Quantum calculations on salt bridges with water: Potentials, structure, and properties

Salt bridges are electrostatic links between acidic and basic amino acids in a protein; quantum calculations are used here to determine the energetics and other properties of one form of these species, in the presence of water molecules. The acidic groups are carboxylic acids (aspartic and glutamic acids); proteins have two bases with pK above physiological pH: one, arginine, with a guanidinium basic group, the other lysine, which is a primary amine. Only arginine is modeled here, by ethyl guanidinium, while propionic acid is used as a model for either carboxylic acid. The salt bridges are accompanied by 0–12 water molecules; for each of the 13 systems, the energy-bond distance relation, natural bond orbitals (NBO), frequency calculations allowing thermodynamic corrections to room temperature, and dielectric constant dependence, were all calculated. The water molecules were found to arrange themselves in hydrogen bonded rings anchored to the oxygens of the salt bridge components. This was not surprising in itself, but it was found that the rings lead to a periodicity in the energy, and to a “water addition” rule. The latter shows that the initial rings, with four oxygen atoms, become five member rings when an additional water molecule becomes available, with the additional water filling in at the bond with the lowest Wiberg index, as calculated using NBO. The dielectric constant dependence is the expected hyperbola, and the fit of the energy to the inverse dielectric constant is determined. There is an energy periodicity related to ring formation upon addition of water molecules. When 10 water molecules have been added, all spaces near the salt bridge are filled, completing the first hydration shell, and a second shell starts to form. The potentials associated with salt bridges depend on their hydration, and potentials assigned without regard to local hydration are likely to cause errors as large as or larger than kBT, thus suggesting a serious problem if these potentials are used in Molecular Dynamics simulations.