Small metal ions play critical roles in numerous biological processes. Of particular interest is how metalloenzymes are allosterically regulated by the binding of specific ions. Understanding how ion binding affects these biological processes requires atomic models that accurately treat the microscopic interactions with the protein ligands. Theoretical approaches at different levels of sophistication can contribute to a deeper understanding of these systems, although computational models must strike a balance between accuracy and efficiency in order to enable long molecular dynamics simulations. In this study, we present a systematic effort to optimize the parameters of a polarizable force field based on classical Drude oscillators to accurately represent the interactions between ions (K+, Na+, Ca2+, and Cl–) and coordinating amino-acid residues for a set of 30 biologically important proteins. By combining ab initio calculations and experimental thermodynamic data, we derive a polarizable force field that is consistent with a wide range of properties, including the geometries and interaction energies of gas-phase ion/protein-like model compound clusters, and the experimental solvation free-energies of the cations in liquids. The resulting models display significant improvements relative to the fixed-atomic-charge additive CHARMM C36 force field, particularly in their ability to reproduce the many-body electrostatic nonadditivity effects estimated from ab initio calculations. The analysis clarifies the fundamental limitations of the pairwise additivity assumption inherent in classical fixed-charge force fields, and shows its dramatic failures in the case of Ca2+ binding sites. These optimized polarizable models, amenable to computationally efficient large-scale MD simulations, set a firm foundation and offer a powerful avenue to study the roles of the ions in soluble and membrane transport proteins.

We have investigated the structure and electronic structure of single-and double-walled imogolite nanotubes with Ge and Si as group IV element. While it is known from experiment, and in the case of single-walled tubes confirmed by theory, imogolite nanotubes are monodisperse in diameter. We show that imogolite tubes are also showing a preferred chirality (zigzag), resulting from the hydrogen-bond network on the tube surfaces, and that there is an exceptionally stable form of intertube interaction that supports the formation of monodisperse double-walled imogolite nanotubes. The strongest stabilization of double-walled tubes has been found for tube indexes with nine units of difference around the circumference, and the minimum structure is found for the (12,0)@(21,0) tube in the case of germanium imogolite and (9,0)@(18,0) for imogolite. The electronic structure is only slightly affected by these geometric factors, as are the mechanical properties, which show Young moduli of 320−370 GPa, thus being in the same range as other clay mineral nanotubes.

Supercell models are often used to calculate the electronic structure of local deviations from the ideal periodicity in the bulk or on the surface of a crystal or in wires. When the defect or adsorbent is charged, a jellium counter charge is applied to maintain overall neutrality, but the interaction of the artificially repeated charges has to be corrected, both in the total energy and in the one-electron eigenvalues and eigenstates. This becomes paramount in slab or wire calculations, where the jellium counter charge may induce spurious states in the vacuum. We present here a self-consistent potential correction scheme and provide successful tests of it for bulk and slab calculations.