age kernel, and GPR with a system-specific sum kernel, is conducted to evaluate the impact<br> of permutational invariance and atomistic learning on the model’s quality. Additionally, this<br> dissertation introduces the adaptation of the GAP method to be compatible with the sparse<br> variational Gaussian processes scheme and the streaming sparse GPR scheme, enhancing<br> their efficiency and applicability. Through these four ∆-Machine learning schemes, this dis-<br> sertation makes significant contributions to the field of computational chemistry, advancing<br> the quest for accurate potential energy surfaces, reliable force descriptions, and informative<br> free energy profiles in QM/MM simulations.<br> </p>