Mechanism of a proton pump analyzed with computer simulations

Abstract

Understanding the mechanism of proton pumping requires a detailed description of the energetics and sequence of events associated with the proton transfers, and of how proton transfer couples to conformational rearrangements of the protein. Here, we discuss our recent advances in using computer simulations to understand how bacteriorhodopsin pumps protons. We emphasize the importance of accurately describing the retinal geometry and the location of water molecules.

A Modified QM/MM Hamiltonian with the Self-Consistent-Charge Density-Functional-Tight-Binding Theory for Highly Charged QM Regions

“…This is not unexpected because significant imbalance of proton affinities for phosphate and non-phosphate species remains in SCC-DFTBPR 78 . Our recent studies indicate that this deficiency is largely removed when the complete third-order contributions are included 23 (M. Gaus and Q. Cui, work in progress).…”

“…Similar to the Gaussian-blur models 10,72 for ab initio QM/MM, the KO model takes charge penetration effects into consideration and therefore significantly improves the description of charge-charge interactions at short range; at the same time, the computation remains efficient. To be consistent with the third-order formulation of SCC-DFTB 23 , the Hubbard parameter in the KO functional is dependent on the QM charge. In this way, the effective size of the QM charge distribution naturally adjusts as the QM region undergoes chemical transformations, making the KO based QM/MM scheme particularly attractive for describing chemical reactions in the condensed phase.…”

“…In other words, the Hubbard parameter is closely related to the effective size of the atom (charge distribution). In recent studies 12,23,77 , it has been shown that including the charge dependence of the Hubbard parameter, which effectively extends the DFTB energy to third order in density (charge) fluctuation, significantly improves properties such as proton affinities. Physically this highlights that the size of an atom (charge distribution) changes considerably as it deprotonates.…”

“…$${\widehat{H}}_{\mathit{elec},KO}^{QM/MM}=\sum _{\alpha \in QM}\sum _{A\in MM}\frac{\mathrm{\Delta }{q}_{\alpha }{Q}_A}{\sqrt{R_{\alpha A}^2+0.25{false[1/U_{\alpha }false(\mathrm{normal\Delta }{q}_{\alpha }false)+1/U_{A}false]}^2}},$$ where we emphasize that U α (Δ q α ) is dependent on the Mulliken charge of the QM atom; i.e., $U_{\alpha }(\mathrm{\Delta }{q}_{\alpha })=U_{\alpha }^0+\mathrm{\Delta }{q}_{\alpha }{U}_{\alpha }^d$, in which the Hubbard derivative with respect to atomic charge ( $U_{\alpha }^d$) is either calculated from atomic properties or fitted based on properties of interest 23,77 (e.g., proton affinity 23 ). The the MM “Hubbard” parameter ( U A ) can be taken from atomic electronic structure calculations or treated as a parameter similar to the width of the “Gaussian blur” in the approach introduced by Brooks and co-workers 10 , or simply set to ∞ (the point charge limit).…”

“…In principle, the MM Hubbard parameters can also be optimized to allow additional flexibility. In this work, we test two models: simply set the MM Hubbard parameters to ∞ (referred to as the KO- ∞ model), or use the calculated Hubbard from atoms 23 (referred to as the KO-MM model).…”